Full Versus Limited Information Estimation of a Rational Expectations Model: Some Numerical Comparisons

This paper compares numerically the asymptotic distributions of parameter estimates and test statistics associated with two estimation techniques: (a)a limited information one, which uses instrumental variables to estimate a single equation (Hansen and Singleton (1982)), and (b)a full information one, which uses a procedure asymptotically equivalent to maximum likelihood to simultaneously estimate multiple equations (Hansen and Sargent (1980)). The paper compares the two with respect to both (1)asymptotic efficiency under the null hypothesis of no misspecification, and (2)asymptotic bias and power in the presence of certain local alternatives. It is found that: (l)Full information standard errors are only moderately smaller than limited information standard errors. (2)When the model is misspecified, full information tests tend to be more powerful, and its parameter estimates tend to be more biased. This suggests that at least in the model considered here, the gains from the use of the less robust and computationally more complex full information technique are not particularly large.