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A Comparative Study of Alternative Estimators in a Distributed Lag Model

Takeshi Amemiya
Wayne A. Fuller

Abstract

Hannan in "Regression for Time Series" [4] proposed an interesting method of estimating regression coefficients using spectral techniques, and later in "The Estimation of Relationship Involving Distributed Lags" [5] applied the method to the estimation of parameters in a distributed lag model. This paper first illustrates that Hannan's method in his former article is asymptotically equal to Aitken's least-squares estimation in which the covariance matrix of the regression residual is estimated in a certain consistent manner from the calculated residuals. Next it proves that Hannan's method in his latter article is asymptotically equal to maximum likelihood estimation of the distributed lag model. Hannan's method is useful when the investigator's a priori knowledge about the stochastic process of the residual is minimal. But if the process can be specified to be, say, a first order or second order autoregressive system, it is desirable to use such knowledge in estimation. For such a case, the paper proposes an estimator of the distributed lag model based on the Gauss-Newton iterative method and proves it to be asymptotically equal to the maximum likelihood estimator. The paper evaluates the asymptotic distribution of two other estimators of the distributed lag model, including the one proposed by Klein [7].