Aitken Estimator Research Articles

The Use of Error Components Models in Combining Cross Section with Time Series Data

A mixed model of regression with error components is proposed as one of possible interest for combining cross section and time series data. For known variances, it is shown that Aitken estimators and covariance estimators are in one sense asymptotically equivalent, even though the Aitken estimators are more efficient in small samples. Turning to unknown variance components, Zellner-type iterative estimators are compared with covariance estimators. Here, few small sample properties are obtained. However, it is shown that covariance and Zellner-type estimators have equivalent asymptotic distributions and equivalent limits of sequences of first and second order moments for weakly nonstochastic regressors. For the model analyzed, the theoretical results obtained, as well as ease of computation, tend to support traditional covariance estimators of the regression parameters. An additional interesting result presented in an appendix is that ordinary least squares estimates of the fl's (ignoring the error components) have unbounded asymptotic variances. On efficiency grounds, this argues rather strongly for some care in combining data from alternative sources in regression analysis.

Small Sample Properties of Alternative Estimators of Seemingly Unrelated Regressions

Abstract A Monte Carlo experiment is carried out to examine the small sample properties of five alternative estimators of a set of linear regression equations with mutually correlated disturbances. The estimators considered are ordinary least squares, Zellner's two-stage Aitken, Zellner's iterative Aitken, Telser's iterative, and maximum likelihood. The experiment, based on 100 samples, provides approximate sampling distributions for samples of size 10, 20 and 100 for various model specifications. The results show that three of the five estimation methods lead to identical estimates for any sample size, that in many cases the two-stage Aitken estimator performs as well as or better than the other estimators, and that most of the asymptotic properties of this estimator tend to hold in small samples as well.

Small Sample Properties of Alternative Estimators of Seemingly Unrelated Regressions

Abstract A Monte Carlo experiment is carried out to examine the small sample properties of five alternative estimators of a set of linear regression equations with mutually correlated disturbances. The estimators considered are ordinary least squares, Zellner's two-stage Aitken, Zellner's iterative Aitken, Telser's iterative, and maximum likelihood. The experiment, based on 100 samples, provides approximate sampling distributions for samples of size 10, 20 and 100 for various model specifications. The results show that three of the five estimation methods lead to identical estimates for any sample size, that in many cases the two-stage Aitken estimator performs as well as or better than the other estimators, and that most of the asymptotic properties of this estimator tend to hold in small samples as well.

Efficient Estimation of a System of Regression Equations when Disturbances are Both Serially and Contemporaneously Correlated

Abstract This paper considers the problem of obtaining efficient estimates for the parameters of a system of M regression equations. The disturbance terms of this system are assumed to be related by both serial and contemporaneous correlation. Under the further assumption that the serial correlation is a first order autoregressive process, the paper develops an estimator that is consistent and has the same asymptotic normal distribution as the Aitken estimator which assumes the covariance matrix to be known. The paper concludes with a discussion of some alternative covariance specifications and points out certain difficulties with the standard single equation procedures for handling auto-regressive schemes.

Asymptotic Efficiency of the Maximum Likelihood Estimator

Asymptotic Efficiency of the Maximum Likelihood Estimator