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Bootstrap With Cluster‐Dependence in Two or More Dimensions

双维及更高维聚类依赖下的自助法

We propose a bootstrap procedure for data that may exhibit cluster‐dependence in two or more dimensions. The asymptotic distribution of the sample mean or other statistics may be non‐Gaussian if observations are dependent but uncorrelated within clusters. We show that there exists no procedure for estimating the limiting distribution of the sample mean under two‐way clustering that achieves uniform consistency. However, we propose bootstrap procedures that achieve adaptivity…

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Economic Predictions With Big Data: The Illusion of Sparsity

大数据经济预测:稀疏性的幻象

We compare sparse and dense representations of predictive models in macroeconomics, microeconomics, and finance. To deal with a large number of possible predictors, we specify a prior that allows for both variable selection and shrinkage. The posterior distribution does not typically concentrate on a single sparse model, but on a wide set of models that often include many predictors.

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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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Location as an Asset

作为资产的区位

The location of individuals determines their job and schooling opportunities, amenities, and housing costs. We conceptualize the location choice of individuals as a decision to invest in a “location asset.” This asset has a current cost equal to the location's rent, and a future payoff through better job and schooling opportunities. As with any asset, savers in the location asset transfer resources into the future by going to expensive locations with high future returns. In…

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Generalized Local‐to‐Unity Models

广义局部单位根模型

We introduce a generalization of the popular local‐to‐unity model of time series persistence by allowing for p autoregressive (AR) roots and p − 1 moving average (MA) roots close to unity. This generalized local‐to‐unity model, GLTU( p ), induces convergence of the suitably scaled time series to a continuous time Gaussian ARMA( p , p − 1) process on the unit interval. Our main theoretical result establishes the richness of this model class, in the sense that it can well…

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Bootstrap Standard Error Estimates and Inference

自助法标准误估计与推断

Asymptotic justification of the bootstrap often takes the form of weak convergence of the bootstrap distribution to some limit distribution. Theoretical literature recognized that the weak convergence does not imply consistency of the bootstrap second moment or the bootstrap variance as an estimator of the asymptotic variance, but such concern is not always reflected in the applied practice. We bridge the gap between the theory and practice by showing that such common…

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Recovering Preferences From Finite Data

从有限数据中恢复偏好

We study preferences estimated from finite choice experiments and provide sufficient conditions for convergence to a unique underlying “true” preference. Our conditions are weak and, therefore, valid in a wide range of economic environments. We develop applications to expected utility theory, choice over consumption bundles, and menu choice. Our framework unifies the revealed preference tradition with models that allow for errors.

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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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Present Bias

现时偏差

Present bias is the inclination to prefer a smaller present reward to a larger later reward, but reversing this preference when both rewards are equally delayed. Such behavior violates stationarity of temporal choices, and hence exponential discounting. This paper provides a weakening of the stationarity axiom that can accommodate present‐biased choice reversals. We call this new behavioral postulate Weak Present Bias and characterize the general class of utility functions…

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Local Projection Inference Is Simpler and More Robust Than You Think

局部投影推断比你想象的更简单、更稳健

Applied macroeconomists often compute confidence intervals for impulse responses using local projections, that is, direct linear regressions of future outcomes on current covariates. This paper proves that local projection inference robustly handles two issues that commonly arise in applications: highly persistent data and the estimation of impulse responses at long horizons. We consider local projections that control for lags of the variables in the regression. We show that…

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Extreme Points and Majorization: Economic Applications

极点与主序关系:经济学应用

We characterize the set of extreme points of monotonic functions that are either majorized by a given function f or themselves majorize f and show that these extreme points play a crucial role in many economic design problems. Our main results show that each extreme point is uniquely characterized by a countable collection of intervals. Outside these intervals the extreme point equals the original function f and inside the function is constant. Further consistency conditions…

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A New Parametrization of Correlation Matrices

相关矩阵的一种新参数化

We introduce a novel parametrization of the correlation matrix. The reparametrization facilitates modeling of correlation and covariance matrices by an unrestricted vector, where positive definiteness is an innate property. This parametrization can be viewed as a generalization of Fisher's Z ‐transformation to higher dimensions and has a wide range of potential applications. An algorithm for reconstructing the unique n × n correlation matrix from any vector in R n ( n − 1 )…

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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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Finite‐Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness

无混杂条件下平均处理效应的有限样本最优估计与推断

We consider estimation and inference on average treatment effects under unconfoundedness conditional on the realizations of the treatment variable and covariates. Given nonparametric smoothness and/or shape restrictions on the conditional mean of the outcome variable, we derive estimators and confidence intervals (CIs) that are optimal in finite samples when the regression errors are normal with known variance. In contrast to conventional CIs, our CIs use a larger critical…

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Aggregate Dynamics in Lumpy Economies

非连续大额投资经济中的总量动态

How does an economy's capital respond to aggregate productivity shocks when firms make lumpy investments? We show that capital's transitional dynamics are structurally linked to two steady‐state moments: the dispersion of capital to productivity ratios—an indicator of capital misallocation—and the covariance of capital to productivity ratios with the time elapsed since their last adjustment—an indicator of asymmetric costs of upsizing and downsizing the capital stock. We…

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Inference for Iterated GMM Under Misspecification

模型错设下迭代 GMM 的统计推断

This paper develops inference methods for the iterated overidentified Generalized Method of Moments (GMM) estimator. We provide conditions for the existence of the iterated estimator and an asymptotic distribution theory, which allows for mild misspecification. Moment misspecification causes bias in conventional GMM variance estimators, which can lead to severely oversized hypothesis tests. We show how to consistently estimate the correct asymptotic variance matrix. Our…

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Information Technology and Government Decentralization: Experimental Evidence From Paraguay

信息技术与政府分权:来自巴拉圭的实验证据

Standard models of hierarchy assume that agents and middle managers are better informed than principals. We estimate the value of the informational advantage held by supervisors—middle managers—when ministerial leadership—the principal—introduced a new monitoring technology aimed at improving the performance of agricultural extension agents (AEAs) in rural Paraguay. Our approach employs a novel experimental design that elicited treatment‐priority rankings from supervisors…

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Strategic Sample Selection

策略性样本选择

Are the highest sample realizations selected from a larger presample more or less informative than the same amount of random data? Developing multivariate accuracy for interval dominance ordered preferences, we show that sample selection always benefits (or always harms) a decision maker if the reverse hazard rate of the data distribution is log‐supermodular (or log‐submodular), as in location experiments with normal noise. We find nonpathological conditions under which the…

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Spurious Factor Analysis

伪因子分析

This paper draws parallels between the principal components analysis of factorless high‐dimensional nonstationary data and the classical spurious regression. We show that a few of the principal components of such data absorb nearly all the data variation. The corresponding scree plot suggests that the data contain a few factors, which is corroborated by the standard panel information criteria. Furthermore, the Dickey–Fuller tests of the unit root hypothesis applied to the…

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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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Quantile Factor Models

分位数因子模型

Quantile factor models (QFM) represent a new class of factor models for high‐dimensional panel data. Unlike approximate factor models (AFM), which only extract mean factors, QFM also allow unobserved factors to shift other relevant parts of the distributions of observables. We propose a quantile regression approach, labeled Quantile Factor Analysis (QFA), to consistently estimate all the quantile‐dependent factors and loadings. Their asymptotic distributions are established…

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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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