{"title":"Asymptotic theory for two-way clustering","authors":"Luther Yap","doi":"10.1016/j.jeconom.2025.106001","DOIUrl":"10.1016/j.jeconom.2025.106001","url":null,"abstract":"<div><div>This paper proves a new central limit theorem for a sample that exhibits two-way dependence and heterogeneity across clusters. Statistical inference for situations with both two-way dependence and cluster heterogeneity has thus far been an open issue. The existing theory for two-way clustering inference requires identical distributions across clusters (implied by the so-called separate exchangeability assumption). Yet no such homogeneity requirement is needed in the existing theory for one-way clustering. The new result therefore theoretically justifies the view that two-way clustering is a more robust version of one-way clustering, consistent with applied practice. In an application to linear regression, I show that a standard plug-in variance estimator is valid for inference.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"249 ","pages":"Article 106001"},"PeriodicalIF":9.9,"publicationDate":"2025-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143816508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Regret analysis in threshold policy design","authors":"Federico Crippa","doi":"10.1016/j.jeconom.2025.105998","DOIUrl":"10.1016/j.jeconom.2025.105998","url":null,"abstract":"<div><div>Threshold policies are decision rules that assign treatments based on whether an observable characteristic exceeds a certain threshold. They are widespread across multiple domains, including welfare programs, taxation, and clinical medicine. This paper examines the problem of designing threshold policies using experimental data, when the goal is to maximize the population welfare. First, I characterize the regret – a measure of policy optimality – of the Empirical Welfare Maximizer (EWM) policy, popular in the literature. Next, I introduce the Smoothed Welfare Maximizer (SWM) policy, which improves the EWM’s regret convergence rate under an additional smoothness condition. The two policies are compared by studying how differently their regrets depend on the population distribution, and investigating their finite sample performances through Monte Carlo simulations. In many contexts, the SWM policy guarantees larger welfare than the EWM. An empirical illustration demonstrates how the treatment recommendations of the two policies may differ in practice.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"249 ","pages":"Article 105998"},"PeriodicalIF":9.9,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantile prediction with factor-augmented regression: Structural instability and model uncertainty","authors":"Yundong Tu , Siwei Wang","doi":"10.1016/j.jeconom.2025.105999","DOIUrl":"10.1016/j.jeconom.2025.105999","url":null,"abstract":"<div><div>The quantile regression is an effective tool in modeling data with heterogeneous conditional distribution. This paper considers the time-varying coefficient quantile predictive regression with factor-augmented predictors, to capture smooth structural changes and incorporate high-dimensional data information in prediction simultaneously. Uniform consistency of the local linear quantile coefficient estimators is established under misspecification. To further improve the forecast accuracy, a novel time-varying model averaging based on local forward-validation is developed. The averaging estimator is shown to be asymptotically optimal in the sense of minimizing out-of-sample forecast risk function. Furthermore, the weight selection consistency and the asymptotic distribution of the averaging coefficient estimator are established. Numerical results from simulations and a real data application to forecasting U.S. inflation demonstrate the nice performance of the averaging estimators.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"249 ","pages":"Article 105999"},"PeriodicalIF":9.9,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143696011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Quantile Granger causality in the presence of instability","authors":"Alexander Mayer , Dominik Wied , Victor Troster","doi":"10.1016/j.jeconom.2025.105992","DOIUrl":"10.1016/j.jeconom.2025.105992","url":null,"abstract":"<div><div>We propose a new framework for assessing Granger causality in quantiles in unstable environments, for a fixed quantile or over a continuum of quantile levels. Our proposed test statistics are consistent against fixed alternatives, they have nontrivial power against local alternatives, and they are pivotal in certain important special cases. In addition, we show the validity of a bootstrap procedure when asymptotic distributions depend on nuisance parameters. Monte Carlo simulations reveal that the proposed test statistics have correct empirical size and high power, even in absence of structural breaks. Moreover, a procedure providing additional insight into the timing of Granger causal regimes based on our new tests is proposed. Finally, an empirical application in energy economics highlights the applicability of our method as the new tests provide stronger evidence of Granger causality.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"249 ","pages":"Article 105992"},"PeriodicalIF":9.9,"publicationDate":"2025-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143687646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Model averaging prediction for possibly nonstationary autoregressions","authors":"Tzu-Chi Lin , Chu-An Liu","doi":"10.1016/j.jeconom.2025.105994","DOIUrl":"10.1016/j.jeconom.2025.105994","url":null,"abstract":"<div><div>As an alternative to model selection (MS), this paper considers model averaging (MA) for integrated autoregressive processes of infinite order (AR(<span><math><mi>∞</mi></math></span>)). We derive a uniformly asymptotic expression for the mean squared prediction error (MSPE) of the averaging prediction with fixed weights and then propose a Mallows-type criterion to select the data-driven weights that minimize the MSPE asymptotically. We show that the proposed MA estimator and its variants, Shibata and Akaike MA estimators, are asymptotically optimal in the sense of achieving the lowest possible MSPE. We further demonstrate that MA can provide significant MSPE reduction over MS in the algebraic-decay case. These theoretical findings are extended to integrated AR(<span><math><mi>∞</mi></math></span>) models with deterministic time trends and are supported by Monte Carlo simulations and real data analysis.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"249 ","pages":"Article 105994"},"PeriodicalIF":9.9,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143687647","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Supervised factor modeling for high-dimensional linear time series","authors":"Feiqing Huang , Kexin Lu , Yao Zheng , Guodong Li","doi":"10.1016/j.jeconom.2025.105995","DOIUrl":"10.1016/j.jeconom.2025.105995","url":null,"abstract":"<div><div>Motivated by Tucker tensor decomposition, this paper imposes low-rank structures to the column and row spaces of coefficient matrices in a multivariate infinite-order vector autoregression (VAR), which leads to a supervised factor model with two factor modelings being conducted to responses and predictors simultaneously. Interestingly, the stationarity condition implies an intrinsic weak group sparsity mechanism of infinite-order VAR, and hence a rank-constrained group Lasso estimation is considered for high-dimensional linear time series. Its non-asymptotic properties are discussed by balancing the estimation, approximation and truncation errors. Moreover, an alternating gradient descent algorithm with hard-thresholding is designed to search for high-dimensional estimates, and its theoretical justifications, including statistical and convergence analysis, are also provided. Theoretical and computational properties of the proposed methodology are verified by simulation experiments, and the advantages over existing methods are demonstrated by analyzing US quarterly macroeconomic variables.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"249 ","pages":"Article 105995"},"PeriodicalIF":9.9,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143687645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Huber Principal Component Analysis for large-dimensional factor models","authors":"Yong He , Lingxiao Li , Dong Liu , Wen-Xin Zhou","doi":"10.1016/j.jeconom.2025.105993","DOIUrl":"10.1016/j.jeconom.2025.105993","url":null,"abstract":"<div><div>Factor models have been widely used in economics and finance. However, the heavy-tailed nature of macroeconomic and financial data is often neglected in statistical analysis. To address this issue, we propose a robust approach to estimate factor loadings and scores by minimizing the Huber loss function, which is motivated by the equivalence between conventional Principal Component Analysis (PCA) and the constrained least squares method in the factor model. We provide two algorithms that use different penalty forms. The first algorithm involves an element-wise-type Huber loss minimization, solved by an iterative Huber regression algorithm. The second algorithm, which we refer to as Huber PCA, minimizes the <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-norm-type Huber loss and performs PCA on the weighted sample covariance matrix. We examine the theoretical minimizer of the element-wise Huber loss function and demonstrate that it has the same convergence rate as conventional PCA when the idiosyncratic errors have bounded second moments. We also derive their asymptotic distributions under mild conditions. Moreover, we suggest a consistent model selection criterion that relies on rank minimization to estimate the number of factors robustly. We showcase the benefits of the proposed two algorithms through extensive numerical experiments and a real macroeconomic data example. An <span>R</span> package named “<span>HDRFA</span>” <span><span><sup>1</sup></span></span> has been developed to conduct the proposed robust factor analysis.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"249 ","pages":"Article 105993"},"PeriodicalIF":9.9,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143642831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Limit theory and inference in non-cointegrated functional coefficient regression","authors":"Ying Wang , Peter C.B. Phillips , Yundong Tu","doi":"10.1016/j.jeconom.2025.105996","DOIUrl":"10.1016/j.jeconom.2025.105996","url":null,"abstract":"<div><div>Functional coefficient (FC) cointegrating regressions offer empirical investigators flexibility in modeling economic relationships by introducing covariates that influence the direction and intensity of comovement among nonstationary time series. FC regression models are also useful when formal cointegration is absent, in the sense that the equation errors may themselves be nonstationary, but where the nonstationary series display well-defined FC linkages that can be meaningfully interpreted as correlation measures involving the covariates. The present paper proposes new nonparametric estimators for such FC regression models where the nonstationary series display linkages that enable consistent estimation of the correlation measures between them. Specifically, we develop <span><math><msqrt><mrow><mi>n</mi></mrow></msqrt></math></span>-consistent estimators for the functional coefficient and establish their asymptotic distributions, which involve mixed normal limits that facilitate inference. Two novel features that appear in the limit theory are (i) the need for non-diagonal matrix normalization due to the presence of stationary and nonstationary components in the regression; and (ii) random bias elements that appear in the asymptotic distribution of the kernel estimators, again resulting from the nonstationary regression components. Numerical studies reveal that the proposed estimators achieve significant efficiency improvements compared to the estimators suggested in earlier work by Sun et al. (2011). Easily implementable specification tests with standard chi-square asymptotics are suggested to check for constancy of the functional coefficient. These tests are shown to have faster divergence rate under local alternatives and enjoy superior performance in simulations than tests proposed in Gan et al. (2014). An empirical application based on the quantity theory of money is included, illustrating the practical use of correlated but non-cointegrated regression relations.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"249 ","pages":"Article 105996"},"PeriodicalIF":9.9,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143642830","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Adjustments with many regressors under covariate-adaptive randomizations","authors":"Liang Jiang , Liyao Li , Ke Miao , Yichong Zhang","doi":"10.1016/j.jeconom.2025.105991","DOIUrl":"10.1016/j.jeconom.2025.105991","url":null,"abstract":"<div><div>Our paper discovers a new trade-off of using regression adjustments (RAs) in causal inference under covariate-adaptive randomizations (CARs). On one hand, RAs can improve the efficiency of causal estimators by incorporating information from covariates that are not used in the randomization. On the other hand, RAs can degrade estimation efficiency due to their estimation errors, which are not asymptotically negligible when the number of regressors is of the same order as the sample size. Ignoring the estimation errors of RAs may result in serious over-rejection of causal inference under the null hypothesis. To address the issue, we construct a new ATE estimator by optimally linearly combining the estimators with and without RAs. We then develop a unified inference theory for this estimator under CARs. It has two features: (1) the Wald test based on it achieves the exact asymptotic size under the null hypothesis, regardless of whether the number of covariates is fixed or diverges no faster than the sample size; and (2) it guarantees weak efficiency improvement over estimators both with and without RAs.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"249 ","pages":"Article 105991"},"PeriodicalIF":9.9,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143629093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Philipp Bach , Sven Klaassen , Jannis Kueck , Martin Spindler
{"title":"Estimation and uniform inference in sparse high-dimensional additive models","authors":"Philipp Bach , Sven Klaassen , Jannis Kueck , Martin Spindler","doi":"10.1016/j.jeconom.2025.105973","DOIUrl":"10.1016/j.jeconom.2025.105973","url":null,"abstract":"<div><div>We develop a novel method to construct uniformly valid confidence bands for a nonparametric component <span><math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> in the sparse additive model <span><math><mrow><mi>Y</mi><mo>=</mo><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>)</mo></mrow><mo>+</mo><mo>…</mo><mo>+</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>p</mi></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>)</mo></mrow><mo>+</mo><mi>ɛ</mi></mrow></math></span> in a high-dimensional setting. Our method integrates sieve estimation into a high-dimensional Z-estimation framework, facilitating the construction of uniformly valid confidence bands for the target component <span><math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>. To form these confidence bands, we employ a multiplier bootstrap procedure. Additionally, we provide rates for the uniform lasso estimation in high dimensions, which may be of independent interest. Through simulation studies, we demonstrate that our proposed method delivers reliable results in terms of estimation and coverage, even in small samples.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"249 ","pages":"Article 105973"},"PeriodicalIF":9.9,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143551236","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}