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Composite Quasi-Maximum Likelihood Estimation of Dynamic Panels with Group-Specific Heterogeneity and Spatially Dependent Errors


  • Chu, Ba


This paper proposes a new method to estimate dynamic panel data models with spatially dependent errors that allows for known/unknown group-specific patterns of slope heterogeneity. Analysis of this model is conducted in the framework of composite quasi-likelihood (CL) maximization. The proposed CL estimator is robust against some misspecification of the unobserved individual/group-specific fixed effects. Since our CL method is based on the idea of doing regressions involving common-group stochastic trends, no endogeneity problem will arise. Therefore, unlike existing methods the proposed estimator does not require the use of intrumental variables nor bias correction/reduction. Clustering and estimation of the parameters of interest involve a large-scale non-convex mixed-integer programming problem, which can then be solved via a new efficient approach developed based on DC (Difference-of-Convex functions) programming and the DCA (DC algorithm). Suppose that the number of time periods and the size of spatial domain grow simultaneously, asymptotic theory is derived for both cases where the covariates are stationary and nonstationary. An extensive Monte Carlo simulation is also provided to examine the finite-sample performance of the proposed estimator. Our method is then applied to study the long-run relationship between saving and investment rates. The empirical findings reconcile various empirical approaches to capital mobility in the literature; and there exists substantial capital mobility in some countries while no conclusion about capital mobility can be drawn in other countries. Applied economists can easily implement the method by using the companion software to this paper.

Suggested Citation

  • Chu, Ba, 2017. "Composite Quasi-Maximum Likelihood Estimation of Dynamic Panels with Group-Specific Heterogeneity and Spatially Dependent Errors," MPRA Paper 79709, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:79709

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    References listed on IDEAS

    1. St├ęphane Bonhomme & Elena Manresa, 2015. "Grouped Patterns of Heterogeneity in Panel Data," Econometrica, Econometric Society, vol. 83(3), pages 1147-1184, May.
    2. Bester, C. Alan & Hansen, Christian B., 2016. "Grouped effects estimators in fixed effects models," Journal of Econometrics, Elsevier, vol. 190(1), pages 197-208.
    3. Thibaut Lamadon & Elena Manresa & Stephane Bonhomme, 2016. "Discretizing Unobserved Heterogeneity," 2016 Meeting Papers 1536, Society for Economic Dynamics.
    4. Tomohiro Ando & Jushan Bai, 2016. "Panel Data Models with Grouped Factor Structure Under Unknown Group Membership," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(1), pages 163-191, January.
    5. Arellano, M, 1987. "Computing Robust Standard Errors for Within-Groups Estimators," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 49(4), pages 431-434, November.
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    Cited by:

    1. Ryo Okui & Wendun Wang, 2018. "Heterogeneous structural breaks in panel data models," Papers 1801.04672,

    More about this item


    Large dynamic panels; spatial data; group-specific heterogeneity; clustering; asymptotics; large-scale non-convex mixed-integer program; difference of convex (d.c.) functions; DCA; Variable Neighborhood Search (VNS);

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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