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Exogeneity tests and weak identification in IV regressions: Asymptotic theory and point estimation
IF 9.9 3区 经济学
Journal of Econometrics Pub Date : 2025-03-01 DOI: 10.1016/j.jeconom.2024.105821
Firmin Doko Tchatoka , Jean-Marie Dufour
{"title":"Exogeneity tests and weak identification in IV regressions: Asymptotic theory and point estimation","authors":"Firmin Doko Tchatoka ,&nbsp;Jean-Marie Dufour","doi":"10.1016/j.jeconom.2024.105821","DOIUrl":"10.1016/j.jeconom.2024.105821","url":null,"abstract":"<div><div>This paper provides new insights on exogeneity tests in linear IV models and their use for estimation, when identification fails or may not be strong. We make two main contributions. <em>First</em>, we show that Durbin–Wu–Hausman (DWH) and Revankar–Hartley (RH) exogeneity tests have correct level asymptotically, even when the first-stage coefficient matrix (which controls identification) is rank-deficient. We provide necessary and sufficient conditions under which these tests are consistent. In particular, we show that test consistency can hold even when identification fails, provided <em>at least one</em> component of the structural parameter vector is identifiable. <em>Second</em>, we study point estimation after estimator (or model) selection, when the outcome of a DWH/RH test determines whether OLS or an IV method is employed in the second-stage. For this purpose, we use (<em>non-local</em>) concepts of <em>asymptotic bias</em>, <em>asymptotic mean squared error</em> (AMSE), and <em>asymptotic relative efficiency</em> (ARE), which remain applicable even when the estimators considered do not have moments (as can happen for 2SLS) or may be inconsistent. We study the asymptotic properties of OLS, 2SLS, and pretest estimators which select OLS or 2SLS based on the outcome of a DWH/RH test. We show that: (i) OLS typically dominates 2SLS estimator asymptotically for MSE across a broad spectrum of cases, including weak identification and moderate endogeneity; (ii) exogeneity-pretest estimators exhibit consistently good performance and asymptotically dominate both OLS and 2SLS. The proposed theoretical findings are documented by Monte Carlo simulations.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"248 ","pages":"Article 105821"},"PeriodicalIF":9.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526833","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}
引用次数: 0
Efficiency bounds for moment condition models with mixed identification strength 具有混合识别强度的矩条件模型的效率边界
IF 9.9 3区 经济学
Journal of Econometrics Pub Date : 2025-03-01 DOI: 10.1016/j.jeconom.2024.105723
Prosper Dovonon , Yves F. Atchadé , Firmin Doko Tchatoka
{"title":"Efficiency bounds for moment condition models with mixed identification strength","authors":"Prosper Dovonon ,&nbsp;Yves F. Atchadé ,&nbsp;Firmin Doko Tchatoka","doi":"10.1016/j.jeconom.2024.105723","DOIUrl":"10.1016/j.jeconom.2024.105723","url":null,"abstract":"<div><div>Moment condition models with mixed identification strength are models that are point identified but with estimating moment functions that are allowed to drift to 0 uniformly over the parameter space. Even though identification fails in the limit, depending on how slow the moment functions vanish, consistent estimation is possible. Existing estimators such as the generalized method of moment (GMM) estimator exhibit a pattern of nonstandard or even heterogeneous rate of convergence that materializes by some parameter directions being estimated at a slower rate than others. This paper derives asymptotic semiparametric efficiency bounds for regular estimators of parameters of these models. We show that GMM estimators are regular and that the so-called two-step GMM estimator – using the inverse of estimating function’s variance as weighting matrix – is semiparametrically efficient as it reaches the minimum variance attainable by regular estimators. This estimator is also asymptotically minimax efficient with respect to a large family of loss functions. Monte Carlo simulations are provided that confirm these results.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"248 ","pages":"Article 105723"},"PeriodicalIF":9.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140154621","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}
引用次数: 0
Spanning latent and observable factors 跨越潜在因素和可观测因素
IF 9.9 3区 经济学
Journal of Econometrics Pub Date : 2025-03-01 DOI: 10.1016/j.jeconom.2024.105743
E. Andreou , P. Gagliardini , E. Ghysels , M. Rubin
{"title":"Spanning latent and observable factors","authors":"E. Andreou ,&nbsp;P. Gagliardini ,&nbsp;E. Ghysels ,&nbsp;M. Rubin","doi":"10.1016/j.jeconom.2024.105743","DOIUrl":"10.1016/j.jeconom.2024.105743","url":null,"abstract":"<div><div><span>Factor analysis is a widely used tool to summarize high dimensional panel data via a small dimensional set of latent factors<span>. Many applications in finance<span><span> and macroeconomics, are often focused on observable factors with an economic interpretation. The objective of this paper is to provide a test to answer a question which naturally comes up in discussions regarding latent versus observable factors: do latent and observable factors span the same space? We derive </span>asymptotic properties of a formal test and propose a bootstrap version with improved small sample properties. We find empirical evidence for a small number of factors common between a small number of traditional Fama–French </span></span></span>risk factors – or returns on a few stocks (i.e. “magnificent” 5 or 7) – and large panels of US, North American and international portfolio returns.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"248 ","pages":"Article 105743"},"PeriodicalIF":9.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141144485","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}
引用次数: 0
Long-run risk in stationary vector autoregressive models
IF 9.9 3区 经济学
Journal of Econometrics Pub Date : 2025-03-01 DOI: 10.1016/j.jeconom.2024.105905
Christian Gourieroux , Joann Jasiak
{"title":"Long-run risk in stationary vector autoregressive models","authors":"Christian Gourieroux ,&nbsp;Joann Jasiak","doi":"10.1016/j.jeconom.2024.105905","DOIUrl":"10.1016/j.jeconom.2024.105905","url":null,"abstract":"<div><div>This paper introduces a local-to-unity/small sigma model for stationary processes with long-range persistence and non-negligible long-run prediction and estimation risks. The model represents a process containing unobserved short and long-run components measured on different time scales. The short-run component is defined in calendar time, while the long-run component evolves in rescaled time with ultra-long units. We develop estimation and long-run prediction methods for time series with multivariate Vector Autoregressive (VAR) short-run components and reveal the impossibility of estimating consistently some of the long-run parameters, which causes significant estimation and prediction risks in the long run. A simulation study and an application to macroeconomic data illustrate the approach.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"248 ","pages":"Article 105905"},"PeriodicalIF":9.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526828","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}
引用次数: 0
Identification robust inference for the risk premium in term structure models
IF 9.9 3区 经济学
Journal of Econometrics Pub Date : 2025-03-01 DOI: 10.1016/j.jeconom.2024.105728
Frank Kleibergen , Lingwei Kong
{"title":"Identification robust inference for the risk premium in term structure models","authors":"Frank Kleibergen ,&nbsp;Lingwei Kong","doi":"10.1016/j.jeconom.2024.105728","DOIUrl":"10.1016/j.jeconom.2024.105728","url":null,"abstract":"<div><div>We propose identification robust statistics for testing hypotheses on the risk premia in dynamic affine term structure models. We do so using the moment equation specification proposed in <span><span>Adrian et al. (2013)</span></span>. Statistical inference based on their three-stage estimator requires knowledge of the risk factors’ quality and can be misleading when the <span><math><mi>β</mi></math></span>’s are weak, which results when sampling errors are of comparable order of magnitude as the risk factor loadings. We extend the subset (factor) Anderson–Rubin test from <span><span>Guggenberger et al. (2012)</span></span> to models with multiple dynamic factors and time-varying risk prices. It provides a computationally tractable manner to conduct identification robust tests on a few risk premia when a larger number is present. We use it to analyze potential identification issues arising in the data from <span><span>Adrian et al. (2013)</span></span> for which we show that some factors, though potentially weak, may drive the time variation of risk prices, and weak identification issues are more prominent in multi-factor models.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"248 ","pages":"Article 105728"},"PeriodicalIF":9.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526835","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}
引用次数: 0
Conditional spectral methods
IF 9.9 3区 经济学
Journal of Econometrics Pub Date : 2025-03-01 DOI: 10.1016/j.jeconom.2024.105863
Federico M. Bandi , Yinan Su
{"title":"Conditional spectral methods","authors":"Federico M. Bandi ,&nbsp;Yinan Su","doi":"10.1016/j.jeconom.2024.105863","DOIUrl":"10.1016/j.jeconom.2024.105863","url":null,"abstract":"<div><div>We model predictive scale-specific cycles. By employing suitable matrix representations, we express the forecast errors of covariance-stationary multivariate time series in terms of conditionally orthonormal scale-specific bases. The representations yield conditionally orthogonal decompositions of these forecast errors. They also provide decompositions of their variances and betas in terms of scale-specific variances and betas capturing predictive variability and co-variability over cycles of alternative lengths without spillovers across cycles. Making use of the proposed representations within the classical family of time-varying conditional volatility models, we document the role of time-varying volatility forecasts in generating orthogonal predictive scale-specific cycles in returns. We conclude by providing suggestive evidence that the conditional variances of the predictive return cycles (<span><math><mi>i</mi></math></span>) may be priced over short-to-medium horizons and (<span><math><mrow><mi>i</mi><mi>i</mi></mrow></math></span>) may offer economically-relevant trading signals over these same horizons.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"248 ","pages":"Article 105863"},"PeriodicalIF":9.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526916","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}
引用次数: 0
Functional ecological inference 功能生态推断
IF 9.9 3区 经济学
Journal of Econometrics Pub Date : 2025-03-01 DOI: 10.1016/j.jeconom.2024.105918
Christian Bontemps , Jean-Pierre Florens , Nour Meddahi
{"title":"Functional ecological inference","authors":"Christian Bontemps ,&nbsp;Jean-Pierre Florens ,&nbsp;Nour Meddahi","doi":"10.1016/j.jeconom.2024.105918","DOIUrl":"10.1016/j.jeconom.2024.105918","url":null,"abstract":"<div><div>In this paper, we consider the problem of ecological inference when one observes the conditional distributions of <span><math><mrow><mi>Y</mi><mo>|</mo><mi>W</mi></mrow></math></span> and <span><math><mrow><mi>Z</mi><mo>|</mo><mi>W</mi></mrow></math></span> from aggregate data and attempts to infer the conditional distribution of <span><math><mrow><mi>Y</mi><mo>|</mo><mi>Z</mi></mrow></math></span> without observing <span><math><mi>Y</mi></math></span> and <span><math><mi>Z</mi></math></span> in the same sample. First, we show that this problem can be transformed into a linear equation involving operators for which, under suitable regularity assumptions, least squares solutions are available. We then propose the use of the least squares solution with the minimum Hilbert–Schmidt norm, which, in our context, can be structurally interpreted as the solution with minimum dependence between <span><math><mi>Y</mi></math></span> and <span><math><mi>Z</mi></math></span>. Interestingly, in the case where the conditioning variable <span><math><mi>W</mi></math></span> is discrete and belongs to a finite set, such as the labels of units/groups/cities, the solution of this minimal dependence has a closed form. In the more general case, we use a regularization scheme and show the convergence of our proposed estimator. A numerical evaluation of our procedure is proposed.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"248 ","pages":"Article 105918"},"PeriodicalIF":9.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526834","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}
引用次数: 0
Identifying the volatility risk price through the leverage effect
IF 9.9 3区 经济学
Journal of Econometrics Pub Date : 2025-03-01 DOI: 10.1016/j.jeconom.2024.105943
Xu Cheng , Eric Renault , Paul Sangrey
{"title":"Identifying the volatility risk price through the leverage effect","authors":"Xu Cheng ,&nbsp;Eric Renault ,&nbsp;Paul Sangrey","doi":"10.1016/j.jeconom.2024.105943","DOIUrl":"10.1016/j.jeconom.2024.105943","url":null,"abstract":"<div><div>In asset pricing models with stochastic volatility, uncertainty about volatility affects risk premia through two channels: aversion to decreasing returns and aversion to increasing volatility. We analyze the identification of and robust inference for structural parameters measuring investors’ aversions to these risks: the return risk price and the volatility risk price. In the presence of a leverage effect (instantaneous causality between the asset return and its volatility), we study the identification of both structural parameters with the price data only, without relying on additional option pricing models or option data. We analyze this identification challenge in a nonparametric discrete-time exponentially affine model, complementing the continuous-time approach of Bandi and Renò (2016). We then specialize to a parametric model and derive the implied minimum distance criterion relating the risk prices to the asset return and volatility’s joint distribution. This criterion is almost flat when the leverage effect is small, and we introduce identification-robust confidence sets for both risk prices regardless of the magnitude of the leverage effect.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"248 ","pages":"Article 105943"},"PeriodicalIF":9.9,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143526862","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}
引用次数: 0
A large confirmatory dynamic factor model for stock market returns in different time zones
IF 9.9 3区 经济学
Journal of Econometrics Pub Date : 2025-02-25 DOI: 10.1016/j.jeconom.2025.105971
Oliver B. Linton , Haihan Tang , Jianbin Wu
{"title":"A large confirmatory dynamic factor model for stock market returns in different time zones","authors":"Oliver B. Linton ,&nbsp;Haihan Tang ,&nbsp;Jianbin Wu","doi":"10.1016/j.jeconom.2025.105971","DOIUrl":"10.1016/j.jeconom.2025.105971","url":null,"abstract":"<div><div>We propose a confirmatory dynamic factor model for a large number of stocks whose returns are observed daily across multiple time zones. The model has a global factor and a continental factor that both drive the individual stock return series. We propose two estimators of the model: a quasi-maximum likelihood estimator (QML-just-identified), and an improved estimator based on an Expectation Maximization (EM) algorithm (QML-all-res). Our estimators are consistent and asymptotically normal under the large approximate factor model setting. In particular, the asymptotic distributions of QML-all-res are the same as those of the infeasible OLS estimators that treat factors as known and utilize all the restrictions on the parameters of the model. We apply the model to MSCI equity indices of 42 developed and emerging markets, and find that most markets are more integrated when the CBOE Volatility Index (VIX) is high.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"249 ","pages":"Article 105971"},"PeriodicalIF":9.9,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479821","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}
引用次数: 0
Multiplicative factor model for volatility
IF 9.9 3区 经济学
Journal of Econometrics Pub Date : 2025-02-21 DOI: 10.1016/j.jeconom.2025.105959
Yi Ding , Robert Engle , Yingying Li , Xinghua Zheng
{"title":"Multiplicative factor model for volatility","authors":"Yi Ding ,&nbsp;Robert Engle ,&nbsp;Yingying Li ,&nbsp;Xinghua Zheng","doi":"10.1016/j.jeconom.2025.105959","DOIUrl":"10.1016/j.jeconom.2025.105959","url":null,"abstract":"<div><div>Facilitated with high-frequency observations, we introduce a remarkably parsimonious one-factor volatility model that offers a novel perspective for comprehending daily volatilities of a large number of stocks. Specifically, we propose a multiplicative volatility factor (MVF) model, where stock daily variance is represented by a common variance factor and a multiplicative idiosyncratic component. We demonstrate compelling empirical evidence supporting our model and provide statistical properties for two simple estimation methods. The MVF model reflects important properties of volatilities, applies to both individual stocks and portfolios, can be easily estimated, and leads to exceptional predictive performance in both US stocks and global equity indices.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"249 ","pages":"Article 105959"},"PeriodicalIF":9.9,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454633","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}
引用次数: 0
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