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Lack-of-Fit Tests for Quantile Regression Models

分位数回归模型的失拟检验

Summary The paper novelly transforms lack-of-fit tests for parametric quantile regression models into checking the equality of two conditional distributions of covariates. Accordingly, by applying some successful two-sample test statistics in the literature, two tests are constructed to check the lack of fit for low and high dimensional quantile regression models. The low dimensional test works well when the number of covariates is moderate, whereas the high dimensional test…

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Robust Causal Structure Learning with Some Hidden Variables

存在部分隐藏变量时的稳健因果结构学习

Summary We introduce a new method to estimate the Markov equivalence class of a directed acyclic graph (DAG) in the presence of hidden variables, in settings where the underlying DAG among the observed variables is sparse, and there are a few hidden variables that have a direct effect on many of the observed variables. Building on the so-called low rank plus sparse framework, we suggest a two-stage approach which first removes the effect of the hidden variables and then…

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A panel quantile approach to attrition bias in Big Data: Evidence from a randomized experiment

大数据流失偏误的面板分位数方法:随机实验背景下的证据

This paper introduces a quantile regression estimator for panel data models with individual heterogeneity and attrition. The method is motivated by the fact that attrition bias is often encountered in Big Data applications. For example, many users sign-up for the latest program but few remain active users several months later, making the evaluation of such interventions inherently very challenging. Building on earlier work by Hausman and Wise (1979), we provide a simple…

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Constructive identification in some nonseparable discrete choice models

若干非可分离散选择模型的构造性识别

This paper introduces new results on the nonparametric identification of separable and nonseparable discrete choice models. It presents constructive methods for recovering the derivatives of the utility functions of the alternatives in a set, when these utility functions are nonparametric and nonseparable in unobservable random terms. When the utility functions are separable, the constructive methods require fewer assumptions. It is assumed that only the probability of…

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Nonseparable multinomial choice models in cross-section and panel data

横截面与面板数据中的非可分多项选择模型

Multinomial choice models are fundamental for empirical modeling of economic choices among discrete alternatives. We analyze identification of binary and multinomial choice models when the choice utilities are nonseparable in observed attributes and multidimensional unobserved heterogeneity with cross-section and panel data. We show that derivatives of choice probabilities with respect to continuous attributes are weighted averages of utility derivatives in cross-section…

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Missing dependent variables in fixed-effects models

固定效应模型中的因变量缺失

This paper considers estimation of linear fixed-effects models in which the dependent variable may be missing. For cross-sectional units with dependent variables missing, use of covariate information from all time periods can provide efficiency gains relative to complete-data methods. A classical minimum distance (CMD) estimator based upon Chamberlain (1982, 1984), which is consistent under a missing-at-random (MAR) type assumption, is proposed for the static fixed-effects…

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Jerry Hausman

杰里·豪斯曼

This paper is in two parts. The first part includes some reminiscences of my life with Jerry since we both arrived at MIT in 1972. The second part discusses what I view as Jerry’s most important and long-lasting contribution to energy economics. Jerry has been an amazing friend and colleague for 45 years. His paper analyzing consumer choice of energy using durable equipment and the estimate of consumer discount rates continues to be the gold standard from an analytical…

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On the structure of IV estimands

工具变量估计目标的结构

When the overidentifying restrictions of the constant-effect linear instrumental variables model fail, common IV estimators converge to different probability limits. I characterize the estimands of two stage least squares, two step GMM, and limited information maximum likelihood as functions of the single-instrument estimands from the just-identified IV regressions which consider each instrument separately. The limited information maximum likelihood estimand is found to be…

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Correlated random effects models with unbalanced panels

非平衡面板中的相关随机效应模型

I propose some strategies for allowing unobserved heterogeneity to be correlated withobserved covariates and sample selection for unbalanced panels. The methods are extensions of the Chamberlain–Mundlak approach for balanced panels when explanatory variables are strictly exogenous conditional on unobserved effects. A byproduct is fully robust Hausman tests for unbalanced panels. Even for nonlinear models, in many cases the estimators can be implemented using standard…

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Labour supply and taxation with restricted choices

选择受限下的劳动供给与税收

A model of labour supply and taxation is developed in which observed hours reflect both the distribution of preferences and restrictions on choices. Hours restrictions are placed in a constrained rational choice setting in which the set of alternative hours on offer is restricted. Choices are made on a random subset of possible hours. We focus on the case where the choice set contains at most two offers. We show that when the choice set distribution is known, preferences can…

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Estimating the Impacts of Program Benefits: Using Instrumental Variables with Underreported and Imputed Data

项目福利影响估计:少报与插补数据下的工具变量方法

Survey nonresponse has risen in recent years, which has increased the share of imputed and underreported values found on commonly used data sets. While this trend has been well documented for earnings, the growth in nonresponse to government transfers questions has received far less attention. We demonstrate analytically that the underreporting and imputation of transfer benefits can lead to program impact estimates that are substantially overstated when using instrumental…

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Regression Discontinuity Designs Using Covariates

使用协变量的回归断点设计

We study regression discontinuity designs when covariates are included in the estimation. We examine local polynomial estimators that include discrete or continuous covariates in an additive separable way, but without imposing any parametric restrictions on the underlying population regression functions. We recommend a covariate-adjustment approach that retains consistency under intuitive conditions and characterize the potential for estimation and inference improvements. We…

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Inference in Differences-in-Differences with Few Treated Groups and Heteroskedasticity

少量处理组与异方差下的双重差分推断

We derive an inference method that works in differences-in-differences settings with few treated and many control groups in the presence of heteroskedasticity. As a leading example, we provide theoretical justification and empirical evidence that heteroskedasticity generated by variation in group sizes can invalidate existing inference methods, even in data sets with a large number of observations per group. In contrast, our inference method remains valid in this case. Our…

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Differential Markov random field analysis with an application to detecting differential microbial community networks

差异马尔可夫随机场分析及微生物群落网络差异检测

Micro-organisms such as bacteria form complex ecological community networks that can be greatly influenced by diet and other environmental factors. Differential analysis of microbial community structures aims to elucidate systematic changes during an adaptive response to changes in environment. In this paper, we propose a flexible Markov random field model for microbial network structure and introduce a hypothesis testing framework for detecting differences between networks,…

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Pseudo-population bootstrap methods for imputed survey data

插补调查数据的伪总体自助法

The most common way to treat item nonresponse in surveys is to replace a missing value by a plausible value constructed on the basis of fully observed variables. Treating the imputed values as if they were observed may lead to invalid inferences. Bootstrap variance estimators for various finite population parameters are obtained using two pseudo-population bootstrap schemes. We establish the asymptotic properties of the resulting bootstrap variance estimators for population…

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Randomization tests of causal effects under interference

干扰下因果效应的随机化检验

Many causal questions involve interactions between units, also known as interference, for example between individuals in households, students in schools, or firms in markets. In this paper we formalize the concept of a conditioning mechanism, which provides a framework for constructing valid and powerful randomization tests under general forms of interference. We describe our framework in the context of two-stage randomized designs and apply our approach to a randomized…

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A robust and efficient approach to causal inference based on sparse sufficient dimension reduction

基于稀疏充分降维的稳健高效因果推断

A fundamental assumption used in causal inference with observational data is that treatment assignment is ignorable given measured confounding variables. This assumption of no missing confounders is plausible if a large number of baseline covariates are included in the analysis, as we often have no prior knowledge of which variables can be important confounders. Thus, estimation of treatment effects with a large number of covariates has received considerable attention in…

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Causal Dantzig: Fast inference in linear structural equation models with hidden variables under additive interventions

因果 Dantzig:加性干预下含隐藏变量线性结构方程模型的快速推断

Causal inference is known to be very challenging when only observational data are available. Randomized experiments are often costly and impractical and in instrumental variable regression the number of instruments has to exceed the number of causal predictors. It was recently shown in Peters, Bühlmann and Meinshausen (2016) (J. R. Stat. Soc. Ser. B. Stat. Methodol. 78 947–1012) that causal inference for the full model is possible when data from distinct observational…

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Distributed inference for quantile regression processes

分位数回归过程的分布式推断

The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big data, we propose a two-step procedure: (i) estimate conditional quantile functions at different levels in a parallel computing environment; (ii) construct a conditional quantile regression process through projection based on these estimated…

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Causal inference by quantile regression kink designs

分位数回归折点设计的因果推断

The quantile regression kink design (QRKD) is proposed by empirical researchers, but its causal interpretation remains unknown. We show that the QRKD estimand measures a weighted average of heterogeneous marginal effects at respective conditional quantiles of outcome given a designed kink point. We also derive limit processes for the QRKD estimator to conduct statistical inference on heterogeneous treatment effects using the QRKD. Applying our methods to the Continuous Wage…

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Specification tests for the propensity score

倾向得分的设定检验

This paper proposes new nonparametric diagnostic tools to assess the asymptotic validity of different treatment effects estimators that rely on the correct specification of the propensity score. We derive a particular restriction relating the propensity score distribution of treated and control groups, and develop specification tests based upon it. The resulting tests do not suffer from the “curse of dimensionality” when the vector of covariates is high-dimensional, are…

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A simple and trustworthy asymptotic t test in difference-in-differences regressions

双重差分回归中简便可靠的渐近 t 检验

We propose an asymptotically valid t test that uses Student’s t distribution as the reference distribution in a difference-in-differences regression. For the asymptotic variance estimation, we adopt the clustering-by-time approach to accommodate cross-sectional dependence. This approach often assumes the clusters to be independent across time, but we allow them to be temporally dependent. The proposed t test is based on a special heteroscedasticity and autocorrelation robust…

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Identification and estimation of linear social interaction models

线性社会互动模型的识别与估计

This paper has two parts. The first part derives the identification conditions for higher-order social interaction models. In the case where social effects depend on the distance between individuals, the upper bounds on the network diameters for non-identified models are derived. Many network properties of non-identified models in the literature can be derived from these upper bounds. This part analyzes which fixed effect elimination methods require less restrictive…

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Identification and estimation of risk aversion in first-price auctions with unobserved auction heterogeneity

存在未观测拍卖异质性时第一价格拍卖风险厌恶的识别与估计

This paper shows point-identification in first-price auctions with risk aversion and unobserved auction heterogeneity, by exploiting multiple bids per auction and variation in the number of bidders. If the exclusion restriction required for point-identification is violated, the recovered primitives are still valid bounds under weaker restrictions. We propose a Sieve Maximum Likelihood Estimator (SMLE). Monte Carlo experiments illustrate that the estimator performs well and…

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