Bayesian model averaging for dynamic panels with an application to a trade gravity model

This paper extends the Bayesian Model Averaging framework to panel data models where the lagged dependent variable as well as endogenous variables appear as regressors. We propose a Limited Information Bayesian Model Averaging (LIBMA) methodology and then test it using simulated data. Simulation results suggest that asymptotically our methodology performs well both in Bayesian model averaging and selection. In particular, LIBMA recovers the data generating process well, with high posterior inclusion probabilities for all the relevant regressors, and parameter estimates very close to their true values. These findings suggest that our methodology is well suited for inference in short dynamic panel data models with endogenous regressors in the context of model uncertainty. We illustrate the use of LIBMA in an application to the estimation of a dynamic gravity model for bilateral trade.

[1]  Brent R. Moulton.  A Bayesian approach to regression selection and estimation, with application to a price index for radio services , 1991 .

[2]  Steven Yamarik,et al.  Are regional trading arrangements trade creating?: An application of extreme bounds analysis , 2004 .

[3]  Giuseppe Ragusa,et al.  Bayesian Likelihoods for Moment Condition Models , 2007 .

[4]  Adrian E. Raftery,et al.  Bayesian model averaging: development of an improved multi-class, gene selection and classification tool for microarray data , 2005, Bioinform..

[5]  Huigang Chen,et al.  Limited Information Bayesian Model Averaging for Dynamic Panels with Short Time Periods , 2009, SSRN Electronic Journal.

[6]  A. Raftery.  Bayesian Model Selection in Social Research , 1995 .

[7]  Charalambos G Tsangarides,et al.  A Bayesian Approach to Model Uncertainty , 2004, SSRN Electronic Journal.

[8]  V. Chernozhukov,et al.  An MCMC Approach to Classical Estimation , 2002, 2301.07782.

[9]  Adrian E. Raftery,et al.  Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors , 1999 .

[10]  J. Bergstrand.  The Gravity Equation in International Trade: Some Microeconomic Foundations and Empirical Evidence , 1985 .

[11]  Jae-Young Kim,et al.  Limited information likelihood and Bayesian analysis , 2002 .

[12]  K. Back,et al.  Implied Probabilities in GMM Estimators , 1993 .

[13]  A. Raftery,et al.  Default Priors and Predictive Performance in Bayesian Model Averaging, with Application to Growth Determinants , 2007 .

[14]  J. Richard,et al.  Specification Searches: Ad Hoc Inference with Nonexperimental Data , 1980 .

[15]  L. Wasserman,et al.  A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion , 1995 .

[16]  D. Madigan,et al.  Bayesian Model Averaging for Linear Regression Models , 1997 .

[17]  Susanne M. Schennach,et al.  Bayesian exponentially tilted empirical likelihood , 2005 .

[18]  Sune Karlsson,et al.  Finding Good Predictors for Inflation: A Bayesian Model Averaging Approach , 2004 .

[19]  J. Temple,et al.  The Geography of Output Volatility , 2006 .

[20]  R. Blundell,et al.  Initial Conditions and Moment Restrictions in Dynamic Panel Data Models , 1998 .

[21]  M. Arellano,et al.  Another look at the instrumental variable estimation of error-components models , 1995 .

[22]  M. Steel,et al.  Benchmark Priors for Bayesian Model Averaging , 2001 .

[23]  Donald W. K. Andrews,et al.  Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models , 2001 .

[24]  A. Rose,et al.  An Estimate of the Effect of Common Currencies on Trade and Income , 2001 .

[25]  Han Hong,et al.  Bayesian Averaging, Prediction and Nonnested Model Selection , 2008 .

[26]  D. Madigan,et al.  Model Selection and Accounting for Model Uncertainty in Graphical Models Using Occam's Window , 1994 .

[27]  Alastair R. Hall,et al.  Generalized Method of Moments , 2005 .

[28]  A. Rose,et al.  One money, one market : the effect of common currencies on trade , 2000 .

[29]  Edward E. Leamer,et al.  Let's Take the Con Out of Econometrics , 1983 .

[30]  James E. Anderson.  A Theoretical Foundation for the Gravity Equation , 1979 .

[31]  Charalambos G Tsangarides.  A Bayesian Approach to Model Uncertainty , 2004 .

[32]  W. Brock,et al.  Growth empirics and reality , 2001 .

[33]  A. Raftery.  Approximate Bayes factors and accounting for model uncertainty in generalised linear models , 1996 .

[34]  M. Arellano,et al.  Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations , 1991 .

[35]  T. J. Mitchell,et al.  Bayesian Variable Selection in Linear Regression , 1988 .

[36]  Danny Quah,et al.  The New Empirics of Economic Growth , 1998 .

[37]  A. Rose.  One Money, One Market: Estimating the Effect of Common Currencies on Trade , 1999 .

[38]  Joseph G. Ibrahim,et al.  Bayesian Model Averaging With Applications to Benchmark Dose Estimation for Arsenic in Drinking Water , 2006 .

[39]  Brendan A. Wintle,et al.  The Use of Bayesian Model Averaging to Better Represent Uncertainty in Ecological Models , 2003 .

[40]  Douglas L. Campbell.  History, culture, and trade: a dynamic gravity approach , 2010 .

[41]  Edward I. George,et al.  The Practical Implementation of Bayesian Model Selection , 2001 .

[42]  Enrique Moral-Benito.  Determinants of Economic Growth: A Bayesian Panel Data Approach , 2009 .

[43]  J. Temple.  Growth Regressions and What the Textbooks Don't Tell You , 1999 .

[44]  Steven N. Durlauf,et al.  Chapter 4 The new empirics of economic growth , 1999 .

[45]  Peter Schmidt,et al.  Efficient estimation of models for dynamic panel data , 1995 .

[46]  Gary Koop,et al.  Measuring the health effects of air pollution: to what extent can we really say that people are dying from bad air? , 2004 .

[47]  M. Steel,et al.  Model uncertainty in cross-country growth regressions , 2001 .

[48]  Charalambos G. Tsangarides,et al.  The Empirics of Exchange Rate Regimes and Trade: Words Vs. Deeds , 2010, SSRN Electronic Journal.

[49]  A. Cuñat,et al.  Can Comparative Advantage Explain the Growth of US Trade? , 2003 .

[50]  Mark F. J. Steel,et al.  On the effect of prior assumptions in Bayesian model averaging with applications to growth regression , 2009 .

[51]  X. Sala-i-Martin,et al.  Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (Bace) Approach , 2000 .

[52]  Silvana Tenreyro,et al.  The Log of Gravity , 2004, The Review of Economics and Statistics.