Title: The second-order bias and MSE of quantile estimators
Authors: Aman Ullah - University of California Riverside (United States) [presenting]
Tae-Hwy Lee - University of California Riverside (United States)
He Wang - University of California Riverside (United States)
Abstract: Analytical results are developed on the finite sample properties of quantile estimators. We expand previous results on the second-order bias and MSE of quantile estimators with i.i.d. samples. We discover that for both unconditional and conditional quantile regressions, the median is unbiased for a symmetric unconditional and conditional distribution, and the bias of the other quantiles is larger at the tails of any unconditional and conditional distributions. We point out that the second-order bias will vanish as the sample size increases. The Monte Carlo simulations indicate that the second-order bias corrected estimator has better behavior than the uncorrected ones. An application of the impact of schooling, experience, and tenure on earnings are illustrated in quantile estimation. We find larger bias at the extreme low and high earning quantiles. With our second-order bias correction, the results of the application show the improvement of quantile forecasting.