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Counterfactual Imputation: Comments on “Imputation of Counterfactual Outcomes when the Errors are Predictable” by Silvia Gonçalves and Serena Ng

反事实插补:对可预测误差下反事实结果插补方法的评论

The measurement of treatment (intervention) effects on a single (or just a few) treated unit(s) based on counterfactuals constructed from artificial controls has become a popular practice in applied statistics and economics since the proposal of the synthetic control method. However, most of the literature has ignored the time-series properties of the data. The work of Gonçalves and Ng fills this gap by proposing a simple correction for existing estimators to take into…

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Discussion of “Imputation of Counterfactual Outcomes when the Errors are Predictable” by Sílvia Gonçalves and Serena Ng

《误差可预测时的反事实结果插补》讨论:从处理选择理解 PUP

I argue that the PUP approach proposed by Goncalves and Ng is not only useful for reducing the mean squared error of treatment effect estimators but can also be motivated from an identification perspective when units select into treatment based on past shocks.

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On “Imputation of Counterfactual Outcomes when the Errors are Predictable”: Discussions on Misspecification and Suggestions of Sensitivity Analyses

《误差可预测时的反事实结果插补》讨论:误设与敏感性分析

Gonçalves and Ng propose an interesting and simple way to improve counterfactual imputation methods when errors are predictable. For unconditional analyses, this approach yields smaller mean-squared error and tighter prediction intervals in large samples, even if the dependence of the errors is misspecified. For conditional analyses, this approach corrects the bias of standard methods, and provides valid asymptotic inference, if the dependence of the errors is correctly…

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On “Imputation of Counterfactual Outcomes When the Errors Are Predictable”: Viewing the PUP as the DID and the LDV

从双重差分与滞后因变量视角理解 PUP

I discuss the practical unbiased predictor (PUP; Gonçalves and Ng) from the viewpoint of the literature on identification in event studies. The PUP can be seen as the prediction based on a generalized estimand that encompasses both the difference-in-differences (DID) and the lagged dependent variable (LDV). This feature of the PUP allows for a doubly robust property that the identification is achieved when either the parallel trend assumption or the LDV assumption holds at…

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Imputation of Counterfactual Outcomes when the Errors are Predictable

误差可预测时的反事实结果插补

A crucial input into causal inference is the imputed counterfactual outcome. Imputation error can arise because of sampling uncertainty from estimating the prediction model using the untreated observations, or from out-of-sample information not captured by the model. While the literature has focused on sampling uncertainty, it vanishes with the sample size. Often overlooked is the possibility that the out-of-sample error can be informative about the missing counterfactual…

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Identification and Auto-Debiased Machine Learning for Outcome-Conditioned Average Structural Derivatives

结果条件平均结构导数的识别与自动去偏机器学习

This study proposes a new class of heterogeneous causal quantities, referred to as outcome-conditioned average structural derivatives (OASDs), in a general nonseparable model. An OASD is the average partial effect of a marginal change in a continuous treatment on individuals located on different parts of an outcome distribution, irrespective of individuals’ characteristics. We show that OASDs extend the unconditional quantile partial effects (UQPE) proposed by Firpo, Fortin,…

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Policy Analysis Using Multilevel Regression Models with Group Interactive Fixed Effects

使用组别交互固定效应多层回归模型进行政策分析

The use of multilevel regression models is prevalent in policy analysis to estimate the effect of group level policies on individual outcomes. In order to allow for the time varying effect of group heterogeneity and the group specific impact of time effects, we propose a group interactive fixed effects approach that employs interaction terms of group factor loadings and common factors in this model. For this approach, we consider the least squares estimator and associated…

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Testing for Equivalence of Pre-Trends in Difference-in-Differences Estimation

双重差分估计中处理前趋势的等价性检验

The plausibility of the “parallel trends assumption” in Difference-in-Differences estimation is usually assessed by a test of the null hypothesis that the difference between the average outcomes of both groups is constant over time before the treatment. However, failure to reject the null hypothesis does not imply the absence of differences in time trends between both groups. We provide equivalence tests that allow researchers to find evidence in favor of the parallel trends…

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Model Checking in Partially Linear Spatial Autoregressive Models

部分线性空间自回归模型的模型检验

This article proposes two new classes of nonparametric tests for the correct specification of linear spatial autoregressive models based on the “integrated conditional moment” approach. Our test statistics are constructed as continuous functionals of a residual marked empirical process as well as its projected version. We derive asymptotic properties of the test statistics under the null hypothesis, the alternative hypothesis, and a sequence of local alternatives. The…

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Noncommon Breaks

非共同结构断点

We develop a new Bayesian approach to estimate noncommon structural breaks in panel regression models. Any subset of the cross-section may be hit at different times within a break window. Break-specific parameters are learned from the cross-section. They reflect whether (i) breaks hit many or few series and (ii) there is a long or short lag between the first and final series hit by a break. In an empirical application to international stock return predictability, the method…

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Nonparametric Identification and Inference of First-Price Auctions with Heterogeneous Bidders

异质竞标者第一价格拍卖的非参数识别与推断

In the auction literature, it is well established that bidders’ asymmetry plays an important role in determining auction revenues. In this article, we propose a nonparametric methodology to analyze first-price auctions with two popularly adopted asymmetries: heterogeneous risk preferences and asymmetric value distributions. We find that the two competing models provide distinct implications for the bid distributions conditional on heterogeneity. By modeling bidders’…

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Unconditional Quantile Regression for Streaming Datasets

流式数据的无条件分位数回归

The Unconditional Quantile Regression (UQR) method, initially introduced by Firpo et al. has gained significant traction as a popular approach for modeling and analyzing data.However, much like Conditional Quantile Regression (CQR), UQR encounters computational challenges when it comes to obtaining parameter estimates for streaming datasets.This is attributed to the involvement of unknown parameters in the logistic regression loss function used in UQR, which presents…

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Oracle Efficient Estimation of Heterogeneous Dynamic Panel Data Models with Interactive Fixed Effects

含交互固定效应的异质动态面板模型:Oracle 有效估计

We propose a two-step procedure to estimate a heterogeneous dynamic panel data model with interactive fixed effects. We establish the asymptotic properties of the estimators and show that the final estimator is oracle efficient. We also propose a specification test for the null hypothesis of homogeneous slopes and study the asymptotic properties of the test statistic under both local and global alternatives. Simulations demonstrate the fine performance of the estimator and…

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Matrix Completion When Missing Is Not at Random and Its Applications in Causal Panel Data Models

非随机缺失下的矩阵补全及其在因果面板模型中的应用

This paper develops an inferential framework for matrix completion when missing is not at random and without the requirement of strong signals. Our development is based on the observation that if the number of missing entries is small enough compared to the panel size, then they can be estimated well even when missing is not at random. Taking advantage of this fact, we divide the missing entries into smaller groups and estimate each group via nuclear norm regularization. In…

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Standard Errors for Two-Way Clustering with Serially Correlated Time Effects

时间效应存在序列相关时的双向聚类标准误

Abstract We propose improved standard errors and an asymptotic theory for two-way clustered panels. Our theory allow for arbitrary serial dependence in the common time effects, which is excluded by existing two-way methods. Our asymptotic distribution theory is the first which allows for this level of inter-dependence. Under weak conditions, we demonstrate that OLS is asymptotically normal, our proposed variance estimator is consistent, and t-ratios are asymptotically…

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Yang Feng and Jiajin Sun’s contribution to the Discussion of ‘Root and community inference on the latent growth process of a network’ by Crane and Xu

Feng 与 Sun 对“网络潜在增长过程的根与社群推断”的讨论

We congratulate Drs. Crane and Xu for their fascinating piece of work. In the multiple roots PAPER model, one assumption is that different trees share the same affine preferential attachment (APA) growth parameters (α,β)⁠. In practice, the multiple trees in a network may have varying growth mechanisms, and it may be of interest to model each tree to have its own growth parameters. We consider such a heterogeneous affine preferential attachment (HAPA) model. Definition 1…

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Fan Wang, Yi Yu and Alessandro Rinaldo's contribution to the Discussion of ‘Root and community inference on the latent growth process of a network’ by Crane and Xu

范旺、余怡与里纳尔多对网络潜在生长过程根与社区推断的讨论

We congratulate Prof. Crane and Dr Xu for introducing a very interesting and appealing statistical model for Markovian network growth. The PAPER model enjoys several qualities. In particular, (i) it strikes a rare balance between analytic elegance and tractability, and expressive power; (ii) it allows for practicable algorithms for statistical inference that scale to networks of very large size, and (iii) it is very flexible and can be readily generalized to model a variety…

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Andrej Srakar’s contribution to the Discussion of ‘Root and community inference on the latent growth process of a network’ by Crane and Xu

Andrej Srakar 对《网络潜在增长过程的根节点与社区推断》的讨论评论

Paper presented by Harry Crane and Min Xu develops a rather novel area of network archaeology, which builds on findings of network science, probability theory and (in Crane and Xu's article) Bayesian statistics. My comments are directed to possible extensions for future work in this promising area of research. Firstly, in terms of network stochastic processes (authors use a combination of preferential attachment and Erdős–Rényi models) paper does little to explain…

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Marta Catalano, Augusto Fasano, Matteo Giordano, and Giovanni Rebaudo’s contribution to the Discussion of ‘Root and community inference on the latent growth process of a network’ by Crane and Xu

Catalano等对《网络潜在生长过程的根与社群推断》的讨论

We congratulate the authors for their methodological and theoretical contribution to the statistical literature on networks. A natural extension of the proposed PAPER model is included, with K communities growing simultaneously and where new nodes are either assigned to an existing community or elected as a new root. The employed assignment rule is of Pólya-urn type, which leads to a logarithmic growth of the number of communities (Korwar & Hollander, 1973) and is known to…

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Proposers of the vote of thanks to Crane and Xu and contribution to the Discussion of ‘Root and community inference on the latent growth process of a network’

对 Crane 与 Xu《网络潜在生长过程的根与社区推断》的致谢与讨论

We commend the authors on an illuminating article which significantly extends the state of the art in network archaeology. Notably, whereas most other literature in the area has provided methods for root inference which are theoretically grounded only in the case of random trees, the techniques in this paper have been designed to model nontree-structured networks, as well. This has important practical implications, as many real-world networks contain one or more cycles. The…

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Qing Yang and Xin Tong’s contribution to the Discussion of ‘Root and community inference on the latent growth process of a network’ by Crane and Xu

杨青与童昕对“网络潜在增长过程的根节点与社区推断”的讨论

First, we congratulate Dr. Crane and Dr. Xu for this important contribution to statistical network analysis. To address an overlooked fact that most real networks are formed through a growth process, the authors introduce a useful PAPER model and its variations and skilfully construct computationally feasible confidence sets for the root node(s). In the data analysis, the authors also use their models as a new approach to community detection. On this note, our interest lies…

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Jason Wyse, James Ng, Arthur White and Michael Fop's contribution to the Discussion of ‘Root and community inference on the latent growth process of a network' by Crane and Xu

Wyse 等对《网络潜在增长过程的根节点与社区推断》的讨论

We congratulate the authors on a thought provoking paper introducing innovative ideas for the statistical modelling of networks. The emphasis on identifying highly probable root nodes is both original and intriguing. In particular, using the root node credible set methods for node clustering within the PAPER(α,β,α0,θ) random K model (Section 6.3) is an interesting perspective. We wonder how these approaches might connect with latent space model-based node clustering methods…

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Yicong Jiang and Zheng Tracy Ke’s contribution to the Discussion of ‘Root and community inference on the latent growth process of a network’ by Crane and Xu

江一聪与柯征对《网络潜在增长过程的根节点与社群推断》的讨论

We congratulate the authors on an excellent paper! Crane and Xu (2021) proposed novel methods for finding ‘root nodes’ from a single snapshot of a dynamic network process, with several interesting real-data examples. We now consider a new application for finding ‘root papers’ in a citation network. The MADStat dataset (Ji et al., 2022; Ke et al., 2023) consists of the bibtex and citation information of over 83 K papers, which we use to construct paper citation networks.…

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