Asymptotic distribution of estimators in reduced rank regression settings when the regressors are integrated

Abstract

In this paper the asymptotic distribution of estimators is derived in a general regression setting where rank restrictions on a submatrix of the coefficient matrix are imposed and the regressors can include stationary or I(1) processes. Such a setting occurs e.g. in factor models. Rates of convergence are derived and the asymptotic distribution is given for least squares estimators as well as fully-modified estimators. The gains in imposing the rank restrictions are investigated. A number of special cases are discussed including the Johansen results in the case of cointegrated VAR(p) processes.