Fixed Effect Estimation of Large T Panel Data Models

This article reviews recent advances in fixed effect estimation of panel data models for long panels, where the number of time periods is relatively large. We focus on semiparametric models with unobserved individual and time effects, where the distribution of the outcome variable conditional on covariates and unobserved effects is specified parametrically, while the distribution of the unobserved effects is left unrestricted. Compared to existing reviews on long panels (Arellano and Hahn 2007; a section in Arellano and Bonhomme 2011) we discuss models with both individual and time effects, split-panel Jackknife bias corrections, unbalanced panels, distribution and quantile effects, and other extensions. Understanding and correcting the incidental parameter bias caused by the estimation of many fixed effects is our main focus, and the unifying theme is that the order of this bias is given by the simple formula p/n for all models discussed, with p the number of estimated parameters and n the total sample size.Comment: 40 pages, 1 tabl

Fitting vast dimensional time-varying covariance models

Estimation of time-varying covariances is a key input in risk management and asset allocation. ARCH-type multivariate models are used widely for this purpose. Estimation of such models is computationally costly and parameter estimates are meaningfully biased when applied to a moderately large number of assets. Here, we propose a novel estimation approach that suffers from neither of these issues, even when the number of assets is in the hundreds. The theory of this new method is developed in some detail. The performance of the proposed method is investigated using extensive simulation studies and empirical examples. Supplementary materials for this article are available online

Combining Multivariate Volatility Models

Forecasting conditional covariance matrices of returns involves a variety of modeling options. First, the choice between models based on daily or intradaily returns. Examples of the former are the Multivariate GARCH (MGARCH) models while models fitted to Realized Covariance (RC) matrices are examples of the latter. A second option, strictly related to the RC matrices, is given by the identification of the frequency at which the intradaily returns are observed. A third option concerns the proper estimation method able to guarantee unbiased parameter estimates even for large (MGARCH) models. Thus, dealing with all these modeling options is not always straightforward. A possible solution is the combination of volatility forecasts. The aim of this work is to present a forecast combination strategy in which the combined models are selected by the Model Confidence Set (MCS) procedure, implemented under two economic loss functions (LFs)