An Alternative Approach to Obtaining Nagar-Type Moment Approximations in Simultaneous Equation Models

Paper number: 99/06

Paper date: December 1998

Year: 1999

Paper Category: Discussion Paper


Kaddour Hadri
City University, London, UK
University of Exeter, UK


Garry D.A. Phillips
University of Exeter, UK


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. This suggested that the approximation might not be accurate and in Mikhail (1972b) he presented the bias approximation to order T-2. 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.

JEL Classification Nos: C22
Keywords: Two stage least squares; higher order bias approximation, exact bias, Monte Carlo simulations

Corresponding Author: Kaddour Hadri, School of Business and Economics, University of Exeter, Streatham Court, Rennes Drive, Exeter, EX4 4PU, UK, email: