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Locally Robust Semiparametric Estimation

局部稳健的半参数估计

Many economic and causal parameters depend on nonparametric or high dimensional first steps. We give a general construction of locally robust/orthogonal moment functions for GMM, where first steps have no effect, locally, on average moment functions. Using these orthogonal moments reduces model selection and regularization bias, as is important in many applications, especially for machine learning first steps. Also, associated standard errors are robust to misspecification…

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The influence function of semiparametric estimators

半参数估计量的影响函数

There are many economic parameters that depend on nonparametric first steps. Examples include games, dynamic discrete choice, average exact consumer surplus, and treatment effects. Often estimators of these parameters are asymptotically equivalent to a sample average of an object referred to as the influence function. The influence function is useful in local policy analysis, in evaluating local sensitivity of estimators, and constructing debiased machine learning…

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Simultaneous selection of optimal bandwidths for the sharp regression discontinuity estimator

尖锐断点回归估计量的两侧最优带宽联合选择

A new bandwidth selection method that uses different bandwidths for the local linear regression estimators on the left and the right of the cut‐off point is proposed for the sharp regression discontinuity design estimator of the average treatment effect at the cut‐off point. The asymptotic mean squared error of the estimator using the proposed bandwidth selection method is shown to be smaller than other bandwidth selection methods proposed in the literature. The approach…

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Simple Estimators for Invertible Index Models

可逆指标模型的简易估计量

This article considers estimation of the unknown linear index coefficients of a model in which a number of nonparametrically identified reduced form parameters are assumed to be smooth and invertible function of one or more linear indices. The results extend the previous literature by allowing the number of reduced form parameters to exceed the number of indices (i.e., the indices are “overdetermined” by the reduced form parameters. The estimator of the unknown index…

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Characterization of the asymptotic distribution of semiparametric M-estimators

半参数 M 估计量渐近分布的刻画

This paper develops a concrete formula for the asymptotic distribution of two-step, possibly non-smooth semiparametric M-estimators under general misspecification. Our regularity conditions are relatively straightforward to verify and also weaker than those available in the literature. The first-stage nonparametric estimation may depend on finite dimensional parameters. We characterize: (1) conditions under which the first-stage estimation of nonparametric components do not…

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Characterizing Selection Bias Using Experimental Data

利用实验数据刻画选择偏差

Semiparametric methods are developed to estimate the bias that arises from using nonexperimental comparison groups to evaluate social programs and to test the identifying assumptions that justify matching, selection models and the method of difference in differences. Using data from an experiment on a prototypical social program and data from nonexperimental comparison groups, the authors reject the assumptions justifying matching and their extensions of it. The evidence…

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Matching As An Econometric Evaluation Estimator

This paper develops the method of matching as an econometric evaluation estimator. A rigorous distribution theory for kernel-based matching is presented. The method of matching is extended to more general conditions than the ones assumed in the statistical literature on the topic. We focus on the method of propensity score matching and show that it is not necessarily better, in the sense of reducing the variance of the resulting estimator, to use the propensity score method…

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Semiparametric least squares (SLS) and weighted SLS estimation of single-index models

单指标模型的半参数最小二乘与加权估计

For the class of single-index models, I construct a semiparametric estimator of coefficients up to a multiplicative constant that exhibits 1 √n-consistency and asymptotic normality. This class of models includes censored and truncated Tobit models, binary choice models, and duration models with unobserved individual heterogeneity and random censoring. I also investigate a weighting scheme that achieves the semiparametric efficiency bound.

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Optimal Smoothing in Single-Index Models

单指标模型中的最优平滑

Single-index models generalize linear regression. They have applications to a variety of fields, such as discrete choice analysis in econometrics and dose response models in biometrics, where high-dimensional regression models are often employed. Single-index models are similar to the first step of projection pursuit regression, a dimension-reduction method. In both cases the orientation vector can be estimated root-n consistently, even if the unknown univariate function (or…

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