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Adaptive Inference on Pure Spatial Models

Author

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  • Jungyoon Lee
  • Peter M Robinson

Abstract

We consider adaptive tests and estimates which are asymptotically efficient in the presence of unknown, nonparametric, distributional form in pure spatial models. A novel adaptive Lagrange Multiplier testing procedure for lack of spatial dependence is proposed and extended to linear regression with spatially correlated errors. Feasibility of adaptive estimation is verified and its efficiency improvement over Gaussian pseudo maximum likelihood is shown to be either less than, or more than, for models with explanatory variables. The paper covers a general class of semiparametric spatial models allowing nonlinearity in the parameters and/or the weight matrix, in addition to unknown distribution.

Suggested Citation

  • Jungyoon Lee & Peter M Robinson, 2018. "Adaptive Inference on Pure Spatial Models," STICERD - Econometrics Paper Series 596, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:596
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    References listed on IDEAS

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    1. Paolo Buonanno & Daniel Montolio & Paolo Vanin, 2009. "Does Social Capital Reduce Crime?," Journal of Law and Economics, University of Chicago Press, vol. 52(1), pages 145-170, February.
    2. Robinson, Peter M. & Rossi, Francesca, 2015. "Refined Tests For Spatial Correlation," Econometric Theory, Cambridge University Press, vol. 31(6), pages 1249-1280, December.
    3. Robinson, Peter M. & Rossi, Francesca, 2015. "Refinements in maximum likelihood inference on spatial autocorrelation in panel data," Journal of Econometrics, Elsevier, vol. 189(2), pages 447-456.
    4. 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.
    5. Robinson, P.M., 2010. "Efficient estimation of the semiparametric spatial autoregressive model," Journal of Econometrics, Elsevier, vol. 157(1), pages 6-17, July.
    6. Maria Kyriacou & Peter C. B. Phillips & Francesca Rossi, 2017. "Indirect inference in spatial autoregression," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 168-189, June.
    7. Robinson, Peter, 2008. "Correlation testing in time series, spatial and cross-sectional data," LSE Research Online Documents on Economics 25470, London School of Economics and Political Science, LSE Library.
    8. Robinson, P.M., 2008. "Correlation testing in time series, spatial and cross-sectional data," Journal of Econometrics, Elsevier, vol. 147(1), pages 5-16, November.
    9. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
    10. Luc Anselin, 2003. "Spatial Externalities, Spatial Multipliers, And Spatial Econometrics," International Regional Science Review, , vol. 26(2), pages 153-166, April.
    11. Maria Kyriacou & Peter C. B. Phillips & Francesca Rossi, 2017. "Indirect inference in spatial autoregression," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 168-189, June.
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    More about this item

    Keywords

    Efficient test; adaptive estimation; spatial models;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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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