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Smoothed GMM for quantile models. (English) Zbl 1456.62281
Summary: We consider estimation of finite-dimensional parameters identified by general conditional quantile restrictions, including instrumental variables quantile regression. Within a generalized method of moments framework, moment functions are smoothed to aid both computation and precision. Consistency and asymptotic normality are established under weaker assumptions than previously seen in the literature, allowing dependent data and nonlinear structural models. Simulations illustrate the finite-sample properties. An in-depth empirical application estimates the consumption Euler equation derived from quantile utility maximization. Advantages of quantile Euler equations include robustness to fat tails, decoupling risk attitude from the elasticity of intertemporal substitution, and error-free log-linearization.

MSC:
62P20 Applications of statistics to economics
62G05 Nonparametric estimation
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
Software:
GenSA; pracma; R
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References:
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