Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/235416 
Year of Publication: 
2021
Series/Report no.: 
CESifo Working Paper No. 9046
Publisher: 
Center for Economic Studies and Ifo Institute (CESifo), Munich
Abstract: 
We study the small sample properties of conditional quantile estimators such as classical and IV quantile regression. First, we propose a higher-order analytical framework for comparing competing estimators in small samples and assessing the accuracy of common inference procedures. Our framework is based on a novel approximation of the discontinuous sample moments by a Hölder-continuous process with a negligible error. For any consistent estimator, this approximation leads to asymptotic linear expansions with nearly optimal rates. Second, we study the higher-order bias of exact quantile estimators up to O (1/n). Using a novel non-smooth calculus technique, we uncover previously unknown non-negligible bias components that cannot be consistently estimated and depend on the employed estimation algorithm. To circumvent this problem, we propose a “symmetric” bias correction, which admits a feasible implementation. Our simulations confirm the empirical importance of bias correction.
Subjects: 
non-smooth estimators
KMT coupling
Hungarian construction
higher-order asymptotic distribution
higher-order stochastic expansion
order statistic
bias correction
mixed integer linear programming (MILP)
exact estimators
k-step estimators
quantile
JEL: 
C21
C26
Document Type: 
Working Paper
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