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A Unified Method for Dynamic and Cross-Sectional Heterogeneity: Introducing Hidden Markov Panel Models


  • Jong Hee Park is Assistant Professor, Department of Political Science, University of Chicago, 5828 S. University Ave., Chicago, IL 60637 (

  • An earlier version of this article appeared under the title “Joint Modeling of Dynamic and Cross-Sectional Heterogeneity” and was awarded the 2010 Harold Gosnell Prize for Excellence in Political Methodology. An earlier version of this article was presented at the 2009 Political Methodology Meeting, Yale University and at the 2010 Political Methodology Colloquium, Princeton University. The author is grateful to John Balz, Patrick Brandt, John Brehm, Christina Davis, John Freeman, Jude C. Hayes, Kosuke Imai, Nathan M. Jensen, John Londreagan, Andrew D. Martin, Michael Peress, Kenneth Scheve, Sebastian Smith, and Gregory J. Wawro for helpful comments. Also, the author appreciates anonymous reviewers and AJPS editor Rick Wilson for excellent advice. The author would like to thank the Division of the Social Sciences at University of Chicago for generous research support. The usual disclaimer applies. R functions for all the proposed methods in this article are provided within MCMCpack v.1.2-1 (Martin, Quinn, and Park, 2011), which was released on November 14, 2011. Supplementary material including web appendices and replication codes can be found at the author’s website ( This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2010-330-B00036).


Conventional statistical methods for panel data are based on the assumption that unobserved heterogeneity is time constant. Despite the central importance of this assumption for panel data methods, few studies have developed statistical methods for testing this assumption and modeling time-varying unobserved heterogeneity. In this article, I introduce a formal test to check the assumption of time-constant unobserved heterogeneity using Bayesian model comparison. Then, I present two panel data methods that account for time-varying unobserved heterogeneity in the context of the random-effects model and the fixed-effects model, respectively. I illustrate the utility of the introduced methods using both simulated data and examples drawn from two important debates in the political economy literature: (1) the identification of shifting relationships between income inequality and economic development in capitalist countries and (2) the effects of the GATT/WTO on bilateral trade volumes.