Higher-order asymptotic expansions of the least-squares estimation bias in first-order dynamic regression models

An approximation to order T-² is obtained for the bias of the full vector of least-
squares estimates in general stable but not necessarily stationary ARX(1) models with
normal disturbances. This yields generalizations, allowing for various forms of initial
conditions, of Kendall's and White's classic results for stationary AR(1) models. The
accuracy of various alternative approximations is examined and compared by simulation
for particular parametrizations of AR(1) and ARX(1) models. The results show that often
the second-order approximation is considerably better than its first order counterpart and
hence opens perspectives for improved bias correction. However, we also find that order
T-² approximations are more vulnerable in the near unit root case than the much simpler
order T-¹ approximations.