A Second-order Approximation to the Bias of OLS Estimates in Bivariate VAR Models

Two terms of a second-order approximation to the bias of the multivariate OLS estimate are derived using the same technique as in Nicholls and Pope (1988). The resulting second-order bias approximation is then tested against first-order alternatives on two bivariate Monte Carlo sijmulated VAR models. Even though the second-order terms do not completely remedy the bias left unadjusted by the first-order approximations, it makes a significant change in the right direction where the first-order approximations fail, notably in the smallest samples and when systems approach non-stationarity.