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Identification and Estimation in a Time-Varying Endogenous Random Coefficient Panel Data Model

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  • Ming Li

Abstract

This paper proposes a correlated random coefficient linear panel data model, where regressors can be correlated with time-varying and individual-specific random coefficients through both a fixed effect and a time-varying random shock. I develop a new panel data-based identification method to identify the average partial effect and the local average response function. The identification strategy employs a sufficient statistic to control for the fixed effect and a conditional control variable for the random shock. Conditional on these two controls, the residual variation in the regressors is driven solely by the exogenous instrumental variables, and thus can be exploited to identify the parameters of interest. The constructive identification analysis leads to three-step series estimators, for which I establish rates of convergence and asymptotic normality. To illustrate the method, I estimate a heterogeneous Cobb-Douglas production function for manufacturing firms in China, finding substantial variations in output elasticities across firms.

Suggested Citation

  • Ming Li, 2021. "Identification and Estimation in a Time-Varying Endogenous Random Coefficient Panel Data Model," Papers 2110.00982, arXiv.org, revised Nov 2024.
  • Handle: RePEc:arx:papers:2110.00982
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    Cited by:

    1. Michele Battisti & Valentino Dardanoni & Stefano Demichelis, 2024. "Inter-firm Heterogeneity in Production," Papers 2411.15980, arXiv.org.
    2. Laage, Louise, 2024. "A Correlated Random Coefficient panel model with time-varying endogeneity," Journal of Econometrics, Elsevier, vol. 242(2).

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