Quantile selection in non-linear GMM quantile models

Abstract This note proposes a non-linear GMM quantile regression model to estimate the quantile as an additional parameter. The limiting distribution is studied. An empirical application to an intertemporal consumption model built on a structural dynamic quantile utility model illustrates the estimator. Using US data, it separately estimates the elasticity of intertemporal substitution and the risk attitude, which is captured by the estimated quantile.