The R2 Ridge Trace in 2SLS Regression Estimation

Abstract

Although the two-stage least squares (2SLS) estimator has several desirable properties, and thus is a preferred method of equation estimation, it is nevertheless extremely sensitive to multicollinearity. In recent years, ridge regression (RR) has become a popular approach for coping with multicollinearity because it usually generates smaller estimator variance than least squares methods. In theory, then, two-stage ridge regression (2SRR) should also generate smaller estimator variance than 2SLS. Although it is well known that the R ² goodness of fit decreases as the biasing parameter, k, introduced by RR estimation increases, it is less well known that for 2SRR estimation the reverse may be true; and, within a range of modest k-values, as the k increases so does the R ² goodness of fit. Using this property of 2SRR, we addressed the question of whether in the presence of multicollinearity the 2SRR estimator would generate better-fitting models than the 2SLS estimator. Comparisons were made for seven RR methods; the R ² ridge trace results demonstrated that the incorporation of RR into 2SLS estimation could significantly improve the goodness of fit of an equation.