Hailong Qian

Redundancy of moment conditions

It is well known that adding moment conditions cannot decrease asymptotic efficiency. However, sometimes additional moment conditions are redundant, in the sense that they do not increase the asymptotic efficiency of estimation for some or all of the parameters of interest. This paper gives a general treatment of redundancy of moment conditions. It provides necessary and sufficient conditions for redundancy, in several equivalent forms. The paper also provides interesting results for the case that there are three (or more) sets of moment conditions.

Improved instrumental variables and generalized method of moments estimators

This paper considers GMM estimation with moment conditions of the usual type, plus extra moment conditions that do not depend on the parameters. The extra moment conditions improve efficiency if they are correlated with the original set of moment conditions. This is true in linear and nonlinear models, but in linear models we provide simple, explicit formulas for the improved estimators. Our results may be useful in rational expectations models, in which an equations error is a forecast error and the extra moment conditions would be forecast errors in related variables.

PARTIALLY SUPERFLUOUS OBSERVATIONS

Necessary and sufficient conditions are established for the second subsample to be partially redundant given the first subsample for the best linear unbiased estimator of a subset of the coefficient vector of a general linear regression model.We thank the Co-editor for his very helpful comments on an earlier draft.

Partial GLS regression

Abstract We derive a novel expression for the GLS estimate of a subset of the regression coefficients. We give conditions for the partial equality of OLS and GLS, and we derive a feasible GLS estimator for the fixed effects panel data model

Efficient GMM and MD estimation of autoregressive models

Abstract This paper considers minimum distance estimation of the AR( p ) model. Given the first p autocorrelations, higher-order autocorrelations are shown to be redundant. Thus, given non-normality, improvements to the normal quasi-MLE must depend on something other than autocorrelations.

REDUNDANCY OF MOMENT CONDITIONS AND THE EFFICIENCY OF OLS IN SUR MODELS

In this note, based on the generalized method of moments (GMM) interpretation of the usual ordinary least squares (OLS) and feasible generalized least squares (FGLS) estimators of seemingly unrelated regressions (SUR) models, we show that the OLS estimator is asymptotically as efficient as the FGLS estimator if and only if the cross-equation orthogonality condition is redundant given the within-equation orthogonality condition. Using the condition for redundancy of moment conditions of Breusch, Qian, Schmidt, and Wyhowski (1999, Journal of Econometrics 99, 89–111), we then derive the necessary and sufficient condition for the equal asymptotic efficiency of the OLS and FGLS estimators of SUR models. We also provide several useful sufficient conditions for the equal asymptotic efficiency of OLS and FGLS estimators that can be interpreted as various mixings of the two famous sufficient conditions of Zellner (1962, Journal of the American Statistical Association 57, 348–368).

PARTIAL REDUNDANCY OF MOMENT CONDITIONS

In this paper, we first transform a set of moment conditions into a set of transformed moment conditions, based on which the efficient partial generalized method of moments estimation for part of a parameter vector is defined. Given the set of transformed moment conditions, we then show that the conditions for partial redundancy of an additional set of moment conditions given an original set of moment conditions simply become the conditions for full redundancy of the second subset of transformed moment conditions given the first subset of transformed moment conditions. Thus the transformed moment conditions proposed in this paper unify partial redundancy of moment conditions with full redundancy of moment conditions. Using transformed moment conditions, we then straightforwardly derive necessary and sufficient conditions for partial redundancy of one or two subset(s) of moment conditions given the other when the large set of moment conditions consists of three subsets of moment conditions. The paper also provides several easily checkable sufficient conditions for partial redundancy of one set of moment conditions given other sets of moment conditions.