A New Asymmetric Interaction Ridge (AIR) Regression Method

Abstract

Despite that interaction terms are standard tools of regression analysis, the side effects of the inclusion of these terms in models estimated by ordinary least squares (OLS) are yet not fully penetrated. The inclusion of interaction effects induces multicollinearity problems since all non zero values are equal between the interaction term and the regressor. In this article, we propose a procedure to remedy this problem by the use of new ridge regression (RR) shrinkage parameters—which we call the asymmetric interaction ridge (AIR) regression method. By means of Monte Carlo simulations we evaluate both OLS and AIR using the mean square error (MSE) performance criterion. The result from the simulation study confirms our hypothesis that AIR always should be preferred to OLS since it has a lower estimated MSE. Moreover, the advantages of our new method are demonstrated in an empirical application where positive asymmetric price transmission effects are exposed for the mortgage interest rates of Handelsbanken Stadshypotek. It is observed that the mortgage interest rates increase more fully and rapidly to an increase in the bank's borrowing costs than to a decrease. This asymmetry is defined as positive asymmetric price transmission (APT).