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Efficient Estimation of the SemiparametricSpatial Autoregressive Model

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  • Peter M Robinson

Abstract

Efficient semiparametric and parametric estimates are developed for aspatial autoregressive model, containing nonstochastic explanatoryvariables and innovations suspected to be non-normal. The main stress ison the case of distribution of unknown, nonparametric, form, where seriesnonparametric estimates of the score function are employed in adaptiveestimates of parameters of interest. These estimates are as efficient asones based on a correct form, in particular they are more efficient thanpseudo-Gaussian maximum likelihood estimates at non-Gaussiandistributions. Two different adaptive estimates are considered. One entails astringent condition on the spatial weight matrix, and is suitable only whenobservations have substantially many "neighbours". The other adaptiveestimate relaxes this requirement, at the expense of alternative conditionsand possible computational expense. A Monte Carlo study of finite sampleperformance is included.

Suggested Citation

  • Peter M Robinson, 2007. "Efficient Estimation of the SemiparametricSpatial Autoregressive Model," STICERD - Econometrics Paper Series 515, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:515
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    References listed on IDEAS

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    1. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-533, May.
    2. Rudolf Beran, 1976. "Adaptive estimates for autoregressive processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 28(1), pages 77-89, December.
    3. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
    4. Potscher, Benedikt M. & Prucha, Ingmar R., 1986. "A class of partially adaptive one-step m-estimators for the non-linear regression model with dependent observations," Journal of Econometrics, Elsevier, vol. 32(2), pages 219-251, July.
    5. 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.
    6. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(3), pages 428-457, December.
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    8. Lung-fei Lee, 2003. "Best Spatial Two-Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances," Econometric Reviews, Taylor & Francis Journals, vol. 22(4), pages 307-335.
    9. Lee, Lung-Fei, 2002. "Consistency And Efficiency Of Least Squares Estimation For Mixed Regressive, Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 18(2), pages 252-277, April.
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    More about this item

    Keywords

    Spatial autoregression; Efficient estimation; Adaptive estimation; Simultaneity bias.© The author. All rights reserved. Short sections of text; not to exceed two paragraphs; may be quoted without explicit permission provided that full credit; including © notice; isgiven to the source.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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