Non-Gaussian dynamic Bayesian modelling for panel data

Juarez, Miguel A. and Steel, Mark F. J. (2006): Non-Gaussian dynamic Bayesian modelling for panel data.

Abstract

A first order autoregressive non-Gaussian model for analysing panel data is proposed. The main feature is that the model is able to accommodate fat tails and also skewness, thus allowing for outliers and asymmetries. The modelling approach is to gain sufficient flexibility, without sacrificing interpretability and computational ease. The model incorporates individual effects and we pay specific attention to the elicitation of the prior. As the prior structure chosen is not proper, we derive conditions for the existence of the posterior. By considering a model with individual dynamic parameters we are also able to formally test whether the dynamic behaviour is common to all units in the panel. The methodology is illustrated with two applications involving earnings data and one on growth of countries.

• Item Type: MPRA Paper
• Language: English
• Keywords: autoregressive modelling; growth convergence; individual effects; labour earnings; prior elicitation; posterior existence; skewed distributions
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C23 - Panel Data Models ; Spatio-temporal Models

References

Arbia, G. and Piras, G. (2005). Convergence in per-capita GDP across European regions using panel data models extended to spatial autocorrelation effects, Working Paper 51, Istituto di Studi e Analisi Economica, Roma.

Arellano, M. (2003). Panel Data Econometrics, Oxford: Oxford University Press.

Arnold, B. C. and Beaver, R. J. (2002). Skewed multivariate models related to hidden truncation and/or selective reporting, Test, 11, 7–54.

Arnold, B. C. and Groeneveld, R. A. (1995). Measuring skewness with respect to the mode,The American Statistician, 49, 34–38.

Azzalini, A. (1985). A class of distributions which include the normal ones, Scandinavian Journal of Statistics, 12, 171–178.

Azzalini, A. and Capitanio, A. (2003). Distributions generated by perturbations of symmetry with emphasis on a multivariate skew t-distribution, Journal of the Royal Statistical Society, B, 65, 367–389.

Baltagi, B. (2001). Econometric Analysis of Panel Data, Chichester: Wiley, second ed.

Barro, R. J. and Sala-i-Martin, X. (2004). Economic Growth, Cambridge: MIT Press, second ed.

Bernard, A. B. and Durlauf, S. N. (1996). Interpreting tests of the convergence hypothesis, Journal of Econometrics, 71, 161–173.

Canova, F. (2004). Testing for convergence clubs in income per capita: A predictive density approach, International Economic Review, 45, 49–77.

Chib, S. and Greenberg, E. (1994). Bayes inference in regression models with ARMA(p,q) errors, Journal of Econometrics, 64, 183–206.

Durlauf, S.N. and Johnson, P.A. (1995). Multiple regimes and cross-country growth behaviour, Journal of Applied Econometrics, 10, 365–384.

Durlauf, S.N. and Quah, D.T. (1999). The new empirics of economic growth, Handbook of Macroeconomics Vol.1 (J.B. Taylor and M. Woodford, eds.), Amsterdam: Elsevier, pp. 235–308.

Evans, P. (1998). Using panel data to evaluate growth theories, International Economic Review, 39, 295–306.

Evans, P. and Karras, G. (1996). Do economies converge? Evidence from a panel of US states, The review of Economics and Statistics, 78, 348–388.

Fernández, C., Osiewalski, J. and Steel, M. F. J. (1997). On the use of panel data in stochastic frontier models with improper priors, Journal of Econometrics, 79, 169–193.

Fernández, C. and Steel, M. F. J. (1998). On Bayesian modeling of fat tails and skewness, Journal of the American Statistical Association, 93, 359–371.

Fernández, C. and Steel, M. F. J. (2000). Bayesian regression analysis with scale mixtures of normals, Econometric Theory, 16, 80–101.

Frühwirth-Schnatter, S. and Kaufmann, S. (2004). Model-based clustering of multiple time series, mimeo, Johannes Kepler Universität Linz.

Gaulier, G., Hurlin, C. and Jean-Pierre, P. (1999). Testing convergence: A panel data approach, Annales D’économie et de Statistique, 55-56, 411–427.

Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models, Bayesian Analysis, 1, 515–534.

Genton, M. G. (2004). Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality, Boca Raton: Chapman & Hall.

Hansen, B.E. (1999). Threshold effects in non-dynamic panels: estimation, testing and inference, Journal of Econometrics, 93, 334–368.

Heston, A., Summers, R. and Aten, B. (2002). Penn world table version 6.1, http://pwt.econ.upenn.edu/php_site/pwt_index.php . Center for International Comparisons at the University of Pennsylvania (CICUP).

Hill, B. M. (1965). Inference about variance components in the one-way model, Journal of the American Statistical Association, 60, 806–825.

Hirano, K. (2002). Semiparametric Bayesian inference in autoregressive panel data models, Econometrica, 70, 781–799.

Ho, T. (2006). Income thresholds and growth convergence: A panel data approach, The Manchester School, 74, 170–189.

Hsiao, C. and Pesaran, M. H. (2004). Random coefficient panel data models, IEPR Working Paper 04.2, University of Southern California.

Islam, N. (1995). Growth empirics: a panel data approach, Quarterly Journal of Economics, 110, 1128–1170.

Jones, M. C. and Faddy, M. J. (2003). A skew extension of the t-distribution, with applications, Journal of the Royal Statistical Society, B, 65, 159–174.

Lee, M., Longmire, R., Mátyás, L. and Harris, M. (1998). Growth convergence: some panel data evidence, Applied Economics, 30, 907–912.

Liu, M. C. and Tiao, G. C. (1980). Random coefficient first-order autoregressive models, Journal of Econometrics, 13, 305–325.

Mátyás, L. and Sevestre, P. (1995). The Econometrics of Panel Data. A handbook of the theory with applications, The Netherlands: Kluwer, second ed.

Nandram, B. and Petruccelli, J. D. (1997). A Bayesian analysis of autoregressive time series panel data, Journal of Business and Economic Statistics, 15, 328–334.

Newton, M. A. and Raftery, A. E. (1994). Approximate Bayesian inference with the weighted likelihood bootstrap, Journal of the Royal Statistical Society, B, 56, 3–48.

Pesaran, M. H. (2006). A pair-wise approach to testing for output and growth convergence, Journal of Econometrics, forthcoming.

Pesaran, M. H., Smith, R. and Im, K. S. (1995). Dynamic linear models for heterogenous panels, The Econometrics of Panel Data (L. Mátyás and P. Sevestre, eds.), The Netherlands: Kluwer, pp. 145–195.

Quah, D. T. (1997). Empirics for growth and distribution: Stratification, polarization and convergence clubs, Journal of Economic Growth, 2, 27–59.

Sáfadi, T. and Morettin, P. A. (2003). A Bayesian analysis of autoregressive models with random Normal coefficients, Journal of Statistical Computation and Simulation, 8, 563–573.

Spiegelhalter, D. J., Abrams, K. R. and Myles, J. P. (2004). Bayesian approaches to clinical trials and health-care evaluation, Chichester: Wiley.

Sun, D., Tsutakawa, R. K. and He, Z. (2001). Property of posteriors with improper priors in hierarchical linear mixed models, Statistica Sinica, 11, 77–95.

Temple, J. (1999). The new growth evidence, Journal of Economic Literature, 37, 112–156.

Verdinelli, I. and Wasserman, L. (1995). Computing Bayes factors using a generalization of the Savage-Dickey density ratio, Journal of the American Statistical Association, 90, 614–618.

Wang, D. and Ghosh, S. K. (2002). Bayesian analysis of random coefficient autoregressive models, Joint Statistical meeting proceedings.

Zellner, A. (1971). An introduction to Bayesian inference in Econometrics, New York: Wiley.