TY - JOUR

T1 - On efficient estimation and correct inference in models with generated regressors

T2 - A general approach

AU - McKenzie, Colin R.

AU - McAleer, Michael

PY - 1997/1/1

Y1 - 1997/1/1

N2 - Two approaches have been developed for deriving the properties of efficiency and consistency of standard errors of two step estimators of linear models containing current or lagged unobserved expectations of a single variable. One method is based on the derivatives of the likelihood function and information matrix, while the other uses the true covariance matrix of the disturbance vector when unknown parameters or variables are replaced by corresponding estimates. In this paper, the second approach is extended to cases where the structural equation is nonlinear and the model contains expectations of more than one variable or expectations of future variables. The properties of a frequently used estimator to deal with missing observations problems, a model involving a variance as an explanatory variable, and a recently developed estimator for autoregressive moving average models can be easily derived using the results of the paper. Methods for improving the efficiency of two step estimators are outlined.

AB - Two approaches have been developed for deriving the properties of efficiency and consistency of standard errors of two step estimators of linear models containing current or lagged unobserved expectations of a single variable. One method is based on the derivatives of the likelihood function and information matrix, while the other uses the true covariance matrix of the disturbance vector when unknown parameters or variables are replaced by corresponding estimates. In this paper, the second approach is extended to cases where the structural equation is nonlinear and the model contains expectations of more than one variable or expectations of future variables. The properties of a frequently used estimator to deal with missing observations problems, a model involving a variance as an explanatory variable, and a recently developed estimator for autoregressive moving average models can be easily derived using the results of the paper. Methods for improving the efficiency of two step estimators are outlined.

KW - Efficiency

KW - Generated regressors

KW - Inference

KW - Rational expectations models

KW - Two step estimation

UR - http://www.scopus.com/inward/record.url?scp=0001161060&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001161060&partnerID=8YFLogxK

U2 - 10.1111/1468-5876.00060

DO - 10.1111/1468-5876.00060

M3 - Article

AN - SCOPUS:0001161060

VL - 48

SP - 368

EP - 389

JO - Japanese Economic Review

JF - Japanese Economic Review

SN - 1352-4739

IS - 4

ER -