Mean Square Error Comparisons of the Alternative Estimators For The Distributed Lag Models

Abstract

The finite distributed lag models include highly correlated variables as well as lagged and unlagged values of the same variables. Some problems are faced for this model when applying the ordinary least squares (OLS) method or econometric models such as Almon and Koyck models. The primary aim of this study is to compare the performances of alternative estimators to the OLS estimator defined by combining the Almon estimator with some other estimators according to the mean square error (MSE) criterion. We use Almon [2] data to illustrate our theoretical results.

Almon-KL estimator for the distributed lag model

“…As earlier mentioned, there is high tendency of multicollinearity among the regressors since lags of the same explanatory variable appear in the model (G€ uler, G€ ultay, & Kac ¸iranlar, 2015;G€ ultay & Kac ¸ıranlar, 2015). It becomes difficult to estimate with the conventional OLS when the lag length (p) is known and large (G€ uler et al, 2015;G€ ultay & Kac ¸ıranlar, 2015;Ozbay, 2019;€ Ozbay & Kac ¸ıranlar, 2017). The Almon polynomial lag distribution was recommended as a replacement to the OLS estimator (Almon, 1965).…”

“…The OLS estimator of b is BLUE when there is no violation of the model assumptions (Lukman et al, 2019). As earlier mentioned, there is high tendency of multicollinearity among the regressors since lags of the same explanatory variable appear in the model (G€ uler, G€ ultay, & Kac ¸iranlar, 2015;G€ ultay & Kac ¸ıranlar, 2015). It becomes difficult to estimate with the conventional OLS when the lag length (p) is known and large (G€ uler et al, 2015;G€ ultay & Kac ¸ıranlar, 2015;Ozbay, 2019;€ Ozbay & Kac ¸ıranlar, 2017).…”

Improvement of the Liu‐type Shiller estimator for distributed lag models

“…Therefore, some alternative methods have been discussed to resolve problems encountered due to these disadvantages of the Almon estimator. Gültay and Kaçıranlar () defined some alternative estimators by way of a matrix‐weighted combination of the Almon estimator with some other estimators (see Hoerl & Kennard, ; Liu, ) when the specification form β = Aα is true. They then compared the performance of the alternative estimators to OLS according to the matrix mean square error (MSE) criterion.…”