Bayesian Quantile Regression with Adaptive Lasso Penalty for Dynamic Panel Data

‎Dynamic panel data models include the important part of medicine‎, ‎social and economic studies‎. ‎Existence of the lagged dependent variable as an explanatory variable is a sensible trait of these models‎. ‎The estimation problem of these models arises from the correlation between the lagged depended variable and the current disturbance‎. ‎Recently‎, ‎quantile regression to analyze dynamic panel data has been taken in to consideration‎. ‎In this paper‎, ‎quantile regression model by adding an adaptive Lasso penalty term to the random effects for dynamic panel data is introduced by assuming correlation between the random effects and initial observations‎. ‎Also‎, ‎this model is illustrated by assuming that the random effects and initial values are independent‎. ‎These two models are analyzed from a Bayesian point of view‎. ‎Since‎, ‎in these models posterior distributions of the parameters are not in explicit form‎, ‎the full conditional posterior distributions of the parameters are calculated and the Gibbs sampling algorithm is used to deduction‎. ‎To compare the performance of the proposed method with the conventional methods‎, ‎a simulation study was conducted and at the end‎, ‎applications to a real data set are illustrated‎.