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Inference for high-dimensional instrumental variables regression

高维工具变量回归的统计推断

This paper concerns statistical inference for the components of a high-dimensional regression parameter despite possible endogeneity of each regressor. Given a first-stage linear model for the endogenous regressors and a second-stage linear model for the dependent variable, we develop a novel adaptation of the parametric one-step update to a generic second-stage estimator. We provide conditions under which the scaled update is asymptotically normal. We then introduce a…

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Estimating derivatives of function-valued parameters in a class of moment condition models

一类矩条件模型中函数值参数的导数估计

We develop a general approach to estimating the derivative of a function-valued parameter θo(u) that is identified for every value of u as the solution to a moment condition. This setup in particular covers interesting models for conditional distributions, such as quantile regression or distribution regression. Exploiting that θo(u) solves a moment condition, we obtain an explicit expression for its derivative from the Implicit Function Theorem, and then estimate the…

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Discussion of ‘Network cross-validation by edge sampling’

对《通过边抽样进行网络交叉验证》的讨论

We congratulate the authors for their exciting paper (Li et al., 2020) on the difficult problem of network model selection. The authors have proposed an interesting cross-validation procedure that selects the best network model according to the criterion ... One of the main novelties of the method is the use of matrix completion to reconstruct a full network |$\{\skew6\hat{A}_{ij}\}_{1\leq i\neq j\leq n}$| from the partial set of observations |$\{A_{ij}\}_{(i,\,j)\in\Omega}$|…

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Rejoinder: ‘Network cross-validation by edge sampling’

《基于边抽样的网络交叉验证》讨论回复

We thank the editor for organizing this discussion and giving us the opportunity to read experts’ perspectives on our work. We are grateful to all the discussants for their insightful contributions, which raise many important points and offer suggestions for potential improvements and generalizations of our method. In this rejoinder we provide some clarifications, remarks and selected numerical results in response to these comments. Lei & Lin (2020) conjecture, and we agree,…

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Discussion of ‘Network cross-validation by edge sampling’

《通过边抽样进行网络交叉验证》的讨论

We congratulate the authors for a nice contribution to the literature on model selection and assessment for complex network data. The article of Li et al. (2020) enriches the collection of tools available for network data analysis, bringing together different fields such as low-rank matrix estimation, cross-validation and network modelling. This discussion will focus on the |$V$|-fold variant of the edge sampling cross-validation method and its combination with other…

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Network cross-validation by edge sampling

通过边抽样进行网络交叉验证

Summary While many statistical models and methods are now available for network analysis, resampling of network data remains a challenging problem. Cross-validation is a useful general tool for model selection and parameter tuning, but it is not directly applicable to networks since splitting network nodes into groups requires deleting edges and destroys some of the network structure. In this paper we propose a new network resampling strategy, based on splitting node pairs…

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Entrywise eigenvector analysis of random matrices with low expected rank

期望低秩随机矩阵的特征向量逐元素分析

Recovering low-rank structures via eigenvector perturbation analysis is a common problem in statistical machine learning, such as in factor analysis, community detection, ranking, matrix completion, among others. While a large variety of bounds are available for average errors between empirical and population statistics of eigenvectors, few results are tight for entrywise analyses, which are critical for a number of problems such as community detection. This paper…

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Statistical inference in two-sample summary-data Mendelian randomization using robust adjusted profile score

利用稳健调整剖面得分进行双样本汇总数据孟德尔随机化推断

Mendelian randomization (MR) is a method of exploiting genetic variation to unbiasedly estimate a causal effect in presence of unmeasured confounding. MR is being widely used in epidemiology and other related areas of population science. In this paper, we study statistical inference in the increasingly popular two-sample summary-data MR design. We show a linear model for the observed associations approximately holds in a wide variety of settings when all the genetic variants…

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Survey weighted estimating equation inference with nuisance functionals

含干扰泛函的调查加权估计方程推断

This paper provides a rigorous treatment on design-based estimating equation inference using complex survey data in the presence of nuisance functionals. The proposed design-based framework covers parameters from inequality measures and measures on performance evaluation in economic, business and financial studies but the scope of the paper is more broad. Unlike nuisance parameters in other settings where profile analysis is commonly used, the nuisance functionals are…

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The dynamic factor network model with an application to international trade

动态因子网络模型及其国际贸易应用

We introduce a dynamic network model with probabilistic link functions that depend on stochastically time-varying parameters. We adopt a blockmodel framework and allow the high-dimensional vector of link probabilities to be a function of a low-dimensional set of dynamic factors. The resulting dynamic factor network model has a basic and transparent structure. However, parameter estimation, signal extraction of stochastic loadings and dynamic factors, and the econometric…

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Counterfactual prediction in complete information games: Point prediction under partial identification

完全信息博弈的反事实预测:部分识别下的点预测

We study the problem of counterfactual prediction in discrete decision games with complete information, pure strategies, and Nash equilibria: the presence of multiple equilibria poses unique challenges. We introduce multiple types of counterfactuals to establish sharp identified bounds for their prediction probabilities. We propose and compare various point prediction methods, namely midpoint prediction, an approach using a Dirichlet-based prior, a maximum entropy method,…

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Unobserved heterogeneity in auctions under restricted stochastic dominance

受限随机占优下拍卖中的不可观测异质性

We study the identification of first-price auctions with nonseparable unobserved heterogeneity. In particular, we extend Hu et al. (2013) by relaxing the first-order stochastic dominance condition. Instead, we assume restricted stochastic dominance relations among value quantile functions and show that the same relations pass to bid quantile functions. An ordered tree summarizes these relations and provides a total ordering. Relying on the proposed restricted stochastic…

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Efficient estimation of heterogeneous coefficients in panel data models with common shocks

共同冲击面板模型中异质系数的有效估计

This paper investigates the estimation and inference issues of heterogeneous coefficients in panel data models with common shocks. We propose a novel two-step method to estimate the heterogeneous coefficients. We establish the asymptotic theory of our estimators, including consistency, asymptotic representation, and limiting distribution. Our two-step method can effectively address the limitations of the existing methods, such as the common correlated effects method proposed…

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Locked in by leverage: Job search during the housing crisis

被杠杆锁定:住房危机期间的求职行为

This paper examines how housing market distress affects job search. Using data from a leading online job search platform during the Great Recession, we find that job seekers in areas with depressed housing markets apply for fewer jobs that require relocation. With their search constrained geographically, job seekers broaden their search for lower-level positions nearby. These effects are stronger for job seekers with recourse mortgages, which we confirm using a spatial…

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IDENTIFICATION AND ESTIMATION IN A THIRD-PRICE AUCTION MODEL

第三价格拍卖模型的识别与估计

The first novelty of this paper is that we show global identification of the private values distribution in a sealed-bid third-price auction model using a fully nonparametric methodology. The second novelty of the paper comes from the study of the identification and estimation of the model using a quantile approach. We consider an i.i.d. private values environment with risk-averse bidders. In the first place, we consider the case where the risk-aversion parameter is known.…

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Estimation of firm‐level productivity in the presence of exports: Evidence from China's manufacturing

存在出口时的企业生产率估计:中国制造业证据

Summary Motivated by the long‐standing interest of economists in understanding the nexus between firm productivity and export behavior, this paper develops a novel structural framework for control‐function‐based nonparametric identification of the gross production function and latent firm productivity in the presence of endogenous export opportunities that is robust to recent unidentification critiques of proxy estimators. We provide a workable identification strategy,…

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Estimation with Aggregate Shocks

存在总量冲击时的估计

Abstract Aggregate shocks affect most households’ and firms’ decisions. Using three stylized models, we show that inference based on cross-sectional data alone generally fails to correctly account for decision making of rational agents facing aggregate uncertainty. We propose an econometric framework that overcomes these problems by explicitly parameterizing the agents’ decision problem relative to aggregate shocks. Our framework and examples illustrate that the…

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Double/debiased machine learning for difference-in-differences models

双重差分模型中的双重/去偏机器学习

Summary This paper provides an orthogonal extension of the semiparametric difference-in-differences estimator proposed in earlier literature. The proposed estimator enjoys the so-called Neyman orthogonality (Chernozhukov et al., 2018), and thus it allows researchers to flexibly use a rich set of machine learning methods in the first-step estimation. It is particularly useful when researchers confront a high-dimensional data set in which the number of potential control…

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Wild bootstrap for fuzzy regression discontinuity designs: obtaining robust bias-corrected confidence intervals

模糊断点回归的野生自助法:构造稳健偏差校正置信区间

Summary This paper develops a novel wild bootstrap procedure to construct robust bias-corrected valid confidence intervals for fuzzy regression discontinuity designs, providing an intuitive complement to existing robust bias-corrected methods. The confidence intervals generated by this procedure are valid under conditions similar to the procedures proposed by Calonico et al. (2014) and related literature. Simulations provide evidence that this new method is at least as…

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Partial identification in nonseparable count data instrumental variable models

非可分计数数据工具变量模型的部分识别

Summary This paper investigates undesirable limitations of widely used count data instrumental variable models. To overcome the limitations, I propose a partially identifying single-equation model that requires neither strong separability of unobserved heterogeneity nor a triangular system. Sharp bounds (identified sets) of structural features are characterised by conditional moment inequalities. Numerical examples show that the size of an identified set can be very small…

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Optimal bandwidth choice for robust bias-corrected inference in regression discontinuity designs

断点回归中稳健偏差校正推断的最优带宽选择

Summary Modern empirical work in regression discontinuity (RD) designs often employs local polynomial estimation and inference with a mean square error (MSE) optimal bandwidth choice. This bandwidth yields an MSE-optimal RD treatment effect estimator, but is by construction invalid for inference. Robust bias-corrected (RBC) inference methods are valid when using the MSE-optimal bandwidth, but we show that they yield suboptimal confidence intervals in terms of coverage error.…

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Double machine learning with gradient boosting and its application to the Big N audit quality effect

梯度提升双重机器学习及其对大型审计机构质量效应的应用

In this paper, we study the double machine learning (DML) approach of Chernozhukov et al. (2018) for estimating average treatment effect and apply this approach to examine the Big N audit quality effect in the accounting literature. This approach relies on machine learning methods and is suitable when a high dimensional nuisance function with many covariates is present in the model. This approach does not suffer from the “regularization bias” when a learning method with a…

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Two-mode network autoregressive model for large-scale networks

大规模二模网络的网络自回归模型

A two-mode network refers to a network where the nodes are classified into two distinct types, and edges can only exist between nodes of different types. In analysis of two-mode networks, one important objective is to explore the relationship between responses of two types of nodes. To this end, we propose a network autoregressive model for two-mode networks. Different network autocorrelation coefficients are allowed. To estimate the model, a quasi-maximum likelihood…

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Inference for the degree distributions of preferential attachment networks with zero-degree nodes

含零度节点的优先连接网络度分布推断

The tail of the logarithmic degree distribution of networks decays linearly with respect to the logarithmic degree is known as the power law and is ubiquitous in daily lives. A commonly used technique in modeling the power law is preferential attachment (PA), which sequentially joins each new node to the existing nodes according to the conditional probability law proportional to a linear function of their degrees. Although effective, it is tricky to apply PA to real networks…

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