There is a large and growing literature concerned with forecasting time series variables using factor-augmented regression models. The workhorse of this literature is a two-step approach in which the factors are first estimated by applying the principal components method to a large panel of variables, and the forecast regression is estimated conditional on the first-step factor estimates. Another stream of research that has attracted much attention is concerned with the use of cross-section averages as common factor estimates in interactive effects panel regression models. The main justification for this second development is the simplicity and good performance of the cross-section averages when compared to estimated principal component factors. In view of this, it is quite surprising that no one has yet considered the use of cross-section averages for forecasting. Indeed, given the purpose to forecast the conditional mean, the use of the cross-sectional average to estimate the factors is only natural. The present paper can be seen as a reaction to this. The purpose is to investigate the asymptotic and small-sample properties of forecasts based on cross-section average-augmented regressions. In contrast to existing studies, the investigation is carried out while allowing the number of factors to be unknown. JEL Classification: C12; C13; C33.
{"title":"Forecasting using cross-section average–augmented time series regressions","authors":"Hande Karabıyık, J. Westerlund","doi":"10.1093/ectj/utaa031","DOIUrl":"https://doi.org/10.1093/ectj/utaa031","url":null,"abstract":"There is a large and growing literature concerned with forecasting time series variables using factor-augmented regression models. The workhorse of this literature is a two-step approach in which the factors are first estimated by applying the principal components method to a large panel of variables, and the forecast regression is estimated conditional on the first-step factor estimates. Another stream of research that has attracted much attention is concerned with the use of cross-section averages as common factor estimates in interactive effects panel regression models. The main justification for this second development is the simplicity and good performance of the cross-section averages when compared to estimated principal component factors. In view of this, it is quite surprising that no one has yet considered the use of cross-section averages for forecasting. Indeed, given the purpose to forecast the conditional mean, the use of the cross-sectional average to estimate the factors is only natural. The present paper can be seen as a reaction to this. The purpose is to investigate the asymptotic and small-sample properties of forecasts based on cross-section average-augmented regressions. In contrast to existing studies, the investigation is carried out while allowing the number of factors to be unknown. JEL Classification: C12; C13; C33.","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":"24 1","pages":"315-333"},"PeriodicalIF":1.9,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/ectj/utaa031","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49181040","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}
This paper presents a multiplicative nonstationary nonparametric regression model which allows for a broad class of nonstationary processes. We propose a three-step estimation procedure to uncover the conditional mean function and establish uniform convergence rates and asymptotic normality of our estimators. The new model can also be seen as a dimension-reduction technique for a general two-dimensional time-varying nonparametric regression model, which is especially useful in small samples and for estimating explicitly multiplicative structural models. We consider two applications: estimating a pricing equation for the US aggregate economy to model consumption growth and estimating the shape of the monthly risk premium for S&P 500 Index data.
{"title":"Estimation of nonstationary nonparametric regression model with multiplicative structure","authors":"Likai Chen, E. Smetanina, W. Wu","doi":"10.1093/ECTJ/UTAB018","DOIUrl":"https://doi.org/10.1093/ECTJ/UTAB018","url":null,"abstract":"\u0000 This paper presents a multiplicative nonstationary nonparametric regression model which allows for a broad class of nonstationary processes. We propose a three-step estimation procedure to uncover the conditional mean function and establish uniform convergence rates and asymptotic normality of our estimators. The new model can also be seen as a dimension-reduction technique for a general two-dimensional time-varying nonparametric regression model, which is especially useful in small samples and for estimating explicitly multiplicative structural models. We consider two applications: estimating a pricing equation for the US aggregate economy to model consumption growth and estimating the shape of the monthly risk premium for S&P 500 Index data.","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43010140","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}
In this paper, we consider efficiency improvement in a nonparametric panel data model with cross-sectional dependence. A generalised least squares (GLS)-type estimator is proposed by taking into account this dependence structure. Parameterising the cross-sectional dependence, a local linear estimator is shown to be dominated by this type of GLS estimator. Also, possible gains in terms of rate of convergence are studied. Asymptotically optimal bandwidth choice is justified. To assess the finite sample performance of the proposed estimators, a Monte Carlo study is carried out. Further, some empirical applications are conducted with the aim of analysing the implications of the European Monetary Union for its member countries.
{"title":"Nonparametric panel data regression with parametric cross-sectional dependence","authors":"A. Soberón, Juan M. Rodríguez-Póo, P. Robinson","doi":"10.1093/ECTJ/UTAB016","DOIUrl":"https://doi.org/10.1093/ECTJ/UTAB016","url":null,"abstract":"\u0000 In this paper, we consider efficiency improvement in a nonparametric panel data model with cross-sectional dependence. A generalised least squares (GLS)-type estimator is proposed by taking into account this dependence structure. Parameterising the cross-sectional dependence, a local linear estimator is shown to be dominated by this type of GLS estimator. Also, possible gains in terms of rate of convergence are studied. Asymptotically optimal bandwidth choice is justified. To assess the finite sample performance of the proposed estimators, a Monte Carlo study is carried out. Further, some empirical applications are conducted with the aim of analysing the implications of the European Monetary Union for its member countries.","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":"1 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42239572","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}
This paper introduces a factor-augmented forecasting regression model in the presence of threshold effects. We consider least squares estimation of the regression parameters and establish asymptotic theories for estimators of both slope coefficients and the threshold parameter. Prediction intervals are also constructed for factor-augmented forecasts. Moreover, we develop a likelihood ratio statistic for tests on the threshold parameter and a sup-Wald test statistic for tests on the presence of threshold effects, respectively. Simulation results show that the proposed estimation method and testing procedures work very well in finite samples. Finally, we demonstrate the usefulness of the proposed model through an application to forecasting stock market returns.
{"title":"Factor-augmented forecasting regressions with threshold effects","authors":"Yayi Yan, Tingting Cheng","doi":"10.1093/ECTJ/UTAB011","DOIUrl":"https://doi.org/10.1093/ECTJ/UTAB011","url":null,"abstract":"\u0000 This paper introduces a factor-augmented forecasting regression model in the presence of threshold effects. We consider least squares estimation of the regression parameters and establish asymptotic theories for estimators of both slope coefficients and the threshold parameter. Prediction intervals are also constructed for factor-augmented forecasts. Moreover, we develop a likelihood ratio statistic for tests on the threshold parameter and a sup-Wald test statistic for tests on the presence of threshold effects, respectively. Simulation results show that the proposed estimation method and testing procedures work very well in finite samples. Finally, we demonstrate the usefulness of the proposed model through an application to forecasting stock market returns.","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43970031","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}
In the literature, a discrepancy in the limiting distributions of least square estimators between the stationary and nonstationary cases exists in various regression models with different persistence level regressors. This hinders further statistical inference since one has to decide which distribution should be used next. In this paper, we develop a semiparametric partially linear regression model with stationary and nonstationary regressors to attenuate this difficulty, and propose a unifying inference procedure for the coefficients. To be specific, we propose a profile weighted estimation equation method that facilitates the unifying inference. The proposed method is applied to the predictive regressions of stock returns, and an empirical likelihood procedure is developed to test the predictability. It is shown that the Wilks theorem holds for the empirical likelihood ratio regardless of predictors being stationary or not, which provides a unifying method for constructing confidence regions of the coefficients of state variables. Simulations show that the proposed method works well and has favourable finite sample performance over some existing approaches. An empirical application examining the predictability of equity returns highlights the value of our methodology.
{"title":"Unifying inference for semiparametric regression","authors":"Shaoxin Hong, Jiancheng Jiang, Xuejun Jiang, Zhijie Xiao","doi":"10.1093/ECTJ/UTAB005","DOIUrl":"https://doi.org/10.1093/ECTJ/UTAB005","url":null,"abstract":"\u0000 In the literature, a discrepancy in the limiting distributions of least square estimators between the stationary and nonstationary cases exists in various regression models with different persistence level regressors. This hinders further statistical inference since one has to decide which distribution should be used next. In this paper, we develop a semiparametric partially linear regression model with stationary and nonstationary regressors to attenuate this difficulty, and propose a unifying inference procedure for the coefficients. To be specific, we propose a profile weighted estimation equation method that facilitates the unifying inference. The proposed method is applied to the predictive regressions of stock returns, and an empirical likelihood procedure is developed to test the predictability. It is shown that the Wilks theorem holds for the empirical likelihood ratio regardless of predictors being stationary or not, which provides a unifying method for constructing confidence regions of the coefficients of state variables. Simulations show that the proposed method works well and has favourable finite sample performance over some existing approaches. An empirical application examining the predictability of equity returns highlights the value of our methodology.","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47822127","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}
G. Anderson, O. Linton, M. G. Pittau, Yoon-Jae Whang, Roberto Zelli
Multilateral comparison of outcomes drawn from multiple groups pervade the social sciences and measurement of their variability, usually involving functions of respective group location and scale parameters, is of intrinsic interest. However, such approaches frequently mask more fundamental differences that more comprehensive examination of relative group distributional structures reveal. Indeed, in categorical data contexts, location and scale based techniques are no longer feasible without artificial and questionable cardinalization of categories. Here, Ginis’ Transvariation measure is extended and employed in providing quantitative and visual multilateral comparison tools in discrete, continuous, categorical, univariate or multivariate settings which are particularly useful in paradigms where cardinal measure is absent. Two applications, one analyzing Eurozone cohesion in terms of the convergence or divergence of constituent nations income distributions, the other, drawn from a study of aging, health and income inequality in China, exemplify their use in a continuous and categorical data environment. Department of Economics, University of Toronto. Faculty of Economics, University of Cambridge. Department of Statistical Sciences, Sapienza University of Rome. Department of Economics, Seoul National University. 1
{"title":"On unit free assessment of the extent of multilateral distributional variation","authors":"G. Anderson, O. Linton, M. G. Pittau, Yoon-Jae Whang, Roberto Zelli","doi":"10.1093/ECTJ/UTAB003","DOIUrl":"https://doi.org/10.1093/ECTJ/UTAB003","url":null,"abstract":"Multilateral comparison of outcomes drawn from multiple groups pervade the social sciences and measurement of their variability, usually involving functions of respective group location and scale parameters, is of intrinsic interest. However, such approaches frequently mask more fundamental differences that more comprehensive examination of relative group distributional structures reveal. Indeed, in categorical data contexts, location and scale based techniques are no longer feasible without artificial and questionable cardinalization of categories. Here, Ginis’ Transvariation measure is extended and employed in providing quantitative and visual multilateral comparison tools in discrete, continuous, categorical, univariate or multivariate settings which are particularly useful in paradigms where cardinal measure is absent. Two applications, one analyzing Eurozone cohesion in terms of the convergence or divergence of constituent nations income distributions, the other, drawn from a study of aging, health and income inequality in China, exemplify their use in a continuous and categorical data environment. Department of Economics, University of Toronto. Faculty of Economics, University of Cambridge. Department of Statistical Sciences, Sapienza University of Rome. Department of Economics, Seoul National University. 1","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42548360","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}
Linear generalised method of moments (GMM) estimators for dynamic panel models with predetermined or endogenous regressors suffer from a weak instruments problem when the data are highly persistent. In this paper, we propose new random- and fixed-effects limited-information quasi–maximum likelihood estimators (LIQMLEs) for such models. We also discuss LIQMLEs for models that contain time-varying individual effects. Unlike system GMM estimators, the LIQMLEs do not require mean stationarity conditions for consistency. Such conditions often do not hold for the models we consider. Our LIQMLEs are based on a two-step control function approach that includes the first-stage model residuals for a predetermined or endogenous regressor in the outcome equation. The LIMLEs are more precise than nonlinear GMM estimators that are based on the original outcome equation. The LIQMLEs also compare favourably to various alternative (quasi–) maximum likelihood estimators in terms of precision, robustness, and/or ease of computation.
{"title":"Identification without assuming mean stationarity: quasi–maximum likelihood estimation of dynamic panel models with endogenous regressors","authors":"H. Kruiniger","doi":"10.1093/ectj/utaa036","DOIUrl":"https://doi.org/10.1093/ectj/utaa036","url":null,"abstract":"\u0000 Linear generalised method of moments (GMM) estimators for dynamic panel models with predetermined or endogenous regressors suffer from a weak instruments problem when the data are highly persistent. In this paper, we propose new random- and fixed-effects limited-information quasi–maximum likelihood estimators (LIQMLEs) for such models. We also discuss LIQMLEs for models that contain time-varying individual effects. Unlike system GMM estimators, the LIQMLEs do not require mean stationarity conditions for consistency. Such conditions often do not hold for the models we consider. Our LIQMLEs are based on a two-step control function approach that includes the first-stage model residuals for a predetermined or endogenous regressor in the outcome equation. The LIMLEs are more precise than nonlinear GMM estimators that are based on the original outcome equation. The LIQMLEs also compare favourably to various alternative (quasi–) maximum likelihood estimators in terms of precision, robustness, and/or ease of computation.","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41774794","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}
This article extends the kink threshold regression model with a constant threshold to a panel data framework with a covariate-dependent threshold, where the threshold is modeled as a function of informative covariates. We suggest an estimator based on the within-group transformation and propose test statistics for kink threshold effect and threshold constancy. We establish the asymptotic joint normality of the slope and threshold estimators and derive the limiting distributions of the test statistics. Our asymptotic results show that the inclusion of a covariate-dependent threshold does not affect the asymptotic joint normality of the slope and threshold estimates in the kink threshold regression model. Monte Carlo simulations show that the finite-sample proprieties of the proposed estimator and test statistics are generally satisfactory.
{"title":"Panel kink threshold regression model with a covariate-dependent threshold","authors":"Lixiong Yang, Chunli Zhang, Chingnun Lee, I‐Po Chen","doi":"10.1093/ectj/utaa035","DOIUrl":"https://doi.org/10.1093/ectj/utaa035","url":null,"abstract":"\u0000 This article extends the kink threshold regression model with a constant threshold to a panel data framework with a covariate-dependent threshold, where the threshold is modeled as a function of informative covariates. We suggest an estimator based on the within-group transformation and propose test statistics for kink threshold effect and threshold constancy. We establish the asymptotic joint normality of the slope and threshold estimators and derive the limiting distributions of the test statistics. Our asymptotic results show that the inclusion of a covariate-dependent threshold does not affect the asymptotic joint normality of the slope and threshold estimates in the kink threshold regression model. Monte Carlo simulations show that the finite-sample proprieties of the proposed estimator and test statistics are generally satisfactory.","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49333303","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}
In this paper we consider estimation of dynamic models of recurring events (event histories) in continuous time using censored data. We develop maximum simulated likelihood estimators where missing data are integrated out using Monte Carlo and importance sampling methods. We allow for random effects and integrate out the unobserved heterogeneity using a quadrature rule. In Monte Carlo experiments, we find that maximum simulated likelihood estimation is practically feasible and performs better than both listwise deletion and auxiliary modelling of initial conditions.
{"title":"Estimation of dynamic models of recurrent events with censored data","authors":"Tue Gørgens, Sanghyeok Lee","doi":"10.1093/ECTJ/UTAA028","DOIUrl":"https://doi.org/10.1093/ECTJ/UTAA028","url":null,"abstract":"In this paper we consider estimation of dynamic models of recurring events (event histories) in continuous time using censored data. We develop maximum simulated likelihood estimators where missing data are integrated out using Monte Carlo and importance sampling methods. We allow for random effects and integrate out the unobserved heterogeneity using a quadrature rule. In Monte Carlo experiments, we find that maximum simulated likelihood estimation is practically feasible and performs better than both listwise deletion and auxiliary modelling of initial conditions.","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":" ","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/ECTJ/UTAA028","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48972155","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}
We propose a novel method for modelling income processes using machine learning. Our method links age-specific regression trees, and returns a discrete state process, which can easily be included in consumption-saving models without further discretizations. A central advantage of our approach is that it does not rely on any parametric assumptions, and because we build on existing machine learning tools it is furthermore easy to apply in practice. Using a 30-year panel of Danish males, we document rich higher-order income dynamics, including substantial skewness and high kurtosis of income levels and growth rates. We also find important changes in income risk over the life-cycle and the income distribution. Our estimated process matches these dynamics closely. Using a consumption-saving model, the implied welfare cost of income risk is more than 10% of income.
{"title":"Higher-order income dynamics with linked regression trees","authors":"Jeppe Druedahl, Anders Munk-Nielsen","doi":"10.1093/ectj/utaa026","DOIUrl":"https://doi.org/10.1093/ectj/utaa026","url":null,"abstract":"\u0000 We propose a novel method for modelling income processes using machine learning. Our method links age-specific regression trees, and returns a discrete state process, which can easily be included in consumption-saving models without further discretizations. A central advantage of our approach is that it does not rely on any parametric assumptions, and because we build on existing machine learning tools it is furthermore easy to apply in practice. Using a 30-year panel of Danish males, we document rich higher-order income dynamics, including substantial skewness and high kurtosis of income levels and growth rates. We also find important changes in income risk over the life-cycle and the income distribution. Our estimated process matches these dynamics closely. Using a consumption-saving model, the implied welfare cost of income risk is more than 10% of income.","PeriodicalId":50555,"journal":{"name":"Econometrics Journal","volume":"23 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/ectj/utaa026","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44416732","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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