Biased estimators for the distributed lag models

The finite distributed lag models include highly correlated variables as well as lagged and unlagged values of the same variables. In this case, the assumptions of independence between the explanatory variables cannot be valid, and this leads to multicollinearity problem. Some problems are faced for these models when applying the ordinary least squares method or econometric models such as Almon and Koyck models. In this study, Almon-kısıtlı ridge, Almon-Liu, Almon-(r-k) sınıf, Almon-(r-d) sınıf, Almon-modified Liu estimators are defined under the nonstochastic restriction in order to overcome the problem of multicollinearity occurred in Almon model. In addition, the performances of the defined estimators are examined with a Monte Carlo simulations. Then, some of these alternative biased estimators are compared according to the mean square error matrix criterion. Another method to eliminate the multicollinearity is to consider the stochastic restricted models. In this sense, the alternative estimators to the Almon estimator are examined under the stochastic restriction and Bayesian Liu type Shiller and Bayesian Liu type Lindley estimators have been proposed. The performance of the proposed estimators is investigated with Almon (1965) data set.