Panel Quantile Regression with Penalized Fixed Effects and Correlated Random Effects (Published)
The crucial difficult in estimating covariates effects in panel analysis, is when there is correlation of the unobserved heterogeneity with the covariates and the fact that estimation of conditional mean effects seems potentially limited. Much consideration has not really been given to curb this difficulty especially in the context of quantile regression. In this work Panel Quantile regression was applied in other to investigate the correlated random effects (i.e. effects of the correlation between the covariates and the unobserved heterogeneity) and the penalized fixed effect (i.e. effects after eliminating the unobserved heterogeneity). We employed the use of real data and simulated data sets at different sample sizes. The results showed significant correlated random effect for both covariates in the real data only at the low level (0.25 quantile), but when the unobserved heterogeneity was eliminated both variables were seen to significantly affect the response at the 0.25, 0.5 and 0.75 quantiles of its distribution. The simulation study also confirmed it. We also noticed that as the sample size increases in the simulation study the correlated random effects become insignificant, while the penalized fixed effect and quantile regression effects were evidently significant at all quantiles considered. Comparison of these methods showed that the penalized fixed effect had the least value for both MSE and RMSE. This analysis was done in R environment using the quantreg package.
Keywords: Panel Data, Quantile Regression., correlated random effect, penalized fixed effect., unobserved heterogeneity