Sensitivity of an estimator to departures from its distributional assumptions is a very important issue that is worth considering. The influence function, which describes the effect of an infinitesimal contamination at point, y, on the estimator we are seeking, standardized by the mass, ε, of the contamination, is bounded for the median. This property of the median is enjoyed by the other quantile points. Quantile regression inherits this robustness property since the minimized objective functions in the case of sample quantile and in the case of quantile regression are the same. This robustness is investigated by analyzing the quarterly implicit price deflator using quantile regression. The coefficients for the median and other quantiles remain unchanged even when outlier is added to the data.

breakdown points, infinitesimal contamination, influence function, quantile regression, robustness, outliers