Microsimulating Residential Mobility and Location Choice Processes within an Integrated Land Use and Transportation Modelling System

Transcription

1 Microsimulating Residential Mobility and Location Choice Processes within an Integrated Land Use and Transportation Modelling System by Muhammad Ahsanul Habib A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Department of Civil Engineering University of Toronto Copyright by Muhammad Ahsanul Habib 2009

2 ii Microsimulating Residential Mobility and Location Choice Processes within an Integrated Land Use and Transportation Modelling System Abstract Muhammad Ahsanul Habib Doctor of Philosophy Department of Civil Engineering University of Toronto 2009 This research investigates motivational and procedural aspects of households long-term decisions of residential locations. The main goal of the research is to develop microbehavioural models of location processes in order to implement this critical land use component within a microsimulation-based model of Integrated Land Use, Transportation and Environment (ILUTE). The research takes a disaggregate and longitudinal approach to develop the models, which is consistent with the real-world decision-making process of households concerning their movements from one residence to another over time. It identifies two sequential model components to represent households relocation behaviour: (1) a model of household residential mobility that determines whether a household decides to become active in the housing market, and (2) a (re) location choice model. Both components are empirically investigated using retrospective surveys of housing careers. For the residential mobility decision, the research tests continuous-time hazard duration models and discrete-time panel logit models, and attempts to capture heterogeneity effects due to repeated choices within both modelling techniques. A discrete-time random parameter model is selected for implementation within ILUTE since it incorporates time-varying covariates. Assuming a sequential decision process, this mobility

3 iii decision model is linked to the (re) location choice model that establishes preference orderings for each active household for a given set of dwelling units that it considers to relocate within the housing market. A unique feature of the (re) location model developed in this research is that it incorporates reference dependence that explicitly recognizes the role of the status quo and captures asymmetric responses towards gains and losses in making location choice decisions. The research then estimates an asking price model, which is used to generate base prices for active dwellings to interact with active households through a market clearing process within a microsimulation environment. A multilevel model that simultaneously accounts for both temporal and spatial heterogeneity is developed in this research using multi-period property transaction data. Finally, this research simulates evolution of households location choices for a twenty-year period ( ) and compares the results against observed location patterns.

4 iv Acknowledgments I am endowed with tremendous amount of support, encouragement and love throughout my PhD study. It was an incredible journey in which I have learned so many things; I have been matured in so many ways; and I have been touched with affection by so many people! First and foremost, I would like to offer my sincere gratitude to my teacher Eric Miller who is an extraordinary academic supervisor as well as an ideal person to follow for all aspects of life. I feel a deep sense of pride and satisfaction to get the opportunity to work so closely with him. Eric, you are a true teacher, a genuine mentor and a good friend. I am grateful to you for your continuous support and constant faith, for providing me full freedom to grow, for infusing your valuable and timely insights, for your endless encouragement to publish, and for being a caring guardian in this distant land where I have pursued my academic dream. I am also thankful to my teachers at U of T, particularly members of my supervisory committee Professor Amer Shalaby, Professor Richard DiFrancesco and Professor Matthew Roorda for their thoughtful suggestions and comments. Special thanks to Matt for providing me full access to him and his resources throughout my doctoral study. I would also like to extend my gratitude to Professor Paul Waddell for offering his valuable time as an external member of the committee, and for providing helpful reviews to improve this dissertation. I am also grateful to Professor Ted Relph, Professor Andre Sorensen and Professor Michael Bunce for giving me opportunities to teach at UTSC. Thanks to Professor Murtaza Haider, Professor Harry Timmermans, Professor Francisco Martinez and Professor Susan Guppy for providing me consultation and inspiration at different stages of my graduate life. Thanks to the ILUTE project team for concurrent development of the population synthesis, demographic updates and market clearing component, which has lead to an operational model. Special thanks to Bilal for his dedicated efforts for coding location choice components of ILUTE. I am also grateful to my friends at the Department - Jesse, Prachi, Marianne, Juan, Medhat, Hossam, Amr, Young-ji, David, Dave, Bryce and many others with whom I have had very good times. I would also like to thank my friends at GTHA for their joyful company.

5 v I am thankful to the funding agencies Transport Canada, NSERC, and SSHRC for supporting my research. Special thanks to CTRF, TAC and CITE for offering me 2008 Awards, which was truly inspirational. I am immensely indebted to my wife Farhana for her understanding, help and compassion to my long commute, schedules, travels and deadlines. I am also proud of my daughter Nuzaira for being such a nice girl and constantly fetching joy to our life. This dissertation has started with her birth, and grown along her first walk, first word, first painting of dad and first school. My student life has ended, she has begun, and who knows it might end up with repeated choices! Last, but not least I would like to thank my parents and siblings (Rony, Snigdha, Supti) for their unconditional love and support throughout my life.

6 vi Table of Contents Acknowledgments... iv Table of Contents... vi List of Tables... ix List of Figures... x CHAPTER 1: INTRODUCTION Background and motivation Objectives Research significance Approach Thesis structure...7 CHAPTER 2: LITERATURE REVIEW Introduction Brief review of integrated urban models Issues in modelling residential location within an IUM framework Concluding remarks...18 CHAPTER 3: CONCEPTUAL FRAMEWORK Introduction Understanding microbehavioural residential location process Conceptual model of residential relocation Decision to move Evaluation and (re) location decision Microsimulating spatial housing markets Concluding remarks...31

7 vii CHAPTER 4: RESIDENTIAL MOBILITY MODEL Introduction Residential mobility model structures Discrete choice models Hazard-based duration models Data for empirical application Model estimation results Panel Logit Models Hazard-based duration models Conclusion...51 CHAPTER 5: RELOCATION CHOICE MODEL Introduction Modelling issues Prospect theory and reference dependent choice model Modelling approach Data for empirical application Data sources Data preparation Model parameter estimation results Variable specification Discussion of results Conclusion...68 CHAPTER 6: DWELLING PRICE MODEL Introduction Modelling housing prices Model structures...76

8 viii 6.4 Data preparation Model parameter estimation results Conclusion...87 CHAPTER 7: SIMULATING LOCATION PROCESSES Introduction Microsimulation framework of residential location component Behaviour of household agents Components of residential location module Market clearing process Interactions with other modules of ILUTE Input data preparation Simulation results Comparison of simulation results Comparison of location patterns Comparison of dwelling prices Comparison of other outputs Potential use of the model for policy analysis Concluding remarks CHAPTER 8: SUMMARY AND CONCLUSION Summary of the research Research contributions Recommendations for future research Final remarks Bibliography Appendix A...136

9 ix List of Tables Table 4.1 Parameter estimation results of binomial panel data logit models Table 4.2 Parameter estimation results of single-episode and repeated events duration models. 50 Table 5.1 Definition of variables used in the reference dependent residential location choice model Table 5.2 Parameter estimation results of conventional location choice logit model Table 5.3 Parameter estimation results of reference dependent location choice mixed logit model Table 6.1 Summary statistics of data used for the housing price modelling Table 6.2 Results of Box-Cox transformation models Table 6.3 Results of multilevel models Table 7.1 Summary list of variables used in residential mobility, (re) location and asking price models Table 7.2 Comparison of dwelling asking prices (simulation vs. TREB observed) Table 7.3 Proposed example scenarios for the Greater Toronto and Hamilton Area

10 x List of Figures Figure 1.1 Population forecast by administrative unit used in the official growth plan (MPIR, 2006)... 2 Figure 2.1 The chronological development of the integrated land use-transportation models towards the target model (Miller et al., 1998)... 9 Figure 3.1 The ILUTE modelling framework Figure 3.2 Conceptual relationships between residence, job and travel models Figure 3.3 Modelling framework of microsimulating housing market Figure 7.1 Microsimulation of relocation decisions Figure 7.2 Relationship-diagram of residential mobility and other modules of ILUTE Figure 7.3 Spatial distribution of households for the simulation year Figure 7.4 Spatial distribution of households for the simulation year Figure 7.5 Spatial distribution of households for the simulation year Figure 7.6 Spatial distribution of households for the simulation year Figure 7.7 Comparison of simulated location patterns against census data (1991) Figure 7.8 Comparison of simulated location patterns against census data (1996) Figure 7.9 Comparison of simulated location patterns against census data (2001) Figure 7.10 Comparison between average observed vs. simulated dwelling prices Figure 7.11 Comparison of observed and predicted asking prices for the simulation year Figure 7.12 Comparison of observed and predicted asking prices for the simulation year

11 1 CHAPTER 1: INTRODUCTION This thesis presents a comprehensive and dynamic modelling framework for households longterm residential location decision processes within a microsimulation environment. Households are one of the key agents active in the urban area that make the urban system a living organism that is constantly changing over time. They decide where to reside, work, shop and participate in different activities. While choice of residential location is a long-term decision, travel decisions are short-term personal day-to-day decisions. But long-term decisions have significant impact on the short-term decisions such as personal travel decisions to reach different types of mandatory and discretionary activities. Therefore, it is important to investigate different aspects of households decision-making processes regarding choice of residences, which has become an integral part of integrated land use and transportation modelling systems. 1.1 Background and motivation Since most North American cities are currently experiencing enormous challenges due to urban sprawl and creation of auto-dependent communities, there is an increasing tendency to adopt integrated land use and transportation planning initiatives over the last decades. While alternative smart growth strategies and transit-oriented design principles have emerged, a comprehensive tool to evaluate the impacts of these policies on the urban system is yet to be developed. Miller (2005) pointed out that although the need for integrated land use and transportation models are well recognized, and while activity-based travel models continue to mature in both their theoretical foundation and their empirical implementation, a corresponding evolution of longerterm decision-making research has not occurred to any significant extent. It is further argued that although several transportation researchers and urban planners have developed integrated land use-transport models since the 1960s, it always has been a subdominant field of interest, especially compared to the modelling of various aspects of transport demand, which typically treated land use as an exogenous variable of the model (Timmermans, 2003).

12 2 With the increasing interest to develop complementary and mutually supportive land use and transportation policies, current practice of the traditional approach to modelling travel demand is neither sufficient nor valid to make informed decisions regarding critical issues of sustainable urban development, balanced growth of spatial systems and evaluation of micro-scale impacts of changes in policies. Since land use policies are being treated as a key catalyst to shape future growth of cities, it is required to model the land use processes in a considerable detail. Taking the Greater Toronto and Hamilton Area (GTHA) as an example, which is the largest urban agglomeration in Canada and an attractive destination of choice for many people and businesses relocating from other parts of Canada and around the world, the Places to Grow Act 1995 provides a framework to implement the Government of Ontario s vision for building stronger, prosperous and sustainable communities by better managing growth in this region to 2031 (MPIR, 2006). It is estimated that the population of this area will grow to 8.62 million by the year 2031, adding a 2.81 million people from the year 2001; this will account for about 60% of the population growth of the entire Province of Ontario (HCL, 2005) over this time period. A growth forecast by administrative boundaries is presented in Figure Population Region of Durham Region of York City of Toronto Region of Peel Region of Halton City of Hamilton Administrative unit Figure 1.1 Population forecast by administrative unit used in the official growth plan (MPIR, 2006)

13 3 The key policy recommendations of the growth plan includes directing growth to built-up areas where the capacity exists to best accommodate the expected population and employment growth, while providing strict criteria for settlement boundary expansion, promoting transit-supportive densities and a healthy mix of residential and employment land uses, preserving employment areas and developing a supportive transportation network (MPIR, 2006). By now, most of the city and regional authorities are using these guidelines to develop their official plans favouring intensification of urban growth centres, corridors, major transit station areas, brownfield sites and greyfields. Since the plan put forward specific population and employment density targets, which should be achieved within a specific time period, planners are experiencing tremendous challenges to adopt specific plans, programs and projects for the successful implementation of the proposed growth plan. Several decisions concerning the growth management issues arise, for example, what kinds and/or combination of policy instruments should they adopt to increase densities, how intense the development should be without impeding the transportation system, how much and what types of dwelling units should they allow to be built, where to restrict settlement boundary expansions. Additionally, since even specific areas are developed in accordance with the proposed plan, there are questions in terms of will people move to those areas, will residences be affordable, what will be the changes in the neighbourhood composition and housing prices. Addressing all these issues might not be possible by any single urban modelling system, but the irony is that planners have very limited resources in terms of decisionsupport tools to assess alternative futures given a particular set of policy and planning initiatives. Since there is no comprehensive land use modelling system, it is not even possible to predict where people will eventually live or work in the long run. As a result, it is a difficult task to ascertain future states of the Greater Toronto and Hamilton Area (GTHA) at a short-term, medium-term and long-term planning horizon. In this context, this research is motivated to investigate a comprehensive framework to model residential location choice behaviour in the GTHA and assist in predicting evolution of location patterns over time. Despite early innovations in aggregate forecasts of land use components in terms of population and employment forecasting and spatial allocation within the integrated urban modelling research field, the aggregate models are not quite effective to address complex types of recent policy instruments and to generate detailed cross-section of future urban states at different points in time. Consequently, research emphasis has shifted towards disaggregate and agent-based

14 4 microsimulation modelling over the last few years. The central idea is to represent individual agents and objects within the modelling system, and simulate the dynamic evolution of agents and objects over time and space to generate the aggregate urban system state at any planning horizon of interest. Since one of the key features of such models is to represent behaviours of individual agents, there is a vital need to develop disaggregate and empirically estimated behavioural models as opposed to rule-based experimentations, which are quite prevalent within current agent-based microsimulation model development practice. Although adoption of rules simplifies modelling complexity in many instances, the validity of the models remains vulnerable due to its shortcomings in theoretical foundations. Hence the primary focus of this research is to develop a modelling system of residential location choice processes that has strong connections to microeconomic theory, econometrics and spatial statistics. In traditional models, residential location choice is treated as a cross-sectional phenomenon, in which the locations of all households are computed within every simulation cycle. Obviously, households do not change their locations at an arbitrary point in time, typically at a year or fiveyear interval, which is chosen for running a land use model by the modellers. Among many other issues, such an implementation is inconsistent with the basic microsimulation principle of evolving agents over time and space. In addition, empirical location choice models are estimated using cross-sectional observations of households existing location that might inform the preference structure at a snapshot in time, but clearly ignores the decision-making processes at different points in time and behavioural responses along human life cycles. Davies and Pickles (1985) claim that cross-sectional analysis of spatial choice is biased and much of the current research, which uses cross-sectional methods, is therefore misleading and must be viewed with suspicion (Davies and Pickles, 1985). No doubt, there is an explicit temporal dimension in residential location choice processes since each household passes through a series of events over time and adjusts its location in response to those changes at internal and external environments. It is self-evident that each household has a housing career or residential biography once it starts living in an urban area. In order to develop a dynamic residential location model, the need to capture these transitions and subsequent investigations on alternative modelling techniques is of utmost interest, hopefully leading to

15 5 formulation of an appropriate modelling framework for microsimulation applications. However, there are virtually no empirical efforts to investigate long-term residential location choice as a process and estimate econometric models of different components of dynamic decision-making for a seamless implementation of residential mobility component within a large-scale microsimulation-based integrated land use and transportation modelling system. This research is motivated to fill this gap by extensively investigating different components of long-term longitudinal process of households location choices. Since changing locations is a complex dynamic process, modelling it is both theoretically and empirically a complicated and challenging task. It not only requires identification of timing of relocation but also necessitates examining alternative modelling methodologies to reflect the continuous nature of relocation decision-making. This research adopts a sequential investigation of different components of relocation decisions to tackle critical modelling issues, and formulates a comprehensive and holistic modelling framework to address behavioural decision dynamics. By modelling underlying behavioural processes by which a household reaches decisions to intermittently relocate from one dwelling to another through life stages will increase the ability to predict evolution of location patterns across space and would act as a vital interface between long-term decisions concerning land uses and short-term travel decisions. 1.2 Objectives The first and foremost goal of this research is to estimate behavioural models of residential location choice processes in order to implement the land use component within an Integrated Land Use, Transportation and Environment (ILUTE) Modelling System. In simple terms, the research attempts to investigate why households move, when they move, and how and where they choose alternative dwellings. The key objectives of the thesis are outlined below: To investigate longitudinal processes of household mobility and location choice decisions To develop econometric models for different components of households relocation processes To develop spatio-temporal models of dwelling asking price, and investigate determinants of housing prices

16 6 To design and formulate a microsimulation modelling framework to generate evolution of location patterns and housing prices To compare predicted location choices against observed location patterns for an extended historical period ( ) 1.3 Research significance This research provides an understanding of how to model longitudinal processes of residential relocation. It has both theoretical and practical implications. Since it investigates several behavioural assumptions such as impact of life cycle events in triggering residential mobility decisions and influence of past location on the subsequent relocation decision, it provides detailed understanding of households movement from one location to another in a given urban area from a behavioural perspective. The research investigates several critical issues of modelling longitudinal processes by testing different model structures with different assumptions, which provides an in-depth understanding of methodological challenges and possible strategies to address those issues. It also examines alternative modelling frameworks by combining behavioural economic theory and common approaches to model spatial choices. A sequential and coherent model development of different parts of long-term decision of dwelling choice significantly contributes to the overall integrated land use and transportation modelling literature. On the other hand, the research contributes to the development of an operational microsimulation-based integrated urban model by providing capacity to endogenously forecast population distribution across space that can directly feed into a travel demand model. The contribution of this thesis added a capacity to the ILUTE modelling system to simulate changes in neighbourhood composition, location patterns, housing prices and commuting patterns in response to changes in different land use and transportation policies. Hence, from a practical perspective, this thesis provides an opportunity to test impacts of different contemporary policies, both land use and transportation, including smart growth strategies and transit-oriented development on the transportation and land use systems.

17 7 1.4 Approach The research takes a disaggregate approach to modelling residential location choice processes. Households are assumed to be decision-making agents concerning choice of residences. Whereas spatial choice is a core focal point in this research, it also brings temporal considerations within its analytic framework. The research approach follows a sequential process of developing behavioural models for different components of household s decision-making. While component-wise investigation provides important behavioural insights pertinent to the respective modelling issue, it also contributes to the incremental implementation of a large-scale integrated land use and transportation modelling system. 1.5 Thesis structure This dissertation has eight chapters. Chapter 2 presents a literature review for the overall integrated urban modelling (IUM) frameworks. Chapter 3 presents the conceptual model developed to proceed with modelling different components of households long-term decision of residential mobility and location choice processes. It also identifies the process of microsimulating residential locations. Chapter 4 formulates and develops models of residential mobility decision. Chapter 5 develops models of (re) location choice. Chapter 6 investigates spatio-temporal models of housing prices. Chapter 7 presents the microsimulation model of residential location process as a part of overall ILUTE model and discusses simulation results. Finally, Chapter 8 concludes with a summary of contribution and future research directions.

18 8 CHAPTER 2: LITERATURE REVIEW 2.1 Introduction This research finds its foundation in the existing literature of integrated land use and transportation modelling and attempts to fill some gaps in the literature in terms of modelling behavioural processes of relocation. Although common emphasis on modelling travel components of an urban system prevails in practice, the importance of modelling land use components is well-recognized among practitioners and modellers due to the fact that integrated land use and transportation planning initiatives are required to address many complicated problems at hand. And, planners should have decision-support tools to forecast future states of urban systems including population and employment distributions across space over time. Clearly, residential location choice models are a vital component within the Integrated Urban Modelling (IUM) framework. As a matter of fact, most of the state-of-art integrated modelling systems only offer population and employment predictions since these are the key inputs into the classical four-stage models and/or advanced activity-based travel models. Despite gradual efforts over the last four decades, most integrated models are criticized for their lack of behavioural representation of different actors that make decisions in terms of places to live and work over time. In addition, in many cases population and employment forecasts follow an accounting framework that, while providing an estimate of future locations, does not provide an integrated framework to compute and respond to price signals. This chapter mainly reviews the existing literature of state-of-art and operational integrated models and investigates how residential locations are handled within those models. The goal is to understand critical gaps and scope to develop improved models for the location component of integrated urban models. Subsequent chapters will provide more specific and focused reviews of relevant literature of different components that this thesis aims to develop to implement an operational model. The rest of the chapter is organized as follows: section 2.2 describes evolution of residential location modelling approaches within the integrated urban modelling (IUM) framework. Section

19 9 2.3 discusses critical issues in modelling location choices within IUM, followed by concluding remarks in section Brief review of integrated urban models Many studies exist that attempt to model land use components, particularly residential locations within integrated land use and transportation modelling system. The variation of residential location models not only depends on the modelling techniques of this particular model component itself, but also on the overall modelling framework, model assumptions, spatial representation, temporal representation, actor representation, etc. The chronological development of the integrated models can be summarized by Miller et al. (1998) s taxonomy of transportationland use modelling capabilities (Figure 2.1): Land Use Model Travel Demand Model No Transit / mode split Transit / no logit (24 hr) Logit / peak-period assignment Activity-based None Activity + Judgement DRAM or equivalent Logit allocation w/ price signals Short-term goal Fully integrated market-based model Ideal Model Long-term goal First Path Advanced Path Figure 2.1 The chronological development of the integrated land use-transportation models towards the target model (Miller et al., 1998) The figure shows that land use models (i.e. location components) are gradually shifting from non-existence to aggregate estimate, and toward more disaggregated and market-based ideal target models. The main purpose of this section is not to review all urban models or every

20 10 aspect of integrated land use and transportation modelling systems, since there are already several reviews that cover various aspects of integrated model development issues (see Wegener, 1994; Miller et al., 1998; Parsons Brinckerhoff, 1998; Waddell et al. 2001, Timmermans, 2003). It will mainly attempt to highlight different major modelling streams and how location processes are represented within those operational and experimental models. Since Lowry s model of metropolis (Lowry, 1964) spatial interaction models have received considerable attention in modelling distributions of population and employment, which predominantly depends on economic base theory. The model postulates that a certain amount of employment is basic that drives an economy. Employees in the basic sector demand housing and other services that in turn create non-basic employment. These employees also create additional demand for services. Thus, an infinite but converging chain of demands are created by basic industries. The theory is translated into a spatial system of zones in which gravity models are applied to allocate service employment into zones in terms of generalized travel cost and population. The population is allocated using the same method in relation to travel cost and employment in a particular zone. The location of basic employment is assumed to be independent of the location distribution of population and service employment. The model is constrained by checking consistency between predicted distributions and the capacity, and solved by iterations for a single period. This aggregate method of predicting population and employment locations was further extended by Garin (1966) and applied for different urban areas, including the Time Oriented Metropolitan Model in Pittsburgh (Crecine, 1964) and the Projection Land Use Model in San Francisco (Golder, 1971). Putman (1983) utilizes spatial interactions as the basis of his Integrated Transportation and Land Use Package (ITLUP), which primarily consists of two components: (1) Disaggregate Residential Allocation Model (DRAM) and (2) Employment Allocation Model (EMPAL). Although the original formulation of the DRAM/EMPAL model system has experienced several changes over the years mainly due to variations in data availability, in general the DRAM module allocates households to the zones based on an attractiveness measure and travel times between zones. Similarly, EMPAL allocates employment by sector to the zones using the basic principles of Lowry (1964). At first, a preliminary activity allocation is performed to generate trip matrices, which are used within a capacity-constrained transportation network model. The resulting travel times are used to recalculate population and employment distributions. DRAM

21 11 and EMPAL typically forecast future states for five or ten year intervals. Key drawbacks of the model are large zone sizes, limited socio-economic disaggregation and static equilibrium without any price signals. In DRAM, zonal attractiveness and accessibility are the only two determining factors for distributing population locations. Parsons Brinckerhoff (1998) criticizes this component for lacking important household/demographic characteristics within the model, which are widely documented to affect residential locations, and concludes that although some testing of additional disaggregation has been completed, it has apparently not led to substantial improvement in the forecasts. We expect that this is more a function of the model construction than the insignificance of these factors in residential location (Parsons Brinckerhoff, 1998). Another major extension of the Lowry model is found in the MEPLAN (Echenique, et al. 1969) and TRANUS (de la Berra et al., 1984) family of models, in which urban spatial economy is modelled through input-output modelling techniques. The models mostly follow a social accounting matrix approach. This approach differs from the original formulation of the inputoutput method (i.e. Leontief, 1936) since it adds the region s households into the computational framework. While the input-output model predicts the change in demand for space, a spatial system is used to allocate the demand to specific zones through the use of random utility models. In addition to providing an important contribution in bringing a detailed representation of industry sectors and regional economic activity, this family of models introduces demand and supply of land/floor-space, by which price is endogenously determined through a static equilibrium assumption. The equilibrium price is increased if the total production in a sector or zone is greater than the maximum; it is decreased if it is less than the minimum through an iterative process to accommodate constraints during activity and household allocation (Echenique et al. 1990). As an extension to the MEPLAN model Hunt and Abraham (2003) develop the Production, Exchange, Consumption Allocation System (PECAS), which is implemented for state-wide models at Ohio and Oregon as well as in Los Angeles and Sacramento Region. PECAS uses an aggregate equilibrium structure with separate flows of exchanges including goods, services, labour and space going from production to consumption. Flows from production zones to exchange zones and exchange zones to consumption zones are allocated using logit function with

22 12 respect to exchange prices and transport disutilites. The exchange zones simulate markets where aggregate supply meets aggregate demand. The space of a particular region is represented by PECAS land use zones, which is recommended to be in the order of 350 zones for the convenience of model convergence. In addition, space is considered to be a commodity in the I/O computational framework, which is broadly classified as office, retail, industrial and residential. For each zone, there are two lowest level logit allocation models that determine the quantities of commodities to be sold or bought by each exchange location. The utility of each alternative depends on the price at the exchange location and travel conditions between zones. A composite utility is calculated from these two lower-level models, which is used in the nexthigher-level logit allocation of production and consumption of commodities by activities. The resulting utilities of production and consumption are feed into the location utilities used at the highest-level to allocate categories of industries and households to the land use zones. The modelling system runs yearly and uses outputs of travel disutilities and changes in space to forecast next year s flows of exchange. Alex Anas developed an integrated model for the Chicago Area (Anas, 1983), which is significantly different from the above-mentioned models in terms of design and estimation. The housing market model is deeply rooted in microeconomic theory. In general, it contains three components of market equilibrium: 1) labour market equilibrium and job assignment, 2) housing market equilibrium and 3) commercial space equilibrium. The model iterates between these markets and the transportation system for equilibrium of land use and transportation flows. The demand and supply sub-models only consider two distinct places: the CBD and the rest of Chicago. In a later implementation of the model in the New York metropolitan area, known as New York Metropolitan Transit Corporation Land Use Model (NYMTC-LUM) divides the space into 3500 zones (Anas, 1998). The land use component of this modelling system is also applied as a stand-alone housing market model, which is known as Chicago Prototype Housing Market Model, CPHMM (Anas and Arnott, 1993). Despite strong microeconomic consistency in the different modules of the model, the model relies on strong market equilibrium assumptions. Additionally, the models do not classify households/workers by type. It forecasts future end year by a single step assuming a full equilibrium. MUSSA, developed by Martinez (1997) follows an auction-based bid choice theory to allocate land uses. Households are segmented into homogeneous categories based on socio-economic

23 13 characteristics and location is defined by housing type and zone. The housing types are defined as detached, semi-detached and back-to-back. Space is subdivided into homogeneous zones based on land use and transportation characteristics. Supply of housing is determined in terms of residential use, non-residential use and mixed use. The allocation of households is primarily performed by an equilibrium solution algorithm that uses a bid function. The model is operational in the city of Santiago, Chile, and generates an aggregate distribution of locations as well as rents (Martinez and Donoso, 2001). Recently, a new supply model has been added into the modelling system, replacing MUSSA s time-series sub-model of deterministic supply (Martinez and Henriquez 2007). A demand-supply interaction within an auction framework is the key feature of this modelling system, which offers a static equilibrium model for the real estate market. The model only deals with the location of existing households. A recent paper claims that movements of relocating households can also be accommodated within the modelling system, it will however require to develop an alternative equilibrium solution algorithm (Martinez and Hurtubia, 2006). UrbanSim, developed by Paul Waddell and his colleagues (Waddell, 1998; Waddell et al., 2003; Waddell and Ulfarsson, 2003) significantly diverges from existing operational models with respect to representation of space, time and choice structure. It is predominantly a microsimulation-based model and closest to the target ideal market-based land use model (Miller et al., 1998). In most applications, UrbanSim models residential location in terms of grid-cell choice 1. The modelling system has separate modules for household location, job location and real estate development and land price models. Although early implementation of UrbanSim follows Martinez s extension of bid-choice theory (Martinez, 1992) to model location choices, it clearly differentiates itself by treating location choice and price determination mechanisms separately, and dropping the equilibrium assumption. In the current implementation of UrbanSim, the residential location choice model has two components: mobility/transition estimates and location choices. The first component determines number of households moving in a specific time period based on the movement probabilities calculated from historical data (Waddell et al., 2003). The second component is a multinomial logit model, which allocates 1 In recent applications, (for example in San Francisco Area) UrbanSim is calibrated for parcel-level residential location choice (Waddell et al., 2008).

24 14 households to grid-cells. Households are grouped into specific categories based on income, age of head, household size, workers and presence of children, The variables used in the household location model include attributes of housing in the grid cell (price, density, age), neighbourhood characteristics (land use mix, density, average property values, local accessibility to retail), and regional accessibility to jobs (Waddell, 2002). Finally, it assumes that land prices are exogenous to the household location choices; hence price determination is executed through a hedonic price model external to the location models. In the UK, David Simmonds Consulting Ltd. developed a microsimulation-based model called SimDelta to replace household decision components of an earlier land use modelling package DELTA. It expands a system of microsimulation components partly based on another microsimulation model MASTER, Micro-Analytical Simulation of Transport, Employment and Residence (see Mackett, 1990; Mackett, 1993), which was previously developed at University College London (Feldman et al., 2007). The model represents individual demographic and socioeconomic changes including ageing, survival, birth, socio-economic status, labour force participation; household changes including marriage, separation, car ownership, income, and household residential mobility and job mobility. In the current implementation, all components of the microsimulation are predominantly rule based and use Monte Carlo simulation approaches to predict future states. Integrated Land Use, Transportation and Environment (ILUTE) is an ongoing research scheme, originally initiated by a consortium of Canadian universities that includes University of Toronto, University of Calgary, Laval University, McMaster University and Wilfred Laurier University. The model is envisioned to be a fully agent-based microsimulation models that would replace conventional, aggregate, static models for the analysis of a broad range of transportation, housing and other urban policies (Miller et al. 2004). The prototype ILUTE modelling software developed by Salvini (2003) is a time-driven microsimulation model in which the system state is evolved from an initial known year to any future state, one time-step at a time. Since the system state is defined in terms of individual persons, households, dwelling units, firms etc., disaggregate information of the model is synthesized from the census data, travel survey data, activity data, and randomly generated proxy data. In addition, the software can import spatial and non-spatial data, and track activities and behaviour of individual objects in the system as they evolve through the model run from an arbitrary date (Salvini and Miller, 2005). The prototype

25 15 model completely implements an auto-ownership sub-module and shows a visionary framework to develop a residential location module at the elemental level of households and dwelling units. This modelling system is under development at the University of Toronto for the last several years and gradually adding capacities to simulate different behavioural processes in an urban system. Integrated Land-Use Modelling and Transportation System Simulation (ILUMASS), a German initiative for Dortmund Region is another group project of the institutes of the universities of Aachen, Bamberg, Dortmund, Cologne, and Wuppertal. The on-going research project aims to include models of demographic development, household formation, firm lifecycle, residential and non-residential construction, labour mobility and household mobility within a microsimulation environment (Moeckel et al. 2002). It is a raster-based model for a population of 2.6 million, where space is subdivided into 100X100 meters raster cells (approximately 207,000 raster cells for a 246 zones). The land use components including residential mobility are still under development; details of realization of individual model components are yet to be observed. Another microsimulation-based experimental model developed for the Northwing of the Dutch Randstad, Predicting Urbanisation with Multi-Agents (PUMA) attempts to represent behaviours of specific actors (Ettema, et al., 2007). The model considers grid-cells for the residential location choice model and conceptualizes an optimization of lifetime utility for relocation decisions (see Devisch et al., 2005). Operationally, the model implements a nested logit model of decision to search, decision to move and location choice model. Although in the current implementation, the models are simple and static in both model design and estimation, it aims to implement richer, new and behavioural models in the future (Ettema, et al. 2007). 2.3 Issues in modelling residential location within an IUM framework Clearly, the above discussion of different models shows that modellers tackle residential location choice within an Integrated Urban Modelling (IUM) framework by at least three different ways: 1) gravity-based aggregate allocation models, 2) aggregate allocation using logit functions, 3) microsimulation models using disaggregate modelling methods. The first two methods of aggregate location allocations are heavily criticized for the aggregate design and lack of

26 16 behavioural choice models. While the use of distance-decay functions seriously undermines the behavioural validity of residential location processes, it is evident that although some models replaced the spatial interaction model component by a multinomial logit model, many essentially remained aggregate in nature, and therefore might as well be characterized as an entropy-maximizing models as opposed to a discrete choice, utility-maximizing models (Timmermans, 2003). In addition, most of these models are static in nature, and instantaneously distribute people at an arbitrary point in time. However, households adjustments of their residential locations are not instantaneous because of the high transaction and relocation costs as well as the physical and psychological burdens associated with a residential move (Ben-Akiva and de Palma, 1986). Although instantaneous allocation of population provides estimates of locations at a certain level of statistical precision, it ignores the fundamental process of continuous movements within an urban area, which is a key determinant of changing dynamics of neighbourhood composition that has immense implications in activity generation and travel patterns over time. Due to their inherent design and computation framework, it is not possible to track households movements in aggregate spatial interaction models, spatial I/O based models and aggregate economic models. In many cases aggregate models deal with counts of households as opposed to explicit representation of individual households in the modelling system. Hence decision-oriented models of residential location are generally missing within those integrated land use and transportation models. On the other hand, the emerging field of microsimulation modelling depicts households as agents, and attempts to simulate the behaviour of agents and their interactions with other agents, objects and processes. Due to the complexity of various interactions and the detailed nature of an agent-object-process representation, there is a general tendency within agent-based modelling to replicate behaviours using rules or heuristic simulations. Unless rules are retrieved from observed behaviours with reasonable statistical confidence, performance and reliability of those models are open to question. However these innovative research projects put together a skeleton for future generation land use models, and raise interest in the disaggregate modelling of socio-economic processes, including residential location that minimizes aggregation bias and increase behavioural fidelity (Goulias and Kitamura, 1992).

27 17 Similar to travel decisions in which a person decides to engage in a certain activity, chooses destination and timing of departure and selects modes and routes, in the case of residential location households also undergo a series of intertwined decisions, including the decision to move, to purchase or rent, and to select an alternative dwelling to relocate. Therefore, modelling these decision components is of utmost interest to provide a behavioural foundation to the land use component of integrated land use and transportation models. Apart from introducing behavioural validity in terms of process representation within microsimulation-based land use models, it is also important to rethink at what spatial level residential location choices should be modelled. The traditional approach of conceiving space as different forms of zones and labeling zones as choice alternatives appears to be problematic, both theoretically and behaviourally. Typically, zones are arbitrary abstraction of the entire space defined by the modellers to allocate households at smaller spatial units. There are numerous reasons why zones are used in spatial choice modelling. It is further augmented by the usual unavailability of micro-data for all the alternatives at the original level of the elemental alternatives, i.e. dwelling units (Lerman, 1983), and a limited willingness to challenge the traditional norm of neighbourhood-choice modelling (Guo, 2004). Theoretically, it raises the question of where to put the boundary of the neighbourhoods, giving rise to the Modifiable Areal Unit Problem, MAUP (see Openshaw, 1984; Fotheringham and Wong, 1991) and leading to potentially inaccurate analytic outcomes of spatial choice processes (Guo and Bhat, 2007). In addition, since housing is a heterogeneous and highly differentiated commodity, assumptions concerning the homogeneity of zones in terms of dwelling properties rarely hold. Behaviourally, consumers choice of location involves specific dwelling unit with associated dwelling characteristics as well as price (Quigley, 1984). Moreover, unless there is a model for dwelling choices, it is not possible to represent dwelling-by-dwelling transactions through a bidding or negotiation protocol between buyers and sellers (as experimented with by Devisch et al., 2005). Therefore it is crucial to model households choice at the elemental level of the dwelling unit, which is also compatible to the central theme and design framework of object-oriented microsimulation. Another important issue is the determination of housing prices within an Integrated Urban Modelling (IUM) system. Aggregate economic models seem attractive since an equilibrium assumption provides a theoretical backbone to generate prices that match demand and supply at

28 18 each point in time. While equilibrium itself can be regarded as a strength for those models in this regard, it is potentially a weakness due to a growing consensus over system disequilibrium, with the valid observation that a market never perfectly clears (Waddell, 1998). How to determine prices within a disaggregate disequilibrium context is still a critical research challenge for the integrated urban modelling community. The most widely implemented operational model across the United States, UrbanSim generate prices through a hedonic price model assuming independence from the location choice processes. 2.4 Concluding remarks Residential location choice is considered to be an essential component of integrated land use and transportation models. However, in many cases this location process is very loosely implemented within the modelling systems. Particularly, it lacks behavioural foundations both in terms of process representation and addressing continuous movements of households over time. Since land use changes are outcomes of combined acts of different agents, next generation land use models should comprise of models of individual decision-making. Similarly, since urban modellers are expecting to use these models for forecasting future urban states and testing policies, it is important to recognize the longitudinal character of residential location processes, i.e. households continuous movements within an urban area, which might be an outcome of policy interventions. Therefore, this research attempts to investigate microbehavioural disaggregate models of households relocation processes to develop a next generation Integrated Land Use, Transportation and Environment (ILUTE) modelling system. In addition, since households competition for space determines price of housing, which is an important outcome of residential location choice processes, this research empirically investigates housing prices and sets a framework to develop market-based housing models.

29 19 CHAPTER 3: CONCEPTUAL FRAMEWORK FOR MODELLING LOCATION PROCESSES 3.1 Introduction Recognizing a need to investigate disaggregate microbehavioural residential location choice models, this chapter conceptualizes residential location choice processes to be implemented within the Integrated Land Use and Transportation (ILUTE) modelling system. Details of the ILUTE modelling framework are documented in Salvini and Miller (2005). The overall model structure is presented in Figure 3.1. Demographics Land Use Regional Economics Location Choice Government Policies Auto Ownership Transport System Activity/Travel & Goods Movement Dynamic Traffic Assignment Model Flows, Times, etc. External Impacts Figure 3.1 The ILUTE modelling framework

30 20 The prototype software of ILUTE 2 developed by Salvini (2003) provides only a conceptual/ computational framework for residential locations. The key goal of this research is to estimate behavioural empirical models of residential location choices to append the capacity of ILUTE software to predict evolution of household locations. This chapter is organized as follows: section 3.2 provides an understanding of microbehavioural relocation processes with discussions of relevant literature. Section 3.3 discusses a conceptual model that identifies different model components of residential relocation, which is empirically investigated in the subsequent chapters. Finally, section 3.4 describes a modelling framework for spatial housing market microsimulation followed by concluding remarks in section Understanding microbehavioural residential location process Since the seminal work of random utility theory and application of discrete choice models for residential location analysis (McFadden, 1974; McFadden, 1978) several authors have investigated modelling of residential location within various contexts. Applications range from examining effects of public services and community attributes (Friedman, 1981), race (Gabriel and Rosenthal, 1989; Sermons, 2000), gender (Sermons and Koppelman, 2001) and transportation factors (Weisbrod et al., 1980; Sermons and Seredich, 2001) on location choice decisions to interdependent models combining other choice dimensions, for example, activity choice and residential location (Ben-Akiva and Bowman, 1998), location, housing, autoownership and mode choice (Lerman, 1976), home, workplace and mode choice (Abraham and Hunt, 1997) and residence and work location (Waddell et al., 2007). Although a separate stream of longitudinal relocation choice modelling has existed for some time (Porell, 1982), this field has only been rediscovered very recently, 3 in terms of the recognition that a household has a housing career/residential biography, i.e., a sequence of dwelling units that it occupies over time (Kendig, 1990). Similar to job careers, households change residences in response to the need for bigger space and better quality housing (Clark and Ledwith, 2005), which, of course does not necessarily mean a 2 The software is written in object oriented programming language C++. 3 For example, Miller and Haroun (2000), Habib and Miller (2005), Eluru et al. (2008).

31 21 linear progression towards higher quality residences (Hamnett, 1999). Rather a complex and dynamic set of interactions of life-cycle events, including aging, seeking and keeping jobs, marriage/divorce and changes in environmental conditions, determine the path to different residences at different points in time during human life stages. The process of residential mobility is therefore of main importance and is one which has been studied by sociologists, economists, geographers and social scientists, particularly those taking an essentially behavioural approach (Pickles and Davies, 1991). The central argument of this approach is that all households do not change their locations at an arbitrary point in time; rather location choice follows a continuous process of adjustments by households through time with respect to mobility and relocation decisions. Brown and Moore (1971) conceptualize relocation as a sequential decision-process that has two distinct phases: (a) the decision to search, and (b) the decision to relocate after evaluating alternative locations. Speare et al. (1974), however, propose a three-stage process of (a) the development of a desire to consider moving, (b) the selection of an alternative location, and (c) the decision to move or stay. Both conceptual models are criticized by Porell (1982) who raised the question of discrete separation of decision components. Although Smith et al. (1979) put forward a simultaneous analytical formulation integrating the decision to search and the search process itself, the concepts were never realized in empirically supported models. Behaviourally, it is conceivable that households make decisions regarding relocation in steps. Unless households have enough reasons to consider a residential move, it is unlikely that they will actively search for alternative dwellings in the housing market. Continuous search is passive in most cases and can be considered as a process of information gathering for decisions to move and subsequent location choices. Practically, a sequential model system is empirically plausible with existing residential mobility/search surveys. In addition, such a simplification facilitates focusing on individual decision components as a practical approach to the piece-wise development of overall empirical relocation choice models (Cadwallader, 1992). Conceptualizing relocation as a process reiterates inclusion of an explicit decision to search model in relation to households continuous movements through time. Rossi s (1955) pioneering work of why families move plays a significant role in perceiving residential mobility as an outcome of residential stressors since he asserts mobility as

32 22 the process by which families adjust their housing to the housing needs that are generated by the shifts in the family composition that accompany life cycle changes (Rossi, 1955). The original stress concept is introduced by Cannon (1932) and Selye (1936) that has wide applications in the field of psychology, physiology and medical sciences, in which stress refers to the state of an organism subjected to the stressors as defined by environmental and physiological changes (Selye, 1956). Since Rossi (1955) s proposition of residential stress and Wolpert (1965) s subsequent discussions of behavioural aspects of household mobility, several authors have investigated mobility decisions theoretically and empirically 4 with respect to residential stress and continuous process of decision-making. The decision to move is assumed to be a function of the household s present level of satisfaction and of the level of satisfaction it believes may be attained elsewhere, and the difference between these two levels is defined as stress (Cadwallader, 1992). Despite appealing theoretical arguments, the early empirical mobility models are largely dependent on subjective ratings of satisfaction for current and future situations obtained through housing surveys. Several statistical methods, primarily event history analysis techniques, are used to explain households mobility behaviour in recent literature, including logistic regressions and hazardbased duration models. Building upon their emphasis on longitudinal modelling, Davies and Pickles (1991) provide the first examination of event history analysis for mobility modelling, using Cardiff, England as their case study. Several authors subsequently aim at pooled crosssectional and longitudinal analysis of residential mobility (Clark, 1992; Clark and Huang, 2003 among others). Although a few studies investigate mobility models at the urban scale (i.e. Hollingworth and Miller, 1996; Clark and Ledwith, 2005), the majority of the studies basically examine national sample data (for example, van der Vlist et al., 2001; Clark, et al., 2003 among others). Hence, very little is known regarding mobility behaviour at the intra-urban level, and modelling of it is of great interest to develop disaggregate procedural models of relocation since it essentially initiates households activity in the urban housing market. 4 See Clark and Cadwallader (1973), Brummer (1981), Phipps and Carter (1984), Phipps (1989), Huff and Clark (1978), Henderson and Ioannides (1989), Porell (1982).

33 23 Once a household decides to move, it enters into a search process in which it evaluates alternative dwellings as candidates for relocation. During search, the household physically visits residences, collects information from active/passive sources, and performs mental simulations concerning detailed trade-offs of dwelling and location characteristics to finalize a residence to which to relocate. A majority of the search activities are latent in nature. Although some authors investigate search behaviours 5, explicitly modelling the search process is found to be difficult since the collection of information during search and the mental information processing of decision-makers are rarely observed. Since only the outcome of location choice is documented in most revealed preference surveys, the modelling of location choices predominantly follows compensatory utility maximization approach that is based on observed outcomes 6. Like many choice problems, representing residential location choice within a utility framework contradicts the psychological concepts of bounded rationality and limited capacity to information processing (Hooimeijer and Oskamp, 1996). Miller and Haroun (2000), however, outline several advantages of using a utility-based approach that include: (a) since the attribute space within which households are working in their evaluation of alternative dwelling units is large and complex, it is difficult to envision a non-utility -based method, which would be capable of dealing with such complex tradeoffs; (b) at the stage of comparing individual vacancies, detailed evaluations among a variety of attributes do occur, and these more often than not involve (at least approximately) marginal, compensatory tradeoffs (more floorspace, smaller yard; better neighbourhood, farther from work; etc.) of the sort assumed in typical utility functions; and (c) operationally, the approach would allow to exploit the considerable methodological experience which has been gained in the use of random utility models over the past thirty years in relation to location choices. 5 For example, search behaviour analysis in Pushkar (1998) and Poon (2000), and modelling search duration and frequency of vacancy visits in Habib and Miller (2007) among others. 6 Transportation planning research field have extensively used this modelling approach in explaining location choices, which is outlined in the beginning of this sub-section.

34 Conceptual model of residential relocation Based on the foregoing discussion of microbehavioural location processes, this research conceptualizes a sequential model that has two distinct model components: (1) decision to move, (2) evaluation and (re) location decision. The distinction of model components conforms to the original formulation of household decision-making process by Brown and Moore (1971) and the dynamic residential location model structure investigated by Ben-Akiva and de Palma (1986). Whereas the first component explores when and why households move, the second component deals with where to move, leading to a relocation decision Decision to move Investigation of the first component is largely motivated by the concept of stress and behavioural arguments made in the social sciences discussed in the previous section. Since it is observed that the household responds to the changes in its states through time, several life cycle events and changes in household conditions through life stages are identified to be residential stressors. Consequently, birth/adoption/death of a household member, increase/decrease in household size, job change, retirement, income change, increase/decrease in jobs in the household and many other life cycle factors as well as changes in neighbourhood quality, market condition and transportation options are hypothesized to be residential stressors. These change of states 7 can easily be computed by comparing two consecutive years conditions if a panel/retrospective dataset is used to develop mobility models. Beyond conceptual clarity and straightforward computation, the use of stressors in the mobility models has at least two additional advantages. First, the notion of stressors is quite compatible with the architectural design of prototype ILUTE software that uses a stress-manager class, which is responsible to resolve stresses arising from different sub-modules of ILUTE modelling system (Salvini, 2003). Identifying common stressors would allow evaluating other decision components, such as auto-ownership in an integrated way in relation to mobility decision. For instance, a change in job location might prompt a decision-maker to buy a car instead of considering a residential move. Since these interdependencies must be addressed in the future, a stressor-based approach provides flexibility 7 Alternatively, it can be termed as dynamic variables as used in auto-transaction models of ILUTE (see Mohammadian, 2002).

35 25 to establish interactions between linked decisions at the household level. Second, this approach might provide a mechanism to link the long-term decision of residential location and the activitybased travel model (for example with TASHA, Miller and Roorda, 2003) without additional conceptual arguments, by identifying appropriate stressors that arise from the changes in travel options and activity schedule 8. Building upon the above discussions, this research intends to model residential mobility and examines the impacts of hypothesized stressors (alternatively, dynamic variables). Basically, this component would determine for each household the timing of mobility decisions. One of the critical model design issues is the treatment of time, i.e. how to represent time in the model structure. Typical event history models assume a continuous temporal profile. Probability of an occurrence of an event is thus modelled in a dynamic time-dependent fashion. On the other hand, time can also be discretized by assuming an approximation to continuous time. Both methods have their advantages and disadvantages. The research will investigate both continuous-time and discrete-time temporal representations, and test alternative model structures to explore the appropriate modelling method of residential mobility to be implemented within the microsimulation model. The second important modelling issue is how to imitate the assumption of housing career or residential biography within the model structure. Housing career essentially incurs a condition of repeated choices by a particular household over time. There is virtually no evidence in the existing mobility literature that attempts to incorporate heterogeneity effects due to observations of such repeated choices. This research specifically attempts to investigate this crucial issue by testing models of alternative specifications Evaluation and (re) location decision This modelling component determines how a household evaluates alternative dwellings and chooses a new location once it decides to move at a particular point in time. Since a relocating household occupies a residential unit while searching for an alternative, the (re) location choice model is formulated in a different manner. As discussed earlier, most residential location choice 8 Roorda, et al. (2006) experimented such concepts with models of auto transaction and activity scheduling.

36 26 models are cross-sectional in nature. Hence there is no assumption of history dependency in those models. However, the notion of constant adjustments of dwelling needs by the household through time implies that a household s preferences might depend on the dwelling units it lived in previously. Presumably, households choose alternative dwellings in reference to the dwelling units and location characteristics it enjoyed in their previous locations. This history dependency can be explained by the psychological descriptive model of the prospect theory (Kahneman and Tversky, 1979), in which the choices are assumed to be made based on a reference point, usually the status quo, and in terms of gains and losses. Tversky and Kahneman (1991) extended the model for the case of riskless choices and demonstrate its application for the job choice situations. For example, in an experimental study they illustrate that an individual currently employed at a job with isolated social contact and ten minutes commute time faces a choice situation to switch a job for two options, job X and job Y. Whereas the job X is characterized by limited social contact with others and twenty minutes commute time, job Y is defined by moderately sociable with sixty minutes commute time. The experiment shows that the individual frames their choice problem in reference to the existing job and evaluates the alternative in terms of advantages and disadvantages for the job switch. The advantage of attaining higher degree of social contact is defined as a gain, while the disadvantage of greater commute time is evaluated as a loss. The experiment reveals that people do evaluate their choices with respect to a reference point and are more sensitive to losses than gains 9. Application of this theory to the modelling of change of residences not only allows the modeller to include a linkage with the previous home and evaluation of alternatives in terms of gains and losses, but also facilitates the examination of loss aversion attitudes of human decision-making, a behaviour that has long been argued to exist by behavioural economists. To implement and test properties of the prospect theory, this research adopts a referencedependent choice model that takes advantage of random utility maximization (RUM) principles (McFadden, 1974). RUM models are used by almost all neighbourhood choice, zone choice and grid-cell choice models in the spatial choice literature. In addition to the evaluation of alternatives with respect to gains and losses, the location choice model developed in this research 9 Similar experimental studies are quite common in psychology and behavioural economics, which affirm existence of reference points and human loss aversion attitudes.

37 27 diverges from conventional models in at least two other ways. First, it models households choice of dwelling units, which enables it to perform dwelling-by-dwelling transactions in the microsimulation application (see Chapter 7). Second, the choice pool for each choice situation is the entire set of dwelling units that is supplied during a particular period. Unavailability of such micro supply data is one of the key obstacles for implementing location choice models at the elemental unit of analysis in most previous models. Household location choice is obviously related to other choice dimensions, for example, job locations. However, this research specifically focuses on developing models for residential location only. Hence it is assumed that households job location is given. This assumption facilitates the use of job-residence distance, travel time and cost in the hypothesis testing procedures during model development. Interdependency with the job location choice processes in terms of whether a job switch follows a residential mobility decision or residential relocation follows job switch are strictly kept for future research. Given its importance for developing a comprehensive land use model within an Integrated Urban Modelling framework, addressing such issues is of immediate priority task for the ILUTE modelling team. Given known job locations, the residential location model is linked with travel demand models through measures of accessibility. In this version of the models, individual commute travel times and costs are considered in hypothesis testing. More comprehensive and dedicated research efforts are needed to measure alternative forms of accessibility since these models are envisioned to integrate with activity-based travel demand models. Figure 3.2 shows a conceptual representation of residential location, job location and travel demand models. In the current stage, it is assumed that the land use models and transportation models will run separately. However, feedbacks of accessibility measures will be provided from the transportation model after each simulation run and vice-versa. In the current implementation of ILUTE, all accessibility measures are expected to be provided exogenously by running a separate travel demand model.

38 28 Synthetic population (Persons, Households) Demographic update Job/employment update Decision to move (Residential mobility) Job change (Job mobility) Residential location choice Job location choice Accessibilities, travel time, travel cost, etc. Transportation network Travel demand model (Mode choice, traffic flows) Figure 3.2 Conceptual relationships between residence, job and travel models

39 Microsimulating spatial housing markets From the discussion in section 3.3, it is clear that this research intends to develop two sequential decision components to microsimulate residential locations. Figure 3.3 shows the modelling framework of the housing market microsimulation. Residential Mobility Decision Model Active Households in the market Active dwelling in the market Active new dwelling in the market New Housing Supply Decision Models Household (re) Location Decision Model Dwelling Asking Price Model Asking price for all dwellings Market Clearing Process Outputs Location patterns of the households Transaction price of the dwelling in the housing market New Dwelling Supply in the market Figure 3.3 Modelling framework of microsimulating housing market

40 30 It is expected that the residential mobility model will provide an estimate of housing demand in terms of who is going to be active in the housing market in a given simulation year. Then, the (re) location choice model can be used to establish preference orderings for each active household for a given set of active dwelling units it considers to relocate. These active dwelling units will come from two different sources. First, relocating households are assumed to put their dwelling as soon as they become active in the market. Second, developers will provide a new stock of dwelling units in the market. These active dwellings require an asking price to mimic auction-type bargaining of buyers and sellers in the housing market, which motivated this research to estimate an asking price model. The existing literature on housing prices is abundant and voluminous. Most of the housing price models are derived from Rosen s (1974) hedonic price methods. The key assumption in housing price modelling is that the price of dwelling units can be described by a vector of distinct characteristics, the marginal values of which measure the implicit prices of housing attributes (Rosen, 1974). Typically, the price of properties is assumed to be a function of structural, neighbourhood, transportation and locational attributes. Several authors review theoretical foundations, basic model structures, estimation procedures and empirical applications (see Anselin, 1988; Can and Megbolugbe, 1997; Baranzini et al., 2008 among others). Investigation of housing prices involves several critical modelling issues. First, since economic theory does not suggest any specific functional form of the hedonic functions, functional specification of the model should be tested, unless there is enough empirical evidence to select one (Halvorsen and Pollakowski, 1981). Second, although spatial autocorrelation is one of the most investigated properties of hedonic price models (Fotheringham et al., 2002), corresponding consideration of temporal autocorrelation is rarely examined despite the use of multi-period data in many housing price models. This research specifically attempts to address this issue in developing a dwelling price model for the Greater Toronto Area (GTA) since it uses a multi-year time-series dataset. In terms of factors that affect property prices in the GTA, the research tests a series of hypotheses concerning transportation access, dwelling characteristics and neighbourhood qualities. In addition, the models examine housing supply attributes that reflect impacts of temporal environment of the housing market on the asking price of properties. As mentioned earlier, this asking price model is used to estimate the initial base price for all dwellings active in the housing market in a given simulation step and initiates the market

41 31 clearing process. The market is cleared through an iterative process. No system equilibrium is assumed for the market clearing process. A primary outcome of the market clearing process is the transaction prices, which are obtained from the processing of dwelling-by-dwelling transactions. Details of the market clearing process are documented elsewhere (Miller et al. 2009). 3.5 Concluding remarks This chapter discusses the conceptual background of this research and develops a conceptual model that addresses behavioural issues of residential location processes. It identifies key modelling components, which are to be empirically tested in order to implement households decision-making process of relocation in tandem within a microsimulation context. The next chapter describes the modelling of the first component, a decision to move. Chapter 5 then introduces an evaluation and (re) location choice model that uses a prospect-theory based reference-dependent choice modelling framework. Housing price models are presented in Chapter 6. Finally, a microsimulation model of the residential location choice process is developed in Chapter 7.

42 Introduction CHAPTER 4: RESIDENTIAL MOBILITY MODEL 10 As discussed in the previous chapter, the first stage of the relocation process is the decision by an individual household to become active in the housing market, which is termed in this research as the residential mobility decision since it implies the household s desire to move from its current residential location to a new location. Although a few current integrated models such as UrbanSim and ILUMASS have residential mobility sub-modules, operationally they simply use historical mobility rates to generate housing demand at a given point in time. This research attempts to empirically investigate this decision component, and examine alternative modelling techniques to implement this model component of residential relocation within the ILUTE modelling system. Note that this chapter solely deals with the housing demands that are created by households who are already resident of the study area. Other types of mobility decisions including in-migration, out-migration and new-household formation are handled separately in a much simpler fashion within the demographic component of the ILUTE system. As indicated earlier, this research investigates a longitudinal process of households change of dwellings at different points in their life-stages. As a result, a sequence of dwellings and span of time can be identified for each household, which is defined as the housing career/residential biography. The objective of this chapter is to develop models to represent the transition probability of changing one dwelling to another at different points in time. It is also evident that in many instances households encounter residential stresses to search for alternative dwelling in the market, but do not end up relocating due to affordability and/or suitability reasons. This research also includes such instances within its empirical investigation, which is quite unique in the existing mobility research. 10 This chapter is derived largely from the paper: Habib, M.A. and Miller, E.J. 2008a. Modelling Residential Mobility and Spatial Search Behaviour: Estimation of Continuous Time Hazard and Discrete Time Panel Logit Models for Residential Mobility. Reviewed CD-ROM. 87 th Annual Meeting of the Transportation Research Board (TRB), Washington, D.C., January

43 33 This chapter presents two modelling techniques, discrete-time panel logit models and hazardbased duration models to represent households decision to consider a move, which are primarily different in terms of their treatment of time within the modelling framework. The first method discretizes time into yearly intervals and assumes a decision situation in which households decide to become active in the market at each time step. On the other hand, the second method assumes a continuous time framework, and the probability of considering a move depends on hazard functions. The first method is similar to various recent applications of mobility models (see Clark and Ledwith, 2005). Inclusion of time-varying covariates is quite straightforward if time is discretized and the mobility decision is formulated as a discrete choice problem through a continuous stretch of time. This research uses a retrospective residential mobility survey dataset for the Greater Toronto and Hamilton Area (GTHA) to test various hypotheses regarding the determinants of the mobility decision. As discussed in the previous chapter, one of the major shortcomings of the existing mobility literature is that, despite housing career being considered to be the principal behavioural base to explore continuous movements of households across space, previous model structures do not adequately address the repeated nature of choices. By definition, a housing career consists of repeated choices within the lifespan of individual households. To rectify this situation, this research explores panel binomial logit models and tests alternative heterogeneity assumptions to capture underlying correlations due to repeated choices. This research also explores continuous-time hazard modelling techniques to model the residential mobility decisions. The models determine the likelihood of entry to the housing market depending on the length of time spent from the beginning of the last occurrence of the event as well as other relevant covariates. Since the first application of hazard-based duration models by Davies and Pickles (1991) several authors use these methods to explain mobility behaviour (for example, Hollingworth and Miller, 1996; van der Vlist et al., 2002 among others). Similar to the discrete-time models, existing models in the mobility literature assume single-spell durations for the events, which lead to the assumption that event timings are independent. But a housing career essentially involves repeated spells for many households if panel/retrospective survey data are considered. Failure to account for this correlated event timings incurs biases and inefficiency in the models for repeated event contexts (Box-Steffensmeier and Boef, 2006).

44 34 Therefore, this research specifically tests random effect/shared frailty models to account for this correlation in the estimation process of continuous-time hazard models. The rest of the chapter is organized as follows: section 4.2 describes the mathematical formulation of the models that are tested and the methods used to estimate their parameters from the available data. Section 4.3 describes the data that are used to develop the models. Section 4.4 presents and discusses the estimation results obtained for the models that are tested. Section 4.5 then concludes the chapter by discussing the choice of the specific model that is implemented in the current version of ILUTE. 4.2 Residential mobility model structures As discussed above, the residential mobility decision involves a household choosing whether to become active in the housing market at a given point of time or not. It is assumed that households are the decision-making unit (DMU) 11 for the residential mobility decisions. Two different modelling techniques suitable for representing this decision are discrete choice methods and hazard-based duration models. In the following sub-sections the model structures used in this study are briefly discussed: Discrete choice models Within the discrete choice framework, this research investigates the use of binomial logit panel data models that incorporate different assumptions concerning heterogeneity effects within the process. The assumptions tested are: Fixed Effects (FE), Random Intercept (RI) and Random Parameter (RP) models. All these three models are estimated using commercial software (LIMDEP 8.0). The theoretical background and estimation methodologies are discussed in detail in Greene (2002). This research uses the FE model specification to accommodate individual heterogeneity in the panel binomial logit models by examining group specific effects: P ( yit i it = 1) = g( α + β x ) (1) 11 In this chapter, DMU specifically refers to the single-family households (couples, couples with/without children, single adult, single parent with children) living in one place.

45 35 where P ( = 1) represents probability of the binary choice of being active in the housing y it market. x it and β are explanatory variables and corresponding parameters to be estimated respectively. And, α i denotes group specific effects (or constants). In this particular application, a group means a DMU that has a sequence of choice occasions (whether to become active in the housing market or not) over time. For a given set of DMUs ( i = 1,2,... N) at different unit time periods (i.e. choice occasions, by: t = 1,2,...T ) the unconditional log-likelihood function is given i LnL = n i ln T i= 1 t= 1 Λ[(2 y it 1)( α + i β xit )] (2) where Λ (.) is the logistic distribution, Λ ( z ) = exp( z) /(1 + exp( z)), and the term ( 2y 1) determines the sign negative for y = 0 and positive for y = 1 (see Greene, 2003 and it Chamberlain, 1980). Depending upon the group size in the panel dataset, the number of parameters to be estimated for this model can be very large. Hence maximization of this loglikelihood function is tricky. One approach to deal with the problem is to condition out the fixed effects from the log-likelihood. Therefore, estimations of group-specific fixed effect parameters are no longer required. The conditional log-likelihood is obtained by conditioning the contribution of each group i to the sum of the observed outcome, which can then be maximized with respect to the slope parameters, β (for details see Chamberlain, 1980). it it The second approach is a direct maximization of the log-likelihood function (equation 2) to fit the model with all parameters including fixed effects (which is referred to be unconditional fixed effects model in this thesis). Obviously, this estimation is non-trivial with traditional method of full maximum likelihood estimation. Greene (2001) proposes a brute force maximization procedure that takes advantage of the properties of the sparse second derivative matrix. It is observed that with the fixed effects parameters, a part of the matrix is actually a diagonal matrix. Therefore, it is not necessary to compute the entire matrix, which significantly minimizes computational burden. Consequently, it is possible to compute a large number of parameters in a fixed effects model through brute force maximization. However, in this case, there is no covariance matrix computed for the fixed effects. So it is not possible to perform any statistical inference for individual fixed effects.

46 36 The second specification, Random Intercept (RI) model introduces heterogeneity in the form of random effects: P = 1) = g( β + ψ ) (3) ( yit x it i where ψ i is the unobserved heterogeneity, which is a single common random effect for all observations in group i. The difference between α i in equation (1) and ψ i in equation (3) is that while α i is fixed group-specific effects, ψ i represents a random component which is usually assumed to be normally distributed. That s why this model simply has a random intercept with a mean and a variance. The primary virtue of this specification is its parsimony, which adds only a single parameter to the model (Greene, 2001). Finally, the third specification is a Random Parameter (RP) model. In fact, it is a variant of RI model in which all the parameters can vary randomly over decision-makers. The structure of the model is given by a conditional probability: Prob[ y it = 1 xit, β i ] = g( β i xit ), i = 1,..., N, t = 1,... Ti (4) If β i is assumed to be a random parameter, each parameter can be defined as follows: β = β + Γ (5) i v i where β is the fixed means of the distribution for the random parameters, v i is a random vector which introduces latent random term for the i th observation in β i, and Γ is lower triangular matrix which produces the variance (i.e. Γ Γ ) for the random parameter. To estimate the parameters of the model, the random terms are integrated out of the conditional distribution, which gives an unconditional likelihood function as follows: Ti = g( y t it, 1 i L ( Φ y, x ) = β x ) f ( v ) dv (6) i i i vi it i i where Φ denotes all structural parameters, β and Γ, which are being estimated. Since this likelihood function (i.e. equation 6) is a multivariate integral, which cannot be evaluated in

47 37 closed form, the parameters are estimated by simulation (Train, 2003). The simulated loglikelihood function is given by: LnL s = 1 R ln r β (7) R N Ti g( y i= = t= it, i r x 1 1 1, it ) The simulation is carried out over R draws on v i, r through i, r β. The maximum simulated likelihood estimator is obtained by maximizing equation (7) over the full set of structural parameters Φ. Eventually, estimates of structural parameters and their asymptotic standard errors are generated from this simulated maximization procedure (see for details Train, 2003; Greene, 2004). In the RI/RP Model, specific distributions for the random parameters must be assumed. Normal or lognormal distributions are assumed in most applications (such as Revelt and Train, 1998; Mehndiratta. 1996; Ben-Akiva and Bolduc, 1996). On the other hand, a few applications (Revelt and Train, 2000; Hensher and Greene, 2007; Train, 2001) have used triangular and uniform distributions. This research assumes all random parameters to be normally distributed with a mean and unknown variance of the corresponding parameter. In practice, it is often found that some of the parameters are random while others are nonrandom. In such cases, nonrandom parameters in the model are implemented by constraining corresponding rows in the lower triangular matrix ( Γ ) to be zero (see Greene, 2004). Note that, in the Random Intercept (RI) model, all parameters are assumed to be nonrandom except the constant term. In other words, the RI model can be seen as the RP model in which only the constant term is random Hazard-based duration models In addition to panel logit models, this research investigates continuous-time hazard-based duration models to analyze mobility decisions. Hazard models recognize the dynamics of duration since the likelihood of termination of duration depends on the length of time spent from the beginning of an event. It has wide applications in the fields of engineering, medical sciences and labour force analysis. The basic principles are well discussed in the literature (e.g., Kalbfeisch and Prentice, 2002; Lancaster, 1990; Hougaard, 2000). For a housing market application, let T be a continuous, non-negative valued random variable representing time until active in the housing market of a DMU. If the probability of a DMU leaving the passive-state

48 38 within a short interval t at or after t is P( t T < t + t T t) while the DMU is still passive in the market at t, then the hazard rate can be obtained simply by dividing the probability by that represents average probability of leaving the state per unit of time. Considering this average over very short intervals, the hazard function λ (t), which is the instantaneous rate of failure at t, is given by P( t T < t + t T t) λ ( t) = lim (8) t 0 t This basic formulation of the hazard function allows relating it with probability density function f (t), cumulative distribution function F( t) = P( T t) and survival function S( t) = P( T > t) = 1 F( t). Since the probability density function of T is t f ( t) P( t T < t + t) df( t) ds( t) lim = =, the hazard function can be written as t 0 t dt dt = f ( t) f ( t) d log S( t) λ ( t) = = = (9) 1 F( t) S( t) dt Since we are interested in investigating factors affecting termination of duration, this nonparametric model is extended to incorporate explanatory covariates leading to semi-parametric and parametric models. In general, semi-parametric models assume the hazard rate to be proportional 12 and the baseline hazard ( λ ( ) ) to be parametrically unspecified. The most 0 t popular proportional model exploits partial likelihood estimation techniques (Cox, 1972) and takes the following form: λ ( t, x) = λ0 ( t) exp( x( t)) (10) where x (t) is the vector of observed covariates, which are constant from the beginning of the measurement period ( T = 0 ), to the time of the measurement, ( T = t ).And, λ ( ) is the baseline hazard, which is not parametrically specified. 0 t 12 Proportional hazard models assume that a covariate has a multiplicative effect. That means, each unit increase of a covariate will results in proportional scaling of the hazard.

49 39 On the other hand, parametric models assume a distribution for the baseline hazard. In many cases knowledge of the baseline hazard is unnecessary. However, in microsimulating urban systems it is useful to have clear inference about λ ( ) since timing of entry and exit in different markets is of interest. Although it is possible to retrieve baseline hazards in semi-parametric models (see Box-Steffensmeier and Jones, 2004; Kalbfeisch and Prentice, 2002) this study prefers parametric models since they provide direct inference on the duration dependence. In addition, this research makes an accelerated failure time (AFT) assumption (i.e. the covariates directly rescale time), which can be expressed as a log-linear model: ln( T ) = β x + σε (11) 0 t where β are the coefficients of the time independent covariates x, and ε is a stochastic error term 13 scaled by σ. One of the key implications of formulating parametric hazard models in AFT representation is that the interpretation of the model becomes very straightforward. Here the effect of a covariate is to alter the rate at which a person proceeds through time by either accelerating or decelerating the termination of the duration. Although there are wide varieties of distributions that can be employed in the parametric models to define the baseline hazards (see Hougaard, 2000 for detail discussions), this study tests Weibull, log-logistic and exponential distributions. While the exponential distribution has the noageing phenomenon, the Weibull distribution provides constant, strictly increasing (or decreasing) hazard functions. Conversely, log-logistic distribution permits non-monotonic hazards. The hazard rates for Weibull and log-logistic distributions are given as follows: t = p t p 1 λ ( ) ϕ ( ϕ ) (12) p λ ( t) = ϕp( ϕt) /(1 + ( ϕt) 1 p ) (13) ( x) If the model is parameterized in terms of the log-linear model (i.e. equation 11), then ϕ e β =. And, p is known as the shape parameter. For Weibull model, when p < 1, the baseline hazard 13 This error term is assumed to be type-i extreme value distribution in case of a Weibull model. If a logistic distribution is specified for ε, then the log-logistic model is implied.

50 40 monotonically decreases and vice versa. For log-logistic model, the hazard decreases monotonically if p 1; but it takes a non-monotonic shape if p > 1, increasing from the origin 1 / p ( t = 0 ) to a maximum of t = ((( p 1) ) / ϕ), and decreasing thereafter as t approaches to infinity. This shape parameter, p and the coefficients, β are estimated from the observed data. The parameters of the parametric hazard models are estimated using a full information maximum likelihood estimation method (see Kalbfeisch and Prentice, 2002). Since our data is right Type-I censored, denoting δ i as the censoring indicator (taking the value zero if case i is censored and the value one if case i experiences the event), the likelihood function is given by n δ i 1 δ i δ i ( t, x )] [ S( t, x )] [ ( t, x )] [ S( t, x )] L = [ f = λ i i i i i i n i i i i (14) This univariate formulation is adequate for analyzing single-spell residential mobility (see an application in van der Vlist, et al., 2002). However, this study uses retrospective data that has repeated events recorded for each DMU. Failure to account for this repeatability might violate the independence assumption on the occurrence of events taken in the single-spell models. Hence this research examines shared frailty/random effects models that assume a stochastic variation, which is shared (common) among individuals. If DMU i has multiple episodes j, the hazard rate for the j th episode of the i th DMU can be expressed as λ ( t v ) = λ( t ) v (15) ij i ij i For a Weibull model, it takes the following form: λ ( = β v (16) p 1 t ij vi ) [exp( ij xij ) pt ] i Note that v i represents group-specific heterogeneity that is distributed across groups (in this case DMUs with repeated episodes) according to some distribution function G v ). Consequently, the likelihood function is given by ( i L = g i= 1 0 ni j= 1 δ ij [ λ ( t ij, xij )] [ S( t ij, xij )] dg( vi ) (17)

51 41 This likelihood function is maximized in order to obtain parameter estimates. The likelihood ratio test is used to assess the need for inclusion of the frailty component v i. The goodness-of-fit of the models are evaluated based on the Akaike Information Criteria (AIC) where AIC = 2 (Log likelihood) + 2(Number of Variables+ Number of Ancillary Parameters +1). The lower the value of the AIC the higher the goodness-of-fit of the corresponding model. 4.3 Data for empirical application Development of a dynamic residential mobility model necessarily requires a panel dataset. A retrospective Residential Mobility Survey (RMS II) for the Greater Toronto and Hamilton Area (GTHA) is used for the purpose. The survey was conducted during summer of 1998 and detailed description of the survey is available in Haroun and Miller (2004). RMS II is a follow-up survey of RMS I (see Hollingworth, 1995 and Hollingworth and Miller, 1996). While RMS I deals with only the last five years housing career of the households, RMS II asked respondents to report their housing careers starting from the formation of the household, or the point of time the household moved to the GTHA, or at least the three previous dwelling units the household had lived in within the GTHA. Thus, the survey provides a rich panel dataset that can be used to derive longitudinal residential mobility data over a long time period ( ). RMS II is a mail-back survey of 1500 randomly selected households. These households are contacted by telephone one week after they have been mailed the survey to encourage their participation in the survey. However, only 281 complete responses are obtained. Haroun and Miller (2004) validate the sample against Statistics Canada 1996 Census data and Transportation Tomorrow Survey (TTS) 1996 data, and find fair consistency in representing the population within a few percentage points in terms of gender, tenure, household size, auto ownership and dwelling types. The survey collects a wide range of information including households housing career, market activity, household composition history, employment history, etc. For each house, detailed information on dwelling type, number of rooms, number of bedrooms, tenure, purchase price etc. are obtained. In addition, location (address) of the house, year of moving and reason of the move are recorded. For each household, person-specific detailed employment history (each of which includes the job location, category, hour of employment etc.) is collected. Finally, detailed

52 42 socioeconomic characteristics of the household supplemented by the history of household composition change (as well as reason for the change) are obtained. An important feature of RMS II is that, apart from actual moves, instances in which the household became active in the market but did not end up moving are also recorded, including explicit information describing the nature of the search activity involved and why the move was not successful. This active but did not move information is unique in the literature and provides an unbiased database for mobility model development. That is, most data sets only include successful moves and so underestimate mobility participation rates. In addition to RMS II data, this research also uses Statistics Canada census data ( ) to create neighbourhood attributes, and Canadian Socio-Economic Information Management System (CANSIM II) data for market condition indicators, such as key interest rates and mortgage rates for the period ( ). In total, a 28-year longitudinal dataset was created from the RMS II survey data, representing yearly snapshots from the year 1971 to All dwelling locations and job locations are geocoded. After cleaning for the missing values and some special cases (such as discontinuous living 14 ), out of the original 281 households 270 households were considered for further investigation. Since this model is only concerned with intra-urban mobility, other mobility decisions resulting from the formation of a new-household and immigration into the GTHA region are excluded from the dataset. For the discrete choice model applications, in total 4097 observations 15 are used for modelling, in which households were active in the housing market at 408 choice occasions in different years between 1971 and Note that the event active in the housing market includes actual moves as well as instances of attempting to move. Typical market activity that defines the second set of active in the housing market includes direct communication with real estate agents, attending open houses and inspecting vacancies. 14 For instance, a household moved to another province after living for a while in the GTHA and then later returning back from that province to the GTHA. 15 Each observation represents a yearly choice-occasion for each DMU

53 43 In order to compute measures of residential stressors (such as increase/decrease of DMU size), each year s observation for each household is compared against that of the previous year and the difference is recorded as the measure of stress. Accordingly, birth of a child, duration at the current home (or immediately prior home), change of job, etc. are identified within the dataset. Data from six census years (1971, 1981, 1986, 1991, 1996, 2001) are utilized to create yearly changes in census tract level aggregate statistics. These include population density, dwelling density, average value of dwellings, non-movers in the last five years, unemployment rate, labour force participation rate, etc. In total, twenty-three variables are created from the census tabulations. Due to changes in census tract boundaries over the years and inter-census variation in the definition of the variables, extensive efforts are needed to create consistent yearly census tract level data. Straight-line interpolation between census years are used to estimate inter-census variable values. Since it is hypothesized that there might be lag or lead effects of the stressors, dummy variables are created indicating lags and leads of the events for three consecutive or preceding years. For example, in the case of a job change, three dummy variables are created for the three consecutive previous years of the occurrence of the change to indicate the lead of the particular stressor for a given household, while additional three dummy variables are created for the years following the change to capture possible lagged responses. The same RMS II dataset is used to estimate the continuous time hazard-based duration models. The 270 selected households had 623 episodes (i.e., household passive-state durations), including censored spells. A censored spell represents an episode in which the event of interest has not yet been occurred at the termination of the observation period. These right-censored spells occur due to the fact that data collection has to be stopped at some point in time, which is in this case the year of the RMS II survey (i.e. 1998). On the other hand, the complete episodes are those duration spells that are a continuous timeperiod within which households are in a passive-state from the beginning of the measurement time to the end. The state terminates with the occurrence of the event decide-to-become active that triggers actively searching the housing market for potential alternative dwellings. The average observed duration for the sample is 7.35 years with a minimum of one year and a maximum of fifty-five years. Covariates (explanatory variables) used for the hazard models are

54 44 also taken from the same sources, but only those that are constant or assumed to be constant for the entire duration of an episode (or time-spell). Time-varying covariates are not tested in these models. As such, year of birth of the household head, number of bedrooms and other structural attributes of the dwellings, and neighbourhood attributes are tested during model development. 4.4 Model estimation results Panel Logit Models Table 4.1 reports results for the binomial panel logit models. The Fixed Effects (FE) model estimated through brute force maximization gives similar results to the conditional FE model where fixed effects parameters are not estimated. In fact, conditional maximum likelihood estimation is carried out due to the presence of the incidental problem (i.e. if there is the same choice throughout the observation period). The results show that the incidental problem is not acute for the sample used for this study. The unconditional fixed effects model is estimated using direct maximization where all the group-specific effects are estimated along with coefficients of explanatory variables at the same time. On the other hand, a randomly varying constant is estimated in case of Random Intercept (RI) model to capture an unobserved heterogeneity component across decision-making units. This RI model shows greater value of goodness-of-fit statistics than that of unconditional FE models. However, the highest goodness-of-fit statistic is achieved in the Random Parameter (RP) Model that captures heterogeneity across the parameters. In addition, by considering randomly varying parameters across DMUs the RP model provides better understanding of the varying effects of different stressors on the mobility decision. Therefore this research selected the RP model as the final model. The adjusted Rho-square for the RP model is It seems reasonable since the model deals with a relatively rare event (becoming active in the housing market) with respect to the long span of households residential history (i.e. total number of years) in the urban area. Among 4097 yearly observations for all DMUs, only 408 (10.04%) instances of market activity are observed in the sample. It should also be noted that although in most cases sign of the parameters are same across alternative models reported in Table 4.1, three variables do not have same sign in the fixed and random effects model in contrast to the finally selected RP model. These differences are mainly attributable to the different assumptions on the heterogeneity structure for alternative models. Since RP model constitutes randomly varying parameters, the model provides better

55 45 estimates in terms of estimating a mean and a standard deviation for the random parameters. Therefore hypothesis testing is predominantly conducted within RP model to establish causeeffect relationships of residential mobility behaviour. Discussion of the results of parameter estimates for the final RP model is given below. It is found that most of the hypothesized residential stressors (such as increase/decrease in number of jobs, birth of a child, job change, decrease in DMU size, retirements etc.) are found to be statistically significant in explaining residential mobility. These variables are termed dynamic variables since they represent changes of states between consecutive years. The fifth column of Table 4.1 reports mean and standard deviation of the parameters estimated for the RP model. It can be seen that most of the dynamic variables are found to be random parameters whereas all of the static variables are nonrandom. Age of the household head (often used as a proxy variable for life cycle stage, see van der Vlist, et al., 2002; Mulder, 1993; Clark, et al., 1986) has a significant effect on the decision to move. Younger-head DMUs are more frequent movers than older heads. However, there is some variability of the effect, indicated by the statistically significant standard deviation. Another significant life-cycle event, birth of children also induces mobility. Similarly, job change increases the probability of moving, where the mean of the parameter is with a standard deviation of This means that although change of job location on average significantly encourages a relocation decision in order to relieve commuting stress, this effect varies considerably across households, with certain DMUs preferring other stress-release mechanisms (possibly, such as buying a new car) and do not become active in the housing market in response to this stressor. While a decrease in number of jobs in the DMU increases the probability of moving, a dummy variable reflecting retirements doubles this effect. Interestingly, these stressors do not have any statistically significant variance and hence are assumed to be non-random across the sample households. However, an increase in jobs shows a very interesting behaviour, having a negative parameter value. Our prior expectation was that such an increase would increase the probability of becoming active in the housing market. But the model result suggests an opposite effect. This could partly be explained by the results of the static variable number of jobs in the household, which is assumed to be nonrandom with a coefficient value of That means if there are

56 46 Table 4.1 Parameter estimation results of binomial panel data logit models Variables Age of head of decision making unit (DMU) Birth of a child in the DMU (dummy) Lag of two years for decrease in DMU size (dummy) Total duration in the dwelling (in years) Change in job (any member in the DMU) Increase in number of jobs in the DMU Decrease in number of jobs in the DMU Dummy variable representing retirement Fixed Effects (Unconditional) Model Fixed Effects (Conditional) Model Random Intercept (RI) Model Random Parameter (RP) Model Coef. (t-stat.) Coef. (t-stat.) Coef. (t-stat.) Coef. (t-stat.) (-9.62) (-9.40) (-12.25) * (-12.64) (1.58) (1.51) (3.55) 0.326* (3.55) (0.42) (0.40) (1.71) (1.78) (7.33) (7.06) (-13.02) * (-11.37) (3.09) (2.96) (8.69) 0.296* (4.29) (0.31) (0.37) (0.02) * (-1.69) (2.47) (2.29) (4.14) (4.51) (0.73) (0.76) (1.56) (1.47) Number of jobs in the DMU (-0.65) (-0.80) (-2.45) (-2.88) Ratio of non-movers in the neighbourhood Labour force participation rate in the neighbourhood (-2.47) (-2.34) (-1.77) (-2.19) (-0.02) (-0.21) (2.29) (1.94) Change in bank interest rate (-0.18) (-0.01) (-1.23) * (-1.23) Constant (-1.75) (-0.50) Standard deviations for random parameter Constant (0.11) --- Age of head of decision making unit (DMU) (2.12) Birth of a child in the DMU (1.51) Total duration in the dwelling (8.84) Change in job (any member in the DMU) Increase in number of jobs in the DMU (8.61) (7.94) Change in bank interest rate (1.98) LR test statistics Adjusted Rho-square * Means for random parameters

57 47 more workers in the household, the probability of becoming active is lower, all else being equal. This presumably reflects inertia effects associated with having more job locations within which mode choice, commuting patterns and other short-term activity agendas have already been determined and may be difficult to change. Therefore, an increase in jobs within a DMU actually encourages a similar stationary effect that prevents considering a residential relocation. However, the parameter of this variable also exhibits a very high variability among the decision makers, having a standard deviation of compared to the mean of This suggests that in some cases an increase in jobs actually does increase the probability of moving. Duration in the current home is also found to be one of the significant determinants of mobility. The longer the duration in the current location, the lower the probability of moving. This supports the hypothesis of inertia that impedes relocation due to strong community linkages created by longer durations of living in a neighbourhood, which is very much consistent with many other previous findings (such as McHugh, et al., 1990). In many cross-sectional studies, tenure was considered to be an important factor in explaining residential mobility. Often it was found that renters are more mobile than owners. It has also been found that highly educated persons tend to have higher mobility rates compared to less educated workers. Similarly, household size, dwelling type, number of rooms, number of bedrooms, number of people per room etc. were found to be contributing factors for mobility (see van der Vlist, et al., 2002 for a recent review). But this research indicates that most of these static attributes of the dwelling as well as decision makers are not significant when dynamic variables are taken into account in the mobility models. It is also found that neither job-residence distance nor distance to CBD is significant in explaining mobility decisions. Rejection of distance to CBD could be explainable due to the GTHA being a multi-centric metropolitan area (although the Toronto CBD is still a very important employment, shopping and cultural centre within the region). However, the study was expecting to see effects of job-residence distance or changes in average job-residence distance within the mobility decision, but these hypotheses are not confirmed. One possible reason for this unexpected result might be that the stressor job change already captures some of the effects of change in commuting distances.

58 48 Although this research examined three years of lag and lead effects for each of the life cycle stressors, the only significant lag/lead effect found is a two-year lagged response to a decrease in DMU size. That is, if the DMU size decreases it takes two years to have an impact on the mobility decision. In other words, the probability of moving increases two years after a DMU size decrease. This is a plausible response, since it may well take a household some time to decide to adjust its dwelling size and/or location in response to a change in household size. Regarding neighbourhood dynamics, the model indicates that if a DMU lives in a stable community, represented by the ratio of non-movers (in the last five years) in the neighbourhood, it is less likely to consider moving. On the other hand, the neighbourhood labour force participation rate has a positive impact on household mobility. Both of these variables are found to be non-random. A large set of other neighbourhood attributes has also been examined (for example, average dwelling value, dwelling density, renter/owner ratio, percentage of immigrants etc.). None of those variables are found to be statistically significant. Since housing supply data for a long period was not available for use in this study, it uses some housing market indicators such as change in mortgage rate, bank interest rate, etc. to include market dynamics in the model. Although this study finds both mortgage rate and bank interest rate to be significant, due to obvious correlation issues, only one of these two variables can be included in the final model. Since mortgage rates can vary for individual cases and RMS II does not provide any information concerning mortgage premiums or equity/savings, the bank interest rate has been retained in the final model. Note that this interest rate only differs across years, not for individual decision makers. Finally, it is found that changes in interest rate are negatively related with mobility decisions. This key market indicator is found to be a random parameter with a statistically significant standard deviation Hazard-based duration models The first set of hazard-based duration models is estimated assuming a single-spell for each termination. This means that each episode in the passive-state in the market for a given DMU is assumed to be independent and considered as separate observation in the analysis. But given the fact that we have collected retrospective data that contains information on the housing career of each household, it is more appropriate to consider repeated events models; this leads to testing shared frailty models. Although frailty components are examined in the single-episode models to

59 49 explore individual episode-level heterogeneity, Table 4.2 presents only the candidate shared frailty models along with two basic single-spell models. Three different distribution assumptions are used for the frailty component in these models: gamma, inverse Gaussian (Hougaard, 2000) and Gaussian distribution (Greene, 2002). The goodness-of-fit of the models are evaluated in terms of the Akaike Information Criteria (AIC), in which the lower the value of AIC the better the fit of the model with respect to the observed data. It is found that the log-logistic model performs better than Weibull models. The finding is consistent with the non-parametric 16 investigation of the duration data that suggest a non-monotonic form of the hazard rate. Finally, the result reveals that the log-logistic model with Gaussian shared frailty describes the termination probability best in terms of the lowest AIC value. Hence the log-logistic Gaussian shared frailty model is selected as the final model among continuous-time hazard models (results of parameter estimates of the final model are shown in the last column of Table 4.2). It should be mentioned that signs of all parameters in the repeated events model (i.e. random effects/shared frailty models) are the same across candidate models. However, a few variables show different sign in a single-episode model, which are considered to be biased and inaccurate due to the omission of random effects within that model. In addition, some variables show statistical insignificance in the final model specification, they are retained in the model based on the assumption that if a larger sample dataset is used those variables might be statistically significant. Detail discussions of individual variables incorporated in the final model are presented in the following sections. Note that a positive coefficient means the duration would increase as a result of increase in a covariate value since the frailty model is in the AFT metric. It is found that age of the DMU head (represented by the year of birth) has significant impact on the passive-state duration. DMUs with older heads stay passive in the housing market longer than those with younger heads. Also, a DMU who has a higher number of rooms in the dwelling unit have longer duration. Similarly, DMUs living in row houses have longer duration; possibly under income constraints they are less likely to become frequently active in the market. Tenure also affects duration; renters are more frequently active in the market than homeowners. 16 Non-parametric investigation refers to the examination of duration dependency without any covariate

60 50 Table 4.2 Parameter estimation results of single-episode and repeated events duration models Covariates Year of birth of the head of the DMU Num. of rooms in the dwelling unit Dummy row-house (1 if row-house) Dummy indicating renters (1 if renter) Dwelling density in the neigh. Single-detached dwelling density Ratio of non-movers in neighbourhood Ratio of immigrant in neighbourhood Labour force participation rate Euclidian Distance to Toronto CBD Dummy, first spell after HH formation Dummy, first spell after immigration Single-episode models Weibull (without frailty component) Coef. (t-stat.) ( ) (-0.035) (0.742) (0.192) (1.782) (3.789) (3.249) (0.301) (1.274) (1.730) (0.569) (0.283) Constant (6.964) Ancillary parameters p (24.500) Log-logistic (without frailty component) Coef. (t-stat.) ( ) (0.836) (0.712) (-0.391) (1.611) (3.001) (2.901) (-0.255) (1.091) (1.908) (0.655) (0.228) (4.817) (22.977) Weibull Gamma Shared frailty Coef. (t-stat.) (-10.19) (0.51) (0.78) (-0.10) (1.28) (2.79) (3.79) (-0.15) (1.43) (1.8) (0.6) (0.46) (5.49) (18.681) θ (2.612) Model information criteria Repeated events models (Shared frailty candidate models) Log-logistic Gamma Shared frailty Coef. (t-stat.) (-8.63) (1.00) (0.75) (-0.42) (1.23) (2.49) (3.33) (-0.36) (1.27) (1.85) (0.75) (0.27) (4.33) (18.597) (1.239) Weibull Gaussian Shared frailty Coef. (t-stat.) ( ) (0.808) (1.652) (-0.054) (2.981) (6.012) (7.001) (-0.052) (2.715) (3.236) (0.981) (0.826) (11.433) (15.542) (36.603) Log-logistic Gaussian Shared frailty Coef. (t-stat.) ( ) (1.355) (1.635) (-0.480) (2.502) (4.891) (5.628) (-0.592) (2.173) (3.225) (1.203) (0.604) (8.233) (10.569) (36.108) AIC

61 51 The results also suggest that DMUs living in neighbourhoods with higher dwelling density and single-detached housing density have longer duration of stay. However, coefficient value is higher for the single-detached housing density than that of all dwellings. This reflects that DMUs that secured housing in a single-detached dominated neighbourhood are very much less likely to change their dwellings frequently. The duration of stay for DMUs increases with higher share of non-movers in the neighbourhood, which is found to be the opposite for the higher share of immigrants in the neighbourhood. This means that DMUs living in a stable neighbourhood are less likely to consider moving, but those who live in an immigrant-dominated area are more prone to move. On the other hand, duration of being passive in the housing market increases for the DMUs living in neighbourhoods with high labour force participation rate. Distances to Toronto CBD also have impact on duration; people living close to the CBD are more frequently active in the market than people in suburban areas. It is intuitive that DMUs living in the suburbia have already obtained a stable location by purchasing dwellings. Both dummy variables indicating new household formation and new immigrants in GTHA show positive impact on duration. That is, the first spells since formation of the household and immigration tend to be longer than subsequent spells. However, DMUs forming new households have longer durations than those of immigrants. This type of spell-specific characteristics presumably could only be incorporated within the continuous-time hazard models. Finally, the ancillary parameter ( p ) value of greater than one suggests that the hazard initially increases to a certain point and decreases thereafter. The model also shows considerable variance of the distribution of the random effects (θ ), which is statistically significant when tested against a Chi-square distribution. That is, the null hypothesis ( θ = 0 ) is rejected for the log-logistic shared frailty model. 4.5 Conclusion This chapter presents panel logit and hazard-based models, which are investigated in an attempt to find the most appropriate model for the implementation of the residential mobility component within ILUTE. In general, both modelling techniques perform well and provide useful results with respect to understanding residential mobility behaviour. Tests and comparison of different

62 52 models within each technique also provide important insights to cope with methodological challenges while working with retrospective data. Particularly, this research addresses correlation issues due to repeated choices in case of residential mobility by testing panel logit models and shared frailty hazard models against conventional models, which is quite unique in the existing mobility research. While the Random Parameter (RP) model shows better performance in incorporating heterogeneity effects for discrete-time framework, shared frailty models are found to be quite satisfactory for continuous-time settings. The two approaches clearly differ in their treatment of time and of time-varying variables. The discrete choice approach assumes a time-driven simulation environment, in which at each discrete time step the model assesses whether the household will become active in that time step or not. It includes dynamic (time-varying) variables that can vary from one time step to another. The hazard models work in continuous time and project the duration that a given household will remain passive, before the occurrence of an event in terms of changing state and becoming active in the housing market. Hence, they are more compatible with an event-driven and continuous-time simulation framework, although they could be adapted to be applied within a time-driven simulation. Time-varying covariates, however, were not tested, due to the wellknown difficulties in dealing with such variables within hazard models, resulting in models in which only static variables are present. Further investigation is needed to develop a continuoustime hazard model that interacts with time-varying covariates. Hence, an obvious next step in the research would be to introduce time-varying covariates into the hazard models. In the random parameter model, it is found that residential stressors mostly related to job and household composition dynamics are significant in explaining households desire to change location at each point of time. Notable stressors are increase and decrease in the number of jobs, change of job location, retirement, birth of children and a two-year lagged effect for decrease in household size. On the other hand, mostly dwelling and neighbourhood characteristics are found significant in the continuous-time shared frailty models in the absence of stressors that vary with time. Given the compatibility of assumptions with the time-driven ILUTE structure and its use of timevarying (dynamic, stress-related) variables, the random parameter binomial logit model presented in this chapter has been implemented in the current version of ILUTE.

63 Introduction CHAPTER 5: RELOCATION CHOICE MODEL 17 This chapter presents a reference dependent location choice model, the second component of the residential location process as identified in Chapter 3. The model deals with the choice of individual dwelling units to facilitate modelling of dwelling-by-dwelling transactions in the housing market microsimulation model within ILUTE modelling system. The model developed in this chapter attempts to address history dependency in terms of capturing influence of previous dwelling in making location choice decisions. Since this model deals with location choices of relocating households, the model is referred as a (re) location choice model in many instances in this dissertation. The research assumes that when active in the housing market the decision-making unit (DMU) first frames its evaluation process with respect to the current dwelling it occupies (i.e. status quo) and then evaluates the alternative dwellings in terms of gains and losses to make the decision about which dwelling to relocate. Following the theoretical framework of prospect theory for riskless choice (Tversky and Kahneman, 1991) and reference dependent models of marketing science literature, this research examines the role of reference points and loss aversion attitudes of decision-makers in making relocation decisions. Loss aversion reflects that preferences of the decision-makers differ in evaluating changes from the reference point depending on whether the change generates advantages (gains) or disadvantages (losses). Particularly, decision-makers are more sensitive to losses than gains. While loss aversion is an important psychological trait, which is quite evident in experimental studies, recently attempts are being made to test the phenomena in empirical settings and incorporate it within traditional choice theory in various fields. Hence this research develops a reference dependent (re) location choice model and tests 17 This chapter is largely based on the paper: Habib, M.A. and Miller, E.J Reference Dependent Residential Location Choice Model within a Relocation Context. Forthcoming in Transportation Research Record: Journal of the Transportation Research Board.

64 54 loss aversion using a random utility based logit formulation. In order to capture unobserved heterogeneity it applies a mixed logit framework that allows varying parameters across decisionmakers and avoids imposing IIA (independence of irrelevant alternatives) restrictions on the choice probabilities. The rest of the chapter is organized as follows: section 5.2 briefly highlights modelling issues in the existing location choice models and how those are addressed within this research. Section 5.3 introduces concepts of the prospect theory and the reference dependent choice modelling framework, followed by section 5.4 that discusses the mathematical structure of the model. Then, section 5.5 describes the data used to empirically estimate the model parameters and section 5.6 discusses the model parameter results. Finally, section 5.7 concludes the chapter with a summary of the research and future research directions. 5.2 Modelling issues Given the importance of location of households on transportation, land use and urban form there is a substantial amount of research in modelling residential location choice 18. While these studies contributed to the location choice modelling field in various ways, most of these models are zone choice models that require a restrictive assumption that all dwelling attributes are the same for a given zone. Although a few studies propose an alternative formulation of a nested structure by aggregating dwellings by type (see, for example, Weisbrod, et al., 1980 and Habib and Kockelman, 2008, among others), they also require a homogeneity condition, which is arbitrary in most cases (Quigley, 1985). These models are widely popular partly due to the convenience of well-known discrete choice methodology and partly unavailability of micro-data for all the alternatives at the elemental level of individual dwelling units (Lerman, 1983; Guo, 2004). Recently, there is a growing interest to model location choice at the disaggregate level of dwelling units (for example, see Axhausen, et al., 2001; Zhou and Kockelman, 2008). However, these studies rely on chosen alternatives in the entire survey to form a pool of alternatives, which is, at best, a partial representation of dwelling supply. This research, on the other hand, uses an 18 See, among many others, McFadden (1978), Friedman (1981), Ben-Akiva and de Palma (1986), Gabriel and Rosenthal (1989), Timmermans, et al. (1992), Hunt, et al. (1994), Ben-Akiva and Bowman (1998), Sermons (2000), Sermons and Koppleman (2001), Sermons and Seredich (2001), de Palma et al. (2007).

65 55 exogenous housing supply dataset obtained from the Toronto Real Estate Board (TREB) and model location choices at the elemental level of dwelling units. Almost all traditional location choice models are also static in nature in that they assume a crosssectional location choice process. As a result, continuity and temporal dynamics are often ignored in these models. But there is an explicit time dimension and process orientation within household location choice processes that demands modelling residential location choice longitudinally (Porell, 1982; Clark, 1992; Dieleman, 2001). Chapter 3 provides a detailed discussion of issues in dynamic modelling. This chapter attempts to take into account effects of previous location on new location choice decision. Such a modelling framework not only brings behavioural perspectives within residential location choice modelling but also calls for new methodology to deal with the relocation decision (Scheiner, 2006). Reference dependent choice models seem an attractive proposition for this purpose. These models have mainly evolved from the seminal work of Kahneman and Tversky (1979) on prospect theory that postulate that choice makers undergo at least two successive events in making choice decisions: framing and evaluation. In the framing stage the decision-maker establishes a reference point to evaluate alternatives. He/she then evaluates alternatives in terms of gains and losses from the reference point. Therefore, this research uses the theory of reference dependent choice as the basis for relocation modelling. It argues that decision-makers (when active in the housing market) evaluate alternative prospective dwellings in relation to a reference dwelling. The key advantage of this approach is that it allows testing loss aversion attitudes (i.e. asymmetric responses towards gains and losses) in making location choice decisions. 5.3 Prospect theory and reference dependent choice model The key elements of prospect theory are a reference point, value function (that describes gain/loss), loss aversion and diminishing marginal sensitivity. In general, prospect theory has been applied for choices under risk and uncertainty in various fields, including transportation (for example, see Avineri and Prashker, 2003; Senbil and Kitamura, 2004; and de Palma and Picard, 2006). Building on Tversky s earlier work, Tversky and Kahneman (1991) provided a

66 56 behavioural model that extends the prospect theory to the case of riskless consumption bundles 19 where the value of a bundle is defined as a function of the deviation of this bundle from a reference alternative (Matsatlioglu and Uler, 2007). Several authors tried to exploit this extended theory for riskless choice occasions (for example, Hardie, et al., 1993; Bell and Lattin, 2000; and Klapper, et al., 2005 among others). The model presented below attempts to model residential location decision-making following this approach. One of the key challenges within reference dependent models is the determination of the reference point. Tversky and Kahneman (1991) suggested the current condition/status quo as the reference point. For instance, they used the current job as the reference point to illustrate choices among alternative jobs. Consequently, many studies assume the status quo or lagged status quo to be the reference point and show that behaviour is consistent with the propositions of prospect theory (see Odean, 1998 and Genesove and Mayer, 2001) 20. Since in the case of relocation, households occupy a residential unit while searching for dwellings, it serves as a natural reference for comparing alternatives. Hence it is assumed that the relocating households frame evaluation of alternative dwelling units for possible relocation in reference to the current residence. This assumption emphasizes the importance of one s current situation on his/her choice behaviour (Masatlioglu and Ok, 2005). Gains and losses associated with each choice alternative are measured relative to this common reference point, where gains are defined as the advantages gained from the alternative (for example, less commute time) and losses are defined as the disadvantages (for example, higher commute time). While most prospect theory-based experiments and models deal with single attribute choices (such as monetary gain/loss in lottery), it is a difficult task to ascertain a model of multi-dimensional consumption bundles, thus limiting application of prospect theory and testing its properties (Matsatlioglu and Uler, 2007). To overcome this hurdle the study utilizes the random utility maximization (RUM) framework and specifies a gain-loss utility structure that clearly separates effects of gains and losses in location choice decisions. Unlike conventional 19 While lottery/investments in financial market are considered to be risky choices due to risky/uncertain prospects, brand choice/dwelling choice can be seen as riskless choice situation. 20 In cases where no natural reference point exists, a few studies assume a probabilistic reference point. See, for example, Bell (1985), Gul (1991), Koszegi and Rabin (2006).

67 57 location choice models such a formulation allows identification of asymmetric responses towards gains and losses, and hence examination of loss aversion attitudes in making relocation decisions. In the following section the modelling framework for the reference dependent location choice model is presented. 5.4 Modelling approach Tversky and Kahneman (1991) explain the theory of reference dependent riskless choice that recognizes the special role of the reference state. Loss aversion is demonstrated by evaluating alternatives in terms of gains (advantages) and losses (disadvantages) relative to a reference point r. Assuming a decomposable and additive reference structure R x ) Tversky and Kahneman (1991) describe a choice situation where the utility of an option x evaluated from the reference point r ( U ) is defined such that U r x, x ) = R ( x ) + R ( ) for the two attributes r ( x2 ( x 1, x 2 ) of the option. Both R 1 and R 2 are called the reference functions associated with the two attribute reference point r (for further details, see Tversky and Kahneman, 1991; Hardie, et al., 1993). Additionally, assuming a constant loss aversion that depicts the degree of loss aversion for each attribute the reference structure is given by: R i ( i xi ) = vi ( xi ) vi ( r ) if xi ri (1a) i ( i R i ( i xi ) = λ [ vi ( xi ) vi ( r )] if x i < ri (1b) where v represents real valued functions and λ denotes the parameter for loss aversion. While this theoretical formulation demonstrates a powerful descriptive behavioural model challenging traditional expected utility theory and has influential impact on various theoretical works and experimental studies, implementation of the theory within an empirical setting requires specification of the utility structure such that it can be mapped into choice probabilities (Bell and Lattin, 2000). In order to demonstrate reference dependence in a relocation choice occasion and test loss aversion, this research follows the marketing science literature (e.g. Hardie, et al., 1993; Bell and Lattin, 2000; Klapper, et al., 2005) and proposes a model within the utility maximization framework for a multi-attribute commodity, like a dwelling. As such, the utility of a dwelling i for a relocating DMU j in a purchase occasion t is given by

68 58 U ijt / r = 0 + β1 Gainijt + λlossijt ) + β 2 β ( X + ε (2) ijt ijt Denoting γ = β 1 λ, the equation (2) can be rewritten in the following form: U ijt / r = β 0 + β1gainijt + γlossijt + β 2 X ijt + ε ijt (3) Here, β 0, β1, β 2 and γ are the parameters to be estimated. Gain ijt refers to the amount of attribute value by which the alternative dwelling i exceeds that of current dwelling for DMU j at choice occasion t. And, Loss ijt refers to the amount of attribute value by which dwelling i is below than that of current dwelling for household j at choice occasion t. X ijt denotes other attributes such as dwelling type, price etc for the dwelling unit i at choice occasion t. The hypothesis of loss aversion is confirmed if the ratio of the loss and gain coefficient in equation (3) is greater than one (i.e. γ / β1 > 1). Collectively denote Gain ijt, Loss ijt and X ijt as Z ijt and all the corresponding coefficients as β. Now, assuming ε ijt as independently and identically distributed (iid) the choice probability of the decision-maker j choosing dwelling unit i in the choice occasion t can be expressed as McFadden s multinomial logit form (McFadden, 1978): P ijt = e β Z j ijt / k i= 1 e β j Zijt (4) However, to acknowledge the potential existence of random taste heterogeneity this research has considered a mixed logit formulation where the choice probabilities are obtained through the integrals of standard logit probabilities over a probability density of parameters (Train, 2003). In general, the density function is assumed to be a continuous function. Normal or lognormal distributions are assumed in most applications (see Revelt and Train, 1998; Mehndiratta. 1996; Ben-Akiva and Bolduc, 1996). This thesis assumes all random parameters to be normally distributed (i.e. β ~ N ( µ, ν ) ) in the mixed logit model. For the mixed logit, conditional on β j, the choice probability of the relocating household j for a single choice occasion choosing dwelling unit i (denoted simply as y j ) can be written as:

69 59 g( y j β Z k j ij β ) = e / e (5) j i= 1 β j Zij The unconditional probability is obtained by integrating g( y j β j ) over all values of β j weighted by the density of β j as shown in the equation (6): P ( y µ, ν ) = g( y β ) f ( β µ, ν dν (6) j j j j j ) where f (.) is the density function assumed to be normal as stated above. Hence the unconditional log likelihood function is given by: J ln L( µ, ν ) = g( y β ) f ( β µ, ν ) dν (7) j= 1 j j j Since this likelihood function is a multivariate integral that cannot be evaluated in closed form, the integral of the choice probabilities is approximated by Monte Carlo simulation (Train, 2003). For each decision-maker, taking draws from f ( µ, ν ) the conditional choice probability g β ) is calculated for each draw. This process is repeated for R times. Finally, the ( y j j integration over f ( µ, ν ) is approximated by averaging the R draws. Hence the resulting β j simulated log-likelihood function can be expressed as: β j LL s = J R ln = j= 1 1 R r 1 ) P ( y j j µ, ν ) (8) where Pˆ j is the simulated probability of the relocating household j choosing dwelling unit i, and µ and ν are parameters to be estimated. This simulated log-likelihood function is maximized to obtain parameter estimates. Under weak regularity conditions the maximum simulated log-likelihood estimator is consistent, asymptotically efficient and asymptotically normal (Hajivassiliou and Ruud, 1994; McFadden and Train, 2000). Several alternative techniques are available for the simulation procedure (Greene, 2004). Since Bhat (2003) shows that Halton draws performs better than traditional random draws used in pseudo-monte Carlo (PMC) method, this study uses Halton sequences to

70 60 draw realizations from the distributions. Halton draws provide better coverage than random draws, on an average, since they are created to progressively fill in the unit interval evenly and ever more densely (Train, 2003). Therefore, a large number of draws can be performed to ensure low simulation error with reasonable estimation run-time. The use of a mixed logit model has two implications. First, instead of specifying fixed parameters for all decision-makers it allows the model parameters to vary across the population. Second, mixed logit does not exhibit the IIA property, since the denominators of the logit formula (equation 5) are inside the integrals and therefore do not cancel. Hence mixed logit formulation can approximate any substitution pattern and choice probability derived through random utility maximization (McFadden and Train, 2000). Finally, the goodness of fit of the estimated models are evaluated in terms of Rho-square, which is calculated by subtracting ratio of log-likelihood of the full model and the null model (constant only model) from one. In addition to the estimation of a reference dependent mixed logit model, this research also estimates a traditional logit location choice model for comparison purposes. 5.5 Data for empirical application Data sources The primary data source used for this study is a retrospective residential search survey (RSS) for the Greater Toronto Area (GTA). It is a mail back questionnaire survey that collected retrospective information on residential location and search process of the households for alternative dwellings. Although the overall initial response rate was 51% (619 out of 1221 households), detailed information was asked only from those who had moved between 1988 and The latest ten years move were considered in an anticipation that people might not be able to provide the kind of detailed information that was asked in the survey. Out of 320 final respondents only 292 were considered as valid responses after cleaning the dataset for ambiguous and incomplete information. Detailed description of the survey design and descriptive analysis of the final survey dataset can be found in Pushkar (1998). The second important dataset used in this study is the Toronto Real Estate Board (TREB) housing supply data for the period of Since one of the key obstacles of modelling residential location choice at the elemental level of dwelling unit is the unavailability of micro

71 61 supply data, several authors used only the chosen dwelling units in the entire survey to form the choice set (for example, Zhou and Kockelman, 2008). But this disaggregate individual dwelling level supply data provides a unique dataset to estimate micro-level location choice model, which contains 80% of the housing supply data in the Greater Toronto Area (GTA). Description of the characteristics of the data is available in Haider (1999). The choice set is generated using this dataset by randomly drawing 18 dwelling units listed for sale plus the chosen alternative. Although the TREB data provides detailed information on dwelling units for sale, the rental vacancy disaggregate data is still unavailable. Hence this study only focused on the owners market and uses only 172 households of the RSS survey who have decided to move and intended to purchase a dwelling unit. Other data sources used in the analysis are a parcel level land use map for the GTA obtained from the Desktop Mapping Technologies Inc. (DMTI), and census data for 1986, 1991 and 1996 obtained from Statistics Canada. In addition, the highway and street network maps, and locations of subway stations; regional transit stations; regional and local parks; education, recreational and entertainment centers; community centers; regional and local shopping centers, major industries and other activity centers are obtained from the DMTI. The zone-to-zone network level-ofservice (LOS) data are generated from the GTAModel-based EMME/2 road and transit network models Data preparation Preparation of the data for this study involves several steps. First, all current and previous residential locations and job locations of the household members are geocoded using GeoPinPoint TM. Second, zonal percentage of different land uses categories such as residential, commercial, industrial, institutional, parks and open land are measured using ArcGIS 9 for each census tract (CT). Third, census GIS data is created for the census year 1986, 1991 and Notable zonal characteristics considered in the investigation include dwelling density, average bedrooms, average rooms, average people per room, labour force participation rate, unemployment rate, population density, average monthly payments by owners, average monthly household income, average dwelling value, etc. Since spatial definition of census tracts varies over different census years, this study uses the 2001 census boundaries for spatial reference for

72 62 all census data used for the research. Hence census data are adjusted to the 2001 CT level by taking weighted averages with respect to the area of the corresponding year s census tracts. Fourth, since this research models dwelling choice for different time periods, these census data are interpolated to generate yearly representative zonal data for corresponding years from the three census databases (1986, 1991 and 1996). Fifth, since all LOS data are generated for traffic analysis zones (TAZ), for consistency corresponding census tract representative LOS data are calculated using GIS techniques. Sixth, given the current and previous home locations all land use and census attributes are assigned to corresponding current and previous home. Similarly, given the job locations, LOS attributes are assigned to the corresponding households. In addition, common accessibility measures such as Euclidian distances to the highway exits, subway stations etc. are created using GIS. Finally, similar operations are carried out for the dwelling units obtained from the TREB supply data. 5.6 Model parameter estimation results Variable specification Several types of variables are considered for modelling residential location choice. These include dwelling characteristics, accessibility measures, land uses, zonal characteristics, and household socio-demographics. Dwelling characteristics considered in the study include number of bedrooms, number of rooms, dwelling type, asking price of the house, number of storeys, etc. Simple accessibility measures that are examined in the models include Euclidian distances to the highway exits, subway stations, regional transit stations, parks, local and regional shopping centers, community centers, schools, etc. In addition, average zonal auto commute travel time, transit travel time and travel costs are also examined in the model specifications. Percentages of different land uses are used to examine land use impacts on the choice of dwelling units. In addition, a land use mix variable (similar to that used in Bhat and Guo, 2007) is created to test effects of land use diversity. Most of the census tract level zonal attributes (such as average person per room, unemployment rate, average household income) are tested in the model specifications. Finally, socio-demographics such as household composition, income, etc. are examined during model estimation. Since the current dwelling is assumed to be the reference point to frame the evaluation process in the reference dependent model, the characteristics of the prospective dwelling and location are

73 63 compared with that of the current dwelling to determine gains and losses with respect to the status quo. Gains and losses are defined as the advantages and disadvantages, and defined based on previous findings of location choice studies. For example, percentage increase of open area is perceived as a gain, whereas percentage decrease of open area is considered as a loss. On the other hand, percentage decrease of industrial land use is hypothesized as a gain and percentage increase of industrial land is defined as a loss. Hence the sign of all gain parameters are expected to be positive and the loss parameters are expected to all be negative. Table 5.1 shows the definition of the variables used in the final model specification. Note that all gain and loss variables act as interaction variables where gains represent only the advantages and losses are disadvantages. To accommodate marginal diminishing sensitivity this study also examined logtransformed gain and loss variables in the model specifications. Table 5.1 Definition of variables used in the reference dependent residential location choice model Variable Variable Definition GBEDS Gain in number of bedrooms LBEDS Loss in number of bedrooms LAAUTTT Loss (increase) in average auto commute travel time in minutes LATRNTT Loss (increase) in average transit commute travel time in minutes LLSTCOST Loss (increase) in total commute travel cost in Canadian dollars 2001 (log) LHIWAY Loss (increase) in distance to the nearest highway exit in kilometers LGOPENLA Gain in percentage of open area in the neighbourhood (log) LLOPENLA Loss in percentage of open area in the neighbourhood (log) LGINDLAN Gain (decrease) in percentage of industrial area in the neighbourhood (log) LLINDLAN Loss in percentage of industrial area in the neighbourhood (log) GUNEMRT Gain (decrease) in unemployment rate in the neighbourhood LUNEMRT Loss in unemployment rate in the neighbourhood DATTHOUE Dummy variable for attached house (semi-detached and row =1, else 0) PRINCLG Dwelling price (2001 $)/household income (log) OWNPPCL Log of dwelling price (2001 $) Discussion of results Table 5.2 shows the results of a traditional location choice model, in which no reference dependence is assumed. Number of bedrooms, which is a proxy for the dwelling size, is found to

74 64 be statistically significant with a positive coefficient. This suggests that the higher the number of bedrooms, the higher the propensity to choose the dwelling unit and vice versa. On the other hand, price of the dwelling has a negative effect, i.e. the higher the price the lower the probability to choose the dwelling, everything else being equal. A similar result is obtained for the price/income ratio. Also, the decision-makers prefer detached houses relative to attached houses. In addition, the auto and transit commute travel times have expected negative signs. Similarly, the total commute travel cost has a negative coefficient, suggesting that the higher the travel cost the less likely the household is to choose the location and vice versa. Again, while households prefer larger percentage of open areas, they want to live in areas where there are fewer amounts of industrial land uses. Finally, the probability of choosing a dwelling unit in areas with low unemployment rate is higher than areas with high unemployment rate. The adjusted Rho-square of this model is Table 5.2 Parameter estimation results of conventional location choice logit model Variable Variable Definition Coefficient t-statistics BEDSC Number of bedrooms AAUTOTT Average auto commute travel time (in minutes) ATRANTT Average transit commute travel time (in minutes) STCOSTDL Total commute travel cost in Canadian dollars 2001 (log) HIGHWAY Distance to the nearest highway exits (in kilometers) POPENL Percentage of open area in the neighbourhood (log) PINDUSTL Percentage of industrial area in the neighbourhood (log) UNEMPRT Unemployment rate in the neighbourhood DATTHOU Dummy variable for attached house (semi-detached and row =1, else 0) PRINCLG Dwelling price (2001 $)-household income ratio (log) OWNPPCL Log of dwelling price (2001 $) Log-likelihood (null model) Log-likelihood at convergence Adjusted Rho-square 0.142

75 65 Table 5.3 reports parameter estimation results of the reference dependent mixed logit model. As discussed earlier, Halton sequences are used for evaluating the multidimensional integrals. Stable parameters are found at 150 Halton draws. The reference dependent mixed logit model shows better model fit than the traditional location choice model. The adjusted Rho-square of this model is Comparing these two models using a log-likelihood ratio test also suggests that the corresponding Chi-square value is statistically significant, which leads to the rejection of the traditional model. In addition, the reference dependent model deals with gains and losses separately, and is capable of capturing asymmetric responses towards gains and losses, which is not possible by the conventional model. Table 5.3 Parameter estimation results of reference dependent location choice mixed logit model Variable Coefficient t-statistics Gain parameters ( β 1 ) GBEDS LGOPENLA Standard deviation of LGOPENLA LGINDLAN GUNEMRT Loss parameters (γ ) LBEDS LAAUTTT LATRNTT LLSTCOST LHIWAY LLOPENLA Standard deviation of LLOPENLA LLINDLAN LUNEMRT Standard deviation of LUNEMRT Dwelling type and price DATTHOUE PRINCLG OWNPPCL Log-likelihood (null model) Log-likelihood at convergence Adjusted Rho-square 0.199

76 66 The results of the final model suggest that a gain in number of bedrooms seems attractive in making relocation decisions. Since many relocating households make residential mobility decisions in response to various life cycle events such as increase in household size (as found in Chapter 4), it is logical that households will try to increase the size of the dwelling while relocating. In addition, with increased economic stability and increasing capability to afford bigger house over the life cycle stages, households value gains in dwelling size for each subsequent move. Similarly, households are very much concerned about loss of number of bedrooms showing a strong negative relationship. In fact, decision-makers are more sensitive to the losses than the equal amount of gains as seen in the corresponding parameters for gains ( ) and losses ( ). The ratio of the two parameters is 1.49, which is higher than one, reflecting a significant loss aversion for the decision-makers in evaluating number of bedrooms while relocating. Again, households have positive attitudes towards percentage gains of open area in the neighbourhood. The log of gains in percentage of open area has a positive coefficient of This means the higher the gains the higher the probability of choosing a dwelling unit in the neighbourhood. On the other hand, the log of loss in percentage of open area has a negative coefficient of The ratio of these two parameters is 2.25, significantly higher than one, indicating that there is a strong loss aversion attitude of the decision-makers with respect to the amount of open areas. In addition to the human behavioural responses of higher sensitivity to the losses evident in many experimental studies, it is also possible that households who lived in the neighbourhood with higher amenity of open space become habituated with it and hence they are unwilling to choose a dwelling unit in a neighbourhood where there is less open areas. However there is a significant heterogeneity among decision-makers as suggested by the standard deviation parameters for both gains and losses of the open area. Decision-makers prefer decreased proportions and dislike higher proportions of industrial area in the neighbourhood where they are relocating. The gain for the household, which is defined as the decrease of the industrial land use, shows a positive coefficient of On the other hand, loss parameter shows a negative value of In this case the loss aversion hypothesis cannot be confirmed since the corresponding ratio is lower than one.

77 67 In terms of level of service attributes, it is found that households are only sensitive to losses and not to gains. The model results suggest that decision-makers are more sensitive to the commute travel cost than commute travel times. The coefficient of the loss in total commute cost is , which indicates that the lower the increase of total travel cost the higher the probability of choosing the location. Note that the variable also shows diminishing marginal sensitivity since the logarithmic transformation of the variable is statistically significant. On the other hand, the coefficients for the loss in auto travel time and transit travel time are and respectively. Therefore the lower the increase of the travel times the higher the probability to choose the location of the alternative dwelling unit. A similar result is also found for the loss in distances to the nearest highway exit. The more a relocating household loses accessibility to the highway, the less likely it is to choose the dwelling unit. Again this study tests various census tract level zonal attributes (such as dwelling and population density, average people per room, unemployment rate, average monthly payments by owners, average household income, average dwelling value, etc.). However, only the gain and loss of the zonal unemployment rate has been found statistically significant with expected sign. The reason for this might be inclusion of the price variable in the model specification since price itself imitates variability of zonal variables. It might also incur an endogeneity problem (as discussed in Guevara and Ben-Akiva. 2006), which is not addressed in this study. While the coefficient of the gains (decrease) in unemployment rate in the zone is , the coefficient of the loss is This suggests that households prefer to relocate to the low unemployment areas and exhibit loss aversion attitudes, since the ratio of the two coefficients are significantly higher than one (4.23). This means decision-makers are very much sensitive to losses compared to equal amounts of gains. The variable loss in unemployment rate also exhibits a statistically significant standard deviation (t-statistics 2.39). Although some socio-demographic variables (such as household composition, changes in household size, education level etc.) interacting with different gain/loss variables are tested, none of the hypotheses are confirmed with reasonable statistical significance. Small sample size might have an influence on these results. Finally, relocating households do not prefer attached houses (i.e. semi-detached and row houses) compared to detached houses, as indicated by the dummy variable DATTHOUE. In terms of the

78 68 price of the dwelling unit, the model finds a negative relationship with more than 99% statistical significance. Hence, the higher the price of the dwelling unit, the lower the probability of choosing the dwelling unit, and vice versa. A similar result is also evident for the ratio of the price and the household income. Although several variables in the mixed logit specification are specified to have random parameters, as indicated earlier, only gains and losses in percentage of open areas and loss in the unemployment rate in the census tract have statistically significant standard deviations, which capture unobserved heterogeneity across the households. In the final model specification, most of the parameters are statistically significant at least at the 95% confidence level. A few parameters are below the threshold t-statistics value; these are retained in the model due to their important policy implications (such as price/income ratio), based on the assumption that if a larger data set were available these parameters might show statistical significance. 5.7 Conclusion Most residential location choice models assume that the choice of a new location is independent to the current location. This research presents an alternative model that demonstrates reference dependency and captures asymmetric responses towards gains and losses. The central tenet of the proposed reference dependent model is that the decision-makers assess changes in relation to a reference point, rather than simply using absolute alternative attribute values (as assumed in traditional consumer theory) in making location choice decisions. Hence the model is capable of testing loss aversion attitude, a tendency to dislike a loss compared to prefer a gain of equal amounts. This asymmetrical evaluation of gains and losses has important implications in explaining relocation behaviour. The reference dependent location choice model performs better than a conventional location choice model in terms of model fit and behavioural significance. The results of the model suggest that while households prefer gains in number of bedrooms they are more sensitive to losses in number of bedrooms. Likewise they exhibit loss aversion attitudes for percentage of open areas and unemployment rate in the zone. It is also found that decision-makers are only sensitive to the losses for the level of service attributes. In addition households prefer detached houses compared to semi-detached and row houses. Finally, the results indicate a negative relationship for the price of the dwelling unit implying that the higher the price of the dwelling,

79 69 the lower the probability of choosing the dwelling unit and vice versa. The model also captures unobserved heterogeneity by assuming varying parameters across decision-makers. This model is implemented within the Integrated Land Use, Transportation and Environment System (ILUTE) modelling system to simulate evolution of households location in the Greater Toronto and Hamilton Area as discussed in Chapter 7. In modelling dwelling choice behaviour this research takes advantages of mixed logit modelling methods that relaxes IIA restrictions. Most importantly, it introduces unobserved preference heterogeneity across decision makers through the model parameters. However, use of random sampling of alternatives to generate choice set within a mixed logit modelling framework poses some concerns, particularly due to its non IIA-based model structure. There is limited discussion in the existing literature regarding implications of random sampling for mixed logit models. As a matter of fact, large number of alternatives is a common problem for any spatial choice model. Random sampling used in this research is basically a practical way of dealing with large number of alternatives since model estimation with the full choice set is intractable due to computational limitations. Behaviourally, it is also evident that households do not evaluate all alternatives in making dwelling choice decisions. How choice set evolves within household decision-making process and what should be an appropriate modelling strategy to tackle the problem are crucial issues that need to be addressed given the growing interest in disaggregate spatial choice modelling. Hence the next step of this research will be to investigate both methodological and behavioural issues with respect to choice set generation processes, particularly dwelling search mechanisms that actually determine choice set/prospect set of dwellings for each relocating household. Again, the location choice model relies on a very small sample data. The hypotheses tested in this Chapter should be examined with a larger dataset. It is particularly important to investigate whether small sample-based model would be representative enough to be applied to the full (synthetic) population of the microsimulation model presented in Chapter 7. In case of larger data collection initiatives, requirements for detailed information in a panel/retrospective survey should not be compromised since historical records are vital for modelling longitudinal processes.

80 70 Finally, although this research investigates properties of prospect theory and proposes a reference dependent location choice model for a single reference point, it will be interesting to extend the modelling framework by considering multiple reference points and/or changes in reference points during dwelling search. In addition, it is important to understand and attempt to model decision-makers search and evaluation process for alternative dwellings, which might help cross-fertilization of random utility models and behavioural choice theories.

81 Introduction CHAPTER 6: DWELLING PRICE MODEL 21 Once a household decides to become active in the housing market (Chapter 4) and put its current dwelling unit up for sale, it must determine an initial asking price for this dwelling. This asking price is essential for initiating the market clearing process in which both buyers and sellers interact. This chapter describes the development of the asking price model used in the current ILUTE implementation. Hedonic modelling techniques are extensively used to investigate housing prices. In the field of transportation planning, these models are predominantly utilized for the analysis of large-scale transportation investments and value-capture of transit systems. Recent advances in microsimulation-based integrated land use and transportation modelling systems also employ such models to estimate land value changes over the years. For instance, UrbanSim uses an exogenous land price module where house prices are estimated in terms of structural, accessibility and neighbourhood characteristics through the use of hedonic techniques (Waddell and Ulfarsson, 2003). This chapter presents a set of dwelling price models that incorporate supply-side attributes in addition to the traditional accessibility, neighbourhood and structural attributes typically used in the literature. A key contribution of this research is that it attempts to incorporate spatial and temporal heterogeneity into the housing price models using multilevel modelling techniques. Multilevel modelling recognizes hierarchical clusters, where units of analysis are nested within higher-level aggregated units. Such clustering occurs in many cases, for example, students nested within a school, individuals nested within households, workers nested within work zones, dwelling units nested within neighbourhoods, traffic flows nested within hours, etc. The key motivation of 21 This chapter is largely based on the paper, Habib, M.A. and Miller, E.J. 2008b. Influence of Transportation Access and Market Dynamics on Property Values: Multilevel Spatio-Temporal Models of Housing Price. Transportation Research Record: Journal of the Transportation Research Board, 2076, pp

82 72 using the multilevel modelling technique in this application is that it clearly identifies and differentiates between-cluster heterogeneity (i.e. intrinsic differences across aggregated units) and heterogeneity among individual, disaggregated units of analysis that are nested within the aggregated clusters. While this study begins with investigating spatial heterogeneity by assuming that dwelling units are nested within a spatial cluster (i.e. neighbourhood), it then extends the model by incorporating a temporal dimension that assumes dwelling units are nested within spatiotemporal clusters (i.e. a neighbourhood at a specific period of time). The spatio-temporal specification captures random effects of a particular neighbourhood at a given time period by explicitly recognizing that each neighbourhood at a given time period is different from other neigbourhoods, as well as that each neighbourhood is different from the same neighbourhood at different time periods. Incorporation of temporal aspects in the housing price model is very important since most of the models deal with multi-period data and failure to account for this might lead to biased parameter estimates and affect use of such results in policy applications. The rest of the chapter is organized as follows: section 6.2 presents a brief overview of the housing price modelling literature. Section 6.3 describes the mathematical formulations of models estimated in this study. Then, section 6.4 provides a description of the data used in the empirical modelling, followed by a presentation and discussion of the empirical parameter estimation results in section 6.5. The chapter concludes with a summary of contributions and future research directions. 6.2 Modelling housing prices There is a substantial amount of research that attempts to identify factors affecting property values using hedonic price modelling techniques. While most of the studies focus on impacts of rail transit (such as, Armstrong and Rodriguez, 2006; Cervero and Duncan, 2002; Haider and Miller, 2000; Al-Mosaind, et al., 1995), renewed interest has been observed in examining effects of neighbourhood and environmental characteristics, even air quality in recent literature (Anselin and Losano-Gracia, 2007, and Hui, et al., 2007). Du and Mulley (2006) review literature since 1990 in both North America and UK, and conclude that transport accessibility has a mostly positive impact on land values. While Benjamin and Sirmans (1996) use 250 residential units at Washington D.C. and find rents decrease by 2.5% from each one-tenth mile increase of distance

83 73 to the rail rapid transit, using 451 single-family property sales in Boston, Armstrong (1997) observes an 18.9% value increase for 400-feet proximity to commuter rail right-of-way. Most of these studies used small sample data (see a comprehensive review in Habib, 2004). However, Voith (1993) uses 59,000 single-family home sales at Philadelphia and finds 1.5 to 8% premium for houses with access to railway stations. Similarly, Haider and Miller (2000) employ 27, 400 freehold sales in the Greater Toronto Area during 1995 and find propinquity to a subway line adds value to the housing price. On the other hand, Knapp et al. (1996) examines all dwelling units within a one-mile radius of three rail transit stations in San Francisco and suggests that property value rises as one moves closer to the rail line, but not closer to the rail stations. In a similar study, Lewis-Workman and Brod (1997) examine prices in a one-mile radius of a single station (Pleasant Hill) and discover a premium of $1578 for every 100 feet closer to the station. In addition, several neighbourhood attributes are found to be significant in explaining housing price. While labour force density, housing density, average income and different land uses are found to be significant in many studies (such as Cervero and Duncan, 2002), a composite neighbourhood index is also used in some studies (Can and Megbolugbe, 1997). Again, environmental qualities are found to have impacts on housing prices (for a recent review see Hui, et al., 2007). There is a significant negative relationship between airport noise and property values (Palmquist, 1992). Residents of Chicago are willing to pay more to reduce exposure to the pollution of particulate matter (Chattopadhyay, 1999). Consumers are also willing to pay extra money for good views (e.g., Mok, et al., 1995). Despite comprehensive efforts in measuring transportation access effects, neighbourhood and environmental qualities, assessments of the impacts of the housing supply market on housing price are rare. Although demand-supply interactions are well recognized, modelling housing supply has received less attention (Miller, 2006). Even inclusion of exogenous supply attributes in analyzing market outcomes is not extensively investigated yet, partly due to data issues and an inability to encompass a temporal dimension within the housing price estimation techniques. But market dynamics such as total supply of dwelling units, average selling price at a given quarter of the year, average active days in the market of the resale/new dwelling units and quarterly interest rates might all have influence on housing prices. Ignoring these important variables

84 74 might cause overestimation of the importance of other attributes, problems of omitted variables 22 and eventually biased parameter estimates. Hence this research tests the influence of these key market variables as well as a comprehensive set of transportation access, dwelling characteristics and neighbourhood qualities. A key issue in modelling housing price is the functional specification. While some studies utilize flexible price functions, others caution that such practice might compromise the ability of the function to tolerate misspecification (Cassel and Mendelsohn, 1985). Prior evidence suggests that simple functional forms such as linear, log-linear and linear Box-Cox forms perform better than more complex ones (Cropper, et al., 1988). In fact, several authors only used linear and/or semi-log specifications (Damm, et al., 1980; Bajic, 1983; Forrest, et al., 1996; Henneberry, 1998; Haider and Miller, 2000) while a few authors employed Box-Cox transformations to confirm the specification to be linear, log-linear or semi-logarithmic (such as Maurer, et al., 2004). Since there is not enough evidence for Toronto to select a specific functional form a priori, this research uses Box-Cox transformations to test functional specifications. The most critical issue in modelling housing price is spatial and temporal autocorrelations. Spatial autocorrelation involves two key econometric elements: spatial dependency and spatial heterogeneity (Anselin, 1988). Spatial heterogeneity means marginal prices of many attributes used in the housing price models vary over space, which is often assumed to be constant throughout the study area. In most of the hedonic price applications the metropolitan area is viewed as a single unified market which in turn yields stationary parameters that are in fact an average value of the parameters over space. If spatial heterogeneity exists, failure to incorporate it into the model will result in biased parameter estimates and loss of explanatory power, and may obscure important dynamics relating to the operation of housing markets (Bitter, et al., 2007). Early approaches to deal with the spatial heterogeneity include delineation of the entire metropolitan area into distinct geographic sub-markets and estimation of separate price models for each spatial sub-market (for example Schnare and Struyk, 1976), which seems problematic 22 For instance, omission of supply variables will increase the unexplained portion of the model and might cause biased/inaccurate estimates for other attributes.

85 75 since it is practically difficult to define sub-markets. A more innovative method is the spatial expansion method pioneered by Casseti (1972), later extended to the spatial autoregressive method (Can, 1992; Can and Megbolugbe, 1997; Haider and Miller, 2000), which was criticized by Orford (2000) as being a technical fix by the autoregressive function to the spatial problem. Recent attempts to incorporate local geographic heterogeneity also include local indicators of spatial association, LISA (Anselin, 1995), geographically weighted regression, GWR (Fotheringham et al., 2002), etc. However, such methods do not in themselves explain the underlying heterogeneity, rather these sophisticated spatial formulations are nothing but models of geographic determinism in disguise (Anselin, 1999). On the other hand, temporal heterogeneity is almost absent in the literature, with only a very few exceptions. It is not at all obvious how best to account for time in empirical investigations (Case, et al., 2004). Many researchers simply ignore the temporal dimension in analyzing housing prices although they worked with multi-period data (for example, Cervero and Duncan, 2002; Voith, 1993). Such formulations often incur misspecification of models, issues of omitted variables, biased parameter estimates and loss of temporal dynamics in the housing price models. Hence there is a need to apply an appropriate framework that can encompass both spatial and temporal heterogeneity, for which the multilevel or hierarchical modelling technique seems an attractive but simple modelling tool that has been widely used in educational research (Goldstein, 1987; Raudenbush and Bryk, 2002). Some authors have attempted to utilize this technique to investigate housing prices in the past, particularly within a spatial context (see Jones, 1991; Jones and Bullen, 1994; Orford, 2000; Brown and Uyar, 2004; Gelfand, et al., 2007), but they are mostly pedagogical papers (i.e. Jones and Bullen, 1994; Brown and Uyar, 2004), limited in dataset and/or predictors (i.e. Jones, 1991; Jones and Bullen, 1994). Hence empirical application of multilevel model is still limited even for the spatial context. Of course, temporal issues are clearly overlooked (such as Gelfand, et al., 2007), despite the use of time-series data. The unique contribution of this research is that it extends the multilevel spatial model to incorporate temporal aspects by introducing spatio-temporal clusters. In the following section, the model structure of multilevel spatial and spatio-temporal models are discussed beginning with a brief discussions of Box-Cox models applied to investigate functional specifications for use in multilevel applications.

86 Model structures Prior to multilevel modelling this research investigates functional specifications for the housing price model since there is not enough evidence for the GTA to select a specific functional form a priori. It uses Box-Cox transformations (Box and Cox, 1964) that yield the following model specification: ( θ ) ( λ1 ) ( λ2 ) P = β + β X + β X + ε (1) 0 m m n n where P represents price of the dwelling unit which is transformed through the parameter θ to ( θ ) θ P = ( P 1) / θ or log(p ) if θ = 0. A similar transformation is done for explanatory variables X m with the parameter λ 1. However, some explanatory variables cannot be transformed if they are not strictly positive (for example dummy variables that can only take the values of zero and one) are represented by maximizing the following likelihood function: X n with the parameter λ 2. All the parameters can be estimated by k k SSR( θ, λ1, λ2, β ) L = ( θ 1) log Pi log (2) i 2 k where SSR denotes sum of squared residuals and θ, λ1, λ2, β are parameters to be estimated. The parameters are estimated by restricting θ and λ 1 to a certain pre-determined values and applying maximum likelihood method by treating the problem as an ordinary optimization problem (Greene, 2003). If any of the parameters θ or λ 1 are assumed to be equal to one, it means that the transformation is linear, whereas a zero parameter value means the transformation approaches to the natural logarithm. Hence a linear functional form is obtained if θ = λ 1 = 1, a double-log if θ = λ 1 = 0, and a semi-logarithmic function if θ = 0 and λ 1 = 1. In all cases, λ 2 is assumed to have a value of one. Various models are estimated based on different transformation assumptions that help in selecting appropriate functional specification for use in subsequent multilevel modelling. Within the multilevel framework, two different model specifications are used: (a) Two-level spatial model, (b) Mixed two-level spatio-temporal model. In the two-level spatial model,

87 77 individual dwelling units are assumed to be nested within neigbourhoods. The second specification hypothesizes that while dwelling units are at the lowest level (level 1), both spatial and temporal dimensions are in the second level. Model structure of the first specification can be illustrated by two equations. The first level equation of two-level spatial model is given by Level 1: P ij β β + ε = 0 j + 1X ij ij (3) where P ij is the price of a dwelling unit i in neighbourhood j. Note that here dwelling units are assumed to be nested within a neighbourhood (i.e. spatial cluster). While equation (3) represents a micro model of within-neighbourhood variations, the macro model (equation (4)) that stands for between-neighbourhood variations, is given by Level 2: β = β β (4) Z 0 j j + u0 j Then the composite model takes the following form: P ij β β β + ε = 0 + 1X ij + 2Z j + u0 j ij (5) where β 0, β 1 and β 2 are the fixed component that represent fixed intercept and parameters for dwelling characteristics ( X ij ), and neighbourhood attributes ( Z j ). u 0 j and ε ij are the random effects for neighbourhood and dwelling units respectively. It is assumed that u 0 j and ε ij are independent and identically distributed (iid) multivariate normal with mean zero and constant variances: 2 u 0 ~ iid N (0, τ ) j 2 ε ~ iid N (0, σ ), and uncorrelated with the covariates. Hence, ij the random variations within a neighbourhood are independent (and independent of those from other neigbourhoods) and the random effects for a neighbourhood are independent of the random effects from the other neighbourhoods that yield a compound symmetrical structure of the residual matrix within neighbourhood with all dwelling units in the neighbourhood having the same variance. It also provides the same correlation for all dwelling units of the same neighbourhood conditional upon the fixed covariates. In the second specification, the temporal dimension is introduced by assuming that dwelling units are nested within spatio-temporal clusters. That means the second level consists of

88 78 neighbourhood ( j ) at a particular time period (t ). Denoting this combined cluster as m, the micro and macro equations are given by Level 1: P im β β + ε = 0 m + 1X im im (6) where P im is the price of a dwelling unit i in spatio-temporal cluster m. Level 2: β = β β (7) Z 0 m m + u0m Finally, the composite model becomes P im β β β + ε = 0 + 1X im + 2Z m + u0m im (8) While ε im and u 0 m are iid distributed random parameters, β 1 and β 2 are the fixed parameters for level 1 and level 2 attributes. The parameter, β 0 is a global fixed intercept. The second specification captures random effects across spatio-temporal clusters and also random effects of the dwelling units within the cluster. Since time period is represented by the quarter (three months) of the year, this specification explicitly recognizes that each neighbourhood at a specific quarter is different from other neighbourhoods in any quarters and also each neighbourhood is different from the same neighbourhood at different quarters. This model can be further extended to incorporate random coefficients to capture dwelling unit attributes varying randomly across the clusters. The composite random coefficient model is given by P im β β β + ε = 0 + 1X im + 2Z m + u0m + u1 m X im im (9) 2 u0m Here, ε im ~ iid N (0, σ ) ; u m = ~ iid N ( 0, Ω) ; u1m 2 τ u = τ u 0 Ω 2 01 τ u1. Also, u 1 m denotes the random effects of the characteristics of the dwelling units that vary across spatio-temporal clusters. There are two distinct approaches in estimating parameters for these two specifications: full maximum likelihood (ML) and restricted likelihood method (REML). Bayesian estimation is however becoming popular (see a housing price application in Gelfand, et al., 2007) with steady improvement of Markov Chain Monte Carlo (MCMC) algorithms. Since likelihood methods are

89 79 computationally faster than MCMC-based Bayesian fitting of multilevel models (Browne and Draper, 2006) this research considers a maximum likelihood method to estimate the parameters for the large dataset it investigates. Unlike the ML method that maximizes the likelihood of the data, REML maximizes the likelihood of the observed residuals. REML first estimates the fixed effects using common techniques like least squares or generalized least squares and then using these estimates it maximizes the likelihood of the residuals by subtracting off the fixed effects to obtain the estimates of the variance parameters. Since it is difficult to compare models estimated by REML using the likelihood ratio test or other goodness-of-fit statistics such as AIC/BIC, this research utilizes the ML method to estimate the parameters. ML method might produce biased parameter estimates if the data sample is small, but with a very large sample of data and reasonable group size for each level the ML estimate will provide unbiased estimates for this case. For the ML method, the likelihood function to be maximized is obtained from the joint density function f, u ), which is given by ( P im m k m= 1 k 2 L( β, σ, τ / P, u ) = f ( P, u ) = g( P u ) h( u ) (10) im m im m m= 1 im m m where g u ) is the distribution of the observed data assuming the values of the random ( P im m effects are known and h( u m ) represents the distribution of the random effects which is assumed 2 to be multivariate normal and a function of variance parameters τ, etc. that are collectively 0, τ 01 denoted as τ. The random effects are generally treated as nuisance parameters and integrated out to obtain the marginal likelihood of the data: 2 L( β, σ, τ / P 2 ) = L( β, σ, τ P, u du im im ) = k m= 1 f ( P im, u ) du m m = k m= 1 g( P u ) h( u ) du (11) im m m m

90 80 Maximization of this likelihood function requires multiple iterative integrals and full information maximum likelihood estimation incurs considerable computational burden. This research uses maximization of likelihood via the EM algorithm (see Bates and Pineiro, 1998). Due to the model s nested structure the goodness-of-fit of the multilevel models are evaluated with respect to the Akaike Information Criteria, AIC and the Bayesian Information Criteria, BIC. The lower the value of the AIC or BIC the higher the goodness-of-fit of the corresponding model. 6.4 Data preparation This research uses Toronto Real Estate Board (TREB) Multiple Listing Service data that contains 262,669 housing transactions during the period of The data represents almost 80% properties listed in the GTA housing market during this period (Haider, 1999). After cleaning for missing information, a total of 253,383 geocoded observations are retained for housing price modelling, which is one of the largest samples ever used in comparable studies. This study involves extensive Geographic Information System (GIS) operations using ArcGIS 9. While dwelling unit attributes are available from the same data source, all transportation accessibility measures are created using GIS techniques. Highway and street network maps, and locations of subway stations; regional transit stations; regional and local parks; education, recreational and entertainment centers; community centers; regional and local shopping centers, major industries and other activity centers are obtained from Desktop Mapping Technologies Inc. (DMTI). Although a variety of complex and sophisticated measures of accessibility are available in the literature (see Armstrong, 1997 for reviews), this research employs simple Euclidian distances to the transit stations and other activity centers of GTA, which is commonly used in most studies of this type (for example, Lewis-Workman and Brod, 1997; Benjamin and Sirmans, 1996; Cervero and Duncan, 2002). Similarly, dummy variables are created to identify proximity to the different key infrastructure and activity locations (see applications in Al- Mosaind, et al., 1995; Knapp, et al., 1996; Haider and Miller, 2000). Table 6.1 shows definitions of accessibility and other variables that are retained in the final models with their summary statistics. This research creates a substantial amount of explanatory variables and extensive efforts have been undertaken in the preparation of data. About eighty variables were tested in the modelling.

91 81 Table 6.1 Summary statistics of data used for the housing price modelling Total observations = Variable Variable Definition Mean/Proportion Std. Dev. Min Max Dependent variable LSTPR01 Asking price of the property (in CAD $) LOGASKPR Natural log of ASKPR Dwelling unit attributes ROOMS Total number of rooms DDETACH Dummy variable (1, if singledetached 74.02% house) D3STOREY Dummy variable (1, if three storey building) 4.94% Accessibility and location attributes SUBWAY Distance to the nearest subway station (Km) RTRANSIT Distance to the nearest regional transit station (Km) D2HIWAY Dummy variable (1, if within % km of highway exits) D2REGSHO Dummy variable (1, if within % km of regional shopping center) D2COMCEN Dummy variable (1, if within % km of community center) D0_5RECC Dummy variable (1, if within % meters of recreation and entertainment center) D15HAZRD Dummy variable (1, if within 15 km of hazardous industries and waste treatment plants) 28.84% Neighbourhood attributes PRESIDEN Percentage of residential land use PCOMMERC Percentage of commercial land use AVGPPLPERR Average people per room in the census tract (CT) UNEMPRATE Unemployment rate in the CT AVGDWVAT Average dwelling value in the CT (in 1000 CAD $) Market variables (temporal) SQALLASP Average selling price in the quarter of the year (in 1000 CAD $) SQALLDAY Average days listed on the market for sale in the quarter of the year

92 82 While land use data for the GTA are obtained from the DMTI, the census tabulations are obtained from Statistics Canada for the year 1986, 1991 and Percentage of different land uses categories such as residential, commercial, industrial, institutional, parks and open land are measured using GIS techniques for each census tract (CT). Since spatial definition of census tracts varies over different census years, this study uses 2001 census boundaries for spatial reference and adjusted CT-level census data accordingly by taking weighted averages with respect to the area of the corresponding year s census tracts. Although enumeration area (EA) level data (which is spatially more disaggregated than CT) were available, this study relied on the CT level data due to privacy-related data suppression procedures used by Statistics Canada for reporting small-area data. Again, since this research uses housing property transactions for the period , interpolated representative yearly data are generated from the three census databases (1986, 1991 and 1996) using GIS. All neighbourhood attributes are created from these census data. Notable neighbourhood characteristics used for investigation are dwelling density, average bedrooms, average rooms, average people per room, labour force participation rate, unemployment rate, population density, average monthly rental payments, average monthly payments by owners, average monthly household income, average dwelling value, etc. in the neighbourhood. All these variables are attached to the individual properties by spatial joins. Key market variables are obtained from Canadian Socio-Economic Information Management System (CANSIM). In addition, housing supply and market behaviours are generated from the whole TREB database since it covers 80% of the residential real estate transactions in the GTA (Haider, 1999). Notable variables tested in the models are total dwelling units active in the market, average days listed in the market until sold, average asking price, average selling price, etc. Similar attributes are created for both new dwellings as well as dwellings for resale. In addition, quarterly supply characteristics for the whole region and local census tracts are also identified and used for model development. 6.5 Model parameter estimation results Table 6.2 summarizes two Box-Cox model specifications with a reference linear model. Model 1 applies a logarithmic transformation to the dependent variable but uses untransformed independent variables, while in Model 2 independent variables are transformed except those that are not strictly positive. Results of other models with different transformation assumptions are

93 83 Table 6.2 Results of Box-Cox transformation models Variables Model 1: Box-Cox Log-transformed Dependent variable Model 2: Box-Cox Log-transformed Independent variables Model 3: Linear OLS Model (Reference Model) Coefficient t-stat. Coefficient t-stat. Coefficient t-stat. ROOMS DDETACH * D3STOREY * SUBWAY RTRANSIT D2HIWAY * D2REGSHO * D2COMCEN * D0_5RECC * D15HAZRD * PRESIDEN PCOMMERC * AVGPPLPERR UNEMPRATE AVGDWVAT Constant Box-Cox transformations θ λ λ 2 * Adjusted R-square AIC *variables that are not strictly positive (not transformed)

94 84 not presented in this research. It is often suggested that the focus of transformation should be on the dependent variable rather than independent variables (Linneman, 1980). Consistent with the prior evidence it is found that model fits are more sensitive to the changes in the transformation of the dependent variables than to the changes for independent variables in general. Since the semi-log model shows superior performance than other models in terms of goodnessof-fit of the data this research uses this specification for the subsequent multilevel models. Table 6.3 shows the results of two specifications of multilevel models. While in the two-level spatial model (Model 4) dwelling units are nested within neighbourhoods, the mixed two-level spatiotemporal model (Model 5) incorporates both spatial and temporal dimensions in the second level. It should be noted that this research only reports random intercept models. This means that the models estimate heterogeneity at the intercept-level only. Spatially and temporally varying coefficients are not estimated due to problems in convergence of the model for the selected estimation method. It is found that Model 5 has a better goodness-of-fit than Model 4, as seen in a lower value of AIC. It has also better statistical significance of the parameters and expected parameters signs. All of parameters are statistically significant at the 95% confidence level or better. In addition, the model accounts for both spatial and temporal heterogeneity in contrast to the spatial model, which only deals with spatial heterogeneity (Model 4). Hence, this research selected Model 5 (Spatio-temporal Model) as the final model and its empirical results are described in details below. Dwelling unit attributes are found to be strong predictors of housing prices within the Greater Toronto Area (GTA). Number of rooms has positive effects on property values; i.e., the higher the number of rooms the higher the price of the dwelling, all else being equal. A dummy variable representing single-family detached house significantly contributes to the housing price in contrast to that of other types of houses. Similarly houses that are three-storied are also higher in price. A considerable number of transportation accessibility variables are found to be significant in explaining GTA housing prices. The higher the distance to the subway stations the lower the price of the dwelling, controlling for all other variables. Regional transit stations also have a similar effect on the housing price. The model suggests that while the asking price decreases by 0.67% for every additional kilometer from a subway station, it goes down by 0.16% per kilometer from regional transit stations.

95 85 Table 6.3 Results of multilevel models Variables Model 1: Box-Cox Semi-log (reference Model) Model 4: Two-level spatial model Model 5: Mixed two-level spatiotemporal model Coefficient t-stat. Coefficient z-stat. Coefficient z-stat. ROOMS DDETACH D3STOREY SUBWAY RTRANSIT D2HIWAY D2REGSHO D2COMCEN D0_5RECC D15HAZRD PRESIDEN PCOMMERC AVGPPLPERR UNEMPRATE AVGDWVAT SQALLASP SQALLDAY Constant Random effects parameters 2 τ (between neighbourhood) 2 τ (between neighbourhood-quarter) σ (dwelling units) AIC BIC χ Prob.> χ Group size (Level-2)

96 86 In addition, the price of the house is higher within two kilometers of highway exits than for locations further away from highways. Proximity to highway by two kilometers adds a 0.31% premium in property values, all else held equal. Similarly, housing prices are higher if they are located within two kilometers of local community centers. However, a significant housing price impact is found for the houses that are within 500 meters of the recreational centers. It has a positive parametric value of that reflects 1.3% premium on the housing value. In addition, there is a premium of 0.47% for being within two kilometers of a regional shopping district. On the other hand, if the dwelling units are within fifteen kilometers of hazardous industries and waste disposal plants, the properties are valued less than rest of the units. Regarding neighbourhood attributes, while housing prices increase with higher percentages of the census tract that is residential, they decrease with increases in the percentage of commercial area. Average persons per room in the neighbourhood (which is used as a proxy for overall neighbourhood conditions) is found to be negatively related with the price, which suggests that areas with crowded dwelling units have lower housing value than neighbourhoods where people have more space per person. Similarly, unemployment rate has a negative impact on housing values. As expected, average dwelling value in the neighbourhood has a significant impact, the higher the average price in the vicinity the higher the price of the property, all else held equal. Although a considerable number of other neighbourhood attributes were tested in the models (as described in the previous section), most of them were found statistically insignificant or provided signs that significantly contrast with a priori expectations. Only two market indicator variables that reflect temporal changes of the housing market, average selling price at a given quarter and average days on the market for sale were found to be statistically significant for the sample data. This result suggests that the higher the average selling prices at a given quarter the higher the price of the house, all else being equal. But if on average houses are on the market for longer times, this reduces the asking price since market clearing process exhibits that supply exceeded the demand. Inclusion of such market variables into the model does change the contribution of other explanatory variables. For example, in the spatial model (Model 4) when there is no such indicator it suggests that asking price decreases by 0.83% for every additional kilometer away from a subway station in contrast to 0.67% found for the case in Model 5. This means that Model 4 overestimates impacts of transit accessibility, which might be an issue of concern if the study is used for policy applications.

97 87 This study also expected that local supply variables might be found to be significant in the spatio-temporal model specification. Time and space-specific variables such as average selling price in the neighbourhood at a given quarter, average days on the list and total supply of resale and/or new dwellings in the neighbourhood for a given quarter, etc. were tested. But none of these variables were found to be significant in the model. These results suggest that overall market supply in a given quarter for the whole region is more important than supply within individual neigbourhood in determining asking price. Results of covariance parameter estimates show that there is significant spatio-temporal 2 heterogeneity. The variance ( τ ) is with a standard error of for Model 5. The 2 reported χ statistics is with 2739 degrees of freedom (DF). The DF is calculated by taking the group-size at level-2 and subtracting the number of explanatory variables included for level-2 plus one. The null hypothesis ( τ 2 = 0 ) is rejected with the corresponding Chi-square distribution at better than 99% confidence level. The estimated variance of the overall error term 2 ( σ ) is found to be , which reflects variations for dwelling units within spatio-temporal clusters. In Model 4 (i.e. the spatial model), the variance at the neighbourhood level is also found 2 to be statistically significant when tested against the Chi-square distribution ( χ = ). While variance in Model 4 implies between neighbourhood variations, Model 5 incorporates between neighbourhood-quarter variations. Finally, it is found that both these models have higher goodness-of-fit statistics than the commonly used semi-log Box-Cox model (Model 1), as seen in the Akaike Information Criteria (AIC) in Table 6.3. Model 5 (Spatio-temporal model) also performs better than Model 4 (spatial only) in terms of explanatory powers, predictive accuracy and ability to encapsulate both spatial and temporal heterogeneity into the housing price model. 6.6 Conclusion This study adds to our understanding of how to incorporate spatial and temporal heterogeneity into dwelling price models. Since it is found that spatio-temporal heterogeneity exists in the housing market of the Greater Toronto Area (GTA), explicitly accounting for it provides reliable and accurate estimates of the influence of transportation accessibility, neighbourhood attributes, and other key spatial and temporal market dynamics, yielding an improved model for urban

98 88 policy analysis applications. The results reveal that while the asking price deceases by 0.67% for every additional kilometer from a subway station, it goes down by 0.16% per kilometer away from regional transit stations. Additionally, proximity to highway exits by two kilometers adds a 0.31% premium in the property values of the GTA. In addition to neighbourhood attributes, the study also finds that market supply attributes such as average selling price in a given quarter of the year and average days listed for sale make significant contributions to dwelling prices. In general, the multilevel models presented in this research show a very good model fit and statistically significant parameter estimates, with a comprehensive set of dwelling, access, neighbourhood and market indicator variables. Application of Box-Cox transformations also provides useful results in selecting the functional form for the housing price models. Although this research investigates and captures spatio-temporal heterogeneity at the intercept level, it will be very interesting to explore how other model coefficients vary over both time and space. Hence the next step of the research will be to examine multilevel models incorporating spatially and temporally varying coefficients. It is also expected that three-level models should be tested where space and time will be the higher two levels, although the notion of neighbourhoods nested within the time-period is still an arguable proposition. In addition, since investigation of spatial or temporal dependence between the error term and the dependent variable is not performed in this current study, future research should address the issue. Finally, among the specifications examined in this study, the spatio-temporal model performs better in terms of goodness-of-fit, expectations and statistical significance of the parameters. This model is implemented within the Integrated Land Use, Transportation and Environment System (ILUTE) modelling system as a means of generating asking dwelling prices in a market clearing process.

99 Introduction CHAPTER 7: SIMULATING LOCATION PROCESSES This chapter presents a microsimulation model of residential location processes developed using estimated models described in the previous chapters. As a part of a large-scale microsimulationbased Integrated Land Use, Transportation and Environment (ILUTE) modelling system, developed at the University of Toronto, this module generates evolution of residential mobility and location choices at the Greater Toronto and Hamilton Area (GTHA). The specific contribution of this thesis regarding simulation application includes estimation of econometric models to implement behavioural processes, establishing relations between key components of residential mobility and location processes as well as interactions with other modules of ILUTE, and running the microsimulation models to forecast location patterns and housing prices in the Greater Toronto and Hamilton Area (GTHA). The rest of the chapter is organized as follows: section 7.2 discusses the microsimulation framework of the residential location component within ILUTE. Section 7.3 describes preparation of input data to run the modelling system. Section 7.4 provides simulation results depicting evolution of household locations at the GTHA over time. Then, section 7.5 presents comparison of the simulation results against observed data for an extended historical period. Finally, section 7.6 briefly highlights the potential use of the model for testing policy scenarios followed by concluding remarks in section Microsimulation framework of residential location component The model is developed at the most disaggregate level. For residential location it is assumed that households are the decision-making units that choose alternative dwelling objects in a given urban area at a given point in time. The model operates at a yearly time step and can proceed over an extended period of time, supposedly to any planning horizon of interest. Given the dynamic and disaggregate nature of the modelling system, the model allows evaluation of system states that evolve over time at the most elemental unit of analysis. As such, the model is capable

100 90 of evaluating micro-scale impacts of different land use and transportation policies. In addition, the model can generate aggregate system behaviour, which is evolved due to interactions of different agents and decision processes in the urban system. Miller and Haroun (2000) discuss the theoretical framework of microsimulating spatial markets that represents both demand and supply processes. In the current version of ILUTE, the demand sub-system consists of (1) a model of household residential mobility that determines whether a household decides to become active in the housing market in each year in the simulation, and (2) a model of household residential location preferences, given that the household is active in the housing market. This housing demand model interfaces with the ILUTE housing supply module through a market clearing process described in Miller, et al. (2009). The housing price model developed in this research is used to generate initial asking prices for all active dwellings in the market clearing process in a particular simulation year (as discussed in Chapter 3). The current implementation of the models operates only for the owner-occupied market. The rental market microsimulation model is expected to be implemented within ILUTE once relevant rental unit data and appropriate modelling components are empirically investigated. Therefore, the following discussion of the simulation application strictly applies to the owner-occupied market only Behaviour of household agents Since households are assumed to be decision-making agents in the case of residential mobility and location choice decisions, behaviour of individual households are represented in the modelling system in a considerable detail. The model is constructed for the full set of households of the GTHA. The initial set of households is obtained from a synthesis procedure (see Pritchard and Miller, 2009), which is updated for subsequent years to form the pool of households for the study area. In addition, updates of life cycle events (such as birth of a child, death, marriage, divorce, migration, jobs) and characteristics of life stages such as age and education are conducted for each year through probabilistic Monte-Carlo simulation methods. While the updates are mostly carried out at the person-level, they are translated into the household-level since persons in effect create individual households, which are being tracked within ILUTE. In the housing market, a household agent is first of all a demander for a dwelling object. As per the conceptualization in Chapter 3, it is assumed that households decide to move and become

101 91 active in the housing market as a demander in response to different types of stressors triggered from changes in household composition, life cycle events, life stages and surrounding environments. These households are placed in a list of demanders that are assumed to be actively searching for alternative dwellings in the housing market, if they decide to move. Unlike several applications of integrated land use and transportation models (for example, MUSSA in Martinez and Hurtubia, 2006) it avoids putting all households in the location choice process at every time step, which is not only behaviourally incorrect but also incurs computational burden. Thus, it clearly separates the households that are staying at the current location (who do not consider a move at a specific point in time), and the households who are choice movers and responding to the stimuli in the form of households need and opportunities in the housing market. The second role households play in the housing market is as suppliers in the resale housing market. Therefore, as soon as a household decides to move, the dwelling unit it occupies goes to the list of vacant dwelling units in the market that forms the supply pool for a given simulation year. Additional dwelling supply comes from the new housing supply component. Thus, the modelling system essentially reflects the resale market operating simultaneously with the new housing supply and transactions. The asking price of each dwelling active in the housing market is determined by the dwelling price model, which is developed in Chapter 6. While this research specifically deals with the behaviours of relocating households, other types of residential movements also occur in an urban area, particularly through migration and new household formation/dissolution. These two types of mobility decisions are separately handled within demographic component of the ILUTE system. In-migrants and new-households are directly added to the list of demanders, and the dwelling units that are associated with the outmigrants are listed to the dwelling supply pool. On the other hand, out-migrants are deleted from the household list. Additionally, in-migrants and new-households must remain active in the housing market until they find residences in which to live, unlike relocating households that are allowed to exit the housing market and to remain in their current location if suitable housing is not found in a given simulation year Components of residential location module As discussed earlier, the model assumes a sequential decision-making process for the relocating households. The first component of the model is a decision to move component that

102 92 determines for a household at each time step whether the given household will become active in the housing market this time period or not. If the household becomes active in the market, it proceeds through the subsequent stages of location choice processes. Otherwise, the household remains at its current residential location for that particular time step. The current version of ILUTE implements the discrete-time random parameter panel logit model (RP model described in Chapter 4) for the households decision to move, since it is compatible with the time-driven simulation architecture of the prototype ILUTE system and captures key triggers such as life cycle events and other dynamic variables in explaining mobility behaviour. This model generates a list of active households searching for alternative dwellings to relocate at each simulation step. Since these households are attached to existing dwelling objects, the model assumes that those dwelling units also become active in the housing market that is put up for sale. Household agents then select a prospective set of dwellings from the list of active dwellings in the market to evaluate alternatives against current residences. The reference dependent (re) location choice model developed in the Chapter 5 is used to specify and estimate the utility function and preference ordering of the alternative dwellings that are considered in the choice set. Given the complexity involved in explicitly modelling the spatial search process in great behavioural detail, a very simplified procedure is adopted to select choice sets within the current ILUTE implementation. This consists of simply generating a random choice set for each household from the set of active dwelling units. Developing an improved search process model is a priority task for future model system improvement. The probability of choosing a specific dwelling unit is calculated based on household and neighbourhood attributes, and dwelling characteristics including price. Allocation of dwellings to specific households is performed by this probability function. The overall model design for the simulation application is presented in Figure 7.1.

103 93 Select a set of active households - Mobility decisions Get choice sets (from active dwellings) - Search rule (random) Get asking prices - Asking price model Get utilities and assess choices - (Re) location choice model MARKET CLEARING - List probabilities by dwelling - Transaction decision one dwelling at a time NO Accept? YES Update lists -Household with new dwelling Figure 7.1 Microsimulation of relocation decisions

104 Market clearing process Once households assess alternative choices and obtain utilities they enter into a market clearing process in which the transaction price of the dwellings are endogenously determined. Details of the market clearing process are presented in Miller et al. (2009). In a nutshell, at a given point in time for a set of active household agents and active dwellings, the sum of probabilities of choosing a given set of alternative dwellings that a particular household considers to relocate adds up to one. But the probabilities placed for alternative active dwellings in the market in that particular point in time will be either greater or less than one. This second set of probabilities identifies the dwelling units that produce maximum utilities for a set of households given a fixed price. An equilibrium solution might be possible by adjusting prices in order to equate the second set of probabilities to one while maintaining the sum of households probabilities equal to one. Since a system-wide equilibrium is not expected in the ILUTE model, Farooq, et al. (2008) develops a solution algorithm to auction one particular dwelling at a time assuming that the sum of probabilities greater than one means the dwelling is under-priced and less than one suggests an over-priced dwelling. The process is iterated until the market handles all dwelling units in a given period of time. To determine the selling prices of the dwelling units this market clearing process searches prices around the asking prices assuming an upper and lower bound Interactions with other modules of ILUTE The starting point of developing a microsimulation model is the population synthesis. Pritchard (2008) created a set of synthetic household agents with relevant initial state for the year 1986, which acts as the base year for the simulation application. Unlike many other population synthesis work conducted in the field of transportation, it relates household agents with the dwelling units that have key dwelling attributes required to simulate dwelling choices. This set of synthesized households attached with respective current dwellings is used to simulate households decision to move, the first component of the households decision process within ILUTE to model relocation processes. The mobility component also takes inputs from other modules of ILUTE. While the demographic module provides information on life cycle events, the labour force module informs employment updates. Figure 7.2 provides a schematic diagram of the relationships between the mobility model and the other modules of ILUTE system.

105 95 Population and dwelling synthesis module Demographic updates module Age of the HH head Birth of a child Decrease in DMU size Labour force module Number of jobs in the DMU Increase/Decrease in number of jobs Change in job Retirement Residential Mobility Component Census data Exogenous inputs Economic data Ratio of non-movers in the CT Labour force participation rate Change in bank interest rate Figure 7.2 Relationship-diagram of residential mobility and other modules of ILUTE

106 96 Similarly, the household agents also interact with other modules of ILUTE at the (re) location choice component to collect information on dwelling, neighbourhood and household characteristics prior to each simulation run. Since the current implementation of ILUTE is not explicitly connected with the travel demand model, the travel times and costs are exogenously provided to the system. It is expected that once the TASHA (Travel Activity Scheduler for Household Agents) system is calibrated for the corresponding base year and zonal-system of ILUTE, feedbacks of travel characteristics for each year can directly be provided to the relocation model component. Finally, to compute the asking prices the dwelling characteristics are obtained from the synthesized data for the base year. New housing supply is also expected to carry dwelling type, and size in terms of number of rooms and bedrooms. Accessibility and location attributes are provided exogenously since ILUTE does not have an endogenous transportation infrastructure supply model. Since in this case, most accessibility measures are calculated in terms of distances, any official plan to increase transportation infrastructure could be directly entered into the modelling system to estimate policy responses towards impacts on property values. In addition, proportions of different land uses are external inputs since ILUTE do not explicitly simulate spatial land use changes. The model also requires inputs for neighbourhood and market conditions. While the neighbourhood attributes are exogenously provided in this version of the implementation, it is possible to endogenously generate these inputs once other components of ILUTE are fully operationalized. For example, ratio of non-movers in the neighbourhood can be obtained from the residential mobility component once the rental mobility model is empirically estimated and implemented within ILUTE system. Again, unemployment rate can be generated from the implementation of a labour market microsimulation model. 7.3 Input data preparation The mobility, (re) location and asking price models implemented in the ILUTE system require a variety of input data. A summary list of different variables used in these three different models is presented in Table 7.1.

107 97 Table 7.1 Summary list of variables used in residential mobility, (re) location and asking price models Data/Variables Component Data Source Household characteristics Age of head of decision making unit (DMU) Mobility Dem. Module Birth of a child in the DMU Mobility Dem. Module Lag of two years for decrease in DMU size Mobility Dem. Module Dwelling characteristics Total number of rooms Asking Price Synthesis Number of bedrooms Location Choice Synthesis Housing type-detached Asking Price Synthesis Housing type-attached (semi-detached and row) Location Choice Synthesis Building type (three storey building) Asking Price Synthesis Total duration in the dwelling Mobility Relocation Module Dwelling price (2001 $)-household income ratio (log) Location Choice Asking Price & LF Module Log of dwelling price (2001 $) Location Choice Asking Price Employment characteristics Change in job (any member in the DMU) Mobility LF Module Increase in number of jobs in the DMU Mobility LF Module Decrease in number of jobs in the DMU Mobility LF Module Dummy variable representing retirement Mobility LF Module Number of jobs in the DMU Mobility LF Module Census attributes Ratio of non-movers in the neighbourhood** Mobility Census Labour force participation rate in the neighbourhood** Mobility Census Average people per room in the census tract (CT)** Asking Price Census Unemployment rate in the neighbourhood** Location Choice & Asking Census Price Average dwelling value in the CT (in 1000 CAD $)** Asking Price Census Land use attributes Percentage of residential land use** Asking Price DMTI GIS Percentage of commercial land use** Asking Price DMTI GIS Percentage of open area in the neighbourhood (log)** Location Choice DMTI GIS Percentage of industrial area in the neighbourhood (log)** Location Choice DMTI GIS Accessibility Distance to the nearest subway station (Km)** Asking Price DMTI GIS Distance to the nearest regional transit station (Km)** Asking Price DMTI GIS Distance to the nearest highway exits (Km)** Location Choice & Asking DMTI GIS Price Distance to the nearest regional shopping center (Km)** Asking Price DMTI GIS Distance to the nearest community center (Km)** Asking Price DMTI GIS Distance to the nearest recreation center (Km)** Asking Price DMTI GIS

108 98 Distance to the nearest hazardous industries (Km)** Asking Price DMTI GIS Travel time/cost Average auto commute travel time (in minutes)** Location Choice EMME2 assignment Average transit commute travel time (in minutes)** Location Choice EMME2 assignment Total commute travel cost in Canadian dollars 2001 (log)** Housing supply characteristics Average days listed on the market for sale in the quarter of the year Location Choice Asking Price EMME2 assignment Supply (lagged) Average selling price in the quarter of the year (in 1000 Asking Price Supply (lagged) CAD $) Economic indicator Change in bank interest rate** Mobility CANSIM Data *Dem. Module = Demography Module, LF Module = Labour Force Module ** Exogenous variables, which are created using census, DMTI and CANSIM data Variables marked in Table 7.1 must be prepared as inputs to a simulation run, since the current version of ILUTE does not explicitly simulate these attributes 23. Since the model runs for an extended period of time, multi-year census databases are interpolated to create yearly representative dataset using GIS techniques for the neighbourhood attributes. During model estimations as described in the earlier chapters the longitudinal census dataset is created using the 2001 census zonal system as the reference. But since the base year for the simulation is 1986, this dataset is prepared in accordance to the 1986 census-tract zonal system. Distances to different transportation and activity centers are measured from a single year GIS dataset since multi-year infrastructure data are not available. Travel times and costs are generated using auto and transit assignment procedures of EMME/2 for the year 1986, 1991, 1996 and Finally, the land use data are created using land use profiles supplied by Desktop Mapping Technologies Inc. (DMTI) using GIS functions. 7.4 Simulation results To verify the behaviour of the models, several runs of the current ILUTE modelling system are conducted with a sample of 50,000 household agents from a total of the 877,254 synthesized 23 Primarily, neighbourhood, land use, economic attributes, and accessibilities.

109 99 Figure 7.3 Spatial distribution of households for the simulation year 1987 Figure 7.4 Spatial distribution of households for the simulation year 1988

110 100 Figure 7.5 Spatial distribution of households for the simulation year 2005 Figure 7.6 Spatial distribution of households for the simulation year 2006

111 101 household owners in the year of Model results are generated for a 20-year period, from the base year 1986 to the year of The key objective is to demonstrate the ability of the model to represent evolution of location patterns over time and compare the model results to the observed available data. Each run of the model requires approximately eight hours run-time in a standard PC (Intel Core 2 Duo, 2.6 GHz and 4 GB RAM). The outputs of the current ILUTE program are exported to the GIS environment to generate location distributions across the Greater Toronto and Hamilton Area for each year. For consistency in comparison of results, the1986 census zone-system is used for all years. Figures 7.3, 7.4, 7.5 and 7.6 show the simulated distribution of households for the years 1987, 1988, 2005 and 2006 across the GTHA respectively. Simulation results for the remaining years are presented in Appendix A. These figures show evolution of households location distribution across census tracts within GTHA for a 20-years historical period. 7.5 Comparison of simulation results Although several examples of operational integrated land use and transportation models that generate residential location patterns exist in the literature, comparison of simulation results against observed data and testing the models forecasting ability is rarely undertaken. This research is perhaps the first attempt to investigate simulation results for an extended historical period for an integrated land use and transportation model. Two key data sources used in this research to compare simulation results are census data from the Statistics Canada and microtransaction data obtained from the Toronto Real Estate Board (TREB) Comparison of location patterns Since residential location is an important input to the travel demand models and a key contribution of this research is to add capacity to the ILUTE system to generate household location choices, this research attempts to compare simulated predictions of household location patterns for the Greater Toronto and Hamilton Area (GTHA) against observed location patterns. Census datasets for the years 1991, 1996 and 2001 are primarily used to compare simulated and observed location patterns at each corresponding census tracts. To visualize predictive performance of the models, the observed total number of households in each census tract is subtracted from the simulated location predictions. Figure 7.7, 7.8 and 7.9

112 102 show the spatial distribution of closeness of observed and predicted location choices, including areas with under or over-predicted households locations for the year 1991, 1996 and While the blue shades represent under-simulated census tracts, the red shades represent oversimulated locations in the respective census tracts. Grey and yellow represents closer match of the predicted location to the observed. In general, the model predicts well in the midtown areas of the GTHA. However, it oversimulates locations in the downtown core and under-simulates in the suburban areas. Particularly, the model under-simulates location choices for the Hamilton Area. Similar trends are observed for all three years (i.e. 1991, 1996 and 2001). However, over-simulation of the locations in the downtown Toronto and adjacent areas have been steadily increased over the years. Two possible reasons may play a role to the outcome of this trend. First, in the housing supply component the new construction is not restricted to the capacity of the dwelling units that Figure 7.7 Comparison of simulated location patterns against census data (1991)

113 103 Figure 7.8 Comparison of simulated location patterns against census data (1996) Figure 7.9 Comparison of simulated location patterns against census data (2001)

114 104 is possible to be built in a particular census tract, which presumably leads to the additional supply in the attractive downtown areas. Second, the utility of choosing a dwelling as specified in Chapter 5 for location preferences is mostly dependent on accessibility and other attractiveness measures, which are highest in the downtown and adjacent areas. Hence many dwellings in these areas are being chosen by the households, leaving more vacant dwellings in the suburban and peripheral areas. Perhaps inclusion of certain life-style choice variables and/or capturing residential self-selection effects (as studied by Bagley and Mokhtarian, 1999; Walker and Li, 2007 among others) might increase the performance of the models Comparison of dwelling prices Since it is expected that microsimulation models will reasonably replicate the aggregate urban system behaviours this research also compares aggregate predicted prices against observed prices of Multiple Listing Service (MLS) data obtained from Toronto Real Estate Board (TREB) for The model estimated in Chapter 6 is used to predict asking prices for each dwelling that become active in the housing market for sale, which acts as an initial price in the market clearing process. Table 7.2 shows a comparison between observed and predicted asking prices for each simulation year. The result suggests that average predicted prices for the GTHA is very close to that of observed prices for each year. However, standard deviations for simulated asking prices are Table 7.2 Comparison of dwelling asking prices (simulation vs. TREB observed) Predicted (simulation application) Observed (TREB Microdata) Predicted average prices Observed average prices Diff. between Percentage difference Year Average Std. deviation Average Std. deviation averages

115 105 higher than that of observed prices. Although the model mostly under-simulates the average prices, the percentage differences between average observed and simulated prices is only 1.39% to 10.22%. Figure 7.10 clearly shows that the predicted average prices follow the trend of the observed average prices over an extended period of time Dwelling price (2001 CAD $) Observed average prices Predicted average prices Year Figure 7.10 Comparison between average observed vs. simulated dwelling prices The research also compares detailed distribution of simulated dwelling asking prices with that of observed prices. Figure 7.11 and 7.12 show the observed and predicted distribution of asking prices for the year 1988 and 1995 respectively. Other year s results are presented in Appendix A. The distributions are not exactly same, but show relatively similar patterns. The model, in general, over-predicts low priced dwellings and under-predicts medium priced dwellings. For example, for the year 1995, 56% of the simulated active dwellings is priced below 200,000 CAD $ in contrast to 37% in the observed dataset. And, 29% of the simulated dwelling have a price range of 200, ,000 CAD $ in comparison to 52% in the MLS dataset. On the other hand, 15% of the simulated dwellings have over 400,000 CAD $ of asking price in contrast to 11% in

116 106 Percent of properties Observed ask ing price (2001 CAD $) Percent Predicted ask ing price (2001 CAD $) Figure 7.11 Comparison of observed and predicted asking prices for the simulation year 1988

117 107 Percent of properties Observed ask ing price (2001 CAD $) Percent Predicted ask ing price (2001 CAD $) Figure 7.12 Comparison of observed and predicted asking prices for the simulation year 1995

118 108 the actual market listing data. These differences are not quite unreasonable given the fact that the set of dwellings that are active in the market in a given simulation year are not exactly the same (in terms of their attributes) to the dwelling units listed for sale in the actual housing market in a given year. The supply of dwellings depends on a complex interplay of household s decision to move, placing the dwelling units in the resale market as well as new housing supply through construction. These detailed comparisons, however, help us to understand the performance of the modelling system at the disaggregate level and will assist in calibrating the modelling system in near future Comparison of other outputs The ILUTE microsimulation model can generate an enormous number of outputs in terms of location of individual agents (for example, person and families), and at any spatial level with variety of attributes (age, sex, education, etc.). Since the model does not perform rental market simulation it is not possible to compare these outputs generated by the modelling system against the full-sample census data (that aggregately represents both owner and rental market) at the current stage. Obviously, developing models for rental market and implementing within the ILUTE system is an immediate priority, which would allow more comprehensive validation of the simulation model and subsequent use of this model for forecasting and policy tests. 7.6 Potential use of the model for policy analysis The overall intent of developing a modelling system of residential location processes in this research is to integrate land uses within a comprehensive land use and transportation modelling system, and to test different land use and transportation policy scenarios. The current ILUTE system implements households choice mechanisms of residential locations. It is able to generate location patterns and dwelling transaction prices for a given supply of housing. If certain types of development occur or planned to happen, the modelling system will be able to generate changes in households location patterns. Therefore, the model system can be applied to simulate future location patterns, neighbourhood composition, housing prices as well as activity and travel patterns, given a specific assumption of urban growth. In addition, the location models implemented in the simulation model is sensitive to the travel times and costs, which in turn, might help in realizing impacts of transportation investments.

119 109 Since this modelling system is still under development and several important components, including a job location choice module, are not fully implemented in the current version, this research introduces the following discussions of policy tests for illustration purposes only. Table 7.4 presents a proposed example list of scenarios that can be tested with the ILUTE modelling system to generate alternative future states at any planning horizon. This type of information will be helpful in making long-range planning decisions and policy formulation. Table 7.3 Proposed example scenarios for the Greater Toronto and Hamilton Area Scenario 1 Compact development scenario Scenario 2 Transit-oriented development scenario Scenario 3 Compact development with transit-oriented development scenario Scenario 4 Compact and transit-oriented development scenario with the proposed transit city plan Scenario 5 Sprawl scenario Application of smart growth strategies including infill development, intensification within urban core, mixed use, restriction on suburban development, urban growth boundary such as implementation of greenbelt Residential and commercial development around existing transit stations (for example, within half kilometer of the existing stations) Combination of the first two scenarios Scenario 3 with recent City of Toronto transit city plan with possible extension of regional GO network expansion Sprawl developments at the outskirts of the GTHA To test the above-mentioned policy scenarios, extensive scenario development schemes are required that involve identification of developable lands and understanding of current provisions in the zoning regulations. Scenario development strategies might also include identification of growth targets as outlined by the Places to Grow Plan by the Province of Ontario, identification of development capacity in the existing built-up areas, assumptions concerning the amount of dwelling supply by type at a given point in time, assumptions about the prospects of such construction that might be undertaken by the developers, etc. Consequently, scenario development requires extensive consultation with the city and provincial planning and regulatory

120 110 authorities as well as several stakeholders including real estate developers. Such detailed scenario development exercises elicit a comprehensive research agenda for the ILUTE research team in the long run. In the short run, however, simple policy tests, for example impacts of hypothetical growth assumptions (compact development vs. sprawling), and percentage reduction of travel times and costs can be tested using the current modelling system. These experiments might help in understanding model development issues and policy sensitivity of the developed models. 7.7 Concluding remarks This chapter presents a microsimulation application to predict evolution of location patterns at the Greater Toronto and Hamilton Area (GTHA). One of the unique features of the model is that it implements disaggregate econometric models within the ILUTE modelling system, which has increased its behavioural validity in predicting future urban states and potential to test policy initiatives. Additionally, since the models are estimated at the household and dwelling unit level, it adds capacity to the modelling system to capture micro-scale impacts of policy instruments. Although the current model deals only with the owner-occupied market, the modelling system can be extended for rental market microsimulation by estimating similar types of econometric models. The residential location component is highly interconnected with other components of ILUTE, such as demographic/employment updates and labour market models, which are still evolving. Particularly, it is important to develop corresponding models of job location, which is a significant limitation of the current version of the model. In addition the modelling system itself will require calibration. Note that this is a first-cut attempt to run the model. Therefore, the simulation results presented in this research are preliminary in nature. However, running the model for 20-year period helps to understand the performance of the individual model components as well as related implementation issues. Comparison of simulation results against observed data for such an extended historical period is unique in the existing literature. It helps to identify areas to improve different components of the modelling system in a process of incremental development of a large-scale microsimulation model and at the same time guides to undertake a comprehensive validation in near future.

121 111 CHAPTER 8: SUMMARY AND CONCLUSION 8.1 Summary of the research Residential relocation generates spatial movements of people within an urban area. Knowledge of these movements is very critical for planners since it affects neighbourhood composition, mode choices, travel patterns as well as housing prices. This research attempts to fill some critical gaps in the existing literature by investigating and empirically estimating models of different stages of household decision-making processes concerning residential location, as well as investigating housing prices in order to facilitate a price determination mechanism through a market clearing process. A review of literature of existing integrated urban models suggests that there are significant differences in dealing with residential location within integrated land use and transportation modelling systems. The fundamental differences derive from the basic model conceptualizations and designs in major modelling streams. Aggregate spatial interaction models largely depend on the economic base theory, which estimates amounts of population serving different industry sectors. The allocation of population follows a gravity-based approach in relation to generalized travel cost and employment at different zones. Extension of these models includes recent improvements in spatial I/O systems that further disaggregate industry sectors, yielding a reasonably detailed representation of the urban economy, which is the most important strength of these modelling systems. The residential location component however continues to consist of aggregate logit allocations as opposed to process-oriented residential location choice models. Similarly, aggregate microeconomic integrated urban models, which better capture demandsupply interactions, deal with counts of population and instantaneously distribute them by matching aggregate demand and supply in a snapshot in time assuming static equilibrium. In effect, the aggregate models provide macro-level estimates of population locations, but submerge important details of residential location choice decision processes. As a result, a decision-based household residential location model is virtually absent within these integrated urban modelling systems. Most importantly, due to inherent design and computational frameworks of aggregate

122 112 spatial interaction models, spatial I/O models and aggregate economic models, it is not possible to track households movements across space through time, which might be useful information to determine the impacts of policy interventions on the future distribution of households locations. In addition, existing spatial choice components of integrated models are also criticized for aggregate representation of space, time and socio-economic characteristics of population within the modelling systems. Although recent model developments, including microsimulation-based models, have made significant progress in representing population by disaggregate socioeconomic categories, the conventional approach of zone-choice models is quite prevalent in most integrated land use and transportation models. The rapidly emerging field of microsimulation models, however, adds significant excitement and promise in terms of explicitly representing individual actors/agents and simulating the behaviour of agents in considerable details. But given the complex nature of behavioural interactions and the detailed requirements of agent-objectprocess representation, there is a general tendency within agent-based modelling to replicate behaviours using rules or heuristic simulations, sometimes without sufficient statistical validity. Such modelling frameworks however provide a skeleton for next generation land use models for which decision-oriented and disaggregate model components are required to be empirically investigated, which provides a pivotal base for this research to examine process-oriented residential location models. Based on the perspectives gained through the review of integrated models this research develops a conceptual model for long-term decisions of households residential location choices. Unlike most traditional location choice models this research has adopted a longitudinal approach, in which the overall modelling framework attempts to capture continuous movements of households from one place to another in the form of relocation. It investigates microbehavioural decision-making processes of households by which they intermittently change dwellings through time. This conceptualization emphasizes the fact that every household has a housing career/residential biography, which should be incorporated into the model estimation procedures. The research reviews the theoretical basis of existing relocation literature and alternative methodological considerations in developing such models. A household s decision to search for an alternative dwelling is perceived as an outcome of residential stressors, which are generated through shifts in household composition, life stages and life cycle events. Assuming relocation as a decision-oriented process the research identifies a two-stage sequential model that has two

123 113 basic components, (1) decision to move, (2) evaluation and (re) location decision. Whereas the first component explores when and why households move, the second component deals with where to move, leading to a relocation decision. One of the critical model design issues within the decision to move component is how to represent the temporal dimensions in the model structure, which can be assumed to be continuous or a discrete approximation of continuous time. This research investigates both approaches and examines alternative model structures to tackle methodological issues of modelling longitudinal processes within both techniques. Particularly, the research attempts to incorporate correlation effects due to repeated choices, which is quite a common case for the investigation of housing careers that uses retrospective/panel observations. In the second component consisting of the (re) location choice decision, the research attempts to model the choice of dwelling units in order to facilitate dwelling-by-dwelling transactions within a microsimulation model of housing market. The notion of households constant adjustments of dwelling needs implies that a household s preferences of dwelling choices might depend on the dwelling unit it lived in immediately prior to a relocation decision. Therefore, this research examines a reference dependent (re) location choice model, which essentially recognizes history dependency and the role of previous location on household preferences while choosing alternative dwellings for relocation. The model is primarily conceptualized using theoretical and experimental evidence drawn from prospect theory with an assumption that households frame their evaluation in reference to the dwelling unit it is living in at the time it has taken a decision to move. To implement the model the research takes advantage of random utility maximization principles and specifies the utility structure in terms of gains and losses such that it can be mapped into choice probabilities. The location choice model is assumed to be interconnected with the travel demand models, which will provide accessibility measures in terms of auto/transit travel times and travel costs. Finally, the research formulates a microsimulation model for residential location in which the aforementioned two model components generate housing demand in terms of who is going to be active in the housing market in a given simulation year and a preference ordering for each active household for a given set of active dwelling units it considers to relocate. Since the housing microsimulation model attempts to mimic auction-type bargaining of buyers and sellers, this

124 114 research estimates a dwelling price model, which is used to generate asking base prices to initiate a market clearing process. In summary, the conceptual model for microsimulating residential location processes sets a framework to investigate three distinct model components: (1) a model for the decision to move, (2) a model for (re) location choice decision, and (3) a model of dwelling asking price. The residential mobility models that investigate factors affecting a decision to move and timing of households relocation are empirically implemented using a retrospective survey for the Greater Toronto and Hamilton Area (GTHA). Two types of econometric approaches are tested: hazard-based duration models and discrete-time panel logit models. While hazard models assume a continuous temporal profile, binomial panel logit models are applied by discretizing time into yearly intervals. Parametric hazard models are estimated by assuming different distributions for the baseline hazard, notably exponential, Weibull and log-logistic distributions. The final model is selected based on the better fit of the observed data among candidate models. The first set of models considers each passive-state duration to be a separate observation in the duration analysis. This assumption of independence between spells leads to single-spell models, which is the common practice in most mobility modelling studies. Since housing career data essentially involves repeated spells for many households, this independence assumption is no longer valid. To account for potential correlations due to repeated events, the research examines shared frailty/random effect models. The results suggest that a log-logistic hazard model with Gaussian shared frailty component describes event termination probability best in terms of goodness-of-fit measures. One interesting finding is that households in the first spell of forming a newhousehold and also the first spell after immigration have higher durations of stay at a dwelling before considering a move to the next compared to other residents of GTHA. In addition, households with older heads stay passive in the housing market longer than those with younger heads. Renters are more frequently active in the market than homeowners. Within the discrete choice modelling approach this research tests and compares alternative model structures to account for correlation effects due to repeated choices in the form of fixed effect, random effect and random parameter models. A random parameter model is selected as the final model since it has greater goodness-of-fit statistics. This model includes time-varying covariates and most of the hypothesized residential stressors are found to be significant in explaining

125 115 mobility behaviour. Results of parameter estimates reveals that factors related to life cycle events, such as job change, birth of a child, increase/decrease in number of jobs are key determinants of households decision to consider a move at each time period. Both a change in job and birth of a child triggers a residential move. Similarly, a decrease in number of jobs in the household increases the probability of moving. An increase in jobs however shows an opposite effect, presumably due to fact that with more fixed job locations the households experience an immediate stationary condition. But the parameter of this variable exhibits high variability in terms of statistically significant standard deviation, which suggests that in some cases an increase in jobs does increase the probability of moving. Additionally, the model suggests that there is a two-year lag response of a decrease in household size in the mobility decision. Since this model is compatible to the software architecture of time-driven simulation of ILUTE system and includes time-varying covariates, the model is selected to be implemented in the current version of ILUTE. The relocation choice model adopts a reference dependent structure that explicitly recognizes the role of the status quo and captures asymmetric responses of the households towards gains and losses in making location choice decisions. The research uses a retrospective residential search survey dataset and a Toronto Real Estate Board s dwelling supply database to develop the model at the elemental level of individual dwelling units. It applies a mixed logit formulation that captures unobserved heterogeneity and avoids imposing IIA restrictions on the choice probabilities. Several types of variables are tested in the model specifications, including dwelling characteristics, land uses and other zonal attributes, accessibility measures and household sociodemographics. While the current dwelling is assumed to be the reference point in framing evaluation of alternative dwellings, all gains and losses are measured comparing current and prospective dwellings during model development. The results reveal that asymmetrical evaluations of gains and losses relative to the current dwelling exist, and the reference dependent model performs better than conventional location choice model in terms of model fit and behavioural insights. The key determinants of location choices are found to be dwelling size in terms of number of bedrooms, dwelling type, travel times, travel costs, distance to the highway exit, amounts of open areas, amounts of industrial land uses, unemployment rate, dwelling price and household income. Results for the reference dependent model reveal that households prefer gains in number of bedrooms but they are more sensitive to equal amounts of losses. A similar

126 116 loss aversion attitude is observed for the percentage of open areas and unemployment rates. Households are also sensitive to the losses for the level of service attributes. In addition, households prefer detached houses compared to attached dwelling types. Finally, the higher the price of the dwelling unit the lower the probability of choosing the dwelling unit, and vice versa, all else being held equal. For modelling dwelling asking prices this research develops multilevel linear models using an extensive sample of over 250,000 housing property transactions during in the Greater Toronto Area (GTA). It examines temporal heterogeneity along with spatial heterogeneity since the model deals with multi-period data. The key motivation of using the multilevel modelling technique is that it clearly identifies and differentiates between-cluster heterogeneity (i.e. across aggregated units) and heterogeneity between units of analysis that are nested within aggregated clusters. Two alternative specifications are tested: two-level spatial and mixed two-level spatiotemporal random effects model. While the first specification assumes dwelling units are nested within spatial clusters (i.e. neighbourhoods), the second specification hypothesizes that dwelling units are nested within spatio-temporal clusters (i.e. neighbourhoods in a given quarter of the year). At first, the research examines alternative functional forms of the asking price model, and then chooses a semi-log model for subsequent multilevel model development. Comparison of models suggests that the spatio-temporal model performs better in terms of explanatory power and parameter estimates. Dwelling unit characteristics are found to be strong predictors of housing prices in the GTA. The model results also reveal that while the price of the dwelling decreases by 0.67% for every additional kilometer from a subway station, it goes down by 0.16% per kilometer away from regional transit stations. Additionally, proximity to highway exits by two kilometer adds a 0.31% premium in the property values of GTA. Temporal market conditions, particularly in terms of quarterly average selling price and average days listed for sale also influence dwelling prices. Since the result suggests that spatio-temporal heterogeneity exists in the housing market of the GTA, accounting for it provides reliable and accurate estimates of the influence of accessibility, neighbourhood characteristics and other key spatial attributes and temporal market dynamics, yielding an improved model for urban policy analysis applications. Finally, this research presents a microsimulation model of residential location processes developed by the ILUTE project team that implements the aforementioned model components.

127 117 The model operates at yearly time steps and can proceed over an extended period of time, supposedly to any planning horizon of interest. The current implementation of the model is for the owner-occupied market only; a rental market model is expected to be implemented once relevant rental data and appropriate modelling components are empirically investigated. The model uses 1986 synthesized households and dwellings of the GTHA for the initial year of simulation, which is subsequently updated through demographic and new housing supply components for subsequent simulation years. The residential mobility model generates a list of active households searching for alternative dwellings to relocate at each simulation step. In the housing market, it is assumed that a household simultaneously acts as a demander (who is looking for an alternative dwelling to relocate) and a supplier (who puts his/her vacant dwelling unit up for sale once it decides to move). Therefore, all existing dwelling objects attached with active household agents are assumed to be active dwellings for sale in the housing market, which generates a list of active dwellings for that particular year. New construction also adds dwelling units to this list. The reference dependent (re) location choice model is used to specify and estimate a utility function for each household. The probability of choosing a specific dwelling is determined based on household, neighbourhood and dwelling characteristics, which is used to generate preference ordering of the alternative dwellings that is considered in the choice set. A simplified procedure of randomly selecting a choice set is implemented in the current version of the model. In the market clearing process, the dwelling price model developed in Chapter 6 is used to generate base asking price for each active dwelling in the market, and the transaction price is determined around the asking price assuming a lower and upper bound through an iterative market-clearing process. This research runs the simulation model for a 20-year historical period ( ) to generate evolution of location patterns in the Greater Toronto and Hamilton Area (GTHA). It also compares the results against observed location patterns obtained from census tabulations. In general, the model predicts household locations in the midtown areas of GTHA well. However, it over-simulates choices in the downtown core and under-simulates in the sub-urban areas. Several components of the current ILUTE modelling system are still under development, particularly the demographic updates and market clearing process. In addition, a comprehensive modelling effort is required to implement job location component. Therefore, comparison of the model results presented in this research is the first and preliminary step in a longer-term, more complete validation exercise. It is expected that these

128 118 comparisons will help in calibrating the model and guide to undertake a comprehensive validation in the near future. 8.2 Research contributions The most important contribution of this research is the estimation of econometric models to implement households long-term decisions regarding residential location within an Integrated Land Use, Transportation and Environment (ILUTE) modelling system. The research empirically investigated residential mobility and location choice behaviour as well as dwelling prices. For residential mobility it investigates models assuming continuous temporal profile as well as within discrete-time settings. One of the unique features of the estimated models is that the models account for correlation effects due to repeated choices, which are quite common for housing career observations. There is virtually no evidence in the existing literature that attempts to incorporate such effects. As such, this research contributes by testing alternative ways to tackle the issue within both modelling approaches in order to generate unbiased parameter estimates, leading to efficient techniques for modelling longitudinal mobility processes. The random parameter model, which is implemented in the current version of ILUTE is novel in several respects, including: It is a dynamic model, developed using disaggregate time-series (panel) data, incorporating a variety of time-varying explanatory variables. It incorporates heterogeneity effects in which parameters are assumed to be varying randomly, something hitherto not attempted in mobility models. It is developed using a database that includes instances in which households became active in the market but then did not subsequently actually relocate. This database is unique in the field and provides an unbiased estimate of residential mobility rates. The (re) location choice model developed in this research establishes a probability function, which is empirically derived by specifying and estimating a discrete location choice model. The key features of this model that differentiate it from conventional location choice models are: It incorporates reference dependencies that explicitly recognize the role of status quo (i.e. the current, default residential location) and that captures asymmetric responses towards

129 119 gains and losses relative to the currently occupied dwelling in making location choice decisions. It applies a mixed logit formulation that captures unobserved heterogeneity (idiosyncratic taste/preference variations) and avoids imposing IIA restrictions on the choice probabilities. It deals explicitly with the choice of an individual dwelling unit from a set of specific dwelling units, rather than the choice of merely a zone of residence. It is developed using a comprehensive micro dwelling supply data, something that usually is not available to modellers. The dwelling asking price model attempts to investigate the influence of transportation access as well as temporal market dynamics. The model is unique in several respects, including: The model accounts for temporal heterogeneity simultaneously with spatial heterogeneity using a multilevel linear modelling approach. It examines a comprehensive set of transportation access, neighbourhood attributes as well as temporal market conditions. It incorporates temporal aspects in the dwelling price model, which is very important since in most cases modellers deal with multi-period data and failure to account for this might lead to biased parameter estimates and affect the use of such results in policy applications. Finally, this research demonstrates a microsimulation application running the model for an extended historical period and compares the predicted location choices against observed location patterns. To our knowledge, comparison of these results for such an historical period is unique in the existing integrated urban modelling literature. The microsimulation model of residential location is also unique in several respects, including: Unlike many emerging microsimulation-based urban models, this model implements empirically estimated econometric models as opposed to totally rule-based microsimulation experimentations.

130 120 It implements households choice of dwelling objects, which is relatively new in the existing integrated urban modelling literature. It clearly separates relocating households and new households in the urban area, thus more realistically representing evolution of households movements across space. In contrast to many operational integrated urban models that are temporarily aggregated to forecast location patterns every 3-5 years interval, this model predicts changes in population locations every year. It provides an opportunity to assess policy intervention at yearly basis. 8.3 Recommendations for future research The research presents a comprehensive modelling framework for residential location choice processes, which is implemented within the ILUTE system to simulate the evolution of location patterns over time. The most immediate priority task to increase forecasting capability of the model is to develop corresponding job location models. In addition, the residential location choice model developed in this research should be integrated with the travel demand forecasting component of ILUTE. Given the complexity of households decision-making process in relation to job location, auto ownership and activity schedule, there is a need to develop a comprehensive research agenda for subsequent incremental development of the current version of the model. Particularly, investigation of the interdependence of residential mobility and job mobility should be an immediate priority to integrate these two long-term decision components more realistically. Simulation results presented in this research deals with only a sample of the synthesized GTHA households. This is a first-cut attempt to investigate the performance of the model. The model should be run for 100% of the population, with an improved demographic component and market clearing process. Particularly, the current market clearing model although meets our immediate need to operationalize housing market, extensive research efforts should be given for an econometric approach of dealing with auction-based dwelling-by-dwelling transactions in which utility maximization of households and profit maximization of homeowners are properly ensured. Another important area to contribute is developing an improved choice set generation process, which currently is basically a random selection of a set of dwellings from all dwellings active in the market. In addition, the current model only deals with the owner-occupied market;

131 121 models of the rental market should be empirically investigated to simulate rental relocation and rent as well. Each modelling component investigated in this research can also be extended to improve the current version of the modelling system. Although this research investigated residential mobility decisions, tenure choice (i.e. transition to renting to ownership/owning to renting) is not considered due to a very small sample size in the available estimation database after market segmentation. A competing risk model within hazard-based duration modelling approach might be an interesting pathway to put forward integrated mobility and tenure choice modelling. In case of (re) location choice, the current model assumes a single reference. It will be interesting to extend the modelling framework to consider multiple reference points and/or changes in reference points during dwelling search. As a matter of fact, the dwelling search process is not adequately addressed in the existing literature. It is important to understand and attempt to model search processes in considerable detail, which might help cross-fertilization of random utility models and behavioural choice theories. One of the key obstacles to proceed through search modelling is the availability of observations of selected dwellings while households evaluate alternatives to relocate. Therefore, documenting such information is very important in any future residential search survey if disaggregate modelling is intended. It is also important to note that all models developed in this research depend on small sample surveys. The hypotheses examined in these models should be tested using larger sample data. Therefore future research should concentrate on gathering larger datasets, however, without compromising the detailed nature of information needed within panel/retrospective surveys, which is a vital requirement for modelling longitudinal processes. In addition, future research should address two-way interdependencies of decision to move and (re) location choice. The approach taken to the location choice model in comparing current dwelling and available alternatives leads towards that direction. But further investigation is required to entangle these closely related decision dimensions of household decision-making within a more compact modelling framework. Finally, concurrent to on-going model improvements, the future research agenda should include development of scenarios to test policy implications. Unless it is possible to demonstrate our ability to develop models which provide useful outcomes in terms of policy interventions, it will

132 122 be hard to overcome most criticisms large-scale urban modelling have experienced in the last two decades. 8.4 Final remarks Urban systems are very complex, with multiple key actors that continuously make decisions to change their conditions and surrounding environments. Modelling of such multifaceted decision processes and system-interactions is very challenging. As such, development of a comprehensive integrated urban model can only be dealt with through step-by-step investigation of different components, which will eventually contribute to the evolution of the target model that urban modellers have in mind. This research attempts to develop models for microsimulating residential location processes, which is one of the key elements of integrated urban models. Since the transportation research field has made significant progress in terms of disaggregate activity generation/scheduling and microscopic traffic simulation in recent times, disaggregate and microsimulation-based modelling of land use systems appears to be a step forward towards meaningful integration of long-term and short-term decisions of urban dwellers. Such a modelling system will assist in predicting future of urban areas and formulating appropriate policy and planning initiatives to deal with forthcoming development challenges.

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146 Appendix A 136

147 137 A 1: Spatial distribution of households for the simulation year 1986 A 2: Spatial distribution of households for the simulation year 1989

148 138 A 3: Spatial distribution of households for the simulation year 1990 A 4: Spatial distribution of households for the simulation year 1991

149 139 A 5: Spatial distribution of households for the simulation year 1992 A 6: Spatial distribution of households for the simulation year 1993

150 140 A 7: Spatial distribution of households for the simulation year 1994 A 8: Spatial distribution of households for the simulation year 1995

151 141 A 9: Spatial distribution of households for the simulation year 1996 A 10: Spatial distribution of households for the simulation year 1997