The Accuracy of the Higher Order Bias Approximation for the 2SLS Estimator.

Mikhail (1972a) found that estimated 2SLS biases, obtained through simulation using antithetic variables and control variate methods, were closer to each other than to Nagar's bias approximation to order T-1. As remarked by Kiviet and Phillips (1996), this result represents one of a very small number of higher order approximations in the econometric literature yet there is no published evidence of its accuracy. In this paper the accuracy of the approximation is explored in the context of a framework similar to that chosen by Mikhail (1972a) and it is found that the higher order approximation is clearly superior. In cases where the bias is severe, the results support the belief that, when the first order approximation is poor but not terrible, the higher order approximation mops up most of the error.