Properties of the maximum likelihood estimator in spacial autoregressive models
The (quasi-) maximum likelihood estimator (MLE) for the autoregressive parameter in a spatial autoregressive model cannot in general be written explicitly in terms of the data. The only known properties of the estimator have hitherto been its first-order asymptotic properties (Lee, 2004, Econometrica), derived under specific assumptions on the evolution of the spatial weights matrix involved. In this paper we show that the exact cumulative distribution function of the estimator can, under mild assumptions, be written down explicitly. A number of immediate consequences of the main result are discussed, and several examples of theoretical and practical interest are analysed in detail. The examples are of interest in their own right, but also serve to illustrate some unexpected features of the distribution of the MLE. In particular, we show that the distribution of the MLE may not be supported on the entire parameter space, and may be nonanalytic at some points in its support. Supplementary material relating to this working paper can be viewed here
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Audretsch, David B & Feldman, Maryann P, 1996. "R&D Spillovers and the Geography of Innovation and Production," American Economic Review, American Economic Association, vol. 86(3), pages 630-40, June.
- Besley, Timothy & Case, Anne, 1995.
"Incumbent Behavior: Vote-Seeking, Tax-Setting, and Yardstick Competition,"
American Economic Review,
American Economic Association, vol. 85(1), pages 25-45, March.
- Timothy Besley & Anne Case, 1992. "Incumbent Behavior: Vote Seeking, Tax Setting and Yardstick Competition," NBER Working Papers 4041, National Bureau of Economic Research, Inc.
- Hillier, Grant & Kan, Raymond & Wang, Xiaolu, 2009.
"Computationally Efficient Recursions For Top-Order Invariant Polynomials With Applications,"
Cambridge University Press, vol. 25(01), pages 211-242, February.
- Grant Hillier & Raymond Kan & Xiaolu Wang, 2008. "Computationally efficient recursions for top-order invariant polynomials with applications," CeMMAP working papers CWP07/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- J. Barkley Rosser, 2009. "Introduction," Chapters, in: Handbook of Research on Complexity, chapter 1 Edward Elgar.
- Giovanni Forchini, .
"The Exact Cumulative Distribution Function of a Ratio of Quadratic Forms in Normal Variables with Application to the AR(1) Model,"
01/02, Department of Economics, University of York.
- Forchini, G., 2002. "The Exact Cumulative Distribution Function Of A Ratio Of Quadratic Forms In Normal Variables, With Application To The Ar(1) Model," Econometric Theory, Cambridge University Press, vol. 18(04), pages 823-852, August.
- Hillier, Grant, 2001. "THE DENSITY OF A QUADRATIC FORM IN A VECTOR UNIFORMLY DISTRIBUTED ON THE n-SPHERE," Econometric Theory, Cambridge University Press, vol. 17(01), pages 1-28, February.
- Joris Pinkse & Margaret E. Slade & Craig Brett, 2002. "Spatial Price Competition: A Semiparametric Approach," Econometrica, Econometric Society, vol. 70(3), pages 1111-1153, May.
- G�ran Therborn & K.C. Ho, 2009. "Introduction," City, Taylor & Francis Journals, vol. 13(1), pages 53-62, March.
- Topa, Giorgio, 2001.
"Social Interactions, Local Spillovers and Unemployment,"
Review of Economic Studies,
Wiley Blackwell, vol. 68(2), pages 261-95, April.
- Topa, Giorgio, 1997. "Social Interactions, Local Spillovers and Unemployment," Working Papers 97-17, C.V. Starr Center for Applied Economics, New York University.
- Bao, Yong, 2013. "Finite-Sample Bias Of The Qmle In Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 29(01), pages 68-88, February.
- Hillier, G.H., 1999. "The density of a quadratic form in a vector uniformly distributed on the n-sphere," Discussion Paper Series In Economics And Econometrics 9902, Economics Division, School of Social Sciences, University of Southampton.
- Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-65, July.
- Martellosio, Federico, 2011. "Efficiency of the OLS estimator in the vicinity of a spatial unit root," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1285-1291, August.
- Harry H. Kelejian & Ingmar R. Prucha & Yevgeny Yuzefovich, 2006. "Estimation Problems In Models With Spatial Weighting Matrices Which Have Blocks Of Equal Elements," Journal of Regional Science, Wiley Blackwell, vol. 46(3), pages 507-515.
- Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
- Giovanni Forchini, . "The Distribution of a Ratio of Quadratic Forms in Noncentral Normal Variables," Discussion Papers 01/12, Department of Economics, University of York.
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