Approximating and reducing bias in 2SLS estimation of dynamic simultaneous equation models

Abstract

An order O(1/T) approximation is made to the bias in 2SLS estimation of a dynamic simultaneous equation model, building on similar large-T moment approximations for non-dynamic models. The expression is long because it contains two distinct parts: a part due to the simultaneity which is directly related to the Nagar bias and a part due to the dynamics which has many component terms. However, the analytically corrected 2SLS estimators resulting from this approximation perform well in terms of remaining estimation bias. The biases of these estimators are compared with the Quenouille half-sample jackknife and the residual bootstrap for 2SLS in dynamic models, and are found to be competitive. The Monte Carlo and bias approximation also suggest that the bias in estimating endogenous variable coefficients in dynamic simultaneous equation models is non monotonic in the sample size, contrary to the well known theoretical result for static models. The effect of using weaker instruments on our numerical and Monte Carlo results is explored.