Limited Information 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.

Bayesian Model Averaging (BMA) provides a coherent mechanism to address the problem of model uncertainty. In this paper we extend the BMA 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 selection and averaging. In particular, LIBMA recovers the data generating process very well, with high posterior inclusion probabilities for all the relevant regressors, and parameter estimates very close to the true values. These findings suggest that our methodology is well suited for inference in dynamic panel data models with short time periods in the presence of endogenous regressors under model uncertainty.

This paper develops the theoretical background for the Limited Information Bayesian Model Averaging (LIBMA). The proposed approach accounts for model uncertainty by averaging over all possible combinations of predictors when making inferences about the variables of interest, and it simultaneously addresses the biases associated with endogenous and omitted variables by incorporating a panel data systems Generalized Method of Moments estimator. Practical applications of the developed methodology are discussed, including testing for the robustness of explanatory variables in the analyses of the determinants of economic growth and poverty.

We consider the problem of variable selection in linear regression models. Bayesian model averaging has become an important tool in empirical settings with large numbers of potential regressors and relatively limited numbers of observations. We examine the effect of a variety of prior assumptions on the inference concerning model size, posterior inclusion probabilities of regressors and on predictive performance. We illustrate these issues in the context of cross-country growth regressions using three datasets with 41-67 potential drivers of growth and 72-93 observations. Finally, we recommend priors for use in this and related contexts.

In sufficient dimension reduction (Li, 1991; Cook, 1998b), original predictors are replaced by their low-dimensional linear combinations while preserving all of the conditional information of the response given the predictors. Sliced inverse regression [SIR; Li, 1991] and principal Hessian directions [PHD; Li, 1992] are two popular sufficient dimension reduction methods, and both SIR and PHD estimators involve all of the original predictor variables. To deal with the cases when the linear combinations involve only a subset of the original predictors, we propose a Bayesian model averaging (Raftery et al., 1997) approach to achieve sparse sufficient dimension reduction. We extend both SIR and PHD under the Bayesian framework. The superior performance of the proposed methods is demonstrated through extensive numerical studies as well as a real data analysis.