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Measurement Error Without the Proxy Exclusion Restriction

不施加代理变量排除限制的测量误差分析

Abstract–This article studies the identification of the coefficients in a linear equation when data on the outcome, covariates, and an error-laden proxy for a latent variable are available. We maintain that the measurement error in the proxy is classical and relax the assumption that the proxy is excluded from the outcome equation. This enables the proxy to directly affect the outcome and allows for differential measurement error. Without the proxy exclusion restriction, we…

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Estimation of Covid-19 prevalence from serology tests: A partial identification approach

利用血清学检测估计新冠感染率:部分识别方法

We propose a partial identification method for estimating disease prevalence from serology studies. Our data are results from antibody tests in some population sample, where the test parameters, such as the true/false positive rates, are unknown. Our method scans the entire parameter space, and rejects parameter values using the joint data density as the test statistic. The proposed method is conservative for marginal inference, in general, but its key advantage over more…

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Identification and estimation of the SEIRD epidemic model for COVID-19

COVID-19 的 SEIRD 疫情模型识别与估计

This paper studies the SEIRD epidemic model for COVID-19. First, I show that the model is poorly identified from the observed number of deaths and confirmed cases. There are many sets of parameters that are observationally equivalent in the short run but lead to markedly different long run forecasts. Second, I show that the basic reproduction number R0 can be identified from the data, conditional on epidemiologic parameters, and propose several nonlinear SUR approaches to…

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Estimation and inference for spatial models with heterogeneous coefficients: An application to US house prices

异质系数空间模型的估计与推断:美国房价应用

Summary This paper considers the estimation and inference of spatial panel data models with heterogeneous spatial lag coefficients, with and without weakly exogenous regressors, and subject to heteroskedastic errors. A quasi maximum likelihood (QML) estimation procedure is developed and the conditions for identification of the spatial coefficients are derived. The QML estimators of individual spatial coefficients, as well as their mean group estimators, are shown to be…

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Identification at the Zero Lower Bound

零利率下限下的识别

I show that the zero lower bound (ZLB) on interest rates can be used to identify the causal effects of monetary policy. Identification depends on the extent to which the ZLB limits the efficacy of monetary policy. I propose a simple way to test the efficacy of unconventional policies, modeled via a “shadow rate.” I apply this method to U.S. monetary policy using a three‐equation structural vector autoregressive model of inflation, unemployment, and the Federal Funds rate. I…

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Econometrics for Decision Making: Building Foundations Sketched by Haavelmo and Wald

面向决策的计量经济学:完善Haavelmo与Wald勾勒的基础

Haavelmo (1944) proposed a probabilistic structure for econometric modeling, aiming to make econometrics useful for decision making. His fundamental contribution has become thoroughly embedded in econometric research, yet it could not answer all the deep issues that the author raised. Notably, Haavelmo struggled to formalize the implications for decision making of the fact that models can at most approximate actuality. In the same period, Wald (1939, 1945) initiated his own…

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An Axiomatic Model of Persuasion

说服的公理化模型

A sender ranks information structures knowing that a receiver processes the information before choosing an action affecting them both. The sender and receiver may differ in their utility functions and/or prior beliefs, yielding a model of dynamic inconsistency when they represent the same individual at two points in time. I take as primitive (i) a collection of preference orderings over all information structures, indexed by menus of acts (the sender's ex ante preferences…

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Heterogeneous Choice Sets and Preferences

异质选择集与偏好

We propose a robust method of discrete choice analysis when agents' choice sets are unobserved. Our core model assumes nothing about agents' choice sets apart from their minimum size. Importantly, it leaves unrestricted the dependence, conditional on observables, between choice sets and preferences. We first characterize the sharp identification region of the model's parameters by a finite set of conditional moment inequalities. We then apply our theoretical findings to…

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Robust Bayesian Inference for Set‐Identified Models

集合识别模型的稳健贝叶斯推断

This paper reconciles the asymptotic disagreement between Bayesian and frequentist inference in set‐identified models by adopting a multiple‐prior (robust) Bayesian approach. We propose new tools for Bayesian inference in set‐identified models and show that they have a well‐defined posterior interpretation in finite samples and are asymptotically valid from the frequentist perspective. The main idea is to construct a prior class that removes the source of the disagreement:…

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Salvaging Falsified Instrumental Variable Models

挽救被证伪的工具变量模型

What should researchers do when their baseline model is falsified? We recommend reporting the set of parameters that are consistent with minimally nonfalsified models. We call this the falsification adaptive set (FAS). This set generalizes the standard baseline estimand to account for possible falsification. Importantly, it does not require the researcher to select or calibrate sensitivity parameters. In the classical linear IV model with multiple instruments, we show that…

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Theory of Weak Identification in Semiparametric Models

半参数模型的弱识别理论

We provide general formulation of weak identification in semiparametric models and an efficiency concept. Weak identification occurs when a parameter is weakly regular, that is, when it is locally homogeneous of degree zero. When this happens, consistent or equivariant estimation is shown to be impossible. We then show that there exists an underlying regular parameter that fully characterizes the weakly regular parameter. While this parameter is not unique, concepts of…

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Errors in the Dependent Variable of Quantile Regression Models

分位数回归模型因变量中的测量误差

We study the consequences of measurement error in the dependent variable of random‐coefficients models, focusing on the particular case of quantile regression. The popular quantile regression estimator of Koenker and Bassett (1978) is biased if there is an additive error term. Approaching this problem as an errors‐in‐variables problem where the dependent variable suffers from classical measurement error, we present a sieve maximum likelihood approach that is robust to…

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Local Projections and VARs Estimate the Same Impulse Responses

局部投影与向量自回归估计相同的脉冲响应

We prove that local projections (LPs) and Vector Autoregressions (VARs) estimate the same impulse responses. This nonparametric result only requires unrestricted lag structures. We discuss several implications: (i) LP and VAR estimators are not conceptually separate procedures; instead, they are simply two dimension reduction techniques with common estimand but different finite‐sample properties. (ii) VAR‐based structural identification—including short‐run, long‐run, or sign…

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Reasonable Doubt: Experimental Detection of Job‐Level Employment Discrimination

合理怀疑:岗位层面就业歧视的实验检测

This paper develops methods for detecting discrimination by individual employers using correspondence experiments that send fictitious resumes to real job openings. We establish identification of higher moments of the distribution of job‐level callback rates as a function of the number of resumes sent to each job and propose shape‐constrained estimators of these moments. Applying our methods to three experimental data sets, we find striking job‐level heterogeneity in the…

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Policy Learning With Observational Data

利用观察数据进行政策学习

In many areas, practitioners seek to use observational data to learn a treatment assignment policy that satisfies application‐specific constraints, such as budget, fairness, simplicity, or other functional form constraints. For example, policies may be restricted to take the form of decision trees based on a limited set of easily observable individual characteristics. We propose a new approach to this problem motivated by the theory of semiparametrically efficient…

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Fixed‐ k inference for volatility

波动率的固定k推断

We present a new theory for the conduct of nonparametric inference about the latent spot volatility of a semimartingale asset price process. In contrast to existing theories based on the asymptotic notion of an increasing number of observations in local estimation blocks, our theory treats the estimation block size k as fixed. While the resulting spot volatility estimator is no longer consistent, the new theory permits the construction of asymptotically valid and…

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A new approach to measuring economic policy shocks, with an application to conventional and unconventional monetary policy

经济政策冲击的新度量:常规与非常规货币政策应用

We propose a new approach to analyze economic shocks. Our new procedure identifies economic shocks as exogenous shifts in a function; hence, we call them “ functional shocks. ” We show how to identify such shocks and how to trace their effects in the economy via VARs using “ VARs with functional shocks ” and “ functional local projections. ” Using our new procedure, we address the crucial question of studying the effects of monetary policy by identifying monetary policy…

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Inference on semiparametric multinomial response models

半参数多项响应模型的统计推断

We explore inference on regression coefficients in semiparametric multinomial response models. We consider cross‐sectional, and both static and dynamic panel settings where we focus throughout on inference under sufficient conditions for point identification. The approach to identification uses a matching insight throughout all three models coupled with variation in regressors: with cross‐section data, we match across individuals while with panel data, we match within…

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Decentralization estimators for instrumental variable quantile regression models

工具变量分位数回归模型的分解估计方法

The instrumental variable quantile regression (IVQR) model (Chernozhukov and Hansen (2005)) is a popular tool for estimating causal quantile effects with endogenous covariates. However, estimation is complicated by the nonsmoothness and nonconvexity of the IVQR GMM objective function. This paper shows that the IVQR estimation problem can be decomposed into a set of conventional quantile regression subproblems which are convex and can be solved efficiently. This reformulation…

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Identification of counterfactuals in dynamic discrete choice models

动态离散选择模型中反事实的识别

Dynamic discrete choice (DDC) models are not identified nonparametrically, but the non‐identification of models does not necessarily imply the nonidentification of counterfactuals. We derive novel results for the identification of counterfactuals in DDC models, such as non‐additive changes in payoffs or changes to agents' choice sets. In doing so, we propose a general framework that allows the investigation of the identification of a broad class of counterfactuals (covering…

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Identification and inference with ranking restrictions

排序限制下的识别与推断

We propose to add ranking restrictions on impulse‐responses to sign restrictions to narrow the identified set in vector autoregressions (VARs). Ranking restrictions come from micro data on heterogeneous industries in VARs, bounds on elasticities, or restrictions on dynamics. Using both a fully Bayesian conditional uniform prior and prior‐robust inference, we show that these restrictions help to identify productivity news shocks in the data. In the prior‐robust paradigm,…

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Partial identification of the distribution of treatment effects with an application to the Knowledge is Power Program (KIPP)

处理效应分布的部分识别及其在 KIPP 项目中的应用

We bound the distribution of treatment effects under plausible and testable assumptions on the joint distribution of potential outcomes, namely that potential outcomes are mutually stochastically increasing. We show how to test the empirical restrictions implied by those assumptions. The resulting bounds substantially sharpen bounds based on classical inequalities. We apply our method to estimate bounds on the distribution of effects of attending a Knowledge is Power Program…

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A conditional test with demonstrated insensitivity to unmeasured bias in matched observational studies

匹配观察研究中对未测偏倚不敏感的条件检验

Summary In an observational study matched for observed covariates, an association between treatment received and outcome exhibited may indicate not an effect caused by the treatment, but merely some bias in the allocation of treatments to individuals within matched pairs. The evidence that distinguishes moderate biases from causal effects is unevenly dispersed among possible comparisons in an observational study: some comparisons are insensitive to larger biases than others.…

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Score tests in GMM: Why use implied probabilities?

GMM 得分检验:为何使用隐含概率?

While simple to implement and thus attractive in practice, the GMM score test of Newey and West (1987) often displays upward size distortion under common scenarios involving skewed moment vectors or models with weak identification. Inference based on the Generalized Empirical Likelihood (GEL) is seen as a general solution to this problem. Kleibergen (2005) and, more generally, Guggenberger and Smith (2005) devised an elegant theory for the GEL score tests. However, strictly…

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