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Abstract

Over the last decades, spatial-interaction models have been increasingly used in economics. However, the development of a sufficiently general asymptotic theory for nonlinear spatial models has been hampered by a lack of relevant central limit theorems (CLTs), uniform laws of large numbers (ULLNs) and pointwise laws of large numbers (LLNs). These limit theorems form the essential building blocks towards developing the asymptotic theory of M-estimators, including maximum likelihood and generalized method of moments estimators. The paper establishes a CLT, ULLN, and LLN for spatial processes or random fields that should be applicable to a broad range of data processes.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 150 (2009)
Issue (Month): 1 (May)
Pages: 86-98

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Handle: RePEc:eee:econom:v:150:y:2009:i:1:p:86-98

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Random field Spatial process Central limit theorem Uniform law of large numbers Law of large numbers;

References

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1. Potscher, Benedikt M. & Prucha, Ingmar R., 1994. "Generic uniform convergence and equicontinuity concepts for random functions : An exploration of the basic structure," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 23-63.
2. Davidson, James, 1993. "An L1-convergence theorem for heterogeneous mixingale arrays with trending moments," Statistics & Probability Letters, Elsevier, vol. 16(4), pages 301-304, March.
3. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-67, July.
4. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
   
   • Donald W.K. Andrews, 1990. "Generic Uniform Convergence," Cowles Foundation Discussion Papers 940, Cowles Foundation for Research in Economics, Yale University.
5. Potscher, Benedikt M. & Prucha, Ingmar R., 1987. "A Uniform Law of Large Numbers for Dependent and Heterogeneous Data Process," Working Papers 87-26, C.V. Starr Center for Applied Economics, New York University.
   
   • Potscher, Benedikt M & Prucha, Ingmar R, 1989. "A Uniform Law of Large Numbers for Dependent and Heterogeneous Data Processes," Econometrica, Econometric Society, vol. 57(3), pages 675-83, May.
6. Conley, T. G., 1999. "GMM estimation with cross sectional dependence," Journal of Econometrics, Elsevier, vol. 92(1), pages 1-45, September.
7. de Jong, Robert M., 1997. "Central Limit Theorems for Dependent Heterogeneous Random Variables," Econometric Theory, Cambridge University Press, vol. 13(03), pages 353-367, June.
8. Benedikt M. Potscher & Ingmar R. Prucha, 1994. "On the Formulation of Uniform Laws of Large Numbers: A Truncation Approach," NBER Technical Working Papers 0085, National Bureau of Economic Research, Inc.
9. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(03), pages 458-467, December.
   
   • Andrews, Donald W. K., 1987. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Working Papers 645, California Institute of Technology, Division of the Humanities and Social Sciences.

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Cited by:

1. Mullally, Conner, 2011. "Development in the Midst of Drought: Evaluating an Agricultural Extension and Credit Program in Nicaragua," 2011 Annual Meeting, July 24-26, 2011, Pittsburgh, Pennsylvania 108723, Agricultural and Applied Economics Association.
2. Luc Anselin, 2009. "Thirty Years of Spatial Econometrics," GeoDa Center Working Papers 1013, GeoDa Center for Geospatial Analysis and Computation.
3. Mullally, Conner, 2011. "Development in the Midst of Drought: Evaluating an Agricultural Extension and Credit Program in Nicaragua," 2011 Annual Meeting, July 24-26, 2011, Pittsburgh, Pennsylvania 108498, Agricultural and Applied Economics Association.
4. Mullally, Conner, 2011. "Development in the Midst of Drought: Evaluating an Agricultural Extension and Credit Program in Nicaragua," 2011 Annual Meeting, July 24-26, 2011, Pittsburgh, Pennsylvania 109664, Agricultural and Applied Economics Association.
5. Min Seong Kim & Yixiao Sun, 2012. "Asymptotic F Test in a GMM Framework with Cross Sectional Dependence," Working Papers 032, Ryerson University, Department of Economics.
6. Debarsy, Nicolas & Ertur, Cem, 2010. "Testing for spatial autocorrelation in a fixed effects panel data model," Regional Science and Urban Economics, Elsevier, vol. 40(6), pages 453-470, November.
   
   • Nicolas Debarsy & Cem Ertur, 2009. "Testing for Spatial Autocorrelation in a Fixed Effects Panel Data Model," Post-Print halshs-00414133, HAL.

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