THE SLX MODEL†
Solmaria Halleck Vega
Faculty of Economics and Business, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
Search for more papers by this authorJ. Paul Elhorst
Faculty of Economics and Business, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
Search for more papers by this authorSolmaria Halleck Vega
Faculty of Economics and Business, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
Search for more papers by this authorJ. Paul Elhorst
Faculty of Economics and Business, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
Search for more papers by this authorThe authors gratefully acknowledge James LeSage and Kelley Pace for their thoughtful review of a previous version in December 2012, as well as valuable comments from participants of the 59th Annual North American Meetings of the Regional Science Association International, Ottawa, November 2012, in particular Dennis Robinson and Oleg Smirnov, the Sorbonne University seminar in Paris, April 2013, the Econometrics of Social Interaction Symposium, University of York, May 2013, the 12th International Workshop Spatial Econometrics and Statistics, Université d’Orléans, June 2013, in particular Raymond Florax, the 53rd European Regional Science Association Congress, Palermo, August 2013. The authors also gratefully acknowledge the managing editor Mark Partridge and four anonymous referees for their numerous insightful comments and constructive suggestions that have helped to significantly improve their work. The authors are responsible for any errors that may remain and for the views expressed in the paper.
ABSTRACT
We provide a comprehensive overview of the strengths and weaknesses of different spatial econometric model specifications in terms of spillover effects. Based on this overview, we advocate taking the SLX model as point of departure in case a well-founded theory indicating which model is most appropriate is lacking. In contrast to other spatial econometric models, the SLX model also allows for the spatial weights matrix W to be parameterized and the application of standard econometric techniques to test for endogenous explanatory variables. This starkly contrasts commonly used spatial econometric specification strategies and is a complement to the critique of spatial econometrics raised in a special theme issue of the Journal of Regional Science (Volume 52, Issue 2). To illustrate the pitfalls of the standard spatial econometrics approach and the benefits of our proposed alternative approach in an empirical setting, the Baltagi and Li (2004) cigarette demand model is estimated.
REFERENCES
- Anselin, Luc. 1988. Spatial Econometrics: Methods and Models. Dordrecht: Kluwer Academic Publishers.
10.1007/978-94-015-7799-1 Google Scholar
- Anselin, Luc. 2003a. “Rao's Score Test in Spatial Econometrics,” Journal of Statistical Planning and Inference, 97, 113–139.
- Anselin, Luc. 2003b. “Spatial Externalities, Spatial Multipliers, and Spatial Econometrics,” International Regional Science Review, 26, 153–166.
- Anselin, Luc, Anil K. Bera, Raymond Florax, and Mann J. Yoon. 1996. “Simple Diagnostic Tests for Spatial Dependence,” Regional Science and Urban Economics, 27, 77–104.
- Arbia, Giuseppe and Bernard Fingleton. 2008. “New Spatial Econometric Techniques and Applications in Regional Science,” Papers in Regional Science, 87, 311–317.
- Baltagi, Badi H. 2008. Econometric Analysis of Panel Data. Chichester: Wiley.
- Baltagi, Badi H. and Dan Levin. 1986. “Estimating Dynamic Demand for Cigarettes using Panel Data: The Effects of Bootlegging, Taxation and Advertising Reconsidered,” The Review of Economics and Statistics, 68, 148–155.
- Baltagi, Badi H. and Dan Levin. 1992. “Cigarette Taxation: Raising Revenues and Reducing Consumption,” Structural Change and Economic Dynamics, 3(2), 321–335.
10.1016/0954-349X(92)90010-4 Google Scholar
- Baltagi, Badi H. and Dong Li. 2004. “ Prediction in the Panel Data Model with Spatial Autocorrelation,” in L. Anselin, R. Florax, and S.J. Rey (eds.), Advances in Spatial Econometrics: Methodology, Tools, and Applications. Berlin: Springer, pp. 283–295.
10.1007/978-3-662-05617-2_13 Google Scholar
- Beenstock, Michael and Daniel Felsenstein. 2012. “Nonparametric Estimation of the Spatial Connectivity Matrix Using Spatial Panel Data,” Geographical Analysis, 44(4), 386–397.
- Bhattacharjee, Arnab and Chris Jensen-Butler. 2013. “Estimation of the Spatial Weights Matrix Under Structural Constraints,” Regional Science and Urban Economics, 43, 617–634.
- Bivand, Roger S. 2012. “After ‘Raising the Bar’: Applied Maximum Likelihood Estimation of Families of Models in Spatial Econometrics,” Estadística Española, 54(177), 71–88.
- Blundell, Richard and Thomas M. Stoker. 2007. “ Models of Aggregate Economic Relationships that Account for Heterogeneity,” in J.J. Heckman and E. Leamer (eds.), Handbook of Econometrics, Volume 6A. Amsterdam: Elsevier, pp. 4609–4663.
10.1016/S1573-4412(07)06068-0 Google Scholar
- Boarnet, Marlon G. 1992. “ Intra-metropolitan Growth Patterns: The Nature and Causes of Population and Employment Changes within an Urban Area,” Ph.D. dissertation, Princeton University.
- Boarnet, Marlon G. 1994a. “An Empirical Model of Intrametropolitan Population and Employment Growth,” Papers in Regional Science, 73(2), 135–152.
10.1111/j.1435-5597.1994.tb00607.x Google Scholar
- Boarnet, Marlon G. 1994b. “The Monocentric Model and Employment Location,” Journal of Urban Economics, 36, 79–97.
- Boarnet, Marlon G. 1998. “Spillovers and the Locational Effects of Public Infrastructure,” Journal of Regional Science, 38(3), 381–400.
- Boarnet, Marlon G., Saksith Chalermpong, and Elizabeth Geho. 2005. “Specification Issues in Models of Population and Employment Growth,” Papers in Regional Science, 84(1), 21–46.
- Bramoullé, Yann, Habiba Djebbari, and Bernard Fortin. 2009. “Identification of Peer Effects through Social Networks,” Journal of Econometrics, 150, 41–55.
- Brueckner, Jan K. 2003. “Strategic Interaction among Governments: An Overview of Empirical Studies,” International Regional Science Review, 26(2), 175–188.
- Brueckner, Jan K. 2006. “ Strategic Interactions among Governments,” in R.J. Arnott and D.P. McMillen (eds.), A Companion to Urban Economics. Malden, MA: Blackwell, pp. 332–347.
10.1002/9780470996225.ch20 Google Scholar
- Buonanno, Paolo, Giacomo Pasini, and Paolo Vanin. 2012. “Crime and Social Sanction,” Papers in Regional Science, 91, 193–218.
- Burridge, Peter. 1981. “Testing for a Common Factor in a Spatial Autoregression Model,” Environment and Planning A, 13, 795–400.
- Burridge, Peter. 2012. “Improving the J Test in the SARAR Model by Likelihood-based Estimation,” Spatial Economic Analysis, 7(1), 75–107.
- Burridge, Peter and Bernard Fingleton. 2010. “Bootstrap Inference in Spatial Econometrics: The J-Test,” Spatial Economic Analysis, 5, 93–119.
- Burridge, Peter and Ian Gordon (1981), “Unemployment in the British Metropolitan Labour Areas,” Oxford Economic Papers, 33(2), 274–297.
- CDC. 2012. (Centers for Disease Control and Prevention), Morbidity and Mortality Weekly Report, 61(12), 201–204.
- Chintagunta, Pradeep K. and Harikesh S. Nair. 2011. “Discrete-Choice Models of Consumer Demand in Marketing,” Marketing Science, 30(6), 977–996.
- Chung, Jae Wan. 1994. Utility and Production Functions. Cambridge: Blackwell Publishing.
- Cliff, Andrew D. and J. Keith Ord. 1981. Spatial Processes. London: Pion.
- Corrado, Luisa and Bernard Fingleton. 2012. “Where is the Economics in Spatial Econometrics?” Journal of Regional Science, 52(2), 210–239.
- Dalenberg, Douglas R., Mark D. Partridge, and Dan S. Rickman. 1998. “Public Infrastructure: Pork or Jobs Creator,” Public Finance Review, 26(1), 24–52.
- Debarsy, Nicolas, Cem Ertur, and James P. LeSage. 2012. “Interpreting Dynamic Space-time Panel Data Models,” Statistical Methodology, 9, 158–171.
- Drukker, David M., Peter Egger, and Ingmar R. Prucha. 2013. “On Two-Step Estimation of a Spatial Autoregressive Model with Autoregressive Disturbances and Endogenous Regressors,” Econometric Reviews, 32(5–6), 686–733.
- Dubin, Robin A. 1988. “Spatial Autocorrelation,” Review of Economics and Statistics, 70, 466–474.
- Dubin, Robin A. 1992. “Spatial Autocorrelation and Neighborhood Quality,” Regional Science and Urban Economics, 22, 433–452.
- Elhorst, J. Paul. 2010. “Applied Spatial Econometrics: Raising the Bar,” Spatial Economic Analysis, 5(1), 9–28.
- Elhorst, J. Paul. 2013. “ Spatial Panel Models,” in M.M. Fischer and P. Nijkamp (eds.), Handbook of Regional Science. Berlin: Springer, pp. 1637–1652.
- Elhorst, J. Paul. 2014. “Matlab Software for Spatial Panels,” International Regional Science Review, 37(3), 389–405.
- Ertur, Cem and Wilfried Koch. 2007. “Growth, Technological Interdependence and Spatial Externalities: Theory and Evidence,” Journal of Applied Econometrics, 22, 1033–1062.
- Fingleton, Bernard and Julie Le Gallo. 2008. “Estimating Spatial Models with Endogenous Variables, a Spatial Lag and Spatially Dependent Disturbances: Finite Sample Properties,” Papers in Regional Science, 87(3), 319–339.
- Fingleton, Bernard and Enrique Lopez-Bazo. 2006. “Empirical Growth Models with Spatial Effects,” Papers in Regional Science, 85(2), 177–198.
- Fischer, Manfred M., Thomas Scherngell, and Martin Reismann. 2009. “Knowledge Spillovers and Total Factor Productivity: Evidence Using a Spatial Panel Data Model,” Geographical Analysis, 41(2), 204–220.
- Florax, Raymond and Henk Folmer. 1992. “Specification and Estimation of Spatial Linear Regression Models: Monte Carlo Evaluation of Pre-test Estimators,” Regional Science and Urban Economics, 22, 405–432.
- Florax, Raymond, Henk Folmer, and Sergio J. Rey. 2003. “Specification Searches in Spatial Econometrics: The Relevance of Hendry's Methodology,” Regional Science and Urban Economics, 33, 557–579.
- Getis, Arthur and Jared Aldstadt. 2004. “Constructing the Spatial Weights Matrix Using a Local Statistic,” Geographical Analysis, 36(2), 90–104.
- Gibbons, Stephen and Henry G. Overman. 2012. “Mostly Pointless Spatial Econometrics?” Journal of Regional Science, 52(2), 172–191.
- Golden, Shelley D., Kurt M. Ribisl, and Krista M. Perreira. 2014. “Economic and Political Influence on Tobacco Tax Rates: A Nationwide Analysis of 31 Years of State Data,” American Journal of Public Health, 104(2), 350–357.
- Harris, Richard, John Moffat, and Victoria Kravtsova. 2011. “In Search of W,” Spatial Economic Analysis, 6(3), 249–270.
- Hill, R. Carter, William E. Griffiths, and Guay C. Lim. 2012. Principles of Econometrics. Asia: Wiley.
- Holtz-Eakin, Douglas and Amy Ellen Schwartz. 1995. “Spatial Productivity Spillovers from Public Infrastructure: Evidence from State Highways,” International Tax and Public Finance, 2, 459–468.
10.1007/BF00872777 Google Scholar
- Huber, Martin, Michael Lechner, and Conny Wunsch. 2013. “The Performance of Estimators Based on the Propensity Score,” Journal of Econometrics, 175(1), 1–12.
- Keeler, Theodore E., Teh-wei Hu, Paul G. Barnett, and Willard G. Manning. 1993. “Taxation, Regulation, and Addiction: A Demand Function for Cigarettes Based on Time-series Evidence,” Journal of Health Economics, 12, 1–18.
- Keeler, Theodore E., Teh-Wei Hu, Paul G. Barnett, Willard G. Manning, Hai-Yen Sung. (1996), “Do Cigarette Producers Price-Discriminate by State? An Empirical Analysis of Local Cigarette Pricing and Taxation,” Journal of Health Economics, 15, 499–512.
- Kelejian, Harry H. 2008. “A Spatial J-Test for Model Specification against a Single or a Set of Non-Nested Alternatives,” Letters in Spatial and Resource Sciences, 1(1), 3–11.
10.1007/s12076-008-0001-9 Google Scholar
- Kelejian, Harry H. and Gianfranco Piras. 2014. “Estimation of Spatial Models with Endogenous Weighting Matrices, and an Application to a Demand Model for Cigarettes,” Regional Science and Urban Economics, 46, 140–149.
- Kelejian, Harry H. and Ingmar R. Prucha. 1998. “A Generalized Spatial Two Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances,” Journal of Real Estate Finance and Economics, 17, 99–121.
- Kelejian, Harry H. and Ingmar R. Prucha. 1999. “A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model,” International Economic Review, 40, 509–533.
- Kelejian, Harry H. and Ingmar R. Prucha. 2010. “Specification and Estimation of Spatial Autoregressive Models with Autoregressive and Heteroskedastic Disturbances,” Journal of Econometrics, 157, 53–67.
- Kelejian, Harry H., Ingmar R. Prucha, and Yevgeny Yuzefovich. 2004. “ Instrumental Variable Estimation of a Spatial Autoregressive Model with Autoregressive Disturbances: Large and Small Sample Results,” in J.P. LeSage and R.K. Pace (eds.), Spatial and Spatiotemporal Econometrics. Amsterdam: Elsevier, pp. 163–198.
- Lacombe, Donald J. and James P. LeSage. 2013. “Using Bayesian Posterior Model Probabilities to Identify Omitted Variables in Spatial Regression Models,” Papers in Regional Science, DOI: 10.1111/pirs.12070.
10.1111/pirs.12070 Google Scholar
- Lee, Lung-Fei. 2004. “Asymptotic Distribution of Quasi-maximum Likelihood Estimators for Spatial Autoregressive Models,” Econometrica, 72, 1899–1925.
- Lee, Lung-Fei and Jihai Yu. 2010. “Some Recent Developments in Spatial Panel Data Models,” Regional Science and Urban Economics, 40, 255–271.
- LeSage, James P. and R. Kelley Pace. 2009. Introduction to Spatial Econometrics. Boca Raton, FL: Taylor and Francis.
- LeSage, James P. and R. Kelley Pace. 2011. “Pitfalls in Higher Order Model Extensions of Basic Spatial Regression Methodology,” The Review of Regional Studies, 41(1), 13–26.
- Lewit, Eugene M. and Douglas Coate. 1982. “The Potential of Using Excise Taxes to Reduce Smoking,” Journal of Health Economics, 1, 121–145.
- Lewit, Eugene M., Douglas Coate, and Michael Grossman. 1987. “The Effects of Government Regulation on Teenage Smoking,” Journal of Law and Economics, 24, 545–569.
- Liu, Xiaodong and Lung-Fei Lee. 2013. “Two-Stage Least Squares Estimation of Spatial Autoregressive Models with Endogenous Regressors and Many Instruments,” Econometric Reviews, 32(5–6), 734–753.
- Lovenheim, Michael F. 2008. “How Far to the Border?: The Extent and Impact of Cross-Border Casual Cigarette Smuggling,” National Tax Journal, 56(1), 7–33.
10.17310/ntj.2008.1.01 Google Scholar
- Meen, Geoff. 1996. “Spatial Aggregation, Spatial Dependence and Predictability in the UK Housing Market,” Housing Studies, 11, 345–372.
- McMillen, Daniel P. 2010. “Issues in Spatial Data Analysis,” Journal of Regional Science, 50(1), 119–141.
- McMillen, Daniel P. 2012. “Perspectives on Spatial Econometrics: Linear Smoothing with Structured Models,” Journal of Regional Science, 52(2), 192–209.
- McMillen, Daniel P. 2013. Quantile Regression for Spatial Data. Heidelberg, New York, Dordrecht, London: Springer.
10.1007/978-3-642-31815-3 Google Scholar
- Moulton, Brent R. 1990. “An Illustration of a Pitfall in Estimating the Effects of Aggregate Variables on Micro Units,” Review of Economics and Statistics, 72, 334–338.
- Mur, Jesus and Ana Angulo. 2009. “Model Selection Strategies in a Spatial Setting: Some Additional Results,” Regional Science and Urban Economics, 39, 200–213.
- Mur, Jesus, Marcos Herrera, and Manuel Ruiz. 2013. “ Selecting the W Matrix: Parametric vs. Non Parametric Approaches,” paper presented at the Econometrics of Social Interaction Symposium, University of York.
- Neumayer, Eric and Thomas Plümper. 2012. “Conditional Spatial Policy Dependence: Theory and Model Specification,” Comparative Political Studies, 45(7), 819–849.
- Neumayer, Eric and Thomas Plümper. 2013. “ W,” available on SSRN at http://ssrn.com/abstract=2208706. Last accessed January 21, 2015.
- Orzechowski and Walker. 2012. The Tax Burden on Tobacco, Historical Compilation, Volume 47, 2012. Arlington, Virginia: Orzechowski and Walker.
- Pace, R. Kelley, Ronald Barry, John M. Clapp, and Mauricio Rodriguez. 1998. “Spatiotemporal Autoregressive Models of Neighborhood Effects,” Journal of Real Estate Finance and Economics, 17(1), 15–33.
- Pace, R. Kelley and Shuang Zhu. 2012. “Separable Spatial Modeling of Spillovers and Disturbances,” Journal of Geographical Systems, 14(1), 75–90.
- Partridge, Mark D., Marlon G. Boarnet, Steven Brakman, and Gianmarco Ottaviano. 2012. “Introduction: Whither Spatial Econometrics?” Journal of Regional Science, 52(2), 167–171.
- Pinkse, Joris and Margaret A. Slade. 2010. “The Future of Spatial Econometrics,” Journal of Regional Science, 50(1), 103–117.
- Qu, Xi and Lung-Fei Lee. 2015. “Estimating a Spatial Autoregressive Model with an Endogenous Spatial Weight Matrix,” Journal of Econometrics, 184, 209–232.
- Soetevent, Adriaan R. and Peter Kooreman. 2007. “A Discrete Choice Model with Social Interactions: with an Application to High School Teen Behavior,” Journal of Applied Econometrics, 22, 599–624.
- Song, Shunfeng. 1996. “Some Tests of Alternative Accessibility Measures: A Population Density Approach,” Land Economics, 72(4), 474–482.
- Staiger, Douglas and James H. Stock. 1997. “Instrumental Variables Regression with Weak Instruments,” Econometrica, 65(3), 557–586.
- Tobler, Waldo R. 1970. “A Computer Movie Simulating Urban Growth in the Detroit Region,” Economic Geography, 46(2), 234–240.
- Wasserman, Jeffrey, Willard G. Manning, Joseph P. Newhouse, and John D. Winkler. 1991. “The Effects of Excise Taxes and Regulations on Cigarette Smoking,” Journal of Health Economics, 10, 43–64.
- Yen, Steven T. and Chung L. Huang. 1996. “Household Demand for Finfish: A Generalized Double-hurdle Model,” Journal of Agricultural and Resource Economics, 21(2), 220–234.