Beveridgean Unemployment Gap with Part-time Employment

This paper extends the sufficient-statistics formula for efficient unemployment developed by Michaillat and Saez (2021) to account for part-time employment. I introduce two additional sufficient statistics that measure the share of part-time employment and part-time hours relative to full-time hours. Applying the framework to the United States (1951-2026) and Japan (1970-2025), I compare the effects of total part-time employment and involuntary part-time employment on efficient unemployment. Total part-time employment has substantially larger effects than involuntary part-time employment. While involuntary part-time employment provides information about labor-market slack, the main change in efficient unemployment comes from part-time work itself because part-time workers supply fewer market hours than full-time workers. Under the total part-time calibration, efficient unemployment averages 4.7 percent in the United States before COVID and 4.2 percent after COVID. In the Japanese application, the full-sample average is 2.7 percent. The distinction is especially important in Japan, where part-time employment is widespread and often reflects flexible work arrangements. These findings suggest that aggregate labor input, rather than involuntary part-time employment alone, is an important determinant of labor-market efficiency.