We also thank Yuto Ishikuro, Marina Eguchi, Taiki Kubo, and Kotaro Shinma for their cooperation in data calculations. The authors thank Naohito Abe, Fumio Funaoka, Yukinobu Kitamura, Chihiro Shimizu, Shigenori Shiratsuka, and the staff of the Bank of Japan for their valuable comments. Price Index, Quality Adjustment, Hedonic Regression Model, Multicollinearity, Omitted Variable Bias, Sparse Estimation, Adaptive Elastic Net These results suggest the possible improvement in the accuracy of the price index while enhancing the usefulness of the hedonic quality adjustment method. 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) reduced overestimation of the product quality improvements due to the omitted variable bias. We conduct an empirical analysis applying the new method to the producer price index of passenger cars in Japan. 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. This study proposes the new hedonic quality adjustment method using 'sparse estimation' in order to overcome these problems. In the application of the hedonic quality adjustment method to the price index, multicollinearity and the omitted variable bias arise as practical issues.

Hedonic quality adjustment