From Econometrics to Spatial Econometrics Liu, Tzu-Ming Kainan University

Function Form Heteroscedasticity

Function Form Serial Correlation AR(1) Unit changed from year to region How about the k? Are the j and the k identical?

Function Form General form Spatial error model Spatial lag model SARMA(p, q) Major difference between econometrics and spatial econometrics is W: Spatial weighting matrix or connectivity matrix

Function Form Fixed effects in Panel data analysis

Empirical questions IDZIPy ::: Fixed effect: local specific effects 2.Dummy 3.Space: relative location provides information

Theoretical questions 1.Externality 2.Spillover 3.Location

A case: suicide Is relative location important? Does location itself say something? Does no difference between townships mean nothing? Is the pattern coincident with our expect? How the pattern influence policy making?

Weighting Matrix A weighting matrix (connectivity matrix) defines spatial process (spatial autocorrelation), spatial structure, or spatial interaction across study regions. A common way to define a weighting matrix is by contingency, and another way is with distance. Moving beyond the traditional spatial realm was the recognition of the importance of spaces other than “geographic,” such as social space (social capital) and the use of distance metrics other than the typical Euclidean (social distance, economic distance).

1. spatially contiguous neighbors; 2. inverse distances raised to some power; 3. lengths of shared borders divided by the perimeter; 4. bandwidth as the nth nearest neighbor distance; 5. ranked distances; 6. constrained weights for an observation equal to some constant; 7. all centroids within distance d; 8. n nearest neighbors, and so on, 9. bandwidth distance decay; 10. Gaussian distance decline; and 11. “tri-cube” distance decline function. Weighting Matrix

Some examples 1. Rook Contiguity The four neighbors of each cell in the cardinal directions are given the value 1, all others 0. This is the most popular formulation of W. 2. Queen Contiguity The eight neighbors of each cell in all directions are given the value 1, all others Inverse Distance (1/d) Taking the distance between near neighbors as 1, reciprocals of all pairs of distances are calculated and entered into W. Weighting Matrix

Weights Matrix Example Simple Contiguity (rook) Matrix Sample Region and Units

Criteria of Choosing Weighting Matrix 1. A specification between four and six neighbors is better than something either above six or below four. 2. A relatively large number of spatial units should be employed, n > Low-order spatial models should be given preference over higher-order ones. 4. In general, it is better to apply a somewhat under- specified (fewer neighbors) rather than an over- specified (extra neighbors) weights matrix. 5. To employ the smallest areal units available for mitigating MAUP effects.

Three Important Ways That Spatial Analysis Can Help The Social Scientist (i)Data integration: Spatial analysis provides a basis for integration and data collection at different spatial scales and time dimensions. Data integration is a central function of the application of GIS. (ii) Exploratory spatial data analysis (ESDA): ESDA is a collection of techniques to describe and visualize spatial distributions, identify atypical locations or spatial outliers, discover patterns of spatial association, clusters or hot spots, and suggest spatial regimes or other forms of spatial heterogeneity (Anselin, 1994, 1999b).

(iii) Confirmatory spatial data analysis: Spatial modeling techniques, such as regression analysis can also be implemented to explicitly incorporate the mechanisms underlying the spatial patterns. Three Important Ways That Spatial Analysis Can Help The Social Scientist

Spatial Analysis: An Opportunity to Improve Policy Making at Diverse Decision Levels Monitoring, evaluation, and proposal of policies at the local level do need studies that account for the effect that space has on the outcome of particular variables. Optimizing the distribution of local services (e.g., hospitals and family planning agencies), and improving the allocation of financial resources are specific areas that benefit from these studies. (de Castro, 2007)

Cluster analysis Moran’s I: Compares the value of the variable at any one location with the value at all other locations. A focus on where the non-randomness may be located, in terms of significant clusters or spatial outliers is provided by an analysis of the local indicators of spatial association (LISA).

Oral Cancer Death Rate Total Male Female

Software 1.ArcGIS 2.GeoDA 3.R 4.SAS 5.Stata 6.Matlab 7.SpaceStat 8.CrimeStat

Review of Applications of SE Four most cited applications of SE: 1. Local spillovers 2. Housing prices 3. Regional income convergence 4. Deforestation Other applications: Population changes Macroeconomic fluctuations Air pollution Crime and residential choice Welfare distribution Water quality Public services Active labor market policy Elections results Commuter rail Mental health expenditure Dairy sector Sarafoglou, N., and J. Paelinck "On diffusion of ideas in the academic world: the case of spatial econometrics." The Annals of regional science.

Agricultural Economics (2002) 27(3): Special issue on spatial analysis for agricultural economists International Regional Science Review (2003) 26(2) International Regional Science Review (2003) 26(3) Geographical Analysis (2004) 36 (2): Methodological Developments in Spatial Econometrics and Statistics Journal of Econometrics (2007) 140(1): Analysis of spatially dependent data Regional Science and Urban Economics (2007) 37(4): A Retrospective/Prospective Special Issue Journal of Agricultural Economics (2007) 58(3): Spatial Issues in Agricultural Economics Spatial Economic Analysis (2006 ~present)

Conferences of SE International Workshop on Spatial Econometrics and Statistics, May, 2006, Rome, Italy The 1st World Conference of the Spatial Econometrics Association, July 2007 at Fitzwilliam College, University of Cambridge.Spatial Econometrics Association The 7th Workshop of the Spatial Econometrics and Statistics, 9–10 June 2008, Paris, France II World Conference of the Spatial Econometrics Association New York, November 17-19, 2008 “Spatial Econometrics Advanced Institute,” Rome, 26th May - 25th June, 2008

Spatial Econometrics Association “The Association wants to promote the development of theoretical tools and sound applications of the discipline of spatial econometrics, including spatial statistics and spatial data analysis. …… An aim of the Association is to disseminating and encourage such a knowledge and good practice in academic and research institutions and in the society at large. “

Key Academic Institute of SE National Science Foundation–funded Center for Spatially Integrated Social Science (CSISS) in CSISS seeks to provide a research infrastructure to enhance and advance a spatial analytic perspective in social sciences by disseminating information on techniques, software, and state of the art applications, among other activities. In addition, CSISS also convenes specialist meetings, small workshops where a selected group of participants address a focused research question.

Key References of SE Franzese, R., Hays, J “Empirical Models of Spatial Interdependence,” in Box-Steffensmeier, J., Brady, H., & Collier, D., eds., Oxford Handbook of Political Methodology Anselin, L., Spatial Econometrics, in: T. Mills and K. Patterson (eds.), Palgrave Handbook of Econometrics: Volume 1, Econometric Theory, Basingstoke: Palgrave Macmillan, pp Anselin, L. "Spatial Externalities, Spatial Multipliers, And Spatial Econometrics." International Regional Science Review 26, no. 2(2003):