Abstract
This paper introduces an unbiased estimator based on least squares involving time-specific cross-sectional averages for a first-order panel autoregression with a strictly exogenous covariate. The proposed estimator is straightforward to implement as long as the variables of interest have sufficient time variation. The number of cross-sections (N) and the number of time periods (T) can be large, and there is no restriction on the growth rate of N relative to T. It is demonstrated via both theory and a simulation study that the estimator is asymptotically unbiased, and it can provide correct empirical coverage probabilities for the ‘true’ coefficients of the model for various combinations of N and T. An empirical application is also provided to confirm the feasibility of the proposed approach.
Funding source: Social Sciences and Humanities Research Council of Canada
Award Identifier / Grant number: 430-2016-00682
Funding source: Canadian Network for Research and Innovation in Machining Technology, Natural Sciences and Engineering Research Council of Canada
Award Identifier / Grant number: RGPIN-2020-04161
Acknowledgments
I would like to sincerely thank the editor (Prof. Bruce Mizrach) and two referees for their insightful comments that led to corrections, clarifications, and various improvements in the paper. The remaining errors are mine.
-
Author contribution: The author has accepted responsibility for the entire content of this submitted manuscript and approved submission.
-
Research funding: I gratefully acknowledge funding from the Social Science and Humanities Research Council of Canada (MBF Grant 430-2016-00682) and the Natural Sciences and Engineering Research Council of Canada (Grant RGPIN-2020-04161).
-
Conflict of interest statement: The author declares no conflicts of interest regarding this article.
References
Alvarez, J., and M. Arellano. 2003. “The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators.” Econometrica 71: 1121–59. https://doi.org/10.1111/1468-0262.00441.Suche in Google Scholar
Anderson, T. W., and C. Hsiao. 1982. “Formulation and Estimation of Dynamic Models using Panel Data.” Journal of Econometrics 18: 47–82. https://doi.org/10.1016/0304-4076(82)90095-1.Suche in Google Scholar
Andrews, D. W. K. 1999. “Consistent Moment Selection Procedures for Generalized Method of Moments Estimation.” Econometrica 67: 543–64. https://doi.org/10.1111/1468-0262.00036.Suche in Google Scholar
Arellano, M., and S. Bond. 1991. “Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations.” The Review of Economic Studies 58: 277–97. https://doi.org/10.2307/2297968.Suche in Google Scholar
Arellano, M., and J. Hahn. 2007. “Understanding Bias in Nonlinear Panel Models: Some Recent Developments.” In Advances in Economics and Econometrics: Theory and Applications, Ninth World Congress, 3, edited by R. Blundell, W. Newey, and T. Persson, 381–409. Cambridge: Cambridge University Press.10.1017/CBO9780511607547.013Suche in Google Scholar
Bai, J. 2009. “Panel Data Models with Interactive Fixed Effects.” Econometrica 77: 1229–79. https://doi.org/10.3982/ecta6135.Suche in Google Scholar
Bun, M. J. G., and M. A. Carree. 2005. “Bias-corrected Estimation in Dynamic Panel Data Models.” Journal of Business & Economic Statistics 23: 200–10. https://doi.org/10.1198/073500104000000532.Suche in Google Scholar
Caselli, F., G. Esquivel, and F. Lefort. 1996. “Reopening the Convergence Debate: a New Look at Cross-Country Growth Empirics.” Journal of Economic Growth 1: 363–89. https://doi.org/10.1007/bf00141044.Suche in Google Scholar
Chu, B. 2018. Composite Quasi-Likelihood Estimation of Dynamic Panels with Group-Specific Heterogeneity and Spatially Dependent Errors. Mimeo. Also available at https://arxiv.org/abs/1704.06613.Suche in Google Scholar
Chudik, A., and M. H. Pesaran. 2015. “Common Correlated Effects Estimation of Heterogeneous Dynamic Panel Data Models with Weakly Exogenous Regressors.” Journal of Econometrics 188: 393–420. https://doi.org/10.1016/j.jeconom.2015.03.007.Suche in Google Scholar
Coakley, J., A.-M. Fuertes, and R. Smith. 2002. A Principal Components Approach to Cross-Section Dependence in Panels. New York City: Mimeo.Suche in Google Scholar
Dhaene, G., and K. Jochmans. 2015. “Split-panel Jackknife Estimation of Fixed-Effect Models.” The Review of Economic Studies 82: 991–1030. https://doi.org/10.1093/restud/rdv007.Suche in Google Scholar
Dhaene, G., and K. Jochmans. 2016a. “Bias-corrected Estimation of Panel Vector Autoregressions.” Economics Letters 145: 98–103. https://doi.org/10.1016/j.econlet.2016.06.010.Suche in Google Scholar
Dhaene, G., and K. Jochmans. 2016b. “Likelihood Inference in an Autoregression with Fixed Effects.” Econometric Theory 32: 1178–215. https://doi.org/10.1017/s0266466615000146.Suche in Google Scholar
Everaert, G., and T. D. Groote. 2016. “Common Correlated Effects Estimation of Dynamic Panels with Cross-Sectional Dependence.” Econometric Reviews 35: 428–63. https://doi.org/10.1080/07474938.2014.966635.Suche in Google Scholar
Galvao, A. F., and K. Kato. 2014. “Estimation and Inference for Linear Panel Data Models under Misspecification when Both N and T are Large.” Journal of Business & Economic Statistics 32: 285–309. https://doi.org/10.1080/07350015.2013.875473.Suche in Google Scholar
Gonçalves, S., and M. Kaffo. 2015. “Bootstrap Inference for Linear Dynamic Panel Data Models with Individual Fixed Effects.” Journal of Econometrics 186: 407–26. https://doi.org/10.1016/j.jeconom.2015.02.017.Suche in Google Scholar
Guidotti, E. 2020. R Package “COVID19”. Neuchâtel: University of Neuchâtel.Suche in Google Scholar
Hahn, J., and G. Kuersteiner. 2002. “Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both N and T are Large.” Econometrica 70: 1639–57. https://doi.org/10.1111/1468-0262.00344.Suche in Google Scholar
Hahn, J., and G. Kuersteiner. 2011. “Bias Reduction for Dynamic Nonlinear Panel Models with Fixed Effects.” Econometric Theory 27: 1152–91. https://doi.org/10.1017/s0266466611000028.Suche in Google Scholar
Hahn, J., and H. R. Moon. 2006. “Reducing Bias of MLE in a Dynamic Panel Model.” Econometric Theory 22: 499–512. https://doi.org/10.1017/s0266466606060245.Suche in Google Scholar
Hahn, J., and W. K. Newey. 2004. “Jackknife and Analytical Bias Reduction for Nonlinear Panel Models.” Econometrica 72: 1295–319. https://doi.org/10.1111/j.1468-0262.2004.00533.x.Suche in Google Scholar
Han, C., and P. C. B. Phillips. 2010. “GMM Estimation for Dynamic Panels with Fixed Effects and Strong Instruments at Unity.” Econometric Theory 26: 119–51. https://doi.org/10.1017/s026646660909063x.Suche in Google Scholar
Han, C., P. C. B. Phillips, and D. Sul. 2014. “X-differencing and Dynamic Panel Model Estimation.” Econometric Theory 30: 201–51. https://doi.org/10.1017/s0266466613000170.Suche in Google Scholar
Hsiao, C., M. H. Pesaran, and A. K. Tahmiscioglu. 2002. “Maximum Likelihood Estimation of Fixed Effects Dynamic Panel Data Models Covering Short Time Periods.” Journal of Econometrics 109: 107–50. https://doi.org/10.1016/s0304-4076(01)00143-9.Suche in Google Scholar
Inoue, A. 2008. “Efficient Estimation and Inference in Linear Pseudo-panel Data Models.” Journal of Econometrics 142: 449–66. https://doi.org/10.1016/j.jeconom.2007.08.003.Suche in Google Scholar
Juodis, A. 2018. “Pseudo Panel Data Models with Cohort Interactive Effects.” Journal of Business & Economic Statistics 36: 47–61. https://doi.org/10.1080/07350015.2015.1137759.Suche in Google Scholar
Moon, H. R., and M. Weidner. 2017. “Dynamic Linear Panel Regression Models with Interactive Fixed Effects.” Econometric Theory 33: 158–95. https://doi.org/10.1017/s0266466615000328.Suche in Google Scholar
Newey, W. K., and D. McFadden. 1994. “Large Sample Estimation and Hypothesis Testing.” In Handbook of Econometrics, vol. vol. IV, edited by D. McFadden, and R. F. Engle, pp. 2111–245. North-Holland, Amsterdam: Elsevier.10.1016/S1573-4412(05)80005-4Suche in Google Scholar
Neyman, J., and E. L. Scott. 1948. “Consistent Estimates Based on Partially Consistent Observations.” Econometrica 16: 1–32. https://doi.org/10.2307/1914288.Suche in Google Scholar
Ng, S. 2008. “A Simple Test for Nonstationarity in Mixed Panels.” Journal of Business & Economic Statistics 26: 113–27. https://doi.org/10.1198/073500106000000675.Suche in Google Scholar
Nickell, S. 1981. “Biases in Dynamic Models with Fixed Effects.” Econometrica 49: 1417–26. https://doi.org/10.2307/1911408.Suche in Google Scholar
Pesaran, M. H., Y. Shin, and R. P. Smith. 1999. “Pooled Mean Group Estimation of Dynamic Heterogeneous Panels.” Journal of the American Statistical Association 94: 621–34. https://doi.org/10.1080/01621459.1999.10474156.Suche in Google Scholar
Phillips, P. C. B., and D. Sul. 2007. “Bias in Dynamic Panel Estimation with Fixed Effects Incidental Trends and Cross Section Dependence.” Journal of Econometrics 137: 162–88. https://doi.org/10.1016/j.jeconom.2006.03.009.Suche in Google Scholar
Rosenblatt, M. 1956. “A Central Limit Theorem and a Strong Mixing Condition.” Proceedings of the National Academy of Sciences of the United States of America 42: 43–7. https://doi.org/10.1073/pnas.42.1.43.Suche in Google Scholar PubMed PubMed Central
Sarafidis, V., and D. Robertson. 2009. “On the Impact of Error Cross-Sectional Dependence in Short Dynamic Panel Estimation.” The Econometrics Journal 12: 62–81. https://doi.org/10.1111/j.1368-423x.2008.00260.x.Suche in Google Scholar
Sartori, N. 2003. “Modified Profile Likelihoods in Models with Stratum Nuisance Parameters.” Biometrika 90: 533–49. https://doi.org/10.1093/biomet/90.3.533.Suche in Google Scholar
Song, M. 2013. “Asymptotic Theory for Dynamic Heterogeneous Panels with Cross-Sectional Dependence and its Applications.” In Working paper.Suche in Google Scholar
Westerlund, J. 2016. “A Simple Test for Nonstationarity in Mixed Panels: A Further Investigation.” Journal of Statistical Planning and Inference 173: 1–30. https://doi.org/10.1016/j.jspi.2016.01.004.Suche in Google Scholar
Westerlund, J., and J.-P. Urbain. 2013. “On the Estimation and Inference in Factor-Augmented Panel Regressions with Correlated Loadings.” Economics Letters 119: 247–50. https://doi.org/10.1016/j.econlet.2013.03.022.Suche in Google Scholar
Supplementary Material
The online version of this article offers supplementary material (https://doi.org/10.1515/snde-2019-0084).
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Research Articles
- What does Google say about credit developments in Brazil?
- Forecasting transaction counts with integer-valued GARCH models
- Asymmetries in the monetary policy reaction function: evidence from India
- A mixture autoregressive model based on Gaussian and Student’s t-distributions
- Time-specific average estimation of dynamic panel regressions
- Rescaled variance tests for seasonal stationarity
Artikel in diesem Heft
- Frontmatter
- Research Articles
- What does Google say about credit developments in Brazil?
- Forecasting transaction counts with integer-valued GARCH models
- Asymmetries in the monetary policy reaction function: evidence from India
- A mixture autoregressive model based on Gaussian and Student’s t-distributions
- Time-specific average estimation of dynamic panel regressions
- Rescaled variance tests for seasonal stationarity