Econometrica: Nov, 1988, Volume 56, Issue 6

Asymptotic Normality, When Regressors Have a Unit Root

https://doi.org/0012-9682(198811)56:6<1397:ANWRHA>2.0.CO;2-K
p. 1397-1417

Kenneth D. West

Under fairly general conditions, ordinary least squares and linear instrumental variables estimators are asymptotically normal when a regression equation has nonstationary right-hand side variables. Standard formulas may be used to calculate a consistent estimate of the asymptotic variance covariance matrix of the estimated parameter vector, even if the disturbances are conditionally heteroskedastic and autocorrelated. So inference may proceed in the usual way. The key requirements are that the nonstationary variables share a common unit root and that the unconditional mean of their first differences is nonzero.