Pub Date : 2021-12-08DOI: 10.1080/07474938.2021.2009705
Natalia Bailey, Dandan Jiang, Jianfeng Yao
Abstract This paper introduces a new test for error cross-sectional independence in large panel data models with exogenous regressors having heterogenous slope coefficients. The proposed statistic, LMRMT , is based on the Lagrange Multiplier (LM) principle and the sample correlation matrix of the model’s residuals. Since in large panels poorly estimates its population counterpart, results from Random Matrix Theory (RMT) are used to establish the high-dimensional limiting distribution of LMRMT under heteroskedastic normal errors and assuming that both the panel size N and the sample size grow to infinity in comparable magnitude. Simulation results show that is largely correctly sized (except for some small values of N and T). Further, the empirical size and power outcomes show robustness of our statistic to deviations from the assumptions of normality for the error terms and of strict exogeneity for the regressors. The test has comparable small sample properties to related tests in the literature which have been developed under different asymptotic theory.
{"title":"A RMT-based LM test for error cross-sectional independence in large heterogeneous panel data models*","authors":"Natalia Bailey, Dandan Jiang, Jianfeng Yao","doi":"10.1080/07474938.2021.2009705","DOIUrl":"https://doi.org/10.1080/07474938.2021.2009705","url":null,"abstract":"Abstract This paper introduces a new test for error cross-sectional independence in large panel data models with exogenous regressors having heterogenous slope coefficients. The proposed statistic, LMRMT , is based on the Lagrange Multiplier (LM) principle and the sample correlation matrix of the model’s residuals. Since in large panels poorly estimates its population counterpart, results from Random Matrix Theory (RMT) are used to establish the high-dimensional limiting distribution of LMRMT under heteroskedastic normal errors and assuming that both the panel size N and the sample size grow to infinity in comparable magnitude. Simulation results show that is largely correctly sized (except for some small values of N and T). Further, the empirical size and power outcomes show robustness of our statistic to deviations from the assumptions of normality for the error terms and of strict exogeneity for the regressors. The test has comparable small sample properties to related tests in the literature which have been developed under different asymptotic theory.","PeriodicalId":11438,"journal":{"name":"Econometric Reviews","volume":"41 1","pages":"564 - 582"},"PeriodicalIF":1.2,"publicationDate":"2021-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43744121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-26DOI: 10.1080/07474938.2021.1889208
Tae-Hwy Lee, Millie Yi Mao, A. Ullah
Abstract The estimation of a large covariance matrix is challenging when the dimension p is large relative to the sample size n. Common approaches to deal with the challenge have been based on thresholding or shrinkage methods in estimating covariance matrices. However, in many applications (e.g., regression, forecast combination, portfolio selection), what we need is not the covariance matrix but its inverse (the precision matrix). In this paper we introduce a method of estimating the high-dimensional “dynamic conditional precision” (DCP) matrices. The proposed DCP algorithm is based on the estimator of a large unconditional precision matrix to deal with the high-dimension and the dynamic conditional correlation (DCC) model to embed a dynamic structure to the conditional precision matrix. The simulation results show that the DCP method performs substantially better than the methods of estimating covariance matrices based on thresholding or shrinkage methods. Finally, we examine the “forecast combination puzzle” using the DCP, thresholding, and shrinkage methods.
{"title":"Estimation of high-dimensional dynamic conditional precision matrices with an application to forecast combination","authors":"Tae-Hwy Lee, Millie Yi Mao, A. Ullah","doi":"10.1080/07474938.2021.1889208","DOIUrl":"https://doi.org/10.1080/07474938.2021.1889208","url":null,"abstract":"Abstract The estimation of a large covariance matrix is challenging when the dimension p is large relative to the sample size n. Common approaches to deal with the challenge have been based on thresholding or shrinkage methods in estimating covariance matrices. However, in many applications (e.g., regression, forecast combination, portfolio selection), what we need is not the covariance matrix but its inverse (the precision matrix). In this paper we introduce a method of estimating the high-dimensional “dynamic conditional precision” (DCP) matrices. The proposed DCP algorithm is based on the estimator of a large unconditional precision matrix to deal with the high-dimension and the dynamic conditional correlation (DCC) model to embed a dynamic structure to the conditional precision matrix. The simulation results show that the DCP method performs substantially better than the methods of estimating covariance matrices based on thresholding or shrinkage methods. Finally, we examine the “forecast combination puzzle” using the DCP, thresholding, and shrinkage methods.","PeriodicalId":11438,"journal":{"name":"Econometric Reviews","volume":"40 1","pages":"905 - 918"},"PeriodicalIF":1.2,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474938.2021.1889208","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42782198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-26DOI: 10.1080/07474938.2021.1889175
Yonghui Zhang, Qiankun Zhou
Abstract We study the nonparametric estimation and specification testing for partially linear functional-coefficient dynamic panel data models, where the effects of some covariates on the dependent variable vary nonparametrically according to a set of low-dimensional variables. Based on the sieve approximation of unknown slope functions, we propose a sieve 2SLS procedure to estimate the model. The asymptotic properties of the estimators of both parametric and nonparametric components are established when sample size N and T tend to infinity jointly. A nonparametric specification test for the constancy of slopes is also proposed. We show that after being appropriately standardized, the test is asymptotically normally distributed under the null hypothesis. The asymptotic properties of the test is also studied under a sequence of local Pitman alternatives and global alternatives. A set of Monte Carlo simulations show that our sieve 2SLS estimators and specification test perform remarkably well in finite samples. We apply our method to study the impact of income on democracy, and find strong evidence of nonlinear/nonconstant effect of income on democracy.
{"title":"Partially linear functional-coefficient dynamic panel data models: sieve estimation and specification testing","authors":"Yonghui Zhang, Qiankun Zhou","doi":"10.1080/07474938.2021.1889175","DOIUrl":"https://doi.org/10.1080/07474938.2021.1889175","url":null,"abstract":"Abstract We study the nonparametric estimation and specification testing for partially linear functional-coefficient dynamic panel data models, where the effects of some covariates on the dependent variable vary nonparametrically according to a set of low-dimensional variables. Based on the sieve approximation of unknown slope functions, we propose a sieve 2SLS procedure to estimate the model. The asymptotic properties of the estimators of both parametric and nonparametric components are established when sample size N and T tend to infinity jointly. A nonparametric specification test for the constancy of slopes is also proposed. We show that after being appropriately standardized, the test is asymptotically normally distributed under the null hypothesis. The asymptotic properties of the test is also studied under a sequence of local Pitman alternatives and global alternatives. A set of Monte Carlo simulations show that our sieve 2SLS estimators and specification test perform remarkably well in finite samples. We apply our method to study the impact of income on democracy, and find strong evidence of nonlinear/nonconstant effect of income on democracy.","PeriodicalId":11438,"journal":{"name":"Econometric Reviews","volume":"40 1","pages":"983 - 1006"},"PeriodicalIF":1.2,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474938.2021.1889175","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48584118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-22DOI: 10.1080/07474938.2021.2002521
Fei Jin, Yuqing Wang
Abstract This paper considers the generalized method of moments (GMM) estimation of a spatial autoregressive (SAR) model with SAR disturbances, where we allow for endogenous regressors in addition to a spatial lag of the dependent variable. We do not assume any reduced form of the endogenous regressors, thus we allow for spatial dependence and heterogeneity in endogenous regressors, and allow for nonlinear relations between endogenous regressors and their instruments. Innovations in the model can be homoscedastic or heteroskedastic with unknown forms. We prove that GMM estimators with linear and quadratic moments are consistent and asymptotically normal. In the homoscedastic case, we derive the best linear and quadratic moments that can generate an optimal GMM estimator with the minimum asymptotic variance.
{"title":"GMM estimation of a spatial autoregressive model with autoregressive disturbances and endogenous regressors","authors":"Fei Jin, Yuqing Wang","doi":"10.1080/07474938.2021.2002521","DOIUrl":"https://doi.org/10.1080/07474938.2021.2002521","url":null,"abstract":"Abstract This paper considers the generalized method of moments (GMM) estimation of a spatial autoregressive (SAR) model with SAR disturbances, where we allow for endogenous regressors in addition to a spatial lag of the dependent variable. We do not assume any reduced form of the endogenous regressors, thus we allow for spatial dependence and heterogeneity in endogenous regressors, and allow for nonlinear relations between endogenous regressors and their instruments. Innovations in the model can be homoscedastic or heteroskedastic with unknown forms. We prove that GMM estimators with linear and quadratic moments are consistent and asymptotically normal. In the homoscedastic case, we derive the best linear and quadratic moments that can generate an optimal GMM estimator with the minimum asymptotic variance.","PeriodicalId":11438,"journal":{"name":"Econometric Reviews","volume":"41 1","pages":"652 - 674"},"PeriodicalIF":1.2,"publicationDate":"2021-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45311372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-22DOI: 10.1080/07474938.2021.1995683
Stan Hurn, Vance L. Martin, Lina Xu
Abstract A new class of specification tests for stochastic differential equations (SDE) is proposed to determine whether the probability integral transform of the estimated model generates an independent and identically distributed uniform random variable. The tests are based on Neyman’s smooth test, appropriately adjusted to correct for both the size distortion arising from having to estimate the unknown parameters of the SDE and possible dependence in the uniform random variable. The suite of tests is compared against other commonly used specification tests for SDEs. The finite sample properties of the tests are investigated using a range of Monte Carlo experiments. The tests are then applied to testing the specification of SDEs used to model the spot interest rate and financial asset volatility.
{"title":"Specification tests for univariate diffusions","authors":"Stan Hurn, Vance L. Martin, Lina Xu","doi":"10.1080/07474938.2021.1995683","DOIUrl":"https://doi.org/10.1080/07474938.2021.1995683","url":null,"abstract":"Abstract A new class of specification tests for stochastic differential equations (SDE) is proposed to determine whether the probability integral transform of the estimated model generates an independent and identically distributed uniform random variable. The tests are based on Neyman’s smooth test, appropriately adjusted to correct for both the size distortion arising from having to estimate the unknown parameters of the SDE and possible dependence in the uniform random variable. The suite of tests is compared against other commonly used specification tests for SDEs. The finite sample properties of the tests are investigated using a range of Monte Carlo experiments. The tests are then applied to testing the specification of SDEs used to model the spot interest rate and financial asset volatility.","PeriodicalId":11438,"journal":{"name":"Econometric Reviews","volume":"41 1","pages":"607 - 632"},"PeriodicalIF":1.2,"publicationDate":"2021-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45941689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-11DOI: 10.1080/07474938.2021.1996994
Dalia Ghanem
Abstract This paper proposes a James-Stein-type (JS) adjustment to analytical bias correction in fixed effects panel models that suffer from the incidental parameters problem. We provide high-level conditions under which the infeasible JS adjustment leads to a higher-order MSE improvement over the bias-corrected estimator, and the former is asymptotically equivalent to the latter. To obtain a feasible JS adjustment, we propose a nonparametric bootstrap procedure to estimate the JS weighting matrix and provide conditions for its consistency. We apply the JS adjustment to two models: (1) the linear autoregressive model with fixed effects, (2) the nonlinear static fixed effects model. For each application, we employ Monte Carlo simulations which confirm the theoretical results and illustrate the finite-sample improvements due to the JS adjustment. Finally, the extension of the JS procedure to a more general class of models and other policy parameters are illustrated.
{"title":"A James-Stein-type adjustment to bias correction in fixed effects panel models","authors":"Dalia Ghanem","doi":"10.1080/07474938.2021.1996994","DOIUrl":"https://doi.org/10.1080/07474938.2021.1996994","url":null,"abstract":"Abstract This paper proposes a James-Stein-type (JS) adjustment to analytical bias correction in fixed effects panel models that suffer from the incidental parameters problem. We provide high-level conditions under which the infeasible JS adjustment leads to a higher-order MSE improvement over the bias-corrected estimator, and the former is asymptotically equivalent to the latter. To obtain a feasible JS adjustment, we propose a nonparametric bootstrap procedure to estimate the JS weighting matrix and provide conditions for its consistency. We apply the JS adjustment to two models: (1) the linear autoregressive model with fixed effects, (2) the nonlinear static fixed effects model. For each application, we employ Monte Carlo simulations which confirm the theoretical results and illustrate the finite-sample improvements due to the JS adjustment. Finally, the extension of the JS procedure to a more general class of models and other policy parameters are illustrated.","PeriodicalId":11438,"journal":{"name":"Econometric Reviews","volume":"41 1","pages":"633 - 651"},"PeriodicalIF":1.2,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44631436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-02DOI: 10.1080/07474938.2021.1991140
Francesco Bravo
Abstract This paper considers estimation of nonparametric moment conditions models with weakly dependent data. The estimator is based on a local linear version of the generalized empirical likelihood approach, and is an alternative to the popular local linear generalized method of moment estimator. The paper derives uniform convergence rates and pointwise asymptotic normality of the resulting local linear generalized empirical likelihood estimator. The paper also develops second order stochastic expansions (under a standard undersmoothing condition) that explain the better finite sample performance of the local linear generalized empirical likelihood estimator compared to that of the efficient local linear generalized method of moments estimator, and can be used to obtain (second order) bias corrected estimators. Monte Carlo simulations and an empirical application illustrate the competitive finite sample properties and the usefulness of the proposed estimators and second order bias corrections.
{"title":"Second order expansions of estimators in nonparametric moment conditions models with weakly dependent data","authors":"Francesco Bravo","doi":"10.1080/07474938.2021.1991140","DOIUrl":"https://doi.org/10.1080/07474938.2021.1991140","url":null,"abstract":"Abstract This paper considers estimation of nonparametric moment conditions models with weakly dependent data. The estimator is based on a local linear version of the generalized empirical likelihood approach, and is an alternative to the popular local linear generalized method of moment estimator. The paper derives uniform convergence rates and pointwise asymptotic normality of the resulting local linear generalized empirical likelihood estimator. The paper also develops second order stochastic expansions (under a standard undersmoothing condition) that explain the better finite sample performance of the local linear generalized empirical likelihood estimator compared to that of the efficient local linear generalized method of moments estimator, and can be used to obtain (second order) bias corrected estimators. Monte Carlo simulations and an empirical application illustrate the competitive finite sample properties and the usefulness of the proposed estimators and second order bias corrections.","PeriodicalId":11438,"journal":{"name":"Econometric Reviews","volume":"41 1","pages":"583 - 606"},"PeriodicalIF":1.2,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47592947","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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