In this paper, we estimate and leverage latent constant group structure to generate the point, set, and density forecasts for short dynamic panel data. We implement a nonparametric Bayesian approach to simultaneously identify coefficients and group membership in the random effects which are heterogeneous across groups but fixed within a group. This method allows us to flexibly incorporate subjective prior knowledge on the group structure that potentially improves the predictive accuracy. In Monte Carlo experiments, we demonstrate that our Bayesian grouped random effects (BGRE) estimators produce accurate estimates and score predictive gains over standard panel data estimators. With a data-driven group structure, the BGRE estimators exhibit comparable accuracy of clustering with the Kmeans algorithm and outperform a two-step Bayesian grouped estimator whose group structure relies on Kmeans. In the empirical analysis, we apply our method to forecast the investment rate across a broad range of firms and illustrate that the estimated latent group structure improves forecasts relative to standard panel data estimators.
In this paper, we develop spectral and post-spectral estimators for grouped panel data models. Both estimators are consistent in the asymptotics where the number of observations $N$ and the number of time periods $T$ simultaneously grow large. In addition, the post-spectral estimator is $\sqrt{NT}$-consistent and asymptotically normal with mean zero under the assumption of well-separated groups even if $T$ is growing much slower than $N$. The post-spectral estimator has, therefore, theoretical properties that are comparable to those of the grouped fixed-effect estimator developed by Bonhomme a…
This paper introduces estimation methods for grouped latent heterogeneity in panel data quantile regression. We assume that the observed individuals come from a heterogeneous population with a finite number of types. The number of types and group membership is not assumed to be known in advance and is estimated by means of a convex optimization problem. We provide conditions under which group membership is estimated consistently and establish asymptotic normality of the resulting estimators. Simulations show that the method works well in finite samples when T is reasonably large. To illustrate…
Forecasting with panel data: Estimation uncertainty versus parameter heterogeneity
University of Cambridge（剑桥大学）；University of Southern California（南加州大学）；Erasmus University Rotterdam（鹿特丹伊拉斯姆斯大学）；Erasmus School of Economics（伊拉斯姆斯经济管理学院）；Tinbergen Institute（蒂宁伯根研究所）；UC San Diego（加州大学圣地亚哥分校）
This paper develops a new model and estimation procedure for panel data that allows us to identify heterogeneous structural breaks. We model individual heterogeneity using a grouped pattern. For each group, we allow common structural breaks in the coefficients. However, the number, timing, and size of these breaks can differ across groups. We develop a hybrid estimation procedure of the grouped fixed effects approach and adaptive group fused Lasso. We show that our method can consistently identify the latent group structure, detect structural breaks, and estimate the regression parameters. Mon…
We use a dynamic panel Tobit model with heteroskedasticity to generate forecasts for a large cross-section of short time series of censored observations. Our fully Bayesian approach allows us to flexibly estimate the cross-sectional distribution of heterogeneous coefficients and then implicitly use this distribution as prior to construct Bayes forecasts for the individual time series. In addition to density forecasts, we construct set forecasts that explicitly target the average coverage probability for the cross-section. We present a novel application in which we forecast bank-level loan char…
This paper considers the problem of forecasting a collection of short time series using cross sectional information in panel data. We construct point predictors using Tweedie's formula for the posterior mean of heterogeneous coefficients under a correlated random effects distribution. This formula utilizes cross-sectional information to transform the unit-specific (quasi) maximum likelihood estimator into an approximation of the posterior mean under a prior distribution that equals the population distribution of the random coefficients. We show that the risk of a predictor based on a non-param…
Institute of Statistics and Data Science, Nanjing Audit University（南京审计大学统计与数据科学学院）
China has made great achievements in electric power industry during the long-term deepening of reform and opening up. However, the complex regional economic, social and natural conditions, electricity resources are not evenly distributed, which accounts for the electricity deficiency in some regions of China. It is desirable to develop a robust electricity forecasting model. Motivated by which, we propose a Panel Semiparametric Quantile Regression Neural Network (PSQRNN) by utilizing the artificial neural network and semiparametric quantile regression. The PSQRNN can explore a potential linear…
In this paper, we forecast euro area inflation and its main components using an econometric model which exploits a massive number of time series on survey expectations for the European Commission's Business and Consumer Survey. To make estimation of such a huge model tractable, we use recent advances in computational statistics to carry out posterior simulation and inference. Our findings suggest that the inclusion of a wide range of firms and consumers' opinions about future economic developments offers useful information to forecast prices and assess tail risks to inflation. These predictive…
In this paper, a statistical model for panel data with unobservable grouped factor structures which are correlated with the regressors and the group membership can be unknown. The factor loadings are assumed to be in different subspaces and the subspace clustering for factor loadings are considered. A method called least squares subspace clustering estimate (LSSC) is proposed to estimate the model parameters by minimizing the least-square criterion and to perform the subspace clustering simultaneously. The consistency of the proposed subspace clustering is proved and the asymptotic properties …
We study linear panel regression models in which the unobserved error term is an unknown smooth function of two-way unobserved fixed effects. In standard additive or interactive fixed effect models the individual specific and time specific effects are assumed to enter with a known functional form (additive or multiplicative). In this paper, we allow for this functional form to be more general and unknown. We discuss two different estimation approaches that allow consistent estimation of the regression parameters in this setting as the number of individuals and the number of time periods grow t…
We study discrete panel data methods where unobserved heterogeneity is revealed in a first step, in environments where population heterogeneity is not discrete. We focus on two-step grouped fixed-effects (GFE) estimators, where individuals are first classified into groups using kmeans clustering, and the model is then estimated allowing for group-specific heterogeneity. Our framework relies on two key properties: heterogeneity is a function - possibly nonlinear and time-varying - of a low-dimensional continuous latent type, and informative moments are available for classification. We illustrat…
We use a decision-theoretic framework to study the problem of forecasting discrete outcomes when the forecaster is unable to discriminate among a set of plausible forecast distributions because of partial identification or concerns about model misspecification or structural breaks. We derive "robust" forecasts which minimize maximum risk or regret over the set of forecast distributions. We show that for a large class of models including semiparametric panel data models for dynamic discrete choice, the robust forecasts depend in a natural way on a small number of convex optimization problems wh…
Accurate estimation for extent of cross{sectional dependence in large panel data analysis is paramount to further statistical analysis on the data under study. Grouping more data with weak relations (cross{sectional dependence) together often results in less efficient dimension reduction and worse forecasting. This paper describes cross-sectional dependence among a large number of objects (time series) via a factor model and parameterizes its extent in terms of strength of factor loadings. A new joint estimation method, benefiting from unique feature of dimension reduction for high dimensional…
We consider estimation and inference in panel data models with additive unobserved individual specific heterogeneity in a high dimensional setting. The setting allows the number of time varying regressors to be larger than the sample size. To make informative estimation and inference feasible, we require that the overall contribution of the time varying variables after eliminating the individual specific heterogeneity can be captured by a relatively small number of the available variables whose identities are unknown. This restriction allows the problem of estimation to proceed as a variable s…
We develop a Bayesian non-parametric quantile panel regression model. Within each quantile, the response function is a convex combination of a linear model and a non-linear function, which we approximate using Bayesian Additive Regression Trees (BART). Cross-sectional information at the pth quantile is captured through a conditionally heteroscedastic latent factor. The non-parametric feature of our model enhances flexibility, while the panel feature, by exploiting cross-country information, increases the number of observations in the tails. We develop Bayesian Markov chain Monte Carlo (MCMC) m…
Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and widespread use for various applications ranging from genomics to finance, this methodology has predominantly remained linear. This study estimates factors nonlinearly through the kernel method, which allows flexible nonlinearities while still avoiding the curse of dimensionality. We focus on factor-augmented forecasting of a single time series in a high-dimension…
Panel Vector Autoregressions (PVARs) are a popular tool for analyzing multi-country datasets. However, the number of estimated parameters can be enormous, leading to computational and statistical issues. In this paper, we develop fast Bayesian methods for estimating PVARs using integrated rotated Gaussian approximations. We exploit the fact that domestic information is often more important than international information and group the coefficients accordingly. Fast approximations are used to estimate the latter while the former are estimated with precision using Markov chain Monte Carlo techniq…
Testing Clustered Equal Predictive Ability with Unknown Clusters
Université Bourgogne Europe（勃艮第欧洲大学）；Paris-Panthéon-Assas University（巴黎先贤祠-阿萨斯大学）；Bayes Business School (formerly Cass)（贝叶斯商学院（原卡斯商学院））；Singapore Management University（新加坡管理大学）
Olin Business School, Washington University in St. Louis（华盛顿大学圣路易斯分校奥林商学院）；Chaifetz School of Business, Saint Louis University（圣路易斯大学蔡菲兹商学院）；Center for Economic Behavior and Decision-Making, Zhejiang University of Finance and Economics（浙江财经大学经济行为与决策研究中心）；Department of Economics, University of Chicago（芝加哥大学经济学系）
The practical importance of coherent forecasts in hierarchical forecasting has inspired many studies on forecast reconciliation. Under this approach, so-called base forecasts are produced for every series in the hierarchy and are subsequently adjusted to be coherent in a second reconciliation step. Reconciliation methods have been shown to improve forecast accuracy, but will, in general, adjust the base forecast of every series. However, in an operational context, it is sometimes necessary or beneficial to keep forecasts of some variables unchanged after forecast reconciliation. In this paper,…
