CHAPTER 3 APPLICATION OF MULTIVARIATE TECHNIQUE SPATIAL ANALYSIS ON RURAL POPULATION UNDER POVERTYLINE FROM OFFICIAL STATISTICS, THE WORLD BANK

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1 CHAPTER 3 APPLICATION OF MULTIVARIATE TECHNIQUE SPATIAL ANALYSIS ON RURAL POPULATION UNDER POVERTYLINE FROM OFFICIAL STATISTICS, THE WORLD BANK 3.1 INTRODUCTION: In regional science, space is a central concept. During the 1970s, attention was paid to a growing body of geographic science literature. Issues like estimating and testing problems about regional econometric models were put into focus. Historically, spatial econometrics, first coined by Jean H.P. Paelinck in the early 1970s, originates as an identifiable field in Europe because sub-country data in regional econometric models are needed to deal with and been fast developed & grown during the 1990s (Anselin,1999). According to Anselin (1988), spatial econometrics addresses issues causes by space in statistical analysis of regional science regressions. In other words, spatial econometrics is the combination of statistical and econometrics methods that deal with problems concerning spatial effects that usually consist of two sections, spatial dependence and spatial heterogeneity, which are causes by using spatial data such as cross-sectional data and panel data. Spatial econometric techniques recently become more and more common in empirical work. As a result, there is a growing literature of spatial data analysis in many fields such as urban and regional economics, criminology as well as demography. 106

2 We have focused on two issues that are often overlooked in technical treatments of the methods of spatial statistics and spatial econometrics. Some examples on different approaches in spatial analysis by in Leamer (1978), Hendry (1980), Sims (1980, 1982), Lovell (1983), Swamy et al. (1985), Zellner (1985, 1988), Efron (1986), Pagan (1987), Kloek and Haitovsky (1988), and Durbin (1988) are very interesting. 3.2 SPATIAL ANALYSIS AND SPATIAL DATA: In general terms, spatial analysis can be considered to be the formal quantitative study of phenomena that manifest themselves in spare. This implies a focus on location, area, distance and interaction, e.g., as expressed in Tobler's (1979) First Law of Geography, where "everything is related to everything else, but near things are more related than distant things." In order to interpret what "near" and "distant" mean in a particular context, observations on the phenomenon of interest need to be referenced in space, e.g., in terms of points, lines or areal units. There are two opposite approaches towards dealing with spatially referenced data (Anselin 1986b; Haining 1986). In one, which we will call the data-driven approach, information is derived from the data without a prior notion of what the theoretical framework should be. In other words, one lets the "data speak for themselves" (Gould, 1981) and attempts to derive information on spatial pattern, spatial structure and spatial interaction without the constraints of a pre-conceived theoretical notion. 107

3 The second approach, which is called model-driven, starts from a theoretical specification, which is subsequently confronted with the data. The theory in question may be spatial (e.g., a spatial process or a spatial interaction model, as in Haining 1978, 1984) or largely a-spatial (e.g., a multi-regional economic model, as in Folmer 1986), but the important characteristic is that its estimation or calibration is carried out by means of spatial data. The properties of this data, i.e., spatial dependence and spatial heterogeneity, necessitate the application of specialized statistical (or econometric) techniques, irrespective of the nature of the theory in the model. Most of the methods under this category deal with estimation and specification diagnostics in linear models in general, and regression models in particular (e.g., Cliff and Ord 1981; Anselin 1980, 1988a). The main conceptual problem associated with this approach is how to formalize the role of "space." This is reflected in three major methodological problems, which are still largely unresolved to date: the choice of the spatial weights matrix (Anselin 1984, 1986a); the modifiable areal unit problem (Openshaw and Taylor 1979, 1981); and the boundary value problem (Griffith 1983, 1985). We have chosen model-driven approach. 3.3 SPATIAL ECONOMETRICS: We usually use a database that includes information concerning geographical locations or regional units to estimate a set of regression in social sciences. However, the traditional econometric modeling has largely ignored or overlooked such 108

4 available information. Therefore, if we want to use such valuable information in an efficient approach, we must take spatial effects into account. Spatial econometrics is the collection of methods that deal with the peculiarities caused by spatial interaction (spatial dependence) and spatial structure (spatial heterogeneity) in the statistical analysis of regional science models for cross- sectional and panel data. (Anselin, 1988). As stated above, traditional econometrics does not often take geographical information into account. Hence, two issues occur when the sample data set has a locational component. First, spatial dependence exists between the sample observations. Second, spatial heterogeneity occurred in residuals of the regressions. According to theoretical studies of Anselin (1988), spatial dependence or spatial autocorrelation usually stands for dependence that often exists among the sample observations in cross-sectional data sets. In other words, the sample observations collected at one point in space are not independent on the sample observations collected at other locations. That is, we need to consider spatial dependence, if data collection associates with units such as states, provinces, countries and so on. In this sense, spatial dependence is determined by the effect of distance. As stated in Tobler (1979), everything is related to everything else, but near things are more related than distant things. In addition, there are rich examples concerning issues of spatial dependence such as data on population and employment, as well as other economic activities collected for location or distance. 109

5 The term spatial heterogeneity is the second category of spatial effects and donates instability or variation in relationships over space; namely, functional forms and parameters vary with location and are not homogeneous throughout the data set (Anselin, 1988). In general, a different relationship should hold for every point in space. There is a host of simple and familiar examples such as the rich are living in the south of the town and the poor are living in the north of the town. Attention has recently been paid to issues of spatial effects not only in regional and urban economics, but also in local public finance, environmental and resource economics, international trade as well as industrial organization. 3.4 SPATIAL ERRORS: Basic to both the data-driven and the model-driven analysis of spatial data is an understanding of the stochastic properties of the data. The use of "space" as the organizing framework leads to a number of features that merit special attention, since they are different from what holds for a-spatial or time series data. The most important concept in this respect is that of error, or, more precisely for data observed in space, spatial error. The distinguishing characteristics of spatial error have important implications for description, explanation and prediction in spatial analysis. 110

6 3.5 SPATIAL AUTOREGRESSIVE MODELS: This section in detail is a class of spatial autoregressive models that will be employed in the empirical applications. A general spatial autoregressive model which is well known as spatial log model is labeled as SAR in this paper and has been introduced to model cross-sectional data, is described in Anselin (1988) and given by y Wy X, 2 N( 0, ) (3.1) Where, Y represents an (nx1) vector of the sample observations on a dependent variable collected ay each of n locations. X contains a (n x k) matrix of exogenous variables, and β is an (k x 1) vectors of parameters associated with exogenous variables x, which reflects the influence of the explanatory variables on variation in the dependent variable y, as well as ρ is the coefficient on the spatially lagged dependent variable, W 1 y W is regarded as spatial weight matrix that indicates the potential interaction between contiguous positions and is known as (n x n) matrix with positive elements, which are associated with the spatially lagged dependent variable. Spatial weight matrix usually contain first-order contiguity relations and have been standardized to have row sums of unity (Le Sage, 1998). This model is a special version of the special model that n 111

7 only contains the spatial lagged term. It is labeled as a mixed regressive- spatial autoregressive model in Anselin (1988), because it combines the standard regression model with a spatially lagged dependent variable. Another model studied in this paper is spatial error model (SEM). It provides another efficient method for dealing with the spatial data set that consists of 14 observations for states in India. The SEM model can be stated as follows: LOG( PUPL ) X u, u=λ W u + ε 2 N( 0, ) (3.2) where, λ is a coefficient on the spatially correlated errors and LOG(PUPL), W, X, as well as β are the same as described in the SAR model. n 3.6 SPATIAL CONTIGUITY MATRIX: Quantifying spatial matrix is a crucial operational issue in spatial econometrics. In this paper, spatial contiguity matrix is used in the spatial autoregressive models. The first task we must undertake before we can introduce the matrix to describe what is the meaning of contiguity. As the name implies, contiguity reflects such geographical locational information that one regional unit of the sample observation is close to other such units in space. Measuring contiguities relies on the information of the outlines of spatial units offered by a map. Intuitively, it is not difficult to distinguish which units are 112

8 contiguous or not from the map. That is, if units share the same borders, these units are considered to be contiguous or neighboring. About spatial dependence neighboring units should display a higher degree of spatial dependence than units located far apart (Le Sage, 1998). Below, there is a map that consists of five regional units. We set up a (5 x 5) binary matrix V including 25 elements evaluating 0 or 1 to obtain the contiguity relationships between the five units on the map. We then use the rook contiguity between regions to define a first-order contiguity matrix for the five regions on the map. Figure 3.1: A diagram A quantifying spatial contiguity Rook contiguity:- Define Vij =1 for two spatial units that own a common border of nonzero length & are considered to be contiguous, else equal zero (Anselin, 1988). In the matrix, each spatial unit is represented both as a row and as a column. By convention, an element is not contiguous or neighboring to itself. As a result, the matrix always has 113

9 zero on the main diagonal. For instance, for row 2, namely region 2 s relations, V 21 = 1 with all other row elements equal to zero. Therefore, the matrix V, first order binary rook contiguity relations, is expressed by : (3.3) As explained above, the first- order contiguity matrix V, contains zeros on the main diagonal and rows that have ones in locations associated with bordering spatial units and zeros in locations referred to non-bordering units. The rook definition of a firstorder contiguity matrix is often used in empirical applications, perhaps because we simply need to locate all regions on a map that have common borders with positive length (Lesage, 1998). In applied work, the matrix V is usually scaled such that the sum of the row element is equal to one. After such row standardization, the weight is asymmetric and positive with elements less than or equal to one. Such a matrix is regarded as a standardized first order contiguity matrix which is indicated as follows: (3.4) 114

10 In general, the standardized first order contiguity matrix, we can be written as ; (3.5) Equivalently w is a row standardized ( n X n ) matrix with elements W ij n W' ij W ' j 1 i j ij (3.6) where, W' ij = 1 if i linked to j 0 otherwise that is, the elements of the weight matrix are derived from information on contiguity, which is defined as two sample observations sharing a common border. 3.7 APPLICATION TO POPULATION UNDER POVERTY LINE DATA: In the previous sections, the study has revolved around the fundamental knowledge of spatial econometrics and spatial autoregressive models. The purposes of 115

11 this research are twofold. In the first part, on a theoretical level, we look at the exiting econometrics literature about spatial autoregressive models. In the second part of the research the spatial autoregressive models employed in the empirical investigation are brought up and as well as the Indian rural poverty data for 14 major states in India in 1994 are used to attempt to explore and examine what determines regional rural poverty difference, and to investigate spatial effects and the other variables that influence rural poverty in India. In this section the focus will in turn be put on attempting to address such an issue as: what are the significant factors that influence rural population under poverty line in India? Since the 1970 s, economists have investigated the effect of geography on the labour markets and poverty outcomes. Recently, it has become more and more popular to explore spatial econometrics. However, most of the existing literature is theoretical & little of the work in this field is empirical. A good application of spatial econometric techniques is to test regional disparity. The subject of regional difference has recently received a great attention in literature of regional economic growth. Romer (1986) and lucas (1988) are the pioneers of this field, who address the issue of long term growth of average income in regions and with comparisons among regional long term growth tracks. Hence we will investigate spatial effect in the analysis of regional difference of rural poverty in India in this section. 116

12 SPATIAL DATA UNER STUDY: According to Anselin (1988), spatial data are the data collected in space or in both space and time. For instance, our familiar data such as cross-sectional data and panel data are spatial data. This kind of data is available in many areas such local finance, crime and policing, as well as education policy. However, as applying spatial data, we must consider the issue regarding the presence of self-correlation or autoregression. To avoid these problems, spatial autoregressive models should be employed in such a situation. The source of the data used for the analysis is from IFPRI research report 110, Linkages between Government Spending, Growth, and poverty in rural India. International Food Policy Research Institute., World Bank From this data 14 major states in India have been selected. The reason why data are chosen from 1993 is that not only this year s data provide the necessary information that is used in the analysis, but also the sample data of this year is available to obtain. We have explored the influence of space on population under poverty line. In this research, the data from World Bank has been used to investigate regional inequality that is measured by a difference of rural population under poverty line in space. In other words, we attempt to examine whether there is an interaction between rural poverty and spatial effects. The analysis is not only focused on spatial influence, but also interested in exploring how rural poverty is affected by other variables such as rural work-employment 117

13 status, literacy rate, irrigation facilities and so on. The data under study is shown in table 3.1 as under. TABLE 3.1 DATA ONPOPULATION UNDER POVERTY LINE AND RELATED VARIABLES Population under poverty line (PUPL) Total rural employment (REMP) Total rural population (TRP) Rural Agricultural employment (RAE) Rural Non- Agricultural employment (RANE) Production growth in agriculture (P-G) Percentage of villages electrified (PVE) Road density in rural India (RD) Changes in rural wages, by state (CRW) States Year Andhra Predesh Bihar Gujarat Haryana Karnataka Madhya Pradesh Maharashtra Orissa Punjab Rajasthan Tamil Nadu Uttar Pradesh West Bengal Kerala

14 Total factor productivity growth in Indian agriculture, by state (TFP) Percentage of rural population that is literate (LR) Development expenditures (DEV) Percentage of cropped area irrigated (IRR) Percentage of cropped area sown with highyielding varieties (HYV) States Year Andhra Predesh Bihar Gujarat Haryana Karnataka Madhya Pradesh Maharashtra Orissa Punjab Rajasthan Tamil Nadu Uttar Pradesh West Bengal Kerala

15 At the state level, World Bank contains information on demography, including: Rural Population under Poverty Line, the variable of interest denoted by (PUPL), Total rural employment, which includes both agricultural and non- agricultural employment symbolized as REMP, Total rural population, marked by TRP, Rural agricultural population, includes agricultural laborers and Rural non- agricultural population that are doing non- agricultural economic activities, marked by RAE and RNAE, respectively, Production Growth is agricultural production growth index which is calculated by the authors of the source report stated above = P-G, Percentage of villages electrified, villages having the facility of electrification indicated by PVE, Road density in rural India measured as the length of roads in kilometers per thousand square kilometers of geographic area = RD, 120

16 Changes in rural wages includes the percentage change in the existing wage rates, revealed by CRW, Total Factor Productivity Growth index is also given in IFPRI research report 110, data source, signified as TFP, Percentage of rural population that is literate, the rural literacy rate = LR, Development expenditure which includes total government spending on various rural development facilities = DEV, Percentage of cropped area irrigated that is area having irrigation facilities represented as IRR, Percentage of cropped area sown with high-yielding varieties denotes as HYV, T he general information such as the mean, standard deviation and range of sample data set for all observations without missing values is summarized in Table 3.2 and all the variables employed in the estimated models are in Table 3.3. These variables will be examined in the empirical models in the next section as well. 121

17 Table 3.2: Descriptive statistics of the sample data. Mean Std. Dev. Maximum Minimum OUTCOMES LOG(PUPL) VARIABLES REMP/TRP RAE RNAE P-G PVE RD CRW TFP LR DEV/TRP IRR/HYV Note: the number of observations N = 14 without missing values. Table 3.3.: Variable definitions in estimated models: VARIABLE TYPE LABELED Dependent variable Logarithm of population under C LOG(PUPL) poverty line Independent variables Ratio of rural employment with total rural population. R REMP/TRP Ratio of rural agricultural R RAE employment with total rural employment Ratio of rural non-agricultural R RANE employment with total rural employment Production growth in agriculture C P-G Percentage of villages electrified, C PVE by state Road density in rural India C RD Changes in rural wages, by state C CRW Total factor productivity growth C TFP in Indian agriculture, by state Percentage of rural population that is literate, by state C LR Ratio of Development R DEV/TRP expenditures with total rural population. Ratio of Percentage of cropped R IRR/HYV area sown with high-yielding varieties with Percentage of cropped area irrigated. NOTE:- C= continuous variable and R= ratio variable. 122

18 3.8 MODELS AND RESULTS: In order to utilize all the available information gained from the sample data set, we will employ all the variables defined in Table 3.3 in model 1 that is a general regression model. In model 1 the dependent response variable (Y) is the logarithm of population under poverty line and denoted as log (pupl), as well as 11 independent variables X ( constant, X 2, X 3,.,X 11 ) which contain 11 variables that are from the sample data shown in Table 3.3 and a constant term. Moreover, model 1 is estimated by Ordinary Least Squares (OLS) method for screening out the insignificant variables that are used in spatial autoregressive models as exogenous variables. By convention, the filter rule of exogenous variables is that the variables are statistically significant at five or ten percent level of significance. In this study, we have used the standard of 5% significant level. Hence, the variance of the error term is assumed to be constant. We start from model 1, the standard linear regression model based on OLS: 2 LOG ( PUPL ) X, N (0, ) (3.7) Where, LOG(PUPL) is an (N 1) vector of observations on logarithm of population under poverty line. X is an (N K) matrix of exogenous variables and these variables are tabled in Table 2 in addition to a constant term 123

19 is an (N 1) vector of parameters, and ε is an (N 1) vector of disturbances. The aim of setting up the following linear regression models estimated by OLS is to filter the variables that are used in spatial autoregressive models. The test steps are as follows: 1. Build up model 1 that contains all the variables described in Table Model 2 consists of the significant variables in Model1. 3. Remove the insignificant variables from Model 2 to obtain Model3... This procedure is done until all the independent variables in one model are found to be statistically significant at 5% level. In our case, the experiment is carried out until step 4, which indicates that the variables in Model 4 are significant to explain reduction in dependent variable, the logarithm of population under poverty line. The results of the OLS estimation are shown in Table 3.4 and Table 3.5 displays the correlation matrix of the variables employed in Model 3. Furthermore, the OLS regressions of the logarithm of population under poverty line on the explanatory variables are presented in Table

20 According to the results given in Table 3.4, it can be seen that model 1 contains 11 variables with a constant term and the independent variables, IRR/HYV is found to be not statistically significant at 5% and will not be included in model 2. Therefore, in model 2 there are 10 explanatory variables left in addition to the constant. After removing the insignificant variable RD from model 2, we gain model 3 that includes 9 exogenous variables and one constant term. Then, we obtained model 3 that contains these 9 significant variables, Ratio of rural employment with total rural population, Ratio of rural agricultural employment with total rural employment, Ratio of rural non-agricultural employment with total rural employment, Production growth in agriculture, Percentage of villages electrified, by state, Changes in rural wages, by state, Total factor productivity growth in Indian agriculture, by state, Percentage of rural population that is literate, by state, Ratio of Development expenditures with total rural population. Here, we found production growth and Total factor productivity growth are highly correlated and statistically insignificant. So, both the variables are removed and finally we got model 4 that consist of 7 significant variables. We see from the result of model 4 in Table 3.5 that all 7 variables exhibit significant effects on the variable we want to explain, the logarithm of population under poverty line. Hence, these variables will be used as explanatory variables in the spatial autoregressive models and model 4 is regarded as the final model for adding the spatial effects. 125

21 Table 3.4: Results of OLS estimation:- Dependent variable : LOG(PUPL) Variables Model 1 Model 2 Model 3 Model 4 REMP/TRP (-2.65) -141 (-3.43) (-4.10) (-3.15) RAE (-1.24) (-1.49) (-1.88) (-0.25) RANE (-1.18) (-2.22) (-2.80) (-1.45) P-G * - (-0.9) (-1.17) (-1.87) PVE (-2.26) (-2.78) (-3.24) (-2.03) RD * - - (-0.28) (-0.27) CRW -0.1 (-0.77) (-0.92) (-1.02) (-1.77) TFP * - (0.57) (0.77) (1.10) LR (-0.23) (-0.42) (-0.85) (-1.71) DEV/TRP (-1.13) (-1.94) (-2.24) (-1.36) IRR/HYV * (0.19) Constant (4.80) (5.99) (7.35) (7.31) N Adj-R % 83.1% 87% 77% Note:- t-statistics in parentheses. * indicates a p-value that is not statistically significant at 5% significance level. N is the number of observations. Variabl es Table 3.5: The correlation matrix of the variables in model 3 LOG (PUPL ) 1 REMP /TRP RAE RANE P-G PVE CRW TFP LR DEV / TRP LOG (PUPL) REMP/T RP RAE RANE P-G PVE CRW TFP LR DEV/ TRP

22 The motivation for estimating different models or regression relationships is to see which variables significantly influence the outcomes for population under poverty line and to find the final model to add in spatial effects. Therefore, we will now present a set of two spatial autoregressive models to analyze the sample data. There are 14 states in the sample dataset. Our interest is to calculate the proportion of the total variation in the population under poverty line that is explained by the spatial dependence. This relies on estimating the spatial lag model (SAR) that is brought up in section 3.2. The SAR model can be written as: 2 LOG ( PUPL ) WLOG( PUPL ) X, N( 0, ) (3.8) n where, LOG(PUPL)= [LOG (PUPL) 1,,LOG(PUPL) 14 ] is a 14 dimensional vector of deviations from the mean of population under poverty line for 14 states, denotes a estimated regression parameter, which reflects the spatial dependence characteristic in the sample data set, and measure the average influence of states on states in population under poverty line or the vector LOG(PUPL) W is spatial weight matrix that is row-standardized and each row sum to one (see 3.8) and X represents a (7 14) matrix containing explanatory variables, which are used in Model 4, as well as 127

23 β is the parameters that reflect the influence of the exogenous variables on variation in the dependent variable population under poverty line. We assume that the error terms ε are independent and identically distributed. So far, one important task is to construct the standardized first-order contiguity matrix W mentioned in section 3.6. to use in our SAR model. In addition, the estimates of the SAR model are shown in Table 3.6. The spatial error model (SEM) provides another efficient method for dealing with the spatial data set that consists of 14 observations for states in India. The SEM model, which is introduced in section 3.5, is stated as follows: LOG( PUPL ) X u, u=λw u +ε 2 N( 0, ) (3.9) n where, λ is a coefficient on the spatially correlated errors and LOG(PUPL), W, X, as well as β are the same as described in the SAR model. The estimates of the SEM model are also shown in Table

24 Table 3.6: Results of spatial autoregressive model estimation Dependent variable : LOG(PUPL) Variables SAR SEM Model 4 Constant (4.04) (6.52) (7.31) REMP/TRP (-2.71) (-3.11) (-3.15) RAE (-0.15) (-0.41) (-0.25) RANE (-1.24) (-1.45) (-1.45) PVE (-1.77) (-0.64) (-2.03) CRW (-1.61) (-1.81) (-1.77) LR (-1.58) (-1.44) (-1.71) DEV/TRP (-1.17) (-1.50) (-1.36) Rho (0.20) Lambda (0.75) N Adj-R % 78% 77% Note:- t-statistics in parentheses. N is the number of observations. * indicates a p-value that is not statistically significant at 5% significance level. Table 3.6 displays the result of both SAR and SEM as well as OLS estimation of model 4. The reason why the estimate results model 4 are shown in Table 3.5 is that it is an easy and clear way to compare the model with spatial effects and without spatial effects. In table 3.6, the adjusted R 2 values of these three regressions range between 0.75 and All coefficients of the independent variables, except rho in SAR model, are found to be statistically significant. Interpretations for the coefficients of the explanatory variables are not our chief focus here. 129

25 The SAR estimates in Table 3.6 show that after taking into account the influence of the independent variables, we do not have spatial correlation in the model, since the spatial autoregressive coefficient ρ is statistically insignificant and not large at all. That is, the dependent variable LOG(PUPL) exhibits insignificant spatial dependence. This indicates that we cannot estimate the SAR model successfully. Therefore, we do believe that the OLS estimates are correct, as there are insignificant spatial autoregressive parameters in the SAR model. On the other hand, estimations in the SEM model display the results we expect, so that our analysis will be focused on comparing estimate results between SEM model and Model 4. The following three aspects are considered in particular. Firstly, taking the spatial heterogeneity into account improves the fit of the model, as the adjusted R 2 statistic rises from 0.77 in Model 4 to 0.78 in SEM model. That is, around one percent of the variation in the logarithm of population under poverty line is explained by spatial structure, because the adjusted R 2 is 0.78 in SEM model that takes the spatial effect into account and 0.77 in the least-square model that ignores such an effect. Secondly, the t-value on the spatial autocorrelation parameter λ is 0.75, indicating that this explanatory variable has a coefficient estimate that is significantly different from zero. Equivalently, the spatial coefficient is found to be statistically significant, showing that there exists spatial heterogeneity in the residuals of the model. 130

26 However, Model 4 based on OLS ignores the spatial information that is provided by the sample dataset. 3.9 CONCLUSIONS: Our purpose of this study is to focus on the theoretical study of spatial econometrics and to explore an empirical application of spatial autoregressive models used on Indian rural poverty cross-sectional data. Recently, spatial econometric techniques have grown rapidly and have increasingly been applied in empirical researches. In general, spatial econometrics is related to spatial statistics and is a subfield of econometrics that deals with the combination of spatial dependence and spatial heterogeneity in regression analysis. Spatial dependence relates to the fact that observations in the sample data set display correlation with regard to location in space. Spatial heterogeneity relates to the fact that the regression models that we estimate may vary systematically over space. A large part of section 3.6 is devoted to introduce spatial contiguity matrices that are applied spatial autoregressive models. After reviewing the primary theory of spatial econometrics, the Indian rural poverty data from World Bank 1997 have been used to further study and to empirically apply to spatial autoregressive models. The basic regressions used in this paper are simply OLS regressions of the logarithm of population under poverty line on the explanatory variables to obtain Model 4 that contains 7 significant variables and one constant. As an illustration of exploring 131

27 SAR and SEM, we estimate Eqs. (4.2.2) and (4.2.3) based on Model 4 to investigate spatial effects in rural population under poverty line of 14 major states in India. The results from the empirical investigation indicate that there are many variables that influence the rural population under poverty line. With respect to our major interest, spatial effects, we do find that in the SAR model, there is a positive sign on rho, but it is not statistically significant, indicating there is no spatial dependency in the model. However, in the SEM model lambda is found to be both positive and significant at 5% significance level, indicating that spatial heterogeneity presents in the residuals of the model. Thus, Model 4 associated with OLS estimation is an inappropriate regression model for the sample data that are the spatial data. The findings are that relative to model 4, the SEM model reveals larger influences on the ratios of the development expenditure and rural employed population with total rural population and a smaller influence on literacy rate. Additionally, the proportion of employed population with total rural population has the strongest negative influences on population under poverty line in our models. In addition, the empirical models of SAR and SEM are selected primarily to illustrate the various spatial effects, and are not supposed to contribute to a substantive understanding of spatial patterns of population under poverty line. 132