Comment: 29 pagesI examine changes in matching efficiency and elasticities in Japan's labor market via Hello Work for unemployed workers from January 1972 to April 2024 using a nonparametric identification approach by y Lange and Papageorgiou (2020). I find a declining trend in matching efficiency, consistent with decreasing job and worker finding rates. The implied match elasticity with respect to unemployment is 0.5-0.9, whereas the implied match elasticity with respect to vacancies varies between -0.4 and 0.4. Decomposing aggregate data into full-time and part-time ones, I find that the sharp decline of matching efficiency after 2015 shown in the aggregate trend is driven by the decline of both full-time and part-time ones. Second, I extend the mismatch index proposed by Sahin et al (2014) to the nonparametric version and develop the computational methodology. I find that the mismatch across occupations is more severe than across prefectures and the original Cobb-Douglas mismatch index is underestimated.