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Limit theory for panel data models with cross sectional dependence and sequential exogeneity

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  • Kuersteiner, Guido M.
  • Prucha, Ingmar R.

Abstract

The paper derives a general Central Limit Theorem (CLT) and asymptotic distributions for sample moments related to panel data models with large n. The results allow for the data to be cross sectionally dependent, while at the same time allowing the regressors to be only sequentially rather than strictly exogenous. The setup is sufficiently general to accommodate situations where cross sectional dependence stems from spatial interactions and/or from the presence of common factors. The latter leads to the need for random norming. The limit theorem for sample moments is derived by showing that the moment conditions can be recast such that a martingale difference array central limit theorem can be applied. We prove such a central limit theorem by first extending results for stable convergence in Hall and Heyde (1980) to non-nested martingale arrays relevant for our applications. We illustrate our result by establishing a generalized estimation theory for GMM estimators of a fixed effect panel model without imposing i.i.d. or strict exogeneity conditions. We also discuss a class of Maximum Likelihood (ML) estimators that can be analyzed using our CLT.

Suggested Citation

  • Kuersteiner, Guido M. & Prucha, Ingmar R., 2013. "Limit theory for panel data models with cross sectional dependence and sequential exogeneity," Journal of Econometrics, Elsevier, vol. 174(2), pages 107-126.
  • Handle: RePEc:eee:econom:v:174:y:2013:i:2:p:107-126
    DOI: 10.1016/j.jeconom.2013.02.004
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    References listed on IDEAS

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    Cited by:

    1. Andersen, Torben G. & Fusari, Nicola & Todorov, Viktor & Varneskov, Rasmus T., 2019. "Unified inference for nonlinear factor models from panels with fixed and large time span," Journal of Econometrics, Elsevier, vol. 212(1), pages 4-25.
    2. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2015. "Parametric Inference and Dynamic State Recovery From Option Panels," Econometrica, Econometric Society, vol. 83(3), pages 1081-1145, May.
    3. Guido M. Kuersteiner & Ingmar R. Prucha, 2015. "Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity," CESifo Working Paper Series 5445, CESifo.
    4. James Wolter, 2015. "Kernel Estimation Of Hazard Functions When Observations Have Dependent and Common Covariates," Economics Series Working Papers 761, University of Oxford, Department of Economics.
    5. Bin Peng & Giovanni Forchini, 2014. "Consistent Estimation of Panel Data Models with a Multifactor Error Structure when the Cross Section Dimension is Large," Working Paper Series 20, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
    6. Haupt, Harry & Schnurbus, Joachim & Semmler, Willi, 2018. "Estimation of grouped, time-varying convergence in economic growth," Econometrics and Statistics, Elsevier, vol. 8(C), pages 141-158.
    7. G. Forchini & Bin Jiang & Bin Peng, 2015. "Common Shocks in panels with Endogenous Regressors," Monash Econometrics and Business Statistics Working Papers 8/15, Monash University, Department of Econometrics and Business Statistics.
    8. Peter Egger & Andreas Lindenblatt, 2015. "Endogenous risk-taking and physical appearance of sex workers," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 16(9), pages 941-949, December.
    9. Denis Kojevnikov & Vadim Marmer & Kyungchul Song, 2019. "Limit Theorems for Network Dependent Random Variables," Papers 1903.01059, arXiv.org, revised May 2020.
    10. Giovanni Forchini & Bin Jiang & Bin Peng, 2018. "TSLS and LIML Estimators in Panels with Unobserved Shocks," Econometrics, MDPI, Open Access Journal, vol. 6(2), pages 1-12, April.
    11. Wolter, James Lewis, 2016. "Kernel estimation of hazard functions when observations have dependent and common covariates," Journal of Econometrics, Elsevier, vol. 193(1), pages 1-16.
    12. repec:gam:jecnmx:v:4:y:2016:i:1:p:4:d:62057 is not listed on IDEAS
    13. Artūras Juodis, 2018. "Pseudo Panel Data Models With Cohort Interactive Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 47-61, January.
    14. Ghysels, Eric, 2014. "Factor Analysis with Large Panels of Volatility Proxies," CEPR Discussion Papers 10034, C.E.P.R. Discussion Papers.
    15. Kalouptsidi, Myrto & Scott, Paul T. & Souza-Rodrigues, Eduardo, 2018. "Linear IV Regression Estimators for Structural Dynamic Discrete Choice Models," CEPR Discussion Papers 13240, C.E.P.R. Discussion Papers.
    16. Giovanni Forchini & Bin Peng, 2016. "A Conditional Approach to Panel Data Models with Common Shocks," Econometrics, MDPI, Open Access Journal, vol. 4(1), pages 1-12, January.
    17. Myrto Kalouptsidi & Paul T. Scott & Eduardo Souza-Rodrigues, 2018. "Linear IV Regression Estimators for Structural Dynamic Discrete Choice Models," NBER Working Papers 25134, National Bureau of Economic Research, Inc.
    18. Eduardo A. Souza-Rodrigues, 2016. "Nonparametric Regression with Common Shocks," Econometrics, MDPI, Open Access Journal, vol. 4(3), pages 1-17, September.
    19. Abdelkamel Alj & Rajae Azrak & Guy Melard, 2014. "On Conditions in Central Limit Theorems for Martingale Difference Arrays Long Version," Working Papers ECARES ECARES 2014-05, ULB -- Universite Libre de Bruxelles.

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