Constrained Conditional Moment Restriction Models
提出一种在条件矩限制模型中施加形状约束的通用推断方法，通过比较有无约束的GMM目标函数最小值，并用自助法获得有效临界值。实证分析显示，在线性工具变量模型中施加形状约束可缩短局部和平均处理效应的置信区间。
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.