Space, time and cities. Analysis of the concentration and dynamics of the Chilean urban system.

Transcription

1 Space, time and cities. Analysis of the concentration and dynamics of the Chilean urban system. Andres Vallone PhD Student 2016

2 Contents Motivation and objectives Data Concentration analysis Dynamics analysis Conclusion

3 Introduction The process of urbanization have not being homogeneous across space, each country faces particular circumstances. Spatial proximity among human settlements affects the evolution of urban systems (Le Gallo and Chasco, 2008; Favaro and Pumain, 2011; Xu and Harriss, 2009). The evolution of an urban system highly depends of the development of its corresponding country history (Jedwab et al, 2013). There is consensus about the fact that an increase in agglomeration during the industrialization periods is followed by a dispersion process in the post industrialization period (Willianson, 1965; Parr, 1985; Brackman et al, 1999; Fujita et al., 2001). The hierarchy of cities tends to an increase in stability between the industrialization and post industrialization period (Vallone and Atienza, 2012)

4 Objective The aim of this paper is analysing the concentration and dynamics of the Chilean urban system during the period , considering the effect that space have over them.

5 Why Chile? Chile has a particular geography. The Chilean urban system has its origin in the Colonial cities, with a low level of spatial concentration (Geisse, 1978). Concentration of the population and economic activities in the Metropolitan Region increase during the industrialization period (Geisse 1977; 1978; De Mattos, 1999). However, after 1975 in the midst of the post industrialization period and despite the growth of some intermediate cities, the primacy of the Metropolitan Region increase.

6 The shape of the Chilean cities distribution I Full System Whitout MR Full System Whitout MR N = 184 Bandwidth = N = 184 Bandwidth = (a) 1930 (b) 2002

7 The shape of the Chilean cities distribution II Full System Metropolitan Region N = 184 Bandwidth = N = 22 Bandwidth = (c) Full system (d) Metropolitan Region

8 Data The source of data is National Statistics Institute of Chile City are urban entities of more than 5000 inhabitants Since 184 cities in 2002 a balanced panel data was build min max 698, ,946 1,401,558 1,922,807 median 2,408 2,933 3,506 4,708 mean 11, , , , std.dev 53, , , , coef.var min 35 1,132 1,999 5,113 max 2,233,143 3,654,760 4,295,593 5,428,590 median mean 32, , , , std.dev 166, , , , coef.var

9 Concentration Index We use the Zipf s coefficient as concentration index. Like in LeGallo and Chasco (2008), we estimate the Zipf s coefficient for the Chilean cities with an spatial cross-regressive SUR model log R = α + β log P + θw log P + ɛ The W matrix is inverse distance matrix As robustness analysis 2 different sample of cites and 4 types of spatial weight matrix was use.

10 Estimation Result Complete city group Without MR cities OLS SUR SXLSUR OLS SUR LP *** *** *** *** *** LP *** *** *** *** *** LP *** *** *** *** *** LP *** *** *** *** *** LP *** *** *** *** *** LP *** *** *** *** *** LP *** *** *** *** *** LP *** *** *** *** *** W L P W L P W L P W L P W L P W L P W L P W L P Goodness of fit LIK Homogeneity across equations Wald on LP variable *** *** Diagonality of error covariance matrix LM test *** 2394 *** Model comparison Log-likelihood Ratio (LR) test SUR versus OLS *** *** SDSUR versus SAR * SXSUR versus SUR *** SDSUR versus SXSUR Spatial dependence on the residuals (inverse distance spatial weights matrix) LM, spatial error model LM, spatial lag model * p < 0.01; p < 0.05; p < 0.1

11 Estimation Result

12 Concentration evolution

13 Dynamic of the ranking To analyze the dynamic of the system we use two methods: Markov s transition matrix: estimate the spatial transition matrix (Rey, 2001) and LISA transition Matrix (Rey and Janikas 2006) Ranking dynamics analysis: estimate the Spatial Tau and his decomposition Rey (2004) As robustness analysis the spatial transition matrix was make with 3 different weight matrix and 4 different spatial regime was use in the estimation of the spatial tau.

14 Markov s transition matrix Spatial Markov The data are pooled over space and time in quintiles calculated for the pooled data. The Spatial Markov allows us to compare the global transition dynamics to those conditioned on regional context. More specifically, the transition dynamics are split across economies who have spatial lags in different quintiles at the beginning of the period LISA transition Matrix Consider the joint transitions of an observation and its spatial lag in the distribution The states of the chain are defined as the four quadrants in the Moran scatter plot Example

15 Markov transition matrix 2002 State Q1 Q2 Q3 Q4 Q5 Q Q Q Q Q

16 Spatial Markov Matrix Q1 Q2 Q3 Q4 Q5 Q1 Q2 Q3 Q4 Q5 Q Q Q Q L 1 Q L 4 Q Q Q Q Q Q Q Q Q L 2 Q L 5 Q Q Q Q Q Q Q L 3 Q Q Q The Chi-square test and the Likelihood ratio statistic of homogeneity across lag classes (Bickenbach and Bode, 2003) are Q= LR= with d.f=44 (pvalue=(0.000; 0.000))

17 LISA Markov probability matrix HH LH LL HL HH LH LL HL The Chi Square test under the null hypothesis of the dynamics of a city are independent of dynamics of the neighbours is with dof=9 (pvalue=0.0)

18 Spatial Tau Kendall s Tau is based on a comparison of the number of pairs of n observations that have concordant ranks between two variables. τ (f, g) = n 2 i=1 n 1 j=i+1 sgn ( ) ( ) f i f j sgn gi g j n (n 1) 2 = c d n (n 1) 2 Any pair (f i, g i ) and (f j, g j ), where i j, are said to be concordant if the ranks for both elements agree: that is, if both f i > f j and g i > g j or if both f i < f j and g i < g j. The spatial Tau decomposes these pairs into those that are spatial neighbours and those that are not, and examines whether the rank correlation is different between the two sets relative to what would be expected under spatial randomness. Example

19 Rank Dynamics Period M τ τ p-value M W τ W τ W p-value

20 Rank Decomposition For a sequence of time periods, θ measures the extent to which rank changes for a variable measured over n locations are in the same direction within mutually exclusive and exhaustive partitions (regimes) of the n locations R i R i,t θ 1 i,t 0 Θ t1 t 0 = i,t1 θ i,t0 Theta is defined as the sum of the absolute sum of rank changes within the regimes over the sum of all absolute rank changes. If all regime move in the same direction the index assume a value of 1, the absence of cohesion mean a index equal to 0. i

21 Rank Decomposition Period θ Right p-value Left p-value

22 Conclusion Zipf s coefficient show a high level of spatial concentration activity across all analysis period The sprawl of the MR is decremented by the growth of the intermediate cities. The path dependence play an important role in the dynamic of the system. The dynamics of the urban system is spatial no homogeneous Extras

23 Thank your for your attention, comments are welcome

24 Ranking Movility Return

25 Example using block weight based in Rey(2015) Period t Period t pairs 114 concordant pairs τ = discordant pairs are all in the same regime τ W = 0.50 = (18 6)/24, p value = 0.001, τ W = 1.00 Return

26 Example LISA Markov Period 0 Wx Wx F C B E A D x Period 1 D F C E A B t 0 t 0 Point Own Lag Own Lag A L L L L B L H L L C H H H H D L L H H E H L L L F L H H H HH LH LL HL HH LH LL HL Return x

27 Directional LISA Wx t0 t1 Wx t0 t x x Wx x

28 Directional LISA Wx RM norm Wx RM norm x x Wx RM norm Wx RM norm x x Return