Transformation of variables and the condition number in ridge estimation

Abstract

Ridge estimation (RE) is an alternative method to ordinary least squares (OLS) estimation when collinearity is detected in a linear regression model. After applying RE, it is sensible to determine whether such collinearity has been mitigated. The condition number (CN) is a commonly applied measure to detect the presence of collinearity in econometric models, but to the best of our knowledge, it has not been extended to be applied after RE. In OLS estimation, Belsley et al. (Regression diagnostics: identifying influential data and sources of collinearity, Wiley, New York, 1980) established that the regressors must be of unit length and not centered to correctly calculate the CN. This paper reviews this requirement in the context of RE and presents an expression to calculate the CN in RE.