In the application of the hedonic quality adjustment method to the price index, multicollinearity and the omitted variable bias arise as practical issues. This study proposes the new hedonic quality adjustment method using 'sparse estimation' in order to overcome these problems. The new method deals with these problems by ensuring two properties: the 'grouped effect' that gives robustness for multicollinearity and the 'oracle property' that provides the appropriate variable selection and asymptotically unbiased estimators. We conduct an empirical analysis applying the new method to the producer price index of passenger cars in Japan. In comparison with the conventional standard estimation method, the new method brings the following benefits: 1) a significant increase in the number of variables in the regression model; 2) an improvement in the fit of the regression model to actual prices; and 3) reducing overestimation of the product quality improvements due to the omitted variable bias. These results suggest the possible improvement in the accuracy of the price index while enhancing the usefulness of the hedonic quality adjustment method.
Keywords: Price index; Quality adjustment; Hedonic regression model; Multicollinearity; Omitted variable bias; Sparse estimation; Adaptive elastic net
Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.