Pub Date : 2025-10-14DOI: 10.1016/j.jeconom.2025.106110
Jin Seo Cho , Peter C.B. Phillips
In GMM estimation, it is well known that if the moment dimension grows with the sample size, the asymptotics of GMM differ from the standard finite dimensional case. The present work examines the asymptotic properties of infinite dimensional GMM estimation when the weight matrix is formed by inverting Brownian motion or Brownian bridge covariance kernels. These kernels arise in econometric work such as minimum Cramér–von Mises distance estimation when testing distributional specification. The properties of GMM estimation are studied under different environments where the moment conditions converge to a smooth Gaussian or non-differentiable Gaussian process. Conditions are also developed for testing the validity of the moment conditions by means of a suitably constructed -statistic. In case these conditions are invalid we propose another test called the -test. As an empirical application of these infinite dimensional GMM procedures the evolution of cohort labor income inequality indices is studied using the Continuous Work History Sample database. The findings show that labor income inequality indices are maximized at early career years, implying that economic policies to reduce income inequality should be more effective when designed for workers at an early stage in their career cycles.
在GMM估计中，众所周知，当矩维随样本量增长时，GMM的渐近性与标准有限维情况不同。本文研究了当权矩阵由反布朗运动或布朗桥协方差核构成时，无限维GMM估计的渐近性质。这些核函数出现在计量经济学工作中，例如在测试分布规格时的最小cram - von Mises距离估计。研究了矩条件收敛于光滑高斯过程和不可微高斯过程的不同环境下GMM估计的性质。通过适当构造的j统计量，还开发了检验矩条件有效性的条件。如果这些条件无效，我们提出另一种测试，称为u型测试。作为这些无限维GMM程序的实证应用，本文利用连续工作历史样本数据库研究了队列劳动收入不平等指数的演变。研究结果表明，劳动收入不平等指数在职业生涯早期达到最大值，这意味着为处于职业生涯早期阶段的工人设计的减少收入不平等的经济政策应该更有效。
{"title":"GMM estimation with Brownian kernels applied to income inequality measurement","authors":"Jin Seo Cho , Peter C.B. Phillips","doi":"10.1016/j.jeconom.2025.106110","DOIUrl":"10.1016/j.jeconom.2025.106110","url":null,"abstract":"<div><div>In GMM estimation, it is well known that if the moment dimension grows with the sample size, the asymptotics of GMM differ from the standard finite dimensional case. The present work examines the asymptotic properties of infinite dimensional GMM estimation when the weight matrix is formed by inverting Brownian motion or Brownian bridge covariance kernels. These kernels arise in econometric work such as minimum Cramér–von Mises distance estimation when testing distributional specification. The properties of GMM estimation are studied under different environments where the moment conditions converge to a smooth Gaussian or non-differentiable Gaussian process. Conditions are also developed for testing the validity of the moment conditions by means of a suitably constructed <span><math><mi>J</mi></math></span>-statistic. In case these conditions are invalid we propose another test called the <span><math><mi>U</mi></math></span>-test. As an empirical application of these infinite dimensional GMM procedures the evolution of cohort labor income inequality indices is studied using the Continuous Work History Sample database. The findings show that labor income inequality indices are maximized at early career years, implying that economic policies to reduce income inequality should be more effective when designed for workers at an early stage in their career cycles.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106110"},"PeriodicalIF":4.0,"publicationDate":"2025-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145324449","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}
Pub Date : 2025-10-13DOI: 10.1016/j.jeconom.2025.106113
Falong Tan , Xu Guo , Lixing Zhu
This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical process-based tests, both with and without martingale transformations. The asymptotic properties of these tests are derived from the behavior of weighted residual empirical processes and their martingale transformations under the null and alternative hypotheses. The proposed tests without martingale transformations achieve the fastest possible rate of detecting local alternatives, specifically of order , which is unaffected by dimensionality. However, these tests are not asymptotically distribution-free. To address this limitation, we propose a smooth residual bootstrap approximation and establish its validity in diverging-dimension settings. In contrast, tests incorporating martingale transformations are asymptotically distribution-free but exhibit an unexpected limitation: they can only detect local alternatives converging to the null at a much slower rate of order , which remains independent of dimensionality. This finding reveals a theoretical advantage in the power of tests based on weighted residual empirical process without martingale transformations over their martingale-transformed counterparts, challenging the conventional wisdom of existing asymptotically distribution-free tests based on martingale transformations. To validate our approach, we conduct simulation studies and apply the proposed tests to a real-world dataset, demonstrating their practical effectiveness.
{"title":"Weighted residual empirical processes, martingale transformations, and model specification tests for regressions with diverging number of parameters","authors":"Falong Tan , Xu Guo , Lixing Zhu","doi":"10.1016/j.jeconom.2025.106113","DOIUrl":"10.1016/j.jeconom.2025.106113","url":null,"abstract":"<div><div>This paper explores hypothesis testing for the parametric forms of the mean and variance functions in regression models under diverging-dimension settings. To mitigate the curse of dimensionality, we introduce weighted residual empirical process-based tests, both with and without martingale transformations. The asymptotic properties of these tests are derived from the behavior of weighted residual empirical processes and their martingale transformations under the null and alternative hypotheses. The proposed tests without martingale transformations achieve the fastest possible rate of detecting local alternatives, specifically of order <span><math><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></span>, which is unaffected by dimensionality. However, these tests are not asymptotically distribution-free. To address this limitation, we propose a smooth residual bootstrap approximation and establish its validity in diverging-dimension settings. In contrast, tests incorporating martingale transformations are asymptotically distribution-free but exhibit an unexpected limitation: they can only detect local alternatives converging to the null at a much slower rate of order <span><math><msup><mrow><mi>n</mi></mrow><mrow><mo>−</mo><mn>1</mn><mo>/</mo><mn>4</mn></mrow></msup></math></span>, which remains independent of dimensionality. This finding reveals a theoretical advantage in the power of tests based on weighted residual empirical process without martingale transformations over their martingale-transformed counterparts, challenging the conventional wisdom of existing asymptotically distribution-free tests based on martingale transformations. To validate our approach, we conduct simulation studies and apply the proposed tests to a real-world dataset, demonstrating their practical effectiveness.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106113"},"PeriodicalIF":4.0,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145323902","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}
Pub Date : 2025-10-13DOI: 10.1016/j.jeconom.2025.106112
Zixin Yang , Xiaojun Song , Jihai Yu
This paper proposes a sieve generalized method of moments (GMM) method for the estimation of spatial autoregressive panel data models with nonparametric endogenous effect. The new estimator incorporates both linear moments based on the orthogonality of the exogenous regressors with the model disturbances and quadratic moments based on the properties of idiosyncratic errors. We establish the consistency and asymptotic normality of the sieve GMM estimator and show that it is more efficient than the sieve instrumental variable estimator due to additional quadratic moments. We also put forward two new test statistics for testing the linearity of the endogenous effect. Both test statistics are shown to be asymptotic normal under the null and a sequence of local alternatives after proper standardization. Monte Carlo simulations show that the proposed estimators and tests perform well in finite samples. We also apply our method to estimate the environmental Kuznets curve in China and the knowledge spillover effect among 61 countries.
{"title":"Estimation of spatial autoregressive panel data models with nonparametric endogenous effect","authors":"Zixin Yang , Xiaojun Song , Jihai Yu","doi":"10.1016/j.jeconom.2025.106112","DOIUrl":"10.1016/j.jeconom.2025.106112","url":null,"abstract":"<div><div>This paper proposes a sieve generalized method of moments (GMM) method for the estimation of spatial autoregressive panel data models with nonparametric endogenous effect. The new estimator incorporates both linear moments based on the orthogonality of the exogenous regressors with the model disturbances and quadratic moments based on the properties of idiosyncratic errors. We establish the consistency and asymptotic normality of the sieve GMM estimator and show that it is more efficient than the sieve instrumental variable estimator due to additional quadratic moments. We also put forward two new test statistics for testing the linearity of the endogenous effect. Both test statistics are shown to be asymptotic normal under the null and a sequence of local alternatives after proper standardization. Monte Carlo simulations show that the proposed estimators and tests perform well in finite samples. We also apply our method to estimate the environmental Kuznets curve in China and the knowledge spillover effect among 61 countries.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106112"},"PeriodicalIF":4.0,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145324448","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}
Pub Date : 2025-10-13DOI: 10.1016/j.jeconom.2025.106114
Tom Boot , Johannes W. Ligtenberg
Identification-robust hypothesis tests are commonly based on the continuous updating GMM objective function. When the number of moment conditions grows proportionally with the sample size, the large-dimensional weighting matrix prohibits the use of conventional asymptotic approximations and the behavior of these tests remains unknown. We show that the structure of the weighting matrix opens up an alternative route to asymptotic results when, under the null hypothesis, the distribution of the moment conditions satisfies a symmetry condition known as reflection invariance. We provide several examples in which the invariance follows from standard assumptions. Our results show that existing tests will be asymptotically conservative, and we propose an adjustment to attain nominal size in large samples. We illustrate our findings through simulations for various linear and nonlinear models, and an empirical application on the effect of the concentration of financial activities in banks on systemic risk.
{"title":"Identification- and many moment-robust inference via invariant moment conditions","authors":"Tom Boot , Johannes W. Ligtenberg","doi":"10.1016/j.jeconom.2025.106114","DOIUrl":"10.1016/j.jeconom.2025.106114","url":null,"abstract":"<div><div>Identification-robust hypothesis tests are commonly based on the continuous updating GMM objective function. When the number of moment conditions grows proportionally with the sample size, the large-dimensional weighting matrix prohibits the use of conventional asymptotic approximations and the behavior of these tests remains unknown. We show that the structure of the weighting matrix opens up an alternative route to asymptotic results when, under the null hypothesis, the distribution of the moment conditions satisfies a symmetry condition known as reflection invariance. We provide several examples in which the invariance follows from standard assumptions. Our results show that existing tests will be asymptotically conservative, and we propose an adjustment to attain nominal size in large samples. We illustrate our findings through simulations for various linear and nonlinear models, and an empirical application on the effect of the concentration of financial activities in banks on systemic risk.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106114"},"PeriodicalIF":4.0,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145324450","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}
Pub Date : 2025-10-13DOI: 10.1016/j.jeconom.2025.106108
Frank Kleibergen , Zhaoguo Zhan
We propose the continuous updating estimator (CUE) for estimating ex-post risk premia from large cross-sections of individual asset returns over limited time periods. We analyze its properties while also allowing for an unknown number of unobserved factors. The CUE then provides an estimator of its, so-called, pseudo-true value, the risk premia on the observed factors without assuming that they comprise all priced factors. We develop size-correct procedures for testing hypotheses on the estimand of the CUE, which are more precise than existing ones. The proposed methodology is used to examine risk factors widely analyzed using a small number of portfolios. Our findings are that market, size, and momentum factors carry largely positive risk premia, while many other factors much less so. Different factors therefore stand out in the cross-section of individual assets.
{"title":"Risk premia from the cross-section of individual assets","authors":"Frank Kleibergen , Zhaoguo Zhan","doi":"10.1016/j.jeconom.2025.106108","DOIUrl":"10.1016/j.jeconom.2025.106108","url":null,"abstract":"<div><div>We propose the continuous updating estimator (CUE) for estimating ex-post risk premia from large cross-sections of individual asset returns over limited time periods. We analyze its properties while also allowing for an unknown number of unobserved factors. The CUE then provides an estimator of its, so-called, pseudo-true value, <span><math><mrow><mi>i</mi><mo>.</mo><mi>e</mi><mo>.</mo><mo>,</mo></mrow></math></span> the risk premia on the observed factors without assuming that they comprise all priced factors. We develop size-correct procedures for testing hypotheses on the estimand of the CUE, which are more precise than existing ones. The proposed methodology is used to examine risk factors widely analyzed using a small number of portfolios. Our findings are that market, size, and momentum factors carry largely positive risk premia, while many other factors much less so. Different factors therefore stand out in the cross-section of individual assets.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106108"},"PeriodicalIF":4.0,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145324447","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}
Pub Date : 2025-10-10DOI: 10.1016/j.jeconom.2025.106111
Gregory Fletcher Cox
When parameters are weakly identified, bounds on the parameters may provide a valuable source of information. Existing weak identification estimation and inference results are unable to combine weak identification with bounds. Within a class of minimum distance models, this paper proposes identification-robust inference that incorporates information from bounds when parameters are weakly identified. This paper demonstrates the value of the bounds and identification-robust inference in a simple latent factor model and a simple GARCH model. This paper also demonstrates the identification-robust inference in an empirical application, a factor model for parental investments in children.
{"title":"Weak identification with bounds in a class of minimum distance models","authors":"Gregory Fletcher Cox","doi":"10.1016/j.jeconom.2025.106111","DOIUrl":"10.1016/j.jeconom.2025.106111","url":null,"abstract":"<div><div>When parameters are weakly identified, bounds on the parameters may provide a valuable source of information. Existing weak identification estimation and inference results are unable to combine weak identification with bounds. Within a class of minimum distance models, this paper proposes identification-robust inference that incorporates information from bounds when parameters are weakly identified. This paper demonstrates the value of the bounds and identification-robust inference in a simple latent factor model and a simple GARCH model. This paper also demonstrates the identification-robust inference in an empirical application, a factor model for parental investments in children.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106111"},"PeriodicalIF":4.0,"publicationDate":"2025-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266919","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}
Pub Date : 2025-10-09DOI: 10.1016/j.jeconom.2025.106100
Alexandre Belloni , Mingli Chen , Victor Chernozhukov
We propose two types of Quantile Graphical Models: (i) Conditional Independence Quantile Graphical Models (CIQGMs) characterize the conditional independence by evaluating the distributional dependence structure at each quantile index, as such, those can be used for validation of the graph structure in the causal graphical models; (ii) Prediction Quantile Graphical Models (PQGMs) characterize the statistical dependencies through the graphs of the best linear predictors under asymmetric loss functions. PQGMs make weaker assumptions than CIQGMs as they allow for misspecification. One advantage of these models is that we can apply them to large collections of variables driven by non-Gaussian and non-separable shocks. Because of QGMs’ ability to handle large collections of variables and focus on specific parts of the distributions, we could apply them to quantify tail interdependence. The resulting tail risk network can be used for measuring systemic risk contributions that help make inroads in understanding international financial contagion and dependence structures of returns under downside market movements.
We develop estimation and inference methods focusing on the high-dimensional case, where the number of nodes in the graph is large as compared to the number of observations. For CIQGMs, these results include valid simultaneous choices of penalty functions, uniform rates of convergence, and confidence regions that are simultaneously valid. We also derive analogous results for PQGMs, which include new results for penalized quantile regressions in high-dimensional settings to handle misspecification, many controls, and a continuum of additional conditioning events.
{"title":"Quantile graphical models: Prediction and conditional independence with applications to systemic risk","authors":"Alexandre Belloni , Mingli Chen , Victor Chernozhukov","doi":"10.1016/j.jeconom.2025.106100","DOIUrl":"10.1016/j.jeconom.2025.106100","url":null,"abstract":"<div><div>We propose two types of Quantile Graphical Models: (i) Conditional Independence Quantile Graphical Models (CIQGMs) characterize the conditional independence by evaluating the distributional dependence structure at each quantile index, as such, those can be used for validation of the graph structure in the causal graphical models; (ii) Prediction Quantile Graphical Models (PQGMs) characterize the statistical dependencies through the graphs of the best linear predictors under asymmetric loss functions. PQGMs make weaker assumptions than CIQGMs as they allow for misspecification. One advantage of these models is that we can apply them to large collections of variables driven by non-Gaussian and non-separable shocks. Because of QGMs’ ability to handle large collections of variables and focus on specific parts of the distributions, we could apply them to quantify tail interdependence. The resulting tail risk network can be used for measuring systemic risk contributions that help make inroads in understanding international financial contagion and dependence structures of returns under downside market movements.</div><div>We develop estimation and inference methods focusing on the high-dimensional case, where the number of nodes in the graph is large as compared to the number of observations. For CIQGMs, these results include valid simultaneous choices of penalty functions, uniform rates of convergence, and confidence regions that are simultaneously valid. We also derive analogous results for PQGMs, which include new results for penalized quantile regressions in high-dimensional settings to handle misspecification, many controls, and a continuum of additional conditioning events.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106100"},"PeriodicalIF":4.0,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266918","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}
Pub Date : 2025-10-04DOI: 10.1016/j.jeconom.2025.106103
James A. Duffy , Sophocles Mavroeidis , Sam Wycherley
In the literature on nonlinear cointegration, a long-standing open problem relates to how a (nonlinear) vector autoregression, which provides a unified description of the short- and long-run dynamics of a vector of time series, can generate ‘nonlinear cointegration’ in the profound sense of those series sharing common nonlinear stochastic trends. We consider this problem in the setting of the censored and kinked structural VAR (CKSVAR), which provides a flexible yet tractable framework within which to model time series that are subject to threshold-type nonlinearities, such as those arising due to occasionally binding constraints, of which the zero lower bound (ZLB) on short-term nominal interest rates provides a leading example. We provide a complete characterisation of how common linear and nonlinear stochastic trends may be generated in this model, via unit roots and appropriate generalisations of the usual rank conditions, providing the first extension to date of the Granger–Johansen representation theorem to a nonlinearly cointegrated setting, and thereby giving the first successful treatment of the open problem. The limiting common trend processes include regulated, censored and kinked Brownian motions, none of which have previously appeared in the literature on cointegrated VARs. Our results and running examples illustrate that the CKSVAR is capable of supporting a far richer variety of long-run behaviour than is a linear VAR, in ways that may be particularly useful for the identification of structural parameters.
{"title":"Cointegration with occasionally binding constraints","authors":"James A. Duffy , Sophocles Mavroeidis , Sam Wycherley","doi":"10.1016/j.jeconom.2025.106103","DOIUrl":"10.1016/j.jeconom.2025.106103","url":null,"abstract":"<div><div>In the literature on nonlinear cointegration, a long-standing open problem relates to how a (nonlinear) vector autoregression, which provides a unified description of the short- and long-run dynamics of a vector of time series, can generate ‘nonlinear cointegration’ in the profound sense of those series sharing common nonlinear stochastic trends. We consider this problem in the setting of the censored and kinked structural VAR (CKSVAR), which provides a flexible yet tractable framework within which to model time series that are subject to threshold-type nonlinearities, such as those arising due to occasionally binding constraints, of which the zero lower bound (ZLB) on short-term nominal interest rates provides a leading example. We provide a complete characterisation of how common linear and <em>nonlinear</em> stochastic trends may be generated in this model, via unit roots and appropriate generalisations of the usual rank conditions, providing the first extension to date of the Granger–Johansen representation theorem to a nonlinearly cointegrated setting, and thereby giving the first successful treatment of the open problem. The limiting common trend processes include regulated, censored and kinked Brownian motions, none of which have previously appeared in the literature on cointegrated VARs. Our results and running examples illustrate that the CKSVAR is capable of supporting a far richer variety of long-run behaviour than is a linear VAR, in ways that may be particularly useful for the identification of structural parameters.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106103"},"PeriodicalIF":4.0,"publicationDate":"2025-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266930","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}
Pub Date : 2025-09-26DOI: 10.1016/j.jeconom.2025.106105
Clifford Lam , Zetai Cen
We introduce the matrix-valued time-varying Main Effects Factor Model (MEFM). MEFM is a generalization to the traditional matrix-valued factor model (FM). We give rigorous definitions of MEFM and its identifications, and propose estimators for the time-varying grand mean, row and column main effects, and the row and column factor loading matrices for the common component. Rates of convergence for different estimators are spelt out, with asymptotic normality shown. The core rank estimator for the common component is also proposed, with consistency of the estimators presented. As time series, the row and column main effects and can be non-stationary without affecting the estimation accuracy of our estimators. The number of main effects factors contributing to row or column main effects is also consistently estimated by our proposed estimators. We propose a test for testing if FM is sufficient against the alternative that MEFM is necessary, and demonstrate the power of such a test in various simulation settings. We also demonstrate numerically the accuracy of our estimators in extended simulation experiments. A set of NYC Taxi traffic data is analyzed and our test suggests that MEFM is indeed necessary for analyzing the data against a traditional FM.
{"title":"Matrix-valued factor model with time-varying main effects","authors":"Clifford Lam , Zetai Cen","doi":"10.1016/j.jeconom.2025.106105","DOIUrl":"10.1016/j.jeconom.2025.106105","url":null,"abstract":"<div><div>We introduce the matrix-valued time-varying Main Effects Factor Model (MEFM). MEFM is a generalization to the traditional matrix-valued factor model (FM). We give rigorous definitions of MEFM and its identifications, and propose estimators for the time-varying grand mean, row and column main effects, and the row and column factor loading matrices for the common component. Rates of convergence for different estimators are spelt out, with asymptotic normality shown. The core rank estimator for the common component is also proposed, with consistency of the estimators presented. As time series, the row and column main effects <span><math><mrow><mo>{</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>}</mo></mrow></math></span> and <span><math><mrow><mo>{</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>}</mo></mrow></math></span> can be non-stationary without affecting the estimation accuracy of our estimators. The number of main effects factors contributing to row or column main effects is also consistently estimated by our proposed estimators. We propose a test for testing if FM is sufficient against the alternative that MEFM is necessary, and demonstrate the power of such a test in various simulation settings. We also demonstrate numerically the accuracy of our estimators in extended simulation experiments. A set of NYC Taxi traffic data is analyzed and our test suggests that MEFM is indeed necessary for analyzing the data against a traditional FM.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106105"},"PeriodicalIF":4.0,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145155354","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}
Pub Date : 2025-09-23DOI: 10.1016/j.jeconom.2025.106101
Luis A.F. Alvarez , Chang Chiann , Pedro A. Morettin
This paper studies parameter estimation using L-moments, an alternative to traditional moments with attractive statistical properties. The estimation of model parameters by matching sample L-moments is known to outperform maximum likelihood estimation (MLE) in small samples from popular distributions. The choice of the number of L-moments used in estimation remains ad-hoc, though: researchers typically set the number of L-moments equal to the number of parameters, which is inefficient in larger samples. In this paper, we show that, by properly choosing the number of L-moments and weighting these accordingly, one is able to construct an estimator that outperforms MLE in finite samples, and yet retains asymptotic efficiency. We do so by introducing a generalised method of L-moments estimator and deriving its properties in an asymptotic framework where the number of L-moments varies with sample size. We then propose methods to automatically select the number of L-moments in a sample. Monte Carlo evidence shows our approach can provide mean-squared-error improvements over MLE in smaller samples, whilst working as well as it in larger samples. We consider extensions of our approach to the estimation of conditional models and a class semiparametric models. We apply the latter to study expenditure patterns in a ridesharing platform in Brazil.
{"title":"Inference on model parameters with many L-moments","authors":"Luis A.F. Alvarez , Chang Chiann , Pedro A. Morettin","doi":"10.1016/j.jeconom.2025.106101","DOIUrl":"10.1016/j.jeconom.2025.106101","url":null,"abstract":"<div><div>This paper studies parameter estimation using L-moments, an alternative to traditional moments with attractive statistical properties. The estimation of model parameters by matching sample L-moments is known to outperform maximum likelihood estimation (MLE) in small samples from popular distributions. The choice of the number of L-moments used in estimation remains <em>ad-hoc</em>, though: researchers typically set the number of L-moments equal to the number of parameters, which is inefficient in larger samples. In this paper, we show that, by properly choosing the number of L-moments and weighting these accordingly, one is able to construct an estimator that outperforms MLE in finite samples, and yet retains asymptotic efficiency. We do so by introducing a generalised method of L-moments estimator and deriving its properties in an asymptotic framework where the number of L-moments varies with sample size. We then propose methods to automatically select the number of L-moments in a sample. Monte Carlo evidence shows our approach can provide mean-squared-error improvements over MLE in smaller samples, whilst working as well as it in larger samples. We consider extensions of our approach to the estimation of conditional models and a class semiparametric models. We apply the latter to study expenditure patterns in a ridesharing platform in Brazil.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"252 ","pages":"Article 106101"},"PeriodicalIF":4.0,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145118398","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}
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