Constrained Conditional Moment Restriction Models

TL;DR

This paper develops a general inference procedure for shape-restricted models defined by conditional moment restrictions, improving confidence region accuracy and power in economic applications.

Contribution

It introduces a bootstrap-based method for valid inference under shape restrictions in both identified and partially identified models, applicable to various economic contexts.

Findings

Shape restrictions lead to shorter confidence regions in IV models.

Bootstrap critical values are conservatively accurate in simulations.

Tests show good power compared to unrestricted GMM.

Abstract

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. We find in Monte Carlo examples that the critical values are conservatively accurate and that tests about objects of interest have good power relative to unrestricted GMM.