Pub Date : 2026-03-01Epub Date: 2026-01-30DOI: 10.1016/j.jeconom.2026.106202
Wenhao Cui , Jie Hu , Jiandong Wang
We propose nonparametric estimators for the explicative part of the noise in a model where the market microstructure noise is an unknown function of the trading information while allowing for the presence of an additional residual noise component. Our method allows for dependence in the observable trading information and accommodates the presence of infinite variation jumps in the efficient price process. We establish the convergence and asymptotic normality of the proposed estimators. We also propose a two-step Laplace estimator of integrated volatility where we replace the observed price with the estimated price by removing the explicative part of the market microstructure noise. The finite sample properties of both the nonparametric estimators and the two-step Laplace estimator are examined through Monte Carlo simulations. We find that our method is robust to misspecification of the unknown functional form given finite sample size. Furthermore, an empirical application using high-frequency data demonstrates that our method outperforms commonly employed parametric methods.
{"title":"Reprint of: Nonparametric estimation for high-frequency data incorporating trading information","authors":"Wenhao Cui , Jie Hu , Jiandong Wang","doi":"10.1016/j.jeconom.2026.106202","DOIUrl":"10.1016/j.jeconom.2026.106202","url":null,"abstract":"<div><div>We propose nonparametric estimators for the explicative part of the noise in a model where the market microstructure noise is an unknown function of the trading information while allowing for the presence of an additional residual noise component. Our method allows for dependence in the observable trading information and accommodates the presence of infinite variation jumps in the efficient price process. We establish the convergence and asymptotic normality of the proposed estimators. We also propose a two-step Laplace estimator of integrated volatility where we replace the observed price with the estimated price by removing the explicative part of the market microstructure noise. The finite sample properties of both the nonparametric estimators and the two-step Laplace estimator are examined through Monte Carlo simulations. We find that our method is robust to misspecification of the unknown functional form given finite sample size. Furthermore, an empirical application using high-frequency data demonstrates that our method outperforms commonly employed parametric methods.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 106202"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147399598","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 : 2026-03-01Epub Date: 2024-07-16DOI: 10.1016/j.jeconom.2024.105810
Minseog Oh , Donggyu Kim , Yazhen Wang
In this paper, we develop a robust non-parametric realized integrated beta estimator using high-frequency financial data contaminated by microstructure noise, which is robust to the stylized features, such as the time-varying beta and the price-dependent and autocorrelated microstructure noise. With this robust realized integrated beta estimator, we investigate dynamic structures of integrated betas and find a persistent autoregressive structure. To model this dynamic structure, we utilize the autoregressive–moving-average (ARMA) model for daily integrated market betas. We call this the dynamic realized beta (DR Beta). Then, we propose a quasi-likelihood procedure for estimating the parameters of the ARMA model with the robust realized integrated beta estimator as the proxy. We establish asymptotic theorems for the proposed estimator and conduct a simulation study to check the performance of finite samples of the estimator. The proposed DR Beta model with the robust realized beta estimator is also illustrated by using data from the E-mini S&P 500 index futures and the top 50 large trading volume stocks from the S&P 500 and an application to constructing market-neutral portfolios.
{"title":"Robust realized integrated beta estimator with application to dynamic analysis of integrated beta","authors":"Minseog Oh , Donggyu Kim , Yazhen Wang","doi":"10.1016/j.jeconom.2024.105810","DOIUrl":"10.1016/j.jeconom.2024.105810","url":null,"abstract":"<div><div>In this paper, we develop a robust non-parametric realized integrated beta estimator using high-frequency financial data contaminated by microstructure noise, which is robust to the stylized features, such as the time-varying beta and the price-dependent and autocorrelated microstructure noise. With this robust realized integrated beta estimator, we investigate dynamic structures of integrated betas and find a persistent autoregressive structure. To model this dynamic structure, we utilize the autoregressive–moving-average (ARMA) model for daily integrated market betas. We call this the dynamic realized beta (DR Beta). Then, we propose a quasi-likelihood procedure for estimating the parameters of the ARMA model with the robust realized integrated beta estimator as the proxy. We establish asymptotic theorems for the proposed estimator and conduct a simulation study to check the performance of finite samples of the estimator. The proposed DR Beta model with the robust realized beta estimator is also illustrated by using data from the E-mini S&P 500 index futures and the top 50 large trading volume stocks from the S&P 500 and an application to constructing market-neutral portfolios.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 105810"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141714586","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 : 2026-03-01Epub Date: 2024-07-17DOI: 10.1016/j.jeconom.2024.105812
Dachuan Chen , Long Feng , Per A. Mykland , Lan Zhang
This paper presents the first study on high-dimensional regression coefficient tests with high-frequency financial data. These tests allow the number of regressors to be larger than the number of observations within each estimation block and can grow to infinity in asymptotics. In this paper, the sum-type test and max-type test have been proposed, where the former is suitable for the dense alternative (many small betas) and the latter is suitable for the sparse alternative (a very small number of large betas). By showing the asymptotic independence between the sum-type test and max-type test, the paper proposes a third test – Fisher’s combination test, which is robust to both dense and sparse alternatives. The paper derives the limiting null distributions of the three proposed tests and analyzes the asymptotic behavior of their powers. Monte Carlo simulations demonstrate the validity of the theoretical results developed in this paper. Empirical study shows the impact of high frequency (HF) factors when being added to a Fama–French-style factor model. We found that the HF effects are time varying. The proposed tests can help identify those time periods when the HF factors carry (significant) incremental information for the test asset. Our tests could shed light on market timing in a trading strategy.
{"title":"High dimensional regression coefficient test with high frequency data","authors":"Dachuan Chen , Long Feng , Per A. Mykland , Lan Zhang","doi":"10.1016/j.jeconom.2024.105812","DOIUrl":"10.1016/j.jeconom.2024.105812","url":null,"abstract":"<div><div><span>This paper presents the first study on high-dimensional regression coefficient tests with high-frequency financial data. These tests allow the number of regressors to be larger than the number of observations within each estimation block and can grow to infinity in asymptotics. In this paper, the sum-type test and max-type test have been proposed, where the former is suitable for the dense alternative (many small betas) and the latter is suitable for the sparse alternative (a very small number of large betas). By showing the asymptotic independence between the sum-type test and max-type test, the paper proposes a third test – Fisher’s combination test, which is robust to both dense and sparse alternatives. The paper derives the limiting null distributions of the three proposed tests and analyzes the </span>asymptotic behavior of their powers. Monte Carlo simulations demonstrate the validity of the theoretical results developed in this paper. Empirical study shows the impact of high frequency (HF) factors when being added to a Fama–French-style factor model. We found that the HF effects are time varying. The proposed tests can help identify those time periods when the HF factors carry (significant) incremental information for the test asset. Our tests could shed light on market timing in a trading strategy.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 105812"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141841084","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 : 2026-03-01Epub Date: 2026-02-09DOI: 10.1016/j.jeconom.2026.106193
Mikkel Bennedsen , Kim Christensen , Peter Korsbakke Christensen
We develop a framework for composite likelihood estimation of parametric continuous-time stationary Gaussian processes. We derive the asymptotic theory of the associated maximum composite likelihood estimator. We implement our approach on a pair of models that have been proposed to describe the random log-spot variance of financial asset returns. A simulation study shows that it delivers good performance in these settings and improves upon a method-of-moments estimation. In an empirical investigation, we inspect the dynamic of an intraday measure of the spot log-realized variance computed with high-frequency data from the cryptocurrency market. The evidence supports a mechanism, where the short- and long-term correlation structure of stochastic volatility are decoupled in order to capture its properties at different time scales. This is further backed by an analysis of the associated spot log-trading volume.
{"title":"To be or not to be: Roughness or long memory in volatility?","authors":"Mikkel Bennedsen , Kim Christensen , Peter Korsbakke Christensen","doi":"10.1016/j.jeconom.2026.106193","DOIUrl":"10.1016/j.jeconom.2026.106193","url":null,"abstract":"<div><div>We develop a framework for composite likelihood estimation of parametric continuous-time stationary Gaussian processes. We derive the asymptotic theory of the associated maximum composite likelihood estimator. We implement our approach on a pair of models that have been proposed to describe the random log-spot variance of financial asset returns. A simulation study shows that it delivers good performance in these settings and improves upon a method-of-moments estimation. In an empirical investigation, we inspect the dynamic of an intraday measure of the spot log-realized variance computed with high-frequency data from the cryptocurrency market. The evidence supports a mechanism, where the short- and long-term correlation structure of stochastic volatility are decoupled in order to capture its properties at different time scales. This is further backed by an analysis of the associated spot log-trading volume.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 106193"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171155","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 : 2026-03-01Epub Date: 2026-02-10DOI: 10.1016/j.jeconom.2026.106212
Peter Reinhard Hansen , Chen Tong
We introduce a family of multivariate heavy-tailed distributions, termed convolution-t distributions, constructed as convolutions of heterogeneous multivariate t-distributions. Unlike commonly used heavy-tailed distributions, this family captures nonlinear dependencies, accommodates heterogeneous marginal distributions, and reveals cluster structures prevalent in economic data. Importantly, convolution-t distributions admit simple closed-form densities that facilitate estimation and likelihood-based inference. The characteristic features of convolution-t distributions are shown to be important in an empirical analysis of realized volatility measures and help uncover their underlying factor structure.
{"title":"Convolution-t distributions","authors":"Peter Reinhard Hansen , Chen Tong","doi":"10.1016/j.jeconom.2026.106212","DOIUrl":"10.1016/j.jeconom.2026.106212","url":null,"abstract":"<div><div>We introduce a family of multivariate heavy-tailed distributions, termed convolution-<em>t</em> distributions, constructed as convolutions of heterogeneous multivariate <em>t</em>-distributions. Unlike commonly used heavy-tailed distributions, this family captures nonlinear dependencies, accommodates heterogeneous marginal distributions, and reveals cluster structures prevalent in economic data. Importantly, convolution-<em>t</em> distributions admit simple closed-form densities that facilitate estimation and likelihood-based inference. The characteristic features of convolution-<em>t</em> distributions are shown to be important in an empirical analysis of realized volatility measures and help uncover their underlying factor structure.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 106212"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171158","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 : 2026-03-01Epub Date: 2026-02-26DOI: 10.1016/j.jeconom.2026.106219
Yechan Park , Yuya Sasaki
The Average Treatment Effect on the Treated Survivors (ATETS; Vikström et al., 2018) captures a composite effect of time-varying treatment and dynamic selection into the survivor population. We address the problem of identifying this treatment-effect parameter in the absence of long-term experimental data, utilizing available long-term observational data instead. This poses a nontrivial challenge in practice, as dynamic selection compounds static selection in observational data. We establish two theoretical results. First, it is impossible to obtain informative bounds without model restrictions or auxiliary data. Second, to overturn this negative result, we explore the recent econometric developments in combining experimental and observational data (e.g., Athey et al., 2025; 2024) as a promising avenue; we find that exploiting short-term experimental data can be informative without imposing classical model restrictions. Building on Chesher and Rosen (2017), we further explore how to systematically derive sharp identification bounds, leveraging both novel data-combination principles and classical model restrictions. Estimation and inference procedures are also provided. Applying the proposed method, we investigate what can be learned about the long-run effects of job training programs on employment in the absence of long-term experimental data.
{"title":"The informativeness of combined experimental and observational data under dynamic selection","authors":"Yechan Park , Yuya Sasaki","doi":"10.1016/j.jeconom.2026.106219","DOIUrl":"10.1016/j.jeconom.2026.106219","url":null,"abstract":"<div><div>The Average Treatment Effect on the Treated Survivors (ATETS; Vikström et al., 2018) captures a composite effect of time-varying treatment and dynamic selection into the survivor population. We address the problem of identifying this treatment-effect parameter in the absence of long-term experimental data, utilizing available long-term observational data instead. This poses a nontrivial challenge in practice, as dynamic selection compounds static selection in observational data. We establish two theoretical results. First, it is impossible to obtain informative bounds without model restrictions or auxiliary data. Second, to overturn this negative result, we explore the recent econometric developments in combining experimental and observational data (e.g., Athey et al., 2025; 2024) as a promising avenue; we find that exploiting short-term experimental data can be informative without imposing classical model restrictions. Building on Chesher and Rosen (2017), we further explore how to systematically derive sharp identification bounds, leveraging both novel data-combination principles and classical model restrictions. Estimation and inference procedures are also provided. Applying the proposed method, we investigate what can be learned about the long-run effects of job training programs on employment in the absence of long-term experimental data.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 106219"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147384788","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 : 2026-03-01Epub Date: 2026-02-11DOI: 10.1016/j.jeconom.2026.106191
Jeroen Dalderop , Oliver Linton
Option-implied risk-neutral densities are widely used for constructing forward-looking risk measures. Meanwhile, risk aversion introduces a multiplicative pricing kernel between the risk-neutral and true conditional densities of the underlying asset’s return. This paper proposes a simple local estimator of the pricing kernel based on inverse density weighting. We characterize the asymptotic bias and variance of the estimator and its multiplicatively corrected density forecasts. A local exponential linear variant is proposed to include conditioning variables. The estimator performs well in a simulation study, even when the risk-neutral densities are noisy and/or have missing tails. We apply our estimator to a demand-based model for S&P 500 index options, and find U-shaped pricing kernels when end-users sell out-of-the-money options and volatility is high.
{"title":"Estimating a conditional density ratio model for asset returns and option demand","authors":"Jeroen Dalderop , Oliver Linton","doi":"10.1016/j.jeconom.2026.106191","DOIUrl":"10.1016/j.jeconom.2026.106191","url":null,"abstract":"<div><div>Option-implied risk-neutral densities are widely used for constructing forward-looking risk measures. Meanwhile, risk aversion introduces a multiplicative pricing kernel between the risk-neutral and true conditional densities of the underlying asset’s return. This paper proposes a simple local estimator of the pricing kernel based on inverse density weighting. We characterize the asymptotic bias and variance of the estimator and its multiplicatively corrected density forecasts. A local exponential linear variant is proposed to include conditioning variables. The estimator performs well in a simulation study, even when the risk-neutral densities are noisy and/or have missing tails. We apply our estimator to a demand-based model for S&P 500 index options, and find U-shaped pricing kernels when end-users sell out-of-the-money options and volatility is high.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 106191"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171107","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 : 2026-03-01Epub Date: 2026-02-03DOI: 10.1016/j.jeconom.2026.106194
Michael Johannes , Norman J. Seeger , Jonathan R. Stroud
This paper examines an issue overlooked in the finance and economics literature: time variation in announcement volatility or event risk. To identify this, we combine long spans of high-frequency data with a flexible model of returns. The model allows us to separately identify conditional event risk from other factors like time-varying volatility, jumps and intraday periodicity, and long time spans of data are needed given the infrequency of most announcements. We focus on crude oil due to its economic importance, high volatility and complex announcement structure. Results indicate strong evidence for time-varying announcement volatility as announcement event risk varies by as much as a factor of 10 over time.
{"title":"Time-varying macroeconomic announcement risk","authors":"Michael Johannes , Norman J. Seeger , Jonathan R. Stroud","doi":"10.1016/j.jeconom.2026.106194","DOIUrl":"10.1016/j.jeconom.2026.106194","url":null,"abstract":"<div><div>This paper examines an issue overlooked in the finance and economics literature: time variation in announcement volatility or event risk. To identify this, we combine long spans of high-frequency data with a flexible model of returns. The model allows us to separately identify conditional event risk from other factors like time-varying volatility, jumps and intraday periodicity, and long time spans of data are needed given the infrequency of most announcements. We focus on crude oil due to its economic importance, high volatility and complex announcement structure. Results indicate strong evidence for time-varying announcement volatility as announcement event risk varies by as much as a factor of 10 over time.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 106194"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146171154","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 : 2026-03-01Epub Date: 2026-01-23DOI: 10.1016/j.jeconom.2026.106187
Bingxin Zhao , Yuhong Yang
This paper studies minimax rates of convergence for nonparametric location-scale models, which include mean, quantile, expectile and momentile regression settings. Under Hellinger differentiability on the error distribution and other mild conditions, we show that the minimax rate of convergence for estimating the regression function under the squared L2 loss is determined by the metric entropy of the nonparametric function class. Different error distributions, including asymmetric Laplace distribution, asymmetric connected double truncated gamma distribution, connected normal-Laplace distribution, Cauchy distribution and asymmetric normal distribution are studied as examples. Applications on low order interaction models and multiple index models are also given.
{"title":"Minimax rates of convergence for nonparametric location-Scale models","authors":"Bingxin Zhao , Yuhong Yang","doi":"10.1016/j.jeconom.2026.106187","DOIUrl":"10.1016/j.jeconom.2026.106187","url":null,"abstract":"<div><div>This paper studies minimax rates of convergence for nonparametric location-scale models, which include mean, quantile, expectile and momentile regression settings. Under Hellinger differentiability on the error distribution and other mild conditions, we show that the minimax rate of convergence for estimating the regression function under the squared <em>L</em><sub>2</sub> loss is determined by the metric entropy of the nonparametric function class. Different error distributions, including asymmetric Laplace distribution, asymmetric connected double truncated gamma distribution, connected normal-Laplace distribution, Cauchy distribution and asymmetric normal distribution are studied as examples. Applications on low order interaction models and multiple index models are also given.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 106187"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015887","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 : 2026-03-01Epub Date: 2026-01-22DOI: 10.1016/j.jeconom.2026.106181
Ye Yang , Wim P.M. Vijverberg
This paper offers hypothesis and specification tests for the best generalized methods of moment estimator (BGMME) of the matrix exponential spatial specification (MESS) developed by Debarsy et al. (2015). First, as the BGMME is a two-step estimator, we formulate corrected standard errors using a modified version of the finite sample correction method in Windmeijer (2005) that accounts for the fact that the BGMME makes more extensive use of the first-stage estimator than the GMM model analyzed by Windmeijer. Second, since the BGMME uses different moment conditions under normal, non-normal, and heteroskedastic disturbances, we propose a pretest strategy to determine which set of moment conditions is most suitable for the data at hand. Third, we consider and examine the performance of test statistics that help choose between MESS(1,1), MESS(1,0) and MESS(0,1) models. The performance of these tools is examined with Monte Carlo experiments, which also allow for varying degrees of spatial correlation in the explanatory variables. The correction in the standard errors is especially useful when the sample size is small, such as in a study with state-level, provincial or country-level data: the corrected standard errors improve statistical inference, yielding better size properties. The pretest strategy is effective when the heteroskedasticity, if present, is correlated with explanatory variables in the model. Spatial lags in the outcome variable are more easily detected than those in the disturbance. An empirical study of housing prices illustrates the new tools.
{"title":"GMM inference in the matrix exponential spatial specification","authors":"Ye Yang , Wim P.M. Vijverberg","doi":"10.1016/j.jeconom.2026.106181","DOIUrl":"10.1016/j.jeconom.2026.106181","url":null,"abstract":"<div><div>This paper offers hypothesis and specification tests for the best generalized methods of moment estimator (BGMME) of the matrix exponential spatial specification (MESS) developed by Debarsy et al. (2015). First, as the BGMME is a two-step estimator, we formulate corrected standard errors using a modified version of the finite sample correction method in Windmeijer (2005) that accounts for the fact that the BGMME makes more extensive use of the first-stage estimator than the GMM model analyzed by Windmeijer. Second, since the BGMME uses different moment conditions under normal, non-normal, and heteroskedastic disturbances, we propose a pretest strategy to determine which set of moment conditions is most suitable for the data at hand. Third, we consider and examine the performance of test statistics that help choose between MESS(1,1), MESS(1,0) and MESS(0,1) models. The performance of these tools is examined with Monte Carlo experiments, which also allow for varying degrees of spatial correlation in the explanatory variables. The correction in the standard errors is especially useful when the sample size is small, such as in a study with state-level, provincial or country-level data: the corrected standard errors improve statistical inference, yielding better size properties. The pretest strategy is effective when the heteroskedasticity, if present, is correlated with explanatory variables in the model. Spatial lags in the outcome variable are more easily detected than those in the disturbance. An empirical study of housing prices illustrates the new tools.</div></div>","PeriodicalId":15629,"journal":{"name":"Journal of Econometrics","volume":"254 ","pages":"Article 106181"},"PeriodicalIF":4.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015886","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}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号