1、Introduction to Applied Spatial Econometrics,Attila VargaDIMETIC Pcs, July 3, 2009,Prerequisites,Basic statistics (statistical testing) Basic econometrics (Ordinary Least Squares and Maximum Likelihood estimations, autocorrelation),EU Patent applications 2002,Outline,Introduction The nature of spati
2、al data Modelling space Exploratory spatial data analysis Spatial Econometrics: the Spatial Lag and Spatial Error models Specification diagnostics New developments in Spatial Econometrics Software options,Spatial Econometrics,A collection of techniques that deal with the peculiarities caused by spac
3、e in the statistical analysis of regional science models” Luc Anselin (1988),Increasing attention towards Spatial Econometrics in Economics,Growing interest in agglomeration economies/spillovers (Geographical Economics)Diffusion of GIS technology and increased availability of geo-coded data,The natu
4、re of spatial data,Data representation: time series (time line”) vs. spatial data (map)Spatial effects: spatial heterogeneityspatial dependence,Spatial heterogeneity,Structural instability in the forms of: Non-constant error variances (spatial heteroscedasticity) Non-constant coefficients (variable
5、coefficients, spatial regimes),Spatial dependence (spatial autocorrelation/spatial association),In spatial datasets dependence is present in all directions and becomes weaker as data locations become more and more dispersed” (Cressie, 1993)Toblers First Law of Geography: Everything is related to eve
6、rything else, but near things are more related than distant things.” (Tobler, 1979),Spatial dependence (spatial autocorrelation/spatial association),Positive spatial autocorrelation: high or low values of a variable cluster in spaceNegative spatial autocorrelation: locations are surrounded by neighb
7、ors with very dissimilar values of the same variable,EU Patent applications 2002,Spatial dependence (spatial autocorrelation/spatial association),Dependence in time and dependence in space: Time: one-directional between two observations Space: two-directional among several observations,Spatial depen
8、dence (spatial autocorrelation/spatial association),Two main reasons:Measurement error (data aggregation) Spatial interaction between spatial units,Modelling space,Spatial heterogeneity: conventional non-spatial models (random coefficients, error compontent models etc.) are suitableSpatial dependenc
9、e: need for a non-convential approach,Modelling space,Spatial dependence modelling requires an appropriate representation of spatial arrangementSolution: relative spatial positions are represented by spatial weights matrices (W),Modelling space,1. Binary contiguity weights matrices- spatial units as
10、 neighbors in different orders (first, second etc. neighborhood classes)- neighbors:- having a common border,or- being situated within a given distance band2. Inverse distance weights matrices,Modelling space,Binary contiguity matrices (rook, queen)wi,j = 1 if i and j are neighbors, 0 otherwise Neig
11、hborhood classes (first, second, etc),Modelling space,Inverse distance weights matrices,Modelling space,Row-standardization:Row-standardized spatial weights matrices:- easier interpretation of results (averageing of values)- ML estimation (computation),Modelling space,The spatial lag operator: Wy is
12、 a spatially lagged value of the variable y In case of a row-standardized W, Wy is the average value of the variable: in the neighborhood (contiguity weights) in the whole sample with the weight decreasing with increasing distance (inverse distance weights),Exploratory spatial data analysis,Measurin
13、g global spatial association: The Morans I statistic:a) I = N/S0 Si,j wij (xi -m)(xj - m) / Si(xi -m)2normalizing factor: S0 =Si,j wij(w is not row standardized)b) I* = Si,j wij (xi -m)(xj - m) / Si(xi -m)2(w is row standardized),Global spatial association,Basic principle behind all global measures:
14、- The Gamma indexG = Si,j wij cij Neighborhood patterns and value similarity patterns compared,Global spatial association,Significance of global clustering: test statistic compared with values under H0 of no spatial autocorrelation- normality assumption- permutation approach,Local indicatiors of spa
15、tial association (LISA),The Moran scatterplotidea: Morans I is a regression coefficient of a regression of Wz on z when w is row standardized:I=zWz/zz (where z is the variable in deviations from the mean)- regression line: general pattern- points on the scatterplot: local tendencies- outliers: extre
16、me to the central tendency (2 sigma rule)- leverage points: large influence on the central tendency (2 sigma rule),Moran scatterplot,Local indicators of spatial association (LISA),B. The Local Moran statisticIi = ziSjwijzjsignificance tests: randomization approach,Spatial Econometrics,The spatial la
17、g modelThe spatial error model,The spatial lag model,Lagged values in time: yt-kLagged values in space: problem (multi-oriented, two directional dependence) Serious loss of degrees of freedomSolution: the spatial lag operator, Wy,The spatial lag model,The spatial lag model,EstimationProblem: endogen
18、eity of wy (correlated with the error term) OLS is biased and inconsistent Maximum Likelihood (ML) Instrumental Variables (IV) estimation,The spatial lag model,ML estimation: The Log-Likelihood function,The Spatial Lag model,IV estimation (2SLS) Suggested instruments: spatially lagged exogenous vari
19、ables,The Spatial Error model,The Spatial Error model,OLS: unbiased but inefficientML estimation,Specification tests,Steps in estimation,Estimate OLS Study the LM Error and LM Lag statistics with ideally more than one spatial weights matrices The most significant statistic guides you to the right mo
20、del Run the right model (S-Err or S-Lag),Example: Varga (1998),Spatial econometrics: New developments,Estimation: GMM Spatial panel models Spatial Probit, Logit, Tobit,Study materials,Introductory: Anselin: Spacestat tutorial (included in the course material) Anselin: Geoda users guide (included in the course material)Advanced: Anselin: Spatial Econometrics, Kluwer 1988,Software options,GEODA easiest to access and use SpaceStat R Matlab routines,
