Estimation of Dynamic Mixed Double Factors Model in High Dimensional Panel Data

The purpose of this article is to develop the dimension reduction techniques in panel data analysis when the number of individuals and indicators is large. We use Principal Component Analysis (PCA) method to represent large number of indicators by minority common factors in the factor models. We propose the Dynamic Mixed Double Factor Model (DMDFM for short) to re ect cross section and time series correlation with interactive factor structure. DMDFM not only reduce the dimension of indicators but also consider the time series and cross section mixed effect. Different from other models, mixed factor model have two styles of common factors. The regressors factors re flect common trend and reduce the dimension, error components factors re ect difference and weak correlation of individuals. The results of Monte Carlo simulation show that Generalized Method of Moments (GMM) estimators have good unbiasedness and consistency. Simulation also shows that the DMDFM can improve prediction power of the models effectively.Comment: 38 pages, 2 figure

Unbiased Instrumental Variables Estimation Under Known First-Stage Sign

We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first stage coefficients is known. In the case with a single instrument, there is a unique non-randomized unbiased estimator based on the reduced-form and first-stage regression estimates. For cases with multiple instruments we propose a class of unbiased estimators and show that an estimator within this class is efficient when the instruments are strong. We show numerically that unbiasedness does not come at a cost of increased dispersion in models with a single instrument: in this case the unbiased estimator is less dispersed than the 2SLS estimator. Our finite-sample results apply to normal models with known variance for the reduced-form errors, and imply analogous results under weak instrument asymptotics with an unknown error distribution

Panel Data Models with Nonadditive Unobserved Heterogeneity: Estimation and Inference

This paper considers fixed effects estimation and inference in linear and nonlinear panel data models with random coefficients and endogenous regressors. The quantities of interest -- means, variances, and other moments of the random coefficients -- are estimated by cross sectional sample moments of GMM estimators applied separately to the time series of each individual. To deal with the incidental parameter problem introduced by the noise of the within-individual estimators in short panels, we develop bias corrections. These corrections are based on higher-order asymptotic expansions of the GMM estimators and produce improved point and interval estimates in moderately long panels. Under asymptotic sequences where the cross sectional and time series dimensions of the panel pass to infinity at the same rate, the uncorrected estimator has an asymptotic bias of the same order as the asymptotic variance. The bias corrections remove the bias without increasing variance. An empirical example on cigarette demand based on Becker, Grossman and Murphy (1994) shows significant heterogeneity in the price effect across U.S. states.Comment: 51 pages, 4 tables, 1 figure, it includes supplementary appendi

Analytic and bootstrap approximations of prediction errors under a multivariate fay-herriot model

A Multivariate Fay-Herriot model is used to aid the prediction of small area parameters of dependent variables with sample data aggregated to area level. The empirical best linear unbiased predictor of the parameter vector is used, and an approximation of the elements of the mean cross product error matrix is obtained by an extension of the results of Prasad and Rao (1990) to the multiparameter case. Three different bootstrap approximations of those elements are introduced, and a simulation study is developed in order to compare the efficiency of all presented approximations, including a comparison under lack of normality. Further, the number of replications needed for the bootstrap procedures to get stabilized are studied