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Nonparametric Analysis of Random Utility Models: Computational Tools for Statistical Testing

随机效用模型的非参数分析:统计检验的计算工具

Kitamura and Stoye (2018) recently proposed a nonparametric statistical test for random utility models of consumer behavior. The test is formulated in terms of linear inequality constraints and a quadratic objective function. While the nonparametric test is conceptually appealing, its practical implementation is computationally challenging. In this paper, we develop a column generation approach to operationalize the test. These novel computational tools generate considerable…

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The Empirical Content of Binary Choice Models

二元选择模型的经验内容

An important goal of empirical demand analysis is choice and welfare prediction on counterfactual budget sets arising from potential policy interventions. Such predictions are more credible when made without arbitrary functional‐form/distributional assumptions, and instead based solely on economic rationality, that is, that choice is consistent with utility maximization by a heterogeneous population. This paper investigates nonparametric economic rationality in the…

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Structural Change With Long‐Run Income and Price Effects

具有长期收入与价格效应的经济结构转型

We present a new multi‐sector growth model that features nonhomothetic, constant elasticity of substitution preferences, and accommodates long‐run demand and supply drivers of structural change for an arbitrary number of sectors. The model is consistent with the decline in agriculture, the hump‐shaped evolution of manufacturing, and the rise of services over time. We estimate the demand system derived from the model using household‐level data from the United States and…

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Adaptive Treatment Assignment in Experiments for Policy Choice

面向政策选择的实验自适应处理分配

Standard experimental designs are geared toward point estimation and hypothesis testing, while bandit algorithms are geared toward in‐sample outcomes. Here, we instead consider treatment assignment in an experiment with several waves for choosing the best among a set of possible policies (treatments) at the end of the experiment. We propose a computationally tractable assignment algorithm that we call “exploration sampling,” where assignment probabilities in each wave are an…

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Deep Neural Networks for Estimation and Inference

用于估计与推断的深度神经网络

We study deep neural networks and their use in semiparametric inference. We establish novel nonasymptotic high probability bounds for deep feedforward neural nets. These deliver rates of convergence that are sufficiently fast (in some cases minimax optimal) to allow us to establish valid second‐step inference after first‐step estimation with deep learning, a result also new to the literature. Our nonasymptotic high probability bounds, and the subsequent semiparametric…

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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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Panel experiments and dynamic causal effects: A finite population perspective

面板实验与动态因果效应:有限总体视角

In panel experiments, we randomly assign units to different interventions, measuring their outcomes, and repeating the procedure in several periods. Using the potential outcomes framework, we define finite population dynamic causal effects that capture the relative effectiveness of alternative treatment paths. For a rich class of dynamic causal effects, we provide a nonparametric estimator that is unbiased over the randomization distribution and derive its finite population…

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Imposing equilibrium restrictions in the estimation of dynamic discrete games

动态离散博弈估计中的均衡约束实施

Imposing equilibrium restrictions provides substantial gains in the estimation of dynamic discrete games. Estimation algorithms imposing these restrictions have different merits and limitations. Algorithms that guarantee local convergence typically require the approximation of high‐dimensional Jacobians. Alternatively, the Nested Pseudo‐Likelihood (NPL) algorithm is a fixed‐point iterative procedure, which avoids the computation of these matrices, but—in games—may fail to…

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Blurred boundaries: A flexible approach for segmentation applied to the car market

模糊的市场边界:汽车市场细分的灵活建模

Prominent features of differentiated product markets are segmentation and product proliferation blurring the boundaries between segments. I develop a tractable demand model, the Ordered Nested Logit, which allows for asymmetric substitution between segments. I apply the model to the automobile market where segments are ordered from small to luxury. I find that consumers, when substituting outside their vehicle segment, are more likely to switch to a neighboring segment.…

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A job ladder model with stochastic employment opportunities

具有随机就业机会的工作阶梯模型

We set up a model with on‐the‐job search in which firms infrequently post vacancies for which workers occasionally apply. The model nests the standard job ladder and stock‐flow models as special cases, while remaining analytically tractable and easy to estimate from standard panel data sets. The parameters from a structurally estimated model on US data are significantly different from either the restrictions imposed by a stock‐flow or job ladder model. Imposing these…

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Synthetic controls with imperfect pretreatment fit

处理前拟合不完全的合成控制方法

We analyze the properties of the Synthetic Control (SC) and related estimators when the pre‐treatment fit is imperfect. In this framework, we show that these estimators are generally biased if treatment assignment is correlated with unobserved confounders, even when the number of pre‐treatment periods goes to infinity. Still, we show that a demeaned version of the SC method can improve in terms of bias and variance relative to the difference‐in‐difference estimator. We also…

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Rationalizing rational expectations: Characterizations and tests

理性预期的相容性:刻画与检验

In this paper, we build a new test of rational expectations based on the marginal distributions of realizations and subjective beliefs. This test is widely applicable, including in the common situation where realizations and beliefs are observed in two different data sets that cannot be matched. We show that whether one can rationalize rational expectations is equivalent to the distribution of realizations being a mean‐preserving spread of the distribution of beliefs. The…

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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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Bullying among adolescents: The role of skills

青少年欺凌:技能的作用

Bullying cannot be tolerated as a normal social behavior portraying a child's life. This paper quantifies its negative consequences allowing for the possibility that victims and nonvictims differ in unobservable characteristics. To this end, we introduce a factor analytic model for identifying treatment effects of bullying in which latent cognitive and noncognitive skills determine victimization and multiple outcomes. We use early test scores to identify the distribution of…

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A unified framework for efficient estimation of general treatment models

一般处理模型有效估计的统一框架

This paper presents a weighted optimization framework that unifies the binary, multivalued, and continuous treatment—as well as mixture of discrete and continuous treatment—under a unconfounded treatment assignment. With a general loss function, the framework includes the average, quantile, and asymmetric least squares causal effect of treatment as special cases. For this general framework, we first derive the semiparametric efficiency bound for the causal effect of…

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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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Robust inference in deconvolution

反卷积中的稳健推断

Kotlarski's identity has been widely used in applied economic research based on repeated‐measurement or panel models with latent variables. However, how to conduct inference for these models has been an open question for two decades. This paper addresses this open problem by constructing a novel confidence band for the density function of a latent variable in repeated measurement error model. The confidence band builds on our finding that we can rewrite Kotlarski's identity…

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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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Controlling for presentation effects in choice

选择中的呈现效应控制

Experimenters make theoretically irrelevant decisions concerning user interfaces and ordering or labeling of options. Reanalyzing dictator games, I first show that such decisions may drastically affect comparative statics and cause results to appear contradictory across experiments. This obstructs model testing, preference analyses, and policy predictions. I then propose a simple model of choice incorporating both presentation effects and stochastic errors, and test the…

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Ex Ante Returns and Occupational Choice

事前回报与职业选择

Using data from Duke University undergraduates, we make three main contributions to the literature. First, we show that data on earnings beliefs and probabilities of choosing particular occupations are highly informative of future earnings and occupations. Second, we show how beliefs data can be used to recover ex ante treatment effects and their relationship with individual choices. We find large differences in expected earnings across occupations and provide evidence of…

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Optimal Bayesian estimation for random dot product graphs

随机点积图潜在位置的最优贝叶斯估计

Summary We propose and prove the optimality of a Bayesian approach for estimating the latent positions in random dot product graphs, which we call posterior spectral embedding. Unlike classical spectral-based adjacency, or Laplacian spectral embedding, posterior spectral embedding is a fully likelihood-based graph estimation method that takes advantage of the Bernoulli likelihood information of the observed adjacency matrix. We develop a minimax lower bound for estimating…

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Regression-adjusted average treatment effect estimates in stratified randomized experiments

分层随机实验中经回归调整的平均处理效应估计

Summary Linear regression is often used in the analysis of randomized experiments to improve treatment effect estimation by adjusting for imbalances of covariates in the treatment and control groups. This article proposes a randomization-based inference framework for regression adjustment in stratified randomized experiments. We re-establish, under mild conditions, the finite-population central limit theorem for a stratified experiment, and we prove that both the stratified…

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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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