Difference Identities for Unemployment Rates

Abstract

This paper presents some extremely flexible identities useful in analyzing changes in unemploy- ment rates from month to month, from year to year, and over longer periods. An aggregate unemployment rate change is expressed as a polynomial in labor force stocks and first differences in labor force stocks. Terms of this polynomial are interpreted as the effects of (1) changes in the distribution of the labor force among demographic groups; (2) unexpected changes in labor demand within a demo- graphic group; and (3) unexpected changes in labor supply within a demographic group. A simple exten- sion of the framework shows its relationship to recent work with labor force gross flow data. The framework is applied to the increase in black youth unemployment between 1950 and 1970. Most of it may be attributed to a decline in employment among male in the South.