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Identification and Estimation of Nonlinear Dynamic Panel Data Models with Unobserved Covariates

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  • Ji-Liang Shiu
  • Yingyao Hu

Abstract

This paper considers nonparametric identification of nonlinear dynamic models for panel data with unobserved voariates. Including such unobserved covariates may control for both the individual-specific unobserved heterogeneity and the endogeneity of the explanatory variables. Without specifying the distribution of the initial condition with the unobserved variables, we show that the models are nonparametrically identified from three periods of data. The main identifying assumption requires the evolution of the observed covariates depends on the unobserved covariates but not on the lagged dependent variable. We also propose a sieve maximum likelihood estimator (MLE) and focus on two classes of nonlinear dynamic panel data models, i.e., dynamic discrete choice models and dynamic censored models. We present the asymptotic property of the sieve MLE and investigate the finite sample properties of these sieve-based estimator through a Monte Carlo study. An intertemporal female labor force participation model is estimated as an empirical illustration using a sample from the Panel Study of Income Dynamics (PSID).

Suggested Citation

  • Ji-Liang Shiu & Yingyao Hu, 2010. "Identification and Estimation of Nonlinear Dynamic Panel Data Models with Unobserved Covariates," Economics Working Paper Archive 557, The Johns Hopkins University,Department of Economics.
    • Handle: RePEc:jhu:papers:557
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    3. Hu, Yingyao & Shum, Matthew, 2012. "Nonparametric identification of dynamic models with unobserved state variables," Journal of Econometrics, Elsevier, vol. 171(1), pages 32-44.
    4. Williams, Benjamin, 2020. "Nonparametric identification of discrete choice models with lagged dependent variables," Journal of Econometrics, Elsevier, vol. 215(1), pages 286-304.
    5. Hu, Yingyao, 2017. "The econometrics of unobservables: Applications of measurement error models in empirical industrial organization and labor economics," Journal of Econometrics, Elsevier, vol. 200(2), pages 154-168.
    6. Yingyao Hu & Ji‐Liang Shiu, 2018. "Identification and estimation of semi‐parametric censored dynamic panel data models of short time periods," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 55-85, February.
    7. Gagliardini, Patrick & Gouriéroux, Christian, 2019. "Identification by Laplace transforms in nonlinear time series and panel models with unobserved stochastic dynamic effects," Journal of Econometrics, Elsevier, vol. 208(2), pages 613-637.
    8. Shiu, Ji-Liang, 2014. "An alternative identification of nonlinear dynamic panel data models with unobserved covariates," Economics Letters, Elsevier, vol. 122(2), pages 338-342.
    9. Yingyao Hu, 2015. "Microeconomic models with latent variables: applications of measurement error models in empirical industrial organization and labor economics," CeMMAP working papers 03/15, Institute for Fiscal Studies.
    10. Hu, Yingyao & Schennach, Susanne M. & Shiu, Ji-Liang, 2017. "Injectivity of a class of integral operators with compactly supported kernels," Journal of Econometrics, Elsevier, vol. 200(1), pages 48-58.
    11. Hu, Yingyao & Shiu, Ji-Liang, 2018. "Nonparametric Identification Using Instrumental Variables: Sufficient Conditions For Completeness," Econometric Theory, Cambridge University Press, vol. 34(3), pages 659-693, June.
    12. Hu, Yingyao, 2017. "The Econometrics of Unobservables -- Latent Variable and Measurement Error Models and Their Applications in Empirical Industrial Organization and Labor Economics [The Econometrics of Unobservables]," Economics Working Paper Archive 64578, The Johns Hopkins University,Department of Economics, revised 2021.
    13. Yingyao Hu, 2015. "Microeconomic models with latent variables: applications of measurement error models in empirical industrial organization and labor economics," CeMMAP working papers CWP03/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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