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Using monotonicity restrictions to identify models with partially latent covariates

利用单调性限制识别含部分潜在协变量的模型

This paper develops a new method for identifying econometric models with partially latent covariates. Such data structures arise in industrial organization and labor economics settings where data are collected using an input-based sampling strategy, e.g., if the sampling unit is one of multiple labor input factors. We show that the latent covariates can be nonparametrically identified, if they are functions of a common shock satisfying some plausible monotonicity…

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Profile GMM estimation of panel data models with interactive fixed effects

含交互固定效应的面板模型的剖面 GMM 估计

This paper studies panel data models with interactive fixed effects where the regressors are allowed to be correlated with the idiosyncratic error terms. We propose a two-step profile GMM estimation procedure to estimate the parameters of interest. In the first step we obtain a preliminary consistent estimate of the slope coefficient via a nuclear-norm-regularization (NNR) based profile GMM procedure. In the second step, via an iterative procedure, we conduct post-NNR…

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Uniform inference in linear panel data models with two-dimensional heterogeneity

双维度异质性线性面板模型的一致有效推断

This paper studies uniform inference in a linear panel data model when the slope coefficients may exhibit heterogeneity over both the individual and time dimensions and they can be correlated with the regressors. We propose a generalized two-way fixed effects (GTWFE) estimation procedure to estimate the model. To establish the asymptotic properties of the GTWFE estimators, we invert a number of large dimensional square matrices by approximating them with quasi-Kronecker…

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Prices, profits, proxies, and production

价格、利润、代理变量与生产

This paper studies nonparametric identification and counterfactual bounds for heterogeneous firms that can be ranked in terms of productivity. Our approach works when quantities and prices are latent, rendering standard approaches inapplicable. Instead, we require observation of profits or other optimizing-values such as costs or revenues, and either prices or price proxies of flexibly chosen variables. We extend classical duality results for price-taking firms to a setup…

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Partial identification in nonseparable binary response models with endogenous regressors

含内生解释变量的非可分二元响应模型中的部分识别

This paper considers (partial) identification of a variety of counterfactual parameters in binary response models with possibly endogenous regressors. Our framework allows for nonseparable index functions with multi-dimensional latent variables, and does not require parametric distributional assumptions. We leverage results on hyperplane arrangements and cell enumeration from the literature on computational geometry in order to provide a tractable means of computing the…

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Testing stochastic dominance with many conditioning variables

具有大量条件变量的随机占优检验

We propose tests of the conditional first- and second-order stochastic dominance in the presence of growing numbers of covariates. Our approach builds on a semiparametric location-scale model, where the conditional distribution of the outcome given the covariates is characterized by nonparametric mean and skedastic functions with independent innovations from an unknown distribution. The nonparametric regression functions are estimated by utilizing the ℓ1-penalized…

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Robust inference in first-price auctions: Overbidding as an identifying restriction

一价拍卖中的稳健推断:以过度竞价作为识别限制

Laboratory experiments find consistently that bidding in first-price auctions tends to be more aggressive than predicted by the risk-neutral Bayesian Nash Equilibrium (RNBNE) — a finding known as the overbidding puzzle. Several alternative models can explain the overbidding puzzle, but no canonical alternative to RNBNE has emerged. Instead of estimating a particular model of overbidding, we use the overbidding restriction itself for identification, which allows us to bound…

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Partial identification and inference in moment models with incomplete data

不完整数据矩模型中的部分识别与推断

In this paper, we develop asymptotically valid inference in moment equality models with incomplete data, where the sample information is insufficient to identify the joint distribution of all the variables in the model. Examples of such models include the selection-on-observables framework, the counterfactual distribution, and parametric regressions with incomplete data. In the first two examples, the parameter of interest includes the values of the distribution and quantile…

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Testing for time stochastic dominance

时间随机占优检验

We propose nonparametric tests for the null hypothesis of time stochastic dominance. Time stochastic dominance makes a partial order of different prospects over time based on the net present value criteria for general utility and time discount function classes. For example, time stochastic dominance can be used for ranking investment strategies or environmental policies based on the expected net present value of the future benefits. We consider an Lp-type test statistic and…

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Sieve BLP: A semi-nonparametric model of demand for differentiated products

筛估计 BLP:差异化产品需求的半非参数模型

We develop a semi-nonparametric approach to identify and estimate the demand for differentiated products. The proposed method adopts a random coefficients discrete choice logit model (i.e., mixed logit model) in which the distribution of random coefficients is nonparametrically specified. Our method minimizes misspecification error in the distribution to which routinely used parametric approach is subject. In addition, it overcomes the practical challenge of dimensionality…

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SECOND-ORDER BIAS REDUCTION FOR NONLINEAR PANEL DATA MODELS WITH FIXED EFFECTS BASED ON EXPECTED QUANTITIES

基于期望量的非线性固定效应面板模型二阶偏差修正

In many nonlinear panel data models with fixed effects maximum likelihood estimators suffer from the incidental parameters problem, which often entails that point estimates are markedly biased. While the recent literature has mostly generated methods that yield a first-order bias reduction relative to maximum likelihood, we derive a first- and second-order bias correction of the profile likelihood based on “expected quantities” which differs from the corresponding correction…

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On event studies and distributed‐lags in two‐way fixed effects models: Identification, equivalence, and generalization

双向固定效应中的事件研究与分布滞后:识别、等价及推广

Summary We discuss three important properties of panel data event study designs. First, assuming constant treatment effects before and/or after some event time, also known as binning, is a natural restriction, which identifies dynamic treatment effects in the absence of never‐treated units. Second, event study designs with binned endpoints and distributed‐lag models are numerically identical. Third, classic dummy variable event study designs can be generalized to models that…

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When can we ignore measurement error in the running variable?

何时可以忽略断点运行变量的测量误差?

Summary In many applications of regression discontinuity designs, the running variable used to assign treatment is only observed with error. We show that, provided the observed running variable (i) correctly classifies treatment assignment and (ii) affects the conditional means of potential outcomes smoothly, ignoring the measurement error nonetheless yields an estimate with a causal interpretation: the average treatment effect for units whose observed running variable…

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Causal inference with invalid instruments: post-selection problems and a solution using searching and sampling

无效工具变量下的因果推断:选择后问题及搜索与抽样方案

Abstract Instrumental variable methods are among the most commonly used causal inference approaches to deal with unmeasured confounders in observational studies. The presence of invalid instruments is the primary concern for practical applications, and a fast-growing area of research is inference for the causal effect with possibly invalid instruments. This paper illustrates that the existing confidence intervals may undercover when the valid and invalid instruments are hard…

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The variational method of moments

变分矩方法

Abstract The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. We introduce a very general class of estimators called the variational method of moments (VMM), motivated by a variational minimax reformulation of optimally weighted generalized method of moments for finite sets of moments. VMM controls infinitely for many moments characterized by…

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Statistical testing under distributional shifts

分布偏移下的统计检验

Abstract We introduce statistical testing under distributional shifts. We are interested in the hypothesis P*∈H0 for a target distribution P*, but observe data from a different distribution Q*. We assume that P* is related to Q* through a known shift τ and formally introduce hypothesis testing in this setting. We propose a general testing procedure that first resamples from the observed data to construct an auxiliary data set (similarly to sampling importance resampling) and…

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Elastic integrative analysis of randomised trial and real-world data for treatment heterogeneity estimation

随机试验与真实世界数据的弹性整合:处理效应异质性估计

Abstract We propose a test-based elastic integrative analysis of the randomised trial and real-world data to estimate treatment effect heterogeneity with a vector of known effect modifiers. When the real-world data are not subject to bias, our approach combines the trial and real-world data for efficient estimation. Utilising the trial design, we construct a test to decide whether or not to use real-world data. We characterise the asymptotic distribution of the test-based…

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Proximal causal inference for complex longitudinal studies

复杂纵向研究中的近端因果推断

Abstract A standard assumption for causal inference about the joint effects of time-varying treatment is that one has measured sufficient covariates to ensure that within covariate strata, subjects are exchangeable across observed treatment values, also known as ‘sequential randomization assumption (SRA)’. SRA is often criticized as it requires one to accurately measure all confounders. Realistically, measured covariates can rarely capture all confounders with certainty.…

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Bayesian likelihood-based regression for estimation of optimal dynamic treatment regimes

用于最优动态治疗策略估计的贝叶斯似然回归

Abstract Clinicians often make sequences of treatment decisions that can be framed as dynamic treatment regimes. In this paper, we propose a Bayesian likelihood-based dynamic treatment regime model that incorporates regression specifications to yield interpretable relationships between covariates and stage-wise outcomes. We define a set of probabilistically-coherent properties for dynamic treatment regime processes and present the theoretical advantages that are…

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The Effects of Career and Technical Education: Evidence from the Connecticut Technical High School System

职业技术教育的影响:来自康涅狄格州技术高中体系的证据

Abstract We examine the effect of attending stand-alone technical high schools in Connecticut using regression discontinuity. Male students are 10 percentage points more likely to graduate from high school and have half a semester less time enrolled in college. Male students have 32% higher average quarterly earnings. Earnings effects may in part reflect general skills: male students have higher attendance rates and test scores, industry fixed effects explain less than…

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Double Negative Control Inference in Test-Negative Design Studies of Vaccine Effectiveness

疫苗有效性检测阴性设计研究中的双负对照推断

The test-negative design (TND) has become a standard approach to evaluate vaccine effectiveness against the risk of acquiring infectious diseases in real-world settings, such as Influenza, Rotavirus, Dengue fever, and more recently COVID-19. In a TND study, individuals who experience symptoms and seek care are recruited and tested for the infectious disease which defines cases and controls. Despite TND's potential to reduce unobserved differences, in healthcare seeking…

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Bahadur Efficiency of Observational Block Designs

观察性区组设计的Bahadur效率

To be convincing, an observational or nonrandomized study of causal effects must demonstrate that its conclusions cannot be readily explained by a small unmeasured bias in the way individuals were assigned to treatment or control. The Bahadur relative efficiency of a sensitivity analysis compares the performance of different test statistics or different research designs when sensitivity to unmeasured bias is appraised: better statistics and better designs exhibit…

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Optimal Environmental Targeting in the Amazon Rainforest

亚马孙雨林环境政策的最优定向配置

Abstract This article sets out a data-driven approach for targeting environmental policies optimally in order to combat deforestation. We focus on the Amazon, the world’s most extensive rainforest, where Brazil’s federal government issued a “Priority List” of municipalities in 2008—a blacklist to be targeted with more intense environmental monitoring and enforcement. First, we estimate the causal impact of the Priority List on deforestation (along with other relevant…

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An Instrumental Variable Approach to Dynamic Models

动态模型的工具变量方法

Abstract We present a new class of methods for identification and inference in dynamic models with serially correlated unobservables, which typically imply that state variables are econometrically endogenous. In the context of Industrial Organization, these state variables often reflect econometrically endogenous market structure. We propose the use of Generalized Instrument Variables methods to identify those dynamic policy functions that are consistent with instrumental…

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