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当回归变量被随机分配时的标准误AI 解读

We show that the OLS variance formula simplifies when values of the regressor of interest are assigned randomly and independently of other regressors. When the regressor of interest is independent not only of other regressors but also of the error term, the homoskedastic variance formula is valid even if regression errors are correlated. When the error term is heteroscedastic with respect to the regressor of interest, the variance formula has to be adjusted not only for…

工具变量模型中的识别：Abadie 的 Kappa 的核心作用AI 解读

We study instrumental variables models characterized by: (i) Unobserved heterogeneity consisting of potential outcomes and response types that describe how the instrument determines treatment choice; (ii) Conditional independence of the instrument and the unobserved heterogeneity; and (iii) Convex restrictions on the distribution of unobserved heterogeneity. We show certain causal parameters are identified in these models if and only if a version of the kappa of Abadie…

带约束的条件矩限制模型AI 解读

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)…

已知系数大型线性系统的推断AI 解读

This paper considers the problem of testing whether there exists a non‐negative solution to a possibly under‐determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of settings, including random coefficient, treatment effect, and discrete choice models, as well as a class of linear programming problems. As a first contribution, we obtain a novel geometric characterization of the null hypothesis in terms of…

检验大量矩不等式的两步方法AI 解读

This article considers the problem of testing a finite number of moment inequalities. For this problem, Romano, Shaikh, and Wolf proposed a two-step testing procedure. In the first step, the procedure incorporates information about the location of moments using a confidence region. In the second step, the procedure accounts for the use of the confidence region in the first step by adjusting the significance level of the test appropriately. Its justification, however, has so…

Abstract This paper studies the wild bootstrap–based test proposed in Cameron, Gelbach, and Miller (2008). Existing analyses of its properties require that number of clusters is “large.” In an asymptotic framework in which the number of clusters is “small,” we provide conditions under which an unstudentized version of the test is valid. These conditions include homogeneity-like restrictions on the distribution of covariates. We further establish that a studentized version of…

对《描述性统计对结构估计的信息含量》的评论AI 解读

ANDREWS, GENTZKOW, AND SHAPIRO (2020), henceforth AGS, make important progress on a challenging and fundamental question. The authors consider a setting in which a researcher reports an estimate ĉn that is unbiased under the researcher’s model. The researcher also reports a statistic γ̂n and a measure of informativeness of γ̂n for ĉn, denoted by . AGS show can be related to properties of the distribution of ĉn under models larger than the one employed by the researcher. As a…

This article studies an asymptotic framework for conducting inference on parameters of the form $\phi(\theta_0)$, where $\phi$ is a known directionally differentiable function and $\theta_0$ is estimated by $\hat \theta_n$. In these settings, the asymptotic distribution of the plug-in estimator $\phi(\hat \theta_n)$ can be derived employing existing extensions to the Delta method. We show, however, that (full) differentiability of $\phi$ is a necessary and sufficient…

正则模型中的过度识别AI 解读

In the unconditional moment restriction model of Hansen (), specification tests and more efficient estimators are both available whenever the number of moment restrictions exceeds the number of parameters of interest. We show that a similar relationship between potential refutability of a model and existence of more efficient estimators is present in much broader settings. Specifically, a condition we name local overidentification is shown to be equivalent to both the…

利用工具变量推断政策相关处理参数AI 解读

We propose a method for using instrumental variables (IV) to draw inference about causal effects for individuals other than those affected by the instrument at hand. Policy relevance and external validity turn on the ability to do this reliably. Our method exploits the insight that both the IV estimand and many treatment parameters can be expressed as weighted averages of the same underlying marginal treatment effects. Since the weights are identified, knowledge of the IV…

对缺失数据假设的敏感性：理论与美国工资结构评估AI 解读

This paper develops methods for assessing the sensitivity of empirical conclusions regarding conditional distributions to departures from the missing at random (MAR) assumption.We index the degree of nonignorable selection governing the missing data process by the maximal Kolmogorov-Smirnov distance between the distributions of missing and observed outcomes across all values of the covariates.Sharp bounds on minimum mean square approximations to conditional quantiles are…

模型误设下野生自助法的高阶性质AI 解读

We examine the higher order properties of the wild bootstrap (Wu, 1986) in a linear regression model with stochastic regressors. We find that the ability of the wild bootstrap to provide a higher order refinement is contingent upon whether the errors are mean independent of the regressors or merely uncorrelated with them. In the latter case, the wild bootstrap may fail to match some of the terms in an Edgeworth expansion of the full sample test statistic. Nonetheless, we…

恢复连续线性泛函的工具变量方法AI 解读

This paper develops methods for estimating continuous linear functionals in nonparametric instrumental variable problems. Examples of such functionals include consumer surplus and weighted average derivatives. The estimation procedure is robust to a setting where the underlying model is not identified but the linear functional is. In order to attain such robustness, it is necessary to employ a partially identified nuisance parameter. We address this problem by consistently…