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

Abstract

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 (1) full-information standard errors are only moderately smaller than limited-information standard errors, and (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.

Monetary Policy Indeterminacy and Identification Failures in the U.S.: Results from a Robust Test

“…The marginal rejection frequency of the test AR T ( s ) for H 0 1 ranges from 54.4% for = 0:10, to 88.9% for = 0:35, and is equal to 63.9% and 80.9% for = 0:15 and = 0:25, respectively. We notice that the marginal rejection frequency of the LR T (^ s ) test is systematically larger than the marginal rejection frequency of the AR T ( s ) test, con…rming West's (1986) …ndings that when linear rational expectations models are misspeci…ed, 'full-information' tests tend to be more powerful than 'limited-information'tests.…”

Instrumental Variables Estimation of Heteroskedastic Linear Models Using All Lags of Instruments

“…The ML estimator of $ 1 lowers asymptotic variance by at most 12 percent relative to optimal GMM. Thus, ML may increase efficiency only modestly relative to GMM, a result also found in West (1986) and West and Wilcox (1994). This underscores the potential importance of our approach, in light of the computational and robustness advantages noted in the previous section.…”

Testing for Cointegration in Linear Quadratic Models

“…To illustrate the issues in as clear a manner as possible, we outline the basic experiment whose results appear in Table 1. The design is similar to that of Gregory et al (1990) and West (1986). The computer package used in the analysis is GAUSS.…”