Panel data models with long-range dependence

Abstract

This thesis comprises of three chapters that study panel data models with long-range dependence. The first chapter is a coauthored paper with Prof. Carlos Velasco. We consider large N; T panel data models with fixed effects, common factors allowing cross-section dependence, and persistent data and shocks, which are assumed fractionally integrated. In a basic setup, the main interest is on the fractional parameter of the idiosyncratic component, which is estimated in first differences after factor removal by projection on the cross-section average. The pooled conditional-sum-of-squares estimate is √NT consistent but the normal asymptotic distribution might not be centered, requiring the time series dimension to grow faster than the cross-section size for correction. Generalizing the basic setup to include covariates and heterogeneous parameters, we propose individual and common-correlation estimates for the slope parameters, while error memory parameters are estimated from regression residuals. The two parameter estimates are √T consistent and asymptotically normal and mutually uncorrelated, irrespective of possible cointegration among idiosyncratic components. A study of small-sample performance and an empirical application to realized volatility persistence are included. The second chapter extends the first chapter. In this paper, a general dynamic panel data model is considered that incorporates individual and interactive fixed effects and possibly correlated innovations. The model accommodates general stationary or nonstationary long-range dependence through interactive fixed effects and innovations, removing the necessity to perform a priori unitroot or stationarity testing. Moreover, persistence in innovations and interactive fixed effects allows for cointegration; innovations can also have vector-autoregressive dynamics; deterministic trends can be nested. Estimations are performed using conditional-sum-of-squares criteria based on projected series by which latent characteristics are proxied. Resulting estimates are consistent and asymptotically normal at parametric rates. A simulation study provides reliability on the estimation method. The method is then applied to the long-run relationship between debt and GDP. The third and final chapter of the thesis is a coauthored paper with Prof. Abderrahim Taamouti. In this paper, a parametric portfolio policy function is considered that incorporates common stock volatility dynamics to optimally determine portfolio weights. Reducing dimension of the traditional portfolio selection problem signifficantly, only a number of policy parameters corresponding to first- and second-order characteristics are estimated based on a standard methodof- moments technique. The method, allowing for the calculation of portfolio weight and return statistics, is illustrated with an empirical application to 30 U.S. industries to study the economic activity before and after the recent financial crisis.