CFE 2015: Start Registration
View Submission - CFE
A1680
Topic: Contributed on Large dimensional panel models Title: Generalized least squares estimation of panel with common shocks Authors:  Marco Avarucci - University of Glasgow (United Kingdom) [presenting]
Paolo Zaffaroni - Imperial College London (United Kingdom)
Abstract: The estimation of linear regression such as $Y_i=X_i\beta_{i0}+u_i$ is considered, where $Y_i=(y_{i1},...y_{iT})'$ is a $Tx1$ vector of dependent variables, $X_i$ is a $T\times K$ matrix of regressor and $\beta_{i0}$ are individual-specific parameters. The innovation $u_i=(u_{i1},...,u_{iT})'$ has a factor structure $u_i=Fb_i+e_i$, for a TxM matrix of latent factors $F=(f_1,...,f_T)'$ with loadings $b_i$ and $e_i=(e_{i1},...,e_{iT})'$ is a vector of idiosyncratic innovations. A factor structure in both the innovation $u_i$ and the regressors $X_i$ can make the ordinary least squares estimator inconsistent for the true regression coefficients. To overcome this problem, we propose a GLS-type estimator. The procedure can be summarized as follows: (i) Obtain the $T\times 1$ vector of residuals $\hat{u}_i$ by OLS. (ii) Construct the $T\times T$ variance covariance matrix $W=N^{1}\sum_{i=1}^N \hat{u}_i\hat{u}_i'$. (iii) Compute the GLS estimator using the matrix $W$. We show that, if $T^2/N$ approaches zero for $T,N$ diverging to infinity, the GLS estimator is consistent and asymptotically normal. This result is due to an important insight, namely the existence of a form of asymptotic orthogonality between the latent factor $F$ and inverse of $W$. This result holds despite the inconsistency of the OLS and does not require a preliminary estimate of the factor or a priory knowledge of their number.