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Bayesian Analysis of a Probit Panel Data Model with Unobserved Individual Heterogeneity and Autocorrelated Errors

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  • Martin Burda
  • Roman Liesenfeld
  • Jean-Francois Richard

Abstract

In this paper, we perform Bayesian analysis of a panel probit model with unobserved individual heterogeneity and serially correlated errors. We augment the data with latent variables and sample the unobserved heterogeneity component as one Gibbs block per individual using a flexible piecewise linear approximation to the marginal posterior density. The latent time effects are simulated as another Gibbs block. For this purpose we develop a new user-friendly form of the Efficient Importance Sampling proposal density for an Acceptance-Rejection Metropolis-Hastings step. We apply our method to the analysis of product innovation activity of a panel of German manufacturing firms in response to imports, foreign direct investment and other control variables. The dataset used here was analyzed under more restrictive assumptions by Bertschek and Lechner (1998) and Greene (2004). Although our results differ to a certain degree from these benchmark studies, we confirm the positive effect of imports and FDI on firms' innovation activity. Moreover, unobserved firm heterogeneity is shown to play a far more significant role in the application than the latent time effects.

Suggested Citation

  • Martin Burda & Roman Liesenfeld & Jean-Francois Richard, 2008. "Bayesian Analysis of a Probit Panel Data Model with Unobserved Individual Heterogeneity and Autocorrelated Errors," Working Papers tecipa-321, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:tecipa-321
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    References listed on IDEAS

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    1. Axel Borsch-Supan & Vassilis Hajivassiliou & Laurence J. Kotlikoff, 1992. "Health, Children, and Elderly Living Arrangements: A Multiperiod-Multinomial Probit Model with Unobserved Heterogeneity and Autocorrelated Errors," NBER Chapters, in: Topics in the Economics of Aging, pages 79-108, National Bureau of Economic Research, Inc.
    2. Roman Liesenfeld & Jean-Francois Richard, 2006. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 335-360.
    3. Inkmann, Joachim, 2000. "Misspecified heteroskedasticity in the panel probit model: A small sample comparison of GMM and SML estimators," Journal of Econometrics, Elsevier, vol. 97(2), pages 227-259, August.
    4. Bertschek, Irene, 1995. "Product and Process Innovation as a Response to Increasing Import and Foreign Direct Investment," Journal of Industrial Economics, Wiley Blackwell, vol. 43(4), pages 341-357, December.
    5. William Greene, 2004. "Convenient estimators for the panel probit model: Further results," Empirical Economics, Springer, vol. 29(1), pages 21-47, January.
    6. Dean R. Hyslop, 1999. "State Dependence, Serial Correlation and Heterogeneity in Intertemporal Labor Force Participation of Married Women," Econometrica, Econometric Society, vol. 67(6), pages 1255-1294, November.
    7. Jean-Francois Richard, 2007. "Efficient High-Dimensional Importance Sampling," Working Paper 321, Department of Economics, University of Pittsburgh, revised Jan 2007.
    8. Richard Paap, 2002. "What are the advantages of MCMC based inference in latent variable models?," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(1), pages 2-22, February.
    9. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, October.
    10. Butler, J S & Moffitt, Robert, 1982. "A Computationally Efficient Quadrature Procedure for the One-Factor Multinomial Probit Model," Econometrica, Econometric Society, vol. 50(3), pages 761-764, May.
    11. Elisabetta Falcetti & Merxe Tudela, 2006. "Modelling Currency Crises in Emerging Markets: A Dynamic Probit Model with Unobserved Heterogeneity and Autocorrelated Errors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(4), pages 445-471, August.
    12. Bertschek, Irene & Lechner, Michael, 1998. "Convenient estimators for the panel probit model," Journal of Econometrics, Elsevier, vol. 87(2), pages 329-371, September.
    13. Richard, Jean-Francois & Zhang, Wei, 2007. "Efficient high-dimensional importance sampling," Journal of Econometrics, Elsevier, vol. 141(2), pages 1385-1411, December.
    14. Philip Hans Franses, 2006. "On modeling panels of time series," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 60(4), pages 438-456, November.
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    Cited by:

    1. Bekierman Jeremias & Gribisch Bastian, 2016. "Estimating stochastic volatility models using realized measures," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(3), pages 279-300, June.

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    More about this item

    Keywords

    Dynamic latent variables; Markov Chain Monte Carlo; importance sampling;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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