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Inference in Models Defined by Conditional Moment Inequalities with Continuous Covariates,” Working Paper (2010)
| Citations: | 12 - 1 self |
BibTeX
@MISC{Ponomareva10inferencein,
author = {Maria Ponomareva},
title = {Inference in Models Defined by Conditional Moment Inequalities with Continuous Covariates,” Working Paper},
year = {2010}
}
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Abstract
In this paper I present a novel approach to inference in models where the partially identified parameter is defined by a set of conditional moment inequalities with con-tinuous covariates. This class of models covers many economic applications, including treatment response models and regression with missing or interval outcome data. De-pending on the assumptions that a researcher is willing to make on conditional moment functions that define the inequalities, I propose inference procedure that is based on the distance between the set of conditional moment functions and the cone of non-positive (or non-negative) functions. If a researcher is reluctant to impose any assumptions about the shape of conditional moment functions except certain smoothness conditions, I offer a method that relies on bootstrapping of the simultaneous lower confidence bands for nonparametric estimators of conditional moments. In general, this inference procedure may lead to a conservative coverage. However, I show that under a particular set of shape restrictions on conditional moment functions one can construct confidence sets based on a Gaussian asymptotic approximation that is relatively easy to implement and attains accurate coverage in small samples. Finally, I conduct Monte Carlo simulations to illustrate both procedures. ∗I am indebted to Elie Tamer for his constant encouragement and support throughout this project. I am very grateful to Ivan Canay and Wenxin Jiang for valuable comments and suggestions. I want to thank Vasiliy Ponomarev and Daniil Manaenkov for helpful discussions.
Keyphrases
conditional moment function conditional moment working paper model defined continuous covariates inference procedure shape restriction daniil manaenkov confidence set particular set wenxin jiang novel approach attains accurate coverage model cover many economic application helpful discussion confidence band treatment response model ivan canay small sample elie tamer nonparametric estimator conservative coverage conditional moment inequality gaussian asymptotic approximation vasiliy ponomarev con-tinuous covariates interval outcome data valuable comment constant encouragement certain smoothness condition monte carlo simulation
