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LARGE SAMPLE PROPERTIES OF BAYESIAN ESTIMATION OF SPATIAL ECONOMETRIC MODELS

Published online by Cambridge University Press:  11 August 2020

Xiaoyi Han ,
Lung-Fei Lee  and
Xingbai Xu
Xiaoyi Han
Affiliation:
The Wang Yanan Institute for Studies in Economics, Xiamen University
Lung-Fei Lee
Affiliation:
The Ohio State University
Xingbai Xu*
Affiliation:
Xiamen University
*
Address correspondence to Xingbai Xu, MOE Key Laboratory of Econometrics, Fujian Key Laboratory of Statistical Science, The Wang Yanan Institute for Studies in Economics, Department of Statistics, School of Economics, Xiamen University, Xiamen, China; e-mail: [email protected].
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Abstract

This paper studies asymptotic properties of a posterior probability density and Bayesian estimators of spatial econometric models in the classical statistical framework. We focus on the high-order spatial autoregressive model with spatial autoregressive disturbance terms, due to a computational advantage of Bayesian estimation. We also study the asymptotic properties of Bayesian estimation of the spatial autoregressive Tobit model, as an example of nonlinear spatial models. Simulation studies show that even when the sample size is small or moderate, the posterior distribution of parameters is well approximated by a normal distribution, and Bayesian estimators have satisfactory performance, as classical large sample theory predicts.

Type
ARTICLES
Information
Econometric Theory , Volume 37 , Issue 4 , August 2021 , pp. 708 - 746
Copyright
© Cambridge University Press 2020

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Footnotes

We are grateful to the editor, the co-editor, and four anonymous referees for their helpful comments. X.H. gratefully acknowledges the financial support of the Chinese Natural Science Fund (Nos. 71501163 and 71973113), and the Fundamental Research Funds for the Central Universities (20720151144) to Xiamen University. X.X. gratefully acknowledges the financial support of the Fundamental Research Funds for the Central Universities (Nos. 20720171072 and 20720181052) to Xiamen University, and the Chinese Natural Science Fund (Nos. 71703135 and 11771361). We also thank the help from IT Engineer Xiang Li at the School of Economics, Xiamen University.

References

REFERENCES

Andrews, D. (1992) Generic uniform convergence. Econometric Theory 8, 241–257.CrossRefGoogle Scholar
Chen, C.F. (1985) On asymptotic normality of limiting density functions with Bayesian implications. Journal of the Royal Statistical Society: Series B 47(3), 540–546.Google Scholar
Cheng, T., Gao, J., & Phillips, P.C.B. (2018) A frequency approach to Bayesian asymptotics. Journal of Econometrics 206, 359–378.CrossRefGoogle Scholar
Congdon, P. (2006) Bayesian Statistical Modelling, Second Edition, John Wiley & Sons, Ltd.Google Scholar
Chernozhukov, V. & Hong, H. (2003) An MCMC approach to classical estimation. Journal of Econometrics 115(2), 293–346.CrossRefGoogle Scholar
Creel, M., Gao, J., Hong, H., & Kristensen, D. (2016) Bayesian Indirect Inference and the ABC of GMM. Universitat Autonoma de Barcelona, Monash University, Stanford University, University College London. Working Paper.Google Scholar
Gelman, A., Roberts, G., & Gilks, W. (1996) Efficient metropolis jumping rules. Bayesian Statistics 5, 599–607.Google Scholar
Golub, G., Heath, M., & Wahba, G. (1979) Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21, 215–223.CrossRefGoogle Scholar
Gupta, A. (2019) Estimation of spatial autoregressions with stochastic weight matrices. Econometric Theory 35(2), 417–463.CrossRefGoogle Scholar
Gupta, A. & Robinson, P. (2015) Inference on higher-order spatial autoregressive models with increasingly many parameters. Journal of Econometrics 186, 19–31.CrossRefGoogle Scholar
Gupta, A. & Robinson, P. (2018) Pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension. Journal of Econometrics 202, 92–107.CrossRefGoogle Scholar
Haario, H., Saksman, E., & Tamminen, J. (2001) An adaptive metropolis algorithm. Bernoulli 7, 223–242.CrossRefGoogle Scholar
Han, X., Hsieh, C.S., & Lee, L. (2017) Estimation and model selection of higher-order spatial autoregressive model: An efficient Bayesian approach. Regional Science and Urban Economics 63, 97–120.CrossRefGoogle Scholar
Han, X. & Lee, L. (2013) Bayesian estimation and model selection for spatial Durbin error model with finite distributed lags. Regional Science and Urban Economics 643, 816–837.CrossRefGoogle Scholar
Han, X. & Lee, L. (2016). Bayesian analysis of spatial panel autoregressive models with time-varying endogenous spatial weight matrices, common factors, and random coefficients. Journal of Business & Economic Statistics 34(4), 642–660.CrossRefGoogle Scholar
Hoerl, A. & Kennard, R. (1970) Ridge regression: Applications to nonorthogonal problems. Technometrics 12, 55–68.CrossRefGoogle Scholar
Jenish, N. & Prucha, I.R. (2009) Central limit theorems and uniform laws of large numbers for arrays of random fields. Journal of Econometrics 150, 86–98.CrossRefGoogle ScholarPubMed
Jenish, N. & Prucha, I.R. (2012) On spatial processes and asymptotic inference under near-epoch dependence. Journal of Econometrics 170, 178–190.CrossRefGoogle ScholarPubMed
Jin, F. & Lee, L. (2013) Cox-type tests for competing spatial autoregressive models with spatial autoregressive disturbances. Regional Science and Urban Economics 43, 590–616.CrossRefGoogle Scholar
Kelejian, H.H. & Prucha, I.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 17, 99–121.CrossRefGoogle Scholar
Kim, J.Y. (1998) Large sample properties of posterior densities, Bayesian information criterion and the likelihood principle in nonstationary time series models. Econometrica 66(2), 359–380.CrossRefGoogle Scholar
Kyung, M., Gill, J., Ghosh, M., & Casella, G. (2010) Penalized regression, standard errors and Bayesian lasso. Bayesian Analysis 5, 369–412.Google Scholar
Lee, L. (2004) Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica 72, 1899–1925.CrossRefGoogle Scholar
Lee, L. (2007) GMM and 2SLS estimation of mixed regressive, spatial autoregressive models. Journal of Econometrics 137, 489–514.CrossRefGoogle Scholar
Lee, L. & Liu, X. (2010) An efficient GMM estimator of spatial autoregressive models with autoregressive disturbances. Econometric Theory 26(1), 187–230.CrossRefGoogle Scholar
Lee, L. & Yu, J. (2016) Identification of spatial Durbin panel models. Journal of Applied Econometrics 31(1), 133–162.CrossRefGoogle Scholar
Lehmann, E.L. & Casella, G. (1998) Theory of Point Estimation. Springer Science & Business Media.Google Scholar
LeSage, J. & Pace, R.K. (2008) Spatial econometric modeling of origin-destination flows. Journal of Regional Science 48, 941–967.Google Scholar
LeSage, J.P. & Pace, R.K. (2009) Introduction to Spatial Econometrics. CRC Press.CrossRefGoogle Scholar
Li, Q. & Lin, N. (2010) The Bayesian elastic net. Bayesian Analysis 5, 151–170.CrossRefGoogle Scholar
Li, R.C. (1998) Relative perturbation theory: I. Eigenvalue and singular value variations. SIAM Journal on Matrix Analysis and Applications 19(4), 956–982.CrossRefGoogle Scholar
Marquardt, D. (1970) Generalized inverses, ridge regression, bias linear estimation and nonlinear estimation. Technometrics 12, 591–612.CrossRefGoogle Scholar
Murray, I., Ghahramani, Z., & MacKay, D. (2006) MCMC for doubly-intractable distributions. arXiv preprint, arXiv:1206.6848.Google Scholar
Ord, K. (1975) Estimation methods for models of spatial interactions. Journal of American Statistical Association 70, 120–126.CrossRefGoogle Scholar
Pace, R.K., LeSage, J., & Zhu, S. (2012) Spatial dependence in regressors and its effect on performance of likelihood-based and instrumental variable estimator. Advances in Econometrics 30, 257–295.CrossRefGoogle Scholar
Park, T. & Casella, G. (2008) The Bayesian lasso. Journal of the American Statistical Association 103, 681–686.CrossRefGoogle Scholar
Phillips, P.C.B. (1996) Econometric model determination. Econometrica 64(4), 763–812.CrossRefGoogle Scholar
Phillips, P.C.B. & Ploberger, W. (1996) An asymptotic theory of Bayesian inference for time series. Econometrica 64(2), 381–412.CrossRefGoogle Scholar
Shiller, R. (1973) A distributed lag estimator derived from smoothness priors. Econometrica 41(4), 775–788.CrossRefGoogle Scholar
Qu, X. & Lee, L. (2013) Locally most powerful tests for spatial interactions in the simultaneous sar Tobit model. Regional Science and Urban Economics 43, 307–321.CrossRefGoogle Scholar
Qu, X. & Lee, L. (2015) Estimating a spatial autoregressive model with an endogenous spatial weight matrix. Journal of Econometrics 184, 209–232.Google Scholar
Raiffa, H. & Schlaifer, R. (1961) Applied Statistical Design Theory. Clinton Press.Google Scholar
Roberts, G. & Rosenthal, J.S. (2009) Examples of adaptive MCMC. Journal of Computational and Graphical Statistics 18, 349–367.CrossRefGoogle Scholar
Smith, T.E. (2009) Estimation bias in spatial models with strongly connected weight matrices. Geographical Analysis 41, 307–332.CrossRefGoogle Scholar
Theil, H. & Goldberger, A. (1961) On Pure and Mixed Statistical Estimation in Economics. International Economic Review, 2(1), 65–78.Google Scholar
Theil, H. (1963) On the use of incomplete prior information in regression analysis. Journal of the American Statistical Association 58, 401–414.CrossRefGoogle Scholar
Tibshirani, R. (1996) Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society: Series B 58, 267–288.Google Scholar
Van der Vaart, A.W. (1998) Asymptotic Statistics. Cambridge University Press.CrossRefGoogle Scholar
Van Erp, S., Oberski, D.L., & Mulder, J. (2019) Shrinkage priors for Bayesian penalized regression. Journal of Mathematical Psychology 89, 31–50.CrossRefGoogle Scholar
Xu, X. & Lee, L. (2015) Maximum likelihood estimation of a spatial autoregressive Tobit model. Journal of Econometrics 188, 264–280.CrossRefGoogle Scholar
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