Robust Two-Stage Estimation in General Spatial Dynamic Panel Data Models

DING Hao, JIN Baisuo, WU Yuehua

Journal of Systems Science & Complexity ›› 2023, Vol. 36 ›› Issue (6) : 2580-2604.

PDF(434 KB)
中国科学院数学与系统科学研究院期刊网
JSSC
PDF(434 KB)
Journal of Systems Science & Complexity ›› 2023, Vol. 36 ›› Issue (6) : 2580-2604. DOI: 10.1007/s11424-023-2172-2

Robust Two-Stage Estimation in General Spatial Dynamic Panel Data Models

Author information +
History +

Abstract

This paper proposes a robust two-stage estimation procedure for a general spatial dynamic panel data model in light of the two-stage estimation procedure in Jin, et al. (2020). The authors replace the least squares estimation in the first stage of Jin, et al. (2020) by M-estimation. The authors also provide the justification for not making any change in its second stage when the number of time periods is large enough. The proposed methodology is robust and efficient, and it can be easily implemented. In addition, the authors study the limiting behavior of the parameter estimators, which are shown to be consistent and asymptotic normally distributed under some conditions. Extensive simulation studies are carried out to assess the proposed procedure and a COVID-19 data example is conducted for illustration.

Key words

Asymptotic normality / consistency / M-estimation / model selection / outliers

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations
DING Hao , JIN Baisuo , WU Yuehua. Robust Two-Stage Estimation in General Spatial Dynamic Panel Data Models. Journal of Systems Science and Complexity, 2023, 36(6): 2580-2604 https://doi.org/10.1007/s11424-023-2172-2

References

[1] Ord K, Estimation methods for models of spatial interaction, Journal of the American Statistical Association, 1975, 70(349):120-126.
[2] Whittle P, On stationary processes in the plane, Biometrika, 1954, 41:434-449.
[3] Elhorst J P, Dynamic models in space and time, Geographical Analysis, 2001, 33(2):119-140.
[4] Yu J, de Jong R, and Lee L F, Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large, Journal of Econometrics, 2008, 146:118-134.
[5] Lee L and Yu J, Efficient GMM estimation of spatial dynamic panel data models with fixed effects, Journal of Econometrics, 2014, 180:174-197.
[6] Lee L and Yu J, Identification of spatial Durbin panel models, Journal of Applied Econometrics, 2016, 31:133-162.
[7] Yang Z, Unified M-estimation of fixed-effects spatial dynamic models with short panels, Journal of Econometrics, 2018, 205:423-447.
[8] Bera A K, Doǧ an O, Taşpınar S, et al., Robust LM tests for spatial dynamic panel data models, Regional Science and Urban Economics, 2019, 76:47-66.
[9] Jin B S, Wu Y H, Rao C R, et al., Estimation and model selection in general spatial dynamic panel data models, Proceedings of the National Academy of Sciences, 2020, 117(10):5235-5241.
[10] Huber P J, Robust estimation of a location parameter, The Annals of Mathematical Statistics, 1964, 35(1):73-101.
[11] Huber P J, Robust regression:Asymptotics, conjectures and Monte Carlo, The Annals of Statistics, 1973, 1(5):799-821.
[12] Huber P J, Robust Statistics, Wiley, New York, 1981.
[13] Bickel P J, One-step Huber estimates in the linear model, Journal of the American Statistical Association, 1975, 70(350):428-434.
[14] Yohai V J and Maronna R A, Asymptotic behavior of M-estimators for the linear model, The Annals of Statistics, 1979, 7(2):258-268.
[15] Bai Z D and Wu Y, General M-Estimation, Journal of Multivariate Analysis, 1997, 63:119-135.
[16] Wu Y and Zen M, A strongly consistent information criterion for linear model selection based on M-estimation, Probability Theory and Related Fields, 1999, 113:599-625.
[17] Li G, Peng H, and Zhu L, Nonconcave penalized M-estimation with a diverging number of parameters, Statistica Sinica, 2011, 21(1):391-419.
[18] Loh P L, Statistical consistency and asymptotic normality for high-dimensional robust Mestimators, The Annals of Statistics, 2017, 45(2):866-896.
[19] Bai Z D, Rao C R, and Wu Y, M-estimation of multivariate linear regression parameters under a convex discrepancy function, Statist Sinica, 1992, 2(1):237-254.
[20] Fan J and Li R, Variable selection via nonconcave penalized likelihood and its oracle properties, Journal of the American Statistical Association, 2001, 96(456):1348-1360.
[21] Zhang C H, Nearly unbiased variable selection under minimax concave penalty, The Annals of Statistics, 2010, 38(2):894-942.
[22] Tibshirani R, Regression shrinkage and selection via the lasso, Journal of the Royal Statistical Society:Series B (Methodological), 1996, 58(1):267-288.
[23] Schwarz G, Estimating the dimension of a model, The Annals of Statistics, 1978, 6(2):461-464.
[24] Rockafellar R T, Convex Analysis, Princeton University Press, Princeton, 1970.
[25] Durrett R, Probability:Theory and Examples, Cambridge University Press, Cambridge, 2019.
[26] Hall P and Heyde C C, Martingale Limit Theory and Its Application, Academic Press, New York, 2014.

Funding

This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant No. RGPIN-2017-05720, the National Natural Science Foundation under Grant Nos. 12201601, 71873128, 11571337, 71631006, and 71921001, the Anhui Provincial Natural Science Foundation under Grant No. 2208085QA06.
PDF(434 KB)

169

Accesses

0

Citation

Detail
Sections
Recommended

/

〈 〉