Econometrica

Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Mar, 2023, Volume 91, Issue 2

Constrained Conditional Moment Restriction Models

https://doi.org/10.3982/ECTA13830
p. 709-736

Victor Chernozhukov, Whitney K. Newey, Andres Santos

Shape restrictions have played a central role in economics as both testable implications of theory and sufficient conditions for obtaining informative counterfactual predictions. In this paper, we provide a general procedure for inference under shape restrictions in identified and partially identified models defined by conditional moment restrictions. Our test statistics and proposed inference methods are based on the minimum of the generalized method of moments (GMM) objective function with and without shape restrictions. Uniformly valid critical values are obtained through a bootstrap procedure that approximates a subset of the true local parameter space. In an empirical analysis of the effect of childbearing on female labor supply, we show that employing shape restrictions in linear instrumental variables (IV) models can lead to shorter confidence regions for both local and average treatment effects. Other applications we discuss include inference for the variability of quantile IV treatment effects and for bounds on average equivalent variation in a demand model with general heterogeneity.


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Supplemental Material

Supplement to "Constrained Conditional Moment Restriction Models"

Chernozhukov, Victor, Whitney K. Newey, and Andres Santos

This zip file contains the replication files for the manuscript.

Supplement to "Constrained Conditional Moment Restriction Models"

Chernozhukov, Victor, Whitney K. Newey, and Andres Santos

This Supplemental Appendix to “Constrained Conditional Moment Restriction Models” is organized as follows. Sections A.1 provides a review of AM spaces. Section A.2 specializes the general results of Section 3 to three additional examples: (i) GMM, (ii) Quantile Treatment Effects, and (iii) The Slutsky restriction in a partially linear model. The proofs for all results can be found in the working paper Chernozhukov et al. (2022).