Consistent estimation, model selection and averaging of dynamic panel data models with fixed effect

In the context of an autoregressive panel data model with fixed effect, we examine the relationship between consistent parameter estimation and consistent model selection. Consistency in parameter estimation is achieved by using the tansformation of the fixed effect proposed by Lancaster (2002). We find that such transformation does not necessarily lead to consistent estimation of the autoregressive coefficient when the wrong set of exogenous regressors are included. To estimate our model consistently and to measure its goodness of fit, we argue for comparing different model specifications using the Bayes factor rather than the Bayesian information criterion based on the biased maximum likelihood estimates. When the model uncertainty is substantial, we recommend the use of Bayesian Model Averaging. Finally, we apply our method to study the relationship between financial development and economic growth. Our findings reveal that stock market development is positively related to economic growth, while the effect of bank development is not as significant as the classical literature suggests.