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Maximum likelihood estimation of a spatial autoregressive Tobit model

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  • Xu, Xingbai
  • Lee, Lung-fei

Abstract

This paper examines a Tobit model with spatial autoregressive interactions. We consider the maximum likelihood estimation for this model and analyze asymptotic properties of the estimator based on the spatial near-epoch dependence of the dependent variable process generated from the model structure. We show that the maximum likelihood estimator is consistent and asymptotically normally distributed. Monte Carlo experiments are performed to verify finite sample properties of the estimator.

Suggested Citation

  • Xu, Xingbai & Lee, Lung-fei, 2015. "Maximum likelihood estimation of a spatial autoregressive Tobit model," Journal of Econometrics, Elsevier, vol. 188(1), pages 264-280.
  • Handle: RePEc:eee:econom:v:188:y:2015:i:1:p:264-280
    DOI: 10.1016/j.jeconom.2015.05.004
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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. Jenish, Nazgul, 2012. "Nonparametric spatial regression under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 167(1), pages 224-239.
    3. repec:asg:wpaper:1048 is not listed on IDEAS
    4. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    5. Qu, Xi & Lee, Lung-fei, 2012. "LM tests for spatial correlation in spatial models with limited dependent variables," Regional Science and Urban Economics, Elsevier, vol. 42(3), pages 430-445.
    6. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    7. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    8. Xu, Xingbai & Lee, Lung-fei, 2015. "A spatial autoregressive model with a nonlinear transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 186(1), pages 1-18.
    9. WEGGE, Leon L., 1974. "Mean value theorem for convex functions," LIDAM Reprints CORE 185, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. 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.
    11. Coralio Ballester & Antoni Calvó-Armengol & Yves Zenou, 2006. "Who's Who in Networks. Wanted: The Key Player," Econometrica, Econometric Society, vol. 74(5), pages 1403-1417, September.
    12. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(2), pages 241-257, June.
    13. Antoni Calvó-Armengol & Eleonora Patacchini & Yves Zenou, 2009. "Peer Effects and Social Networks in Education," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(4), pages 1239-1267.
    14. Wegge, Leon L., 1974. "Mean value theorem for convex functions," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 207-208, August.
    15. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    16. Alexander Chudik & M. Hashem Pesaran & Elisa Tosetti, 2011. "Weak and strong cross‐section dependence and estimation of large panels," Econometrics Journal, Royal Economic Society, vol. 14(1), pages 45-90, February.
    17. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    18. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, October.
    19. 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.
    20. Patrick Bajari & Han Hong & Stephen P. Ryan, 2010. "Identification and Estimation of a Discrete Game of Complete Information," Econometrica, Econometric Society, vol. 78(5), pages 1529-1568, September.
    21. Lei, J., 2013. "Smoothed Spatial Maximum Score Estimation of Spatial Autoregressive Binary Choice Panel Models," Discussion Paper 2013-061, Tilburg University, Center for Economic Research.
    22. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    23. Amemiya, Takeshi, 1974. "Multivariate Regression and Simultaneous Equation Models when the Dependent Variables Are Truncated Normal," Econometrica, Econometric Society, vol. 42(6), pages 999-1012, November.
    24. Corinne Autant‐Bernard & James P. LeSage, 2011. "Quantifying Knowledge Spillovers Using Spatial Econometric Models," Journal of Regional Science, Wiley Blackwell, vol. 51(3), pages 471-496, August.
    25. Jenish, Nazgul & Prucha, Ingmar R., 2012. "On spatial processes and asymptotic inference under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 170(1), pages 178-190.
    26. Lei, J., 2013. "Smoothed Spatial Maximum Score Estimation of Spatial Autoregressive Binary Choice Panel Models," Other publications TiSEM d63bf400-7ff2-4a1c-8067-1, Tilburg University, School of Economics and Management.
    27. Jenish, Nazgul & Prucha, Ingmar R., 2009. "Central limit theorems and uniform laws of large numbers for arrays of random fields," Journal of Econometrics, Elsevier, vol. 150(1), pages 86-98, May.
    28. Hermann Pythagore Pierre Donfouet & Pierre Wilner Jeanty & Éric Malin, 2012. "Accounting for spatial interactions in the demand for community-based health insurance: A Bayesian spatial Tobit analysis," Post-Print halshs-00767120, HAL.
    29. Qu, Xi & Lee, Lung-fei, 2015. "Estimating a spatial autoregressive model with an endogenous spatial weight matrix," Journal of Econometrics, Elsevier, vol. 184(2), pages 209-232.
    30. Nelson, Forrest D., 1977. "Censored regression models with unobserved, stochastic censoring thresholds," Journal of Econometrics, Elsevier, vol. 6(3), pages 309-327, November.
    31. 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.
    32. Alfonso Flores‐Lagunes & Kurt Erik Schnier, 2012. "Estimation of sample selection models with spatial dependence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(2), pages 173-204, March.
    33. Olsen, Randall J, 1978. "Note on the Uniqueness of the Maximum Likelihood Estimator for the Tobit Model," Econometrica, Econometric Society, vol. 46(5), pages 1211-1215, September.
    34. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    35. 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.
    36. Qu, Xi & Lee, Lung-fei, 2013. "Locally most powerful tests for spatial interactions in the simultaneous SAR Tobit model," Regional Science and Urban Economics, Elsevier, vol. 43(2), pages 307-321.
    37. Corinne Autant-Bernard & James Lesage, 2011. "Quantifying knowledge spillovers using spatial econometric tools," Post-Print halshs-00617709, HAL.
    38. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Spatial autoregressive model; Tobit model; Censored data; Near-epoch dependence; Maximum likelihood;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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