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

TL;DR

This paper derives the asymptotic distribution of estimators in reduced rank regression models with integrated regressors, including stationary and I(1) processes, and explores the benefits of rank restrictions.

Contribution

It provides a general framework for the asymptotic analysis of estimators under rank restrictions with integrated regressors, extending existing results to broader settings.

Findings

Derived convergence rates for estimators.

Established asymptotic distributions for least squares and fully-modified estimators.

Discussed special cases including cointegrated VAR models.

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.