  I 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 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 is 0.1-0.4. 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 job categories is more severe than across prefectures and
the original Cobb-Douglas mismatch index is underestimated.
