An example of how the control variate method reduces noise in Monte Carlo experiments

Abstract

The control variate method proposed by Mikhail (1972) is used to reexamine the results reported by Kmenta and Gilbert (1968) on the finite sample properties of Zellner's (1962) seemingly unrelated regressions estimator. The results indicate that the Mikhail method does successfully reduce the noise in the Kmenta-Gilbert Monte Carlo results. Additionally, the adjusted Kmenta-Gilbert results indicate that the asymptotic standard deviation of the two step Zellner seemingly unrelated regressions estimator based on restricted estimates of the cross equation variance-covariance matrix is a good approximation of the finite standard deviation in most cases, especially when the correlation between explanatory variables across equations is high and/or the correlation between disturbances across equations is low.

Keywords:

• seemingly unrelated regressions
• restricted residuals
• finite sample properties
• control variable