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A general method for third-order bias and variance corrections on a nonlinear estimator

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  • Yang, Zhenlin

Abstract

Motivated by a recent study of Bao and Ullah (2007a) on finite sample properties of MLE in the pure SAR (spatial autoregressive) model, a general method for third-order bias and variance corrections on a nonlinear estimator is proposed based on stochastic expansion and bootstrap. Working with concentrated estimating equation simplifies greatly the high-order expansions for bias and variance; a simple bootstrap procedure overcomes a major difficulty in analytically evaluating expectations of various quantities in the expansions. The method is then studied in detail using a more general SAR model, with its effectiveness in correcting bias and improving inference fully demonstrated by extensive Monte Carlo experiments. Compared with the analytical approach, the proposed approach is much simpler and has a much wider applicability. The validity of the bootstrap procedure is formally established. The proposed method is then extended to the case of more than one nonlinear estimator.

Suggested Citation

  • Yang, Zhenlin, 2015. "A general method for third-order bias and variance corrections on a nonlinear estimator," Journal of Econometrics, Elsevier, vol. 186(1), pages 178-200.
    • Handle: RePEc:eee:econom:v:186:y:2015:i:1:p:178-200
    DOI: 10.1016/j.jeconom.2014.07.003
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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. Zhenlin Yang, 2010. "Bias-Corrected Estimation for Spatial Autocorrelation," Working Papers 12-2010, Singapore Management University, School of Economics.
    3. 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.
    4. Bun, Maurice J.G. & Carree, Martin A., 2005. "Bias-Corrected Estimation in Dynamic Panel Data Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 200-210, April.
    5. Yang, Zhenlin, 2010. "A robust LM test for spatial error components," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 299-310, September.
    6. Lee, Lung-fei & Yu, Jihai, 2010. "Estimation of spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 154(2), pages 165-185, February.
    7. Yang, Z.L. & Tse, Y.K., 2007. "A Corrected Plug-in Method for Quantile Interval Construction Through a Transformed Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 356-376, July.
    8. Bao, Yong & Ullah, Aman, 2007. "The second-order bias and mean squared error of estimators in time-series models," Journal of Econometrics, Elsevier, vol. 140(2), pages 650-669, October.
    9. 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.
    10. Bao, Yong, 2013. "Finite-Sample Bias Of The Qmle In Spatial Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 29(1), pages 68-88, February.
    11. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, September.
    12. Su, Liangjun, 2012. "Semiparametric GMM estimation of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 167(2), pages 543-560.
    13. Kathleen P. Bell & Nancy E. Bockstael, 2000. "Applying the Generalized-Moments Estimation Approach to Spatial Problems Involving Microlevel Data," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 72-82, February.
    14. Marianne Bertrand & Erzo F. P. Luttmer & Sendhil Mullainathan, 2000. "Network Effects and Welfare Cultures," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 115(3), pages 1019-1055.
    15. Robinson, P.M., 2010. "Efficient estimation of the semiparametric spatial autoregressive model," Journal of Econometrics, Elsevier, vol. 157(1), pages 6-17, July.
    16. Lee, Lung-fei, 2007. "The method of elimination and substitution in the GMM estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 140(1), pages 155-189, September.
    17. Su, Liangjun & Jin, Sainan, 2010. "Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 157(1), pages 18-33, July.
    18. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July.
    19. Bao, Yong & Ullah, Aman, 2007. "Finite sample properties of maximum likelihood estimator in spatial models," Journal of Econometrics, Elsevier, vol. 137(2), pages 396-413, April.
    20. Luc Anselin, 2003. "Spatial Externalities, Spatial Multipliers, And Spatial Econometrics," International Regional Science Review, , vol. 26(2), pages 153-166, April.
    21. Lee, Lung-fei, 2007. "Identification and estimation of econometric models with group interactions, contextual factors and fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 333-374, October.
    22. 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.
    23. Giorgio Topa, 2001. "Social Interactions, Local Spillovers and Unemployment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 261-295.
    24. Kiviet, Jan F., 1995. "On bias, inconsistency, and efficiency of various estimators in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 68(1), pages 53-78, July.
    25. 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.
    26. Hsiao, Cheng & Hashem Pesaran, M. & Kamil Tahmiscioglu, A., 2002. "Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods," Journal of Econometrics, Elsevier, vol. 109(1), pages 107-150, July.
    27. Rilstone, Paul & Srivastava, V. K. & Ullah, Aman, 1996. "The second-order bias and mean squared error of nonlinear estimators," Journal of Econometrics, Elsevier, vol. 75(2), pages 369-395, December.
    28. Ullah, Aman, 2004. "Finite Sample Econometrics," OUP Catalogue, Oxford University Press, number 9780198774488.
    29. Case, Anne C, 1991. "Spatial Patterns in Household Demand," Econometrica, Econometric Society, vol. 59(4), pages 953-965, July.
    30. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    31. Brueckner, Jan K., 1998. "Testing for Strategic Interaction Among Local Governments: The Case of Growth Controls," Journal of Urban Economics, Elsevier, vol. 44(3), pages 438-467, November.
    32. Laskar, M.R. & King, M.L., 1998. "Modified Likelihood and Related Methods for Handling Nuisance Parameters in the Linear Regression Model," Monash Econometrics and Business Statistics Working Papers 5/98, Monash University, Department of Econometrics and Business Statistics.
    33. 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.
    34. Bao, Yong, 2013. "Finite Sample Bias Of The Qmle In Spatial Autoregressive Models – Erratum," Econometric Theory, Cambridge University Press, vol. 29(1), pages 89-89, February.
    35. Mynbaev, Kairat T. & Ullah, Aman, 2008. "Asymptotic distribution of the OLS estimator for a purely autoregressive spatial model," Journal of Multivariate Analysis, Elsevier, vol. 99(2), pages 245-277, February.
    36. Case, Anne C. & Rosen, Harvey S. & Hines, James Jr., 1993. "Budget spillovers and fiscal policy interdependence : Evidence from the states," Journal of Public Economics, Elsevier, vol. 52(3), pages 285-307, October.
    37. Lee, Lung-fei, 2007. "GMM and 2SLS estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 137(2), pages 489-514, April.
    38. 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.
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    2. Christoph Strumann, 2019. "Hodges–Lehmann Estimation of Static Panel Models with Spatially Correlated Disturbances," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 141-168, January.
    3. Baltagi, Badi H. & Pirotte, Alain & Yang, Zhenlin, 2021. "Diagnostic tests for homoskedasticity in spatial cross-sectional or panel models," Journal of Econometrics, Elsevier, vol. 224(2), pages 245-270.
    4. Shew Fan Liu & Zhenlin Yang, 2015. "Asymptotic Distribution and Finite Sample Bias Correction of QML Estimators for Spatial Error Dependence Model," Econometrics, MDPI, vol. 3(2), pages 1-36, May.
    5. Rossi, Francesca & Robinson, Peter M., 2023. "Higher-order least squares inference for spatial autoregressions," Journal of Econometrics, Elsevier, vol. 232(1), pages 244-269.
    6. Kiviet, Jan F. & Phillips, Garry D.A., 2014. "Improved variance estimation of maximum likelihood estimators in stable first-order dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 424-448.
    7. Grant Hillier & Federico Martellosio, 2013. "Properties of the maximum likelihood estimator in spatial autoregressive models," CeMMAP working papers CWP44/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Kyoo Il Kim, 2016. "Higher Order Bias Correcting Moment Equation for M-Estimation and Its Higher Order Efficiency," Econometrics, MDPI, vol. 4(4), pages 1-19, December.
    9. Federico Martellosio & Grant Hillier, 2019. "Adjusted QMLE for the spatial autoregressive parameter," Papers 1909.08141, arXiv.org.
    10. Liu, Shew Fan & Yang, Zhenlin, 2015. "Improved inferences for spatial regression models," Regional Science and Urban Economics, Elsevier, vol. 55(C), pages 55-67.
    11. Francesca Rossi & Peter M. Robinson, 2020. "Higher-Order Least Squares Inference for Spatial Autoregressions," Working Papers 04/2020, University of Verona, Department of Economics.
    12. Ruby Chiu‐Hsing Weng & D. Stephen Coad, 2021. "Bias approximations for likelihood‐based estimators," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1474-1497, December.
    13. Ma, Yingying & Lan, Wei & Zhou, Fanying & Wang, Hansheng, 2020. "Approximate least squares estimation for spatial autoregressive models with covariates," Computational Statistics & Data Analysis, Elsevier, vol. 143(C).
    14. Yang, Zhenlin & Yu, Jihai & Liu, Shew Fan, 2016. "Bias correction and refined inferences for fixed effects spatial panel data models," Regional Science and Urban Economics, Elsevier, vol. 61(C), pages 52-72.
    15. Christian Brownlees & Vladislav Morozov, 2022. "Unit Averaging for Heterogeneous Panels," Papers 2210.14205, arXiv.org, revised May 2024.
    16. Martellosio, Federico & Hillier, Grant, 2020. "Adjusted QMLE for the spatial autoregressive parameter," Journal of Econometrics, Elsevier, vol. 219(2), pages 488-506.

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    More about this item

    Keywords

    Third-order bias; Third-order variance; Bootstrap; Concentrated estimating equation; Monte Carlo; Spatial layout; Stochastic expansion;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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