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A discrete choice model for partially ordered alternatives

部分有序备选项的离散选择模型

In this paper, we analyze a discrete choice model for partially ordered alternatives. The alternatives are differentiated along two dimensions: the first an unordered “horizontal” dimension, and the second an ordered “vertical” dimension. The model can be used in circumstances in which individuals choose among products of different brands, wherein each brand offers an ordered choice menu, for example, by offering products of varying quality. The unordered–ordered nature of…

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Market counterfactuals and the specification of multiproduct demand: A nonparametric approach

市场反事实与多产品需求设定:非参数方法

Demand estimates are essential for addressing a wide range of positive and normative questions in economics that are known to depend on the shape—and notably the curvature—of the true demand functions. The existing frontier approaches, while allowing flexible substitution patterns, typically require the researcher to commit to a parametric specification. An open question is whether these a priori restrictions are likely to significantly affect the results. To address this, I…

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Economic uncertainty and structural reforms: Evidence from stock market volatility

经济不确定性与结构改革:来自股票市场波动的证据

Does economic uncertainty promote the implementation of structural reforms? We answer this question using one of the most exhaustive cross‐country panel data sets on reforms in six major areas and measuring economic uncertainty with stock market volatility. To identify causality, we exploit exogenous differential variation in countries' exposure to foreign volatility shocks due to predetermined and time‐invariant bilateral characteristics. Across all specifications, we find…

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Identification in ascending auctions, with an application to digital rights management

升价拍卖的识别及其数字版权管理应用

This study provides new identification and estimation results for ascending (traditional English or online) auctions with unobserved auction‐level heterogeneity and an unknown number of bidders. When the seller's reserve price and two order statistics of bids are observed, we derive conditions under which the distributions of buyer valuations, unobserved heterogeneity, and number of participants are point identified. We also derive conditions for point identification in…

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A note on the estimation of job amenities and labor productivity

工作非工资属性价值与劳动生产率估计札记

This paper introduces a maximum likelihood estimator of the value of job amenities and labor productivity in a single matching market based on the observation of equilibrium matches and wages. The estimation procedure simultaneously fits both the matching patterns and the wage curve. While our estimator is suited for a wide range of assignment problems, we provide an application to the estimation of the Value of a Statistical Life using compensating wage differentials for…

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Uncertain identification

识别假设的不确定性

Uncertainty about the choice of identifying assumptions is common in causal studies, but is often ignored in empirical practice. This paper considers uncertainty over models that impose different identifying assumptions, which can lead to a mix of point‐ and set‐identified models. We propose performing inference in the presence of such uncertainty by generalizing Bayesian model averaging. The method considers multiple posteriors for the set‐identified models and combines…

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Information theoretic approach to high‐dimensional multiplicative models: Stochastic discount factor and treatment effect

高维乘法模型的信息论方法:随机贴现因子与处理效应

This paper is concerned with estimation of functionals of a latent weight function that satisfies possibly high‐dimensional multiplicative moment conditions. Main examples are functionals of stochastic discount factors in asset pricing, missing data problems, and treatment effects. We propose to estimate the latent weight function by an information theoretic approach combined with the ℓ 1 ‐penalization technique to deal with high‐dimensional moment conditions under sparsity.…

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Testing identifying assumptions in fuzzy regression discontinuity designs

模糊断点回归识别假设的检验

We propose a new specification test for assessing the validity of fuzzy regression discontinuity designs (FRD‐validity). We derive a new set of testable implications, characterized by a set of inequality restrictions on the joint distribution of observed outcomes and treatment status at the cut‐off. We show that this new characterization exploits all of the information in the data that is useful for detecting violations of FRD‐validity. Our approach differs from and…

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The sooner the better: lives saved by the lockdown during the COVID-19 outbreak. The case of Italy

越早越好:意大利新冠疫情封锁挽救的生命

Summary This paper estimates the effects of non-pharmaceutical interventions – mainly, the lockdown – on the COVID-19 mortality rate for the case of Italy, the first Western country to impose a national shelter-in-place order. We use a new estimator, the augmented synthetic control method (ASCM), that overcomes some limits of the standard synthetic control method (SCM). The results are twofold. From a methodological point of view, the ASCM outperforms the SCM in that the…

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Regularised orthogonal machine learning for nonlinear semiparametric models

非线性半参数模型的正则化正交机器学习

Summary This paper proposes a Lasso-type estimator for a high-dimensional sparse parameter identified by a single index conditional moment restriction (CMR). In addition to this parameter, the moment function can also depend on a nuisance function, such as the propensity score or the conditional choice probability, which we estimate by modern machine learning tools. We first adjust the moment function so that the gradient of the future loss function is insensitive (formally,…

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Partially linear models with endogeneity: a conditional moment-based approach

含内生性的部分线性模型:基于条件矩的方法

Summary In a partially linear conditional moment model we propose a new estimator for the slope parameter of the endogenous variable of interest, which combines a Robinson’s transformation to partial out the nonlinear part of the model, with a smooth minimum distance approach to exploit all the information of the conditional mean independence restriction. Our estimator only depends on one tuning parameter, is easy to compute, consistent and $\sqrt{n}$-asymptotically normal…

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Nonparametric panel data regression with parametric cross-sectional dependence

具有参数化截面依赖的非参数面板回归

Summary In this paper, we consider efficiency improvement in a nonparametric panel data model with cross-sectional dependence. A generalised least squares (GLS)-type estimator is proposed by taking into account this dependence structure. Parameterising the cross-sectional dependence, a local linear estimator is shown to be dominated by this type of GLS estimator. Also, possible gains in terms of rate of convergence are studied. Asymptotically optimal bandwidth choice is…

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Synthetic control method with convex hull restrictions: a Bayesian maximum a posteriori approach

带凸包约束的合成控制法:贝叶斯最大后验方法

Summary Synthetic control methods have gained popularity among causal studies with observational data, particularly when estimating the impacts of the interventions implemented to a small number of large units. The synthetic control methods face two major challenges: (a) estimating weights for each donor to create a synthetic control and (b) providing statistical inferences. To overcome these challenges, we propose a Bayesian framework that implements the synthetic control…

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How Does Incarceration Affect Reoffending? Estimating the Dose-Response Function

监禁如何影响再犯?剂量—反应函数的估计

We study the causal effect of incarceration on reoffending using discontinuities in North Carolina’s sentencing guidelines. A regression discontinuity analysis shows that 1 year of incarceration causes a reduction in the likelihood of being reincarcerated within 3, 5, and 8 years from sentencing by 44%, 29%, and 21%, respectively. To parse the potentially heterogeneous dose response relationship underlying these effects, we develop an econometric model of prison sentences…

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Optimal adaptivity of signed-polygon statistics for network testing

网络检验中带符号多边形统计量的最优自适应性

Given a symmetric social network, we are interested in testing whether it has only one community or multiple communities. The desired tests should (a) accommodate severe degree heterogeneity, (b) accommodate mixed memberships, (c) have a tractable null distribution and (d) adapt automatically to different levels of sparsity, and achieve the optimal phase diagram. How to find such a test is a challenging problem. We propose the Signed Polygon as a class of new tests. Fixing…

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Optimal linear discriminators for the discrete choice model in growing dimensions

维度增长下离散选择模型的最优线性判别器

Manski’s celebrated maximum score estimator for the discrete choice model, which is an optimal linear discriminator, has been the focus of much investigation in both the econometrics and statistics literatures, but its behavior under growing dimension scenarios largely remains unknown. This paper addresses that gap. Two different cases are considered: p grows with n but at a slow rate, that is, p/n→0; and p≫n (fast growth). In the binary response model, we recast Manski’s…

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Augmented minimax linear estimation

增广极小极大线性估计

Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized treatments. In this paper, we discuss a general approach to estimating such quantities: we begin with a simple plug-in estimator based on an estimate of the conditional expectation function, and then correct the plug-in estimator by…

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Matching estimators with few treated and many control observations

少量处理观测与大量对照观测下的匹配估计

We analyze the properties of matching estimators when there are few treated, but many control observations. We show that, under standard assumptions, the nearest neighbor matching estimator for the average treatment effect on the treated is asymptotically unbiased in this framework. However, when the number of treated observations is fixed, the estimator is not consistent, and it is generally not asymptotically normal. Since standard inference methods are inadequate, we…

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Permutation test for heterogeneous treatment effects with a nuisance parameter

含干扰参数的异质性处理效应置换检验

This paper proposes an asymptotically valid permutation test for heterogeneous treatment effects in the presence of an estimated nuisance parameter. Not accounting for the estimation error of the nuisance parameter results in statistics that depend on the particulars of the data generating process, and the resulting permutation test fails to control the Type 1 error, even asymptotically.

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Difference-in-differences with variation in treatment timing

处理时点存在差异的双重差分

The canonical difference-in-differences (DD) estimator contains two time periods, ”pre” and ”post”, and two groups, ”treatment” and ”control”. Most DD applications, however, exploit variation across groups of units that receive treatment at different times. This paper shows that the two-way fixed effects estimator equals a weighted average of all possible two-group/two-period DD estimators in the data. A causal interpretation of two-way fixed effects DD estimates requires…

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Covariate-adjusted Fisher randomization tests for the average treatment effect

针对平均处理效应的协变量调整 Fisher 随机化检验

Fisher’s randomization test (frt) delivers exact p-values under the strong null hypothesis of no treatment effect on any units whatsoever and allows for flexible covariate adjustment to improve the power. Of interest is whether the resulting covariate-adjusted procedure could also be valid for testing the weak null hypothesis of zero average treatment effect. To this end, we evaluate two general strategies for conducting covariate adjustment in frts: the pseudo-outcome…

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The identification region of the potential outcome distributions under instrument independence

工具变量独立性下潜在结果分布的识别区域

This paper examines the identifying power of instrument exogeneity in the treatment effect model. We derive the identification region of the potential outcome distributions, which are the collection of distributions that are compatible with data and with the restrictions of the model. We consider identification when (i) the instrument is independent of each of the potential outcomes (marginal independence), (ii) the instrument is independent of the potential outcomes and…

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Difference-in-Differences with multiple time periods

多时期双重差分的识别、估计与推断

In this article, we consider identification, estimation, and inference procedures for treatment effect parameters using Difference-in-Differences (DiD) with (i) multiple time periods, (ii) variation in treatment timing, and (iii) when the “parallel trends assumption” holds potentially only after conditioning on observed covariates. We show that a family of causal effect parameters are identified in staggered DiD setups, even if differences in observed characteristics create…

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Estimating dynamic treatment effects in event studies with heterogeneous treatment effects

异质处理效应下事件研究中的动态效应估计

To estimate the dynamic effects of an absorbing treatment, researchers often use two-way fixed effects regressions that include leads and lags of the treatment. We show that in settings with variation in treatment timing across units, the coefficient on a given lead or lag can be contaminated by effects from other periods, and apparent pretrends can arise solely from treatment effects heterogeneity. We propose an alternative estimator that is free of contamination, and…

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