Model-based clustering of non-Gaussian panel data
Juárez, Miguel A. and Steel, Mark F. J. (2006) Model-based clustering of non-Gaussian panel data. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers).
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In this paper we propose a model-based method to cluster units within a panel. The underlying model is autoregressive and non-Gaussian, allowing for both skewness and fat tails, and the units are clustered according to their dynamic behaviour and equilibrium level. Inference is addressed from a Bayesian perspective and model comparison is conducted using the formal tool of Bayes factors. Particular attention is paid to prior elicitation and posterior propriety. We suggest priors that require little subjective input from the user and possess hierarchical structures that enhance the robustness of the inference. Two examples illustrate the methodology: one analyses economic growth of OECD countries and the second one investigates employment growth of Spanish manufacturing firms.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics
Faculty of Science > Centre for Systems Biology
|Library of Congress Subject Headings (LCSH):||Cluster analysis, Autoregression (Statistics), Panel analysis|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||26|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|References:||Alonso-Borrego, C. and Arellano, M. (1999). Symmetrically normalised intrumental variable estimation using panel data, Journal of Business & Economic Statistics, 17, 36–49. Arellano, M. (2003). Panel Data Econometrics, Oxford: University Press. Baltagi, B. (2001). Econometric Analysis of Panel Data, Chichester: Wiley, second ed. Banfield, J. D. and Raftery, A. E. (1993). Model-based Gaussian and non-Gaussian clustering, Biometrics, 49, 803–821. Bauwens, L. and Rombouts, J.V.K. (2006). Bayesian clustering of many GARCH models, Econometric Reviews, forthcoming. Bensmail, H., Celeux, G., Raftery, A. E. and Robert, C. P. (1997). Inference in model-based cluster analysis, Statistics and Computing, 7, 1–10. Berger, J.O. and Bernardo, J.M. (1992). Ordered group reference priors with application to the multinomial problem, Biometrika, 79, 25–37. Canova, F. (2004). Testing for convergence clubs in income per capita: A predictive density approac, International Economic Review, 45, 49–77. Casella, G., Mengersen, K. L., Robert, C. P. and Titterington, D. M. (2002). Perfect samplers for mixtures of distributions, J. Roy. Statist. Soc. B, 64, 777–790. Casella, G., Robert, C. P. and Wells, M. T. (2004). Mixture models, latent variables and partitioned important sampling, Statistical Methodology, 1, 1–18. Celeux, G., Hurn, M. and Robert, C. P. (2000). Computational and inferential difficulties with mixture posterior distributions, J. Amer. Statist. Assoc., 95, 957–970. Chen, M. H., Shao, Q. M. and Igrahim, J. G. (2000). Monte Carlo Methods in Bayesian Computation, New York: Springer. Chib, S. (1995). Marginal likelihood from the Gibbs output, J. Amer. Statist. Assoc., 90, 1313–1321. DiCiccio, J., Kass, R. E., Raftery, A. E. and Wasserman, L. (1997). Computing Bayes factors by combining simulations and asymptotic approximations, J. Amer. Statist. Assoc., 92, 903–915. Diebolt, J. and Robert, C. P. (1994). Estimation of finite mixture distributions through Bayesian sampling, J. Roy. Statist. Soc. B, 56, 363–375. Diggle, P. J., Heagerty, P., Liand, K. Y. and Zeger, S. L. (2002). Analysis of longitudinal data, Oxford: University Press, second ed. 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. Fernández, C. and Steel, M. F. J. (1998). On Bayesian modeling of fat tails and skewness, J. Amer. Statist. Assoc., 93, 359–371. Fernández, C. and Steel, M. F. J. (2000). Bayesian regression analysis with scale mixtures of normals, Econometric Theory, 16, 80–101. Fraley, C. and Raftery, A. E. (2002). Model-based clustering, discriminant analysis, and density estimation, J. Amer. Statist. Assoc., 97, 611–631. Frühwirth-Schnatter, S. (2004). Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques, Econometrics Journal, 7, 143–167. Frühwirth-Schnatter, S. and Kaufmann, S. (2004). Model-based clustering of multiple time series, mimeo, Johannes Kepler Universität Linz. Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models, Bayesian Analysis, 1, 1–19. Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika, 82, 711–732. 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). Hirano, K. (2002). Semiparametric Bayesian inference in autoregressive panel data models, Econometrica, 70, 781–799. Hoogstrate, A. J., Palm, F. C. and Pfann, G. A. (2000). Pooling in dynamic panel-data models: An application to forecasting GDP growth rates., Journal of Business & Economic Statistics, 18, 274– 283. Hsiao, C. (2003). Analysis of Panel Data, 2nd ed., Cambridge: Cambridge Univ. Press. Ishwaran, H., James, L. F. and Sun, J. (2001). Bayesian model selection in finite mixtures by marginal density decompositions, J. Amer. Statist. Assoc., 96, 1316–1322. Jasra, A., Holmes, C. C. and Stephens, D. A. (2005). Markov chain Monte Carlo methods and the label switching problem in Bayesian mixture modelling, Statistical Science, 20, 50–67. Juárez, M. A. and Steel, M. F. J. (2006). Non-Gaussian dynamic Bayesian modelling for panel data, Working Paper 06-05, CRiSM, University of Warwick. Liu, M. C. and Tiao, G. C. (1980). Random coefficient first-order autoregressive models, Journal of Econometrics, 13, 305–325. Marin, J. M., Mengersen, K. and Robert, C. P. (2005). Bayesian modelling and inference on mixtures of distributions, Handbook of Statistics, vol. 25 (D. Dey and C. R. Rao, eds.), Amsterdam: North- Holland, pp. 459–207. McLachlan, G. J. and Peel, D. (2000). Finite Mixture Models, New York: Wiley. Meng, X. and Wong, W. H. (1996). Simulating ratios of normalising constants via a simple identity: A theoretical exploration, Statistica Sinica, 6, 831–860. 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. Nerlove, M. (2002). Essays in Panel Data Econometrics, Cambridge: University Press. Newton, M. A. and Raftery, A. E. (1994). Approximate Bayesian inference with the weighted likelihood bootstrap, J. Roy. Statist. Soc. B, 56, 3–48. Phillips, D. B. and Smith, A. F. M. (1996). Bayesian model comparison via jump diffusions, Markov chain Monte Carlo in practice (W. R. Gilks, S. Richardson and S. J. Spiegelhalter, eds.), Boca Raton: Chapman & Hall, pp. 215–240. Quah, D. T. (1997). Empirics for growth distribution: stratification, polarization and convergence clubs, Journal of Economic Growth, 2, 27–59. Raftery, A. E. (1996). Hypothesis testing and model selection, Markov chain Monte Carlo in practice (W. R. Gilks, S. Richardson and S. J. Spiegelhalter, eds.), Boca Raton: Chapman & Hall, pp. 163–188. Richardson, S. and Green, P. J. (1997). On Bayesian analysis of mixtures with an unknown number of components, J. Roy. Statist. Soc. B, 59, 731–792. (with discussion). Steele, R. S., Raftery, A. E. and Emond, M. J. (2003). Computing normalizing constants for finite mixture models via incremental mixture important sampling, Tech. Report 436, Department of Statistics, University of Washington. Stephens, M. (2000a). Bayesian analysis of mixtures with an unknown number of components – An alternative to reversible jump methods, Annals of Statistics, 28, 40–74. Stephens, M. (2000b). Dealing with label switching in mixture models, J. Roy. Statist. Soc. B, 62, 795–809. Temple, J. (1999). The new growth evidence, Journal of Economic Literature, 37, 112–156. Titterington, D. M., Smith, A. F. M. and Makov, U. E. (1985). Statistical analysis of finite mixture distributions, Chichester: Wiley. 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. Weiss, R. E. (2005). Modeling longitudinal data, New York: Springer.|
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