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Density Forecasts in Panel Data Models: A Semiparametric Bayesian Perspective

Author

Listed:
  • Laura Liu

    (Indiana University, Bloomington, Indiana)

Abstract
This paper constructs individual-specific density forecasts for a panel of ?rms or households using a dynamic linear model with common and heterogeneous coefficients and cross-sectional heteroskedasticity. The panel considered in this paper features a large cross-sectional dimension N but short time series T. Due to the short T, traditional methods have difficulty in disentangling the heterogeneous parameters from the shocks, which contaminates the estimates of the heterogeneous parameters. To tackle this problem, I assume that there is an underlying distribution of heterogeneous parameters, model this distribution nonparametrically allowing for correlation between heterogeneous parameters and initial conditions as well as individual-speci?c regressors, and then estimate this distribution by pooling the information from the whole cross-section together. Theoretically, I prove that both the estimated common parameters and the estimated distribution of the heterogeneous parameters achieve posterior consistency, and that the density forecasts asymptotically converge to the oracle forecast. Methodologically, I develop a simulation-based posterior sampling algorithm specifically addressing the nonparametric density estimation of unobserved heterogeneous parameters. Monte Carlo simulations and an empirical application to young ?rm dynamics demonstrate improvements in density forecasts relative to alternative approaches.

Suggested Citation

  • Laura Liu, 2020. "Density Forecasts in Panel Data Models: A Semiparametric Bayesian Perspective," CAEPR Working Papers 2020-003, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    • Handle: RePEc:inu:caeprp:2020003
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    References listed on IDEAS

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    1. Omiros Papaspiliopoulos & Gareth O. Roberts, 2008. "Retrospective Markov chain Monte Carlo methods for Dirichlet process hierarchical models," Biometrika, Biometrika Trust, vol. 95(1), pages 169-186.
    2. repec:mpr:mprres:6385 is not listed on IDEAS
    3. Canova, Fabio & Ciccarelli, Matteo, 2013. "Panel Vector Autoregressive Models: A Survey," CEPR Discussion Papers 9380, C.E.P.R. Discussion Papers.
    4. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2006. "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 499-526.
    5. Geweke, John & Amisano, Gianni, 2010. "Comparing and evaluating Bayesian predictive distributions of asset returns," International Journal of Forecasting, Elsevier, vol. 26(2), pages 216-230, April.
    6. Arellano, Manuel & Honore, Bo, 2001. "Panel data models: some recent developments," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 53, pages 3229-3296, Elsevier.
    7. Keisuke Hirano, 2002. "Semiparametric Bayesian Inference in Autoregressive Panel Data Models," Econometrica, Econometric Society, vol. 70(2), pages 781-799, March.
    8. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
    9. Gianni Amisano & John Geweke, 2017. "Prediction Using Several Macroeconomic Models," The Review of Economics and Statistics, MIT Press, vol. 99(5), pages 912-925, December.
    10. Ufuk Akcigit & William R. Kerr, 2018. "Growth through Heterogeneous Innovations," Journal of Political Economy, University of Chicago Press, vol. 126(4), pages 1374-1443.
    11. Evdokimov, Kirill & White, Halbert, 2012. "Some Extensions Of A Lemma Of Kotlarski," Econometric Theory, Cambridge University Press, vol. 28(4), pages 925-932, August.
    12. Manuel Arellano & Stéphane Bonhomme, 2012. "Identifying Distributional Characteristics in Random Coefficients Panel Data Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(3), pages 987-1020.
    13. David B. Dunson, 2009. "Nonparametric Bayes local partition models for random effects," Biometrika, Biometrika Trust, vol. 96(2), pages 249-262.
    14. Youngki Lee & Luis A. N. Amaral & David Canning & Martin Meyer & H. Eugene Stanley, 1998. "Universal features in the growth dynamics of complex organizations," Papers cond-mat/9804100, arXiv.org.
    15. Enrico Santarelli (ed.), 2006. "Entrepreneurship, Growth, and Innovation," International Studies in Entrepreneurship, Springer, number 978-0-387-32314-5, November.
    16. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
    17. Pati, Debdeep & Dunson, David B. & Tokdar, Surya T., 2013. "Posterior consistency in conditional distribution estimation," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 456-472.
    18. Ishwaran H. & James L. F, 2001. "Gibbs Sampling Methods for Stick Breaking Priors," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 161-173, March.
    19. Pelenis, Justinas, 2014. "Bayesian regression with heteroscedastic error density and parametric mean function," Journal of Econometrics, Elsevier, vol. 178(P3), pages 624-638.
    20. Liverani, Silvia & Hastie, David I. & Azizi, Lamiae & Papathomas, Michail & Richardson, Sylvia, 2015. "PReMiuM: An R Package for Profile Regression Mixture Models Using Dirichlet Processes," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 64(i07).
    21. Arellano, Manuel & Bover, Olympia, 1995. "Another look at the instrumental variable estimation of error-components models," Journal of Econometrics, Elsevier, vol. 68(1), pages 29-51, July.
    22. David B. Dunson & Ju-Hyun Park, 2008. "Kernel stick-breaking processes," Biometrika, Biometrika Trust, vol. 95(2), pages 307-323.
    23. Giovanni Compiani & Yuichi Kitamura, 2016. "Using mixtures in econometric models: a brief review and some new results," Econometrics Journal, Royal Economic Society, vol. 19(3), pages 95-127, October.
    24. Laura Liu & Hyungsik Roger Moon & Frank Schorfheide, 2020. "Forecasting With Dynamic Panel Data Models," Econometrica, Econometric Society, vol. 88(1), pages 171-201, January.
    25. Jiaying Gu & Roger Koenker, 2017. "Empirical Bayesball Remixed: Empirical Bayes Methods for Longitudinal Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(3), pages 575-599, April.
    26. Norets, Andriy & Pati, Debdeep, 2017. "Adaptive Bayesian Estimation Of Conditional Densities," Econometric Theory, Cambridge University Press, vol. 33(4), pages 980-1012, August.
    27. Basu S. & Chib S., 2003. "Marginal Likelihood and Bayes Factors for Dirichlet Process Mixture Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 224-235, January.
    28. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    29. Martin Burda & Matthew Harding, 2013. "Panel Probit With Flexible Correlated Effects: Quantifying Technology Spillovers In The Presence Of Latent Heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(6), pages 956-981, September.
    30. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    31. Tony Lancaster, 2002. "Orthogonal Parameters and Panel Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 647-666.
    32. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    33. C. Yau & O. Papaspiliopoulos & G. O. Roberts & C. Holmes, 2011. "Bayesian non‐parametric hidden Markov models with applications in genomics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 37-57, January.
    34. Peter E. Rossi, 2014. "Bayesian Non- and Semi-parametric Methods and Applications," Economics Books, Princeton University Press, edition 1, number 10259.
    35. 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.
    36. Gary Chamberlain & Keisuke Hirano, 1999. "Predictive Distributions based on Longitudinal Earnings Data," Annals of Economics and Statistics, GENES, issue 55-56, pages 211-242.
    37. John Haltiwanger & Ron S. Jarmin & Javier Miranda, 2013. "Who Creates Jobs? Small versus Large versus Young," The Review of Economics and Statistics, MIT Press, vol. 95(2), pages 347-361, May.
    38. Norets, Andriy & Pelenis, Justinas, 2012. "Bayesian modeling of joint and conditional distributions," Journal of Econometrics, Elsevier, vol. 168(2), pages 332-346.
    39. repec:adr:anecst:y:1999:i:55-56:p:08 is not listed on IDEAS
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    Cited by:

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    2. Federico Bassetti & Roberto Casarin & Marco Del Negro, 2022. "A Bayesian Approach to Inference on Probabilistic Surveys," Staff Reports 1025, Federal Reserve Bank of New York.
    3. Liu, Laura & Moon, Hyungsik Roger & Schorfheide, Frank, 2021. "Panel forecasts of country-level Covid-19 infections," Journal of Econometrics, Elsevier, vol. 220(1), pages 2-22.
    4. Boyuan Zhang, 2020. "Forecasting with Bayesian Grouped Random Effects in Panel Data," Papers 2007.02435, arXiv.org, revised Oct 2020.
    5. Laura Liu & Alexandre Poirier & Ji-Liang Shiu, 2021. "Identification and Estimation of Partial Effects in Nonlinear Semiparametric Panel Models," Papers 2105.12891, arXiv.org, revised Jul 2024.

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    More about this item

    Keywords

    Bayesian; Semiparametric Methods; Panel Data; Density Forecasts; Posterior Consistency; Young Firm Dynamics;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • L25 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Performance

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