TEEN-AGE UNEMPLOYMENT AND REAL FEDERAL MINIMUM WAGES DOUGLAS K. ADIE Reprinted for private circulation from the PRINTED IN U.S.A. Teen-Age Unemployment and Real Douglas K. Adie Ohio University A federal minimum wage was first enacted under the Fair Labor Standards Act of 1938 to raise the minimum standard of living without curtailing employment. This note examines the impact of the federal minimum wage on teen-age unemployment to see whether the intentions of the legislators were realized. Department of Labor studies have been criticized elsewhere for suggesting that minimum wages have not reduced employment or damaged the "marginal" firm.1 Peterson (1957), for instance, demonstrated an employment effect from state and federal minimum wages using cross-sectional analysis. Kaun (1965) also found that low-wage industries tended to substitute nonwage factors of production for labor in response to increases in the minimum wage. Brozen's (1969) investigation showed that teen-age unemployment increased each time the federal minimum wage was increased. Except for Moore's (1971) article, however, studies have not measured the extent to which variations in minimum wages are related to variations in unemployment rates.2 To guide policy makers, it is helpful to have some idea of the magnitude of unemployment responses to changes in the mini Received for publication June 16, 1971. Final version received January 20, 1972. I would like to thank Yale Brozen, Sam Peltzman, Finis Welch, Robert J. Gordon, and particularly Gene Chapin for suggestions on earlier work. I am also grateful to an anonymous referee for helpful comments. Computations were performed at the Ohio University Computer Center by John Raisian. Any errors are my responsibility. Financial assistance from the Institute for Humane Studies, the Fred C. Koch Foundation and the Earhart Foundation supported the work in this area. 1 For a discussion of Department of Labor Studies, see U.S. Department of Labor (1970, pp. 30-33). For criticism of Department of Labor studies, see Stewart and Macesich (1960). m deflated by average 2 There are difficulties with Moore's (1971) specification of the real minimumwage variable. It is not the nominal minimum wage in time t hourly carnings in time t that affects the unemployment rate in time t, as Moore's model indicates, but the real minimum wage in time tm, which is the nominal minimum wage in time t Im deflated by the average hourly earnings in time t -m. Also, the weights associated with earlier changes in the nominal minimum wages are constrained by his model to be larger than those associated with recent changes. This weighting pattern requires some theoretical justification, since it is not the normal decay pattern. However, despite the misspecification, Moore's results still show significant teen-age unemployment effects of changes in federal minimum wages. 435 96-478 O 73 13 436 JOURNAL OF POLITICAL ECONOMY mum wage rate. The present study provides estimates of the strength of this relationship for teen-agers. Model Economic theory suggests that the quantity of labor demanded will decrease and the quantity of labor supplied increase if a minimum wage is set above the market clearing wage. The extent of these effects depends on the discrepancy between the minimum wage and the market clearing wage and on the size of the elasticities. Because of union age requirements, statutory age requirements, and low skill levels, the market wage for a large proportion of teen-agers, particularly nonwhite teen-agers, is likely to be below the minimum. Hence, teen-agers will be more severely affected by minimum wages. However, since unemployed teen-agers drop out of the labor force to continue their education, the unemployment effect of federal minimum wages may be understated in the statistics. D= al°Xc, To construct the model, consider a nonlinear demand for labor function, (1) where D is the quantity of labor demanded expressed in number of workers, I is an index of industrial production, a, b, and c are parameters, and X is the real minimum wage. The equality is a nonlinear supply of labor function, where S is the number of workers offering their labor services and d and ƒ are parameters. From (1) and (2), (SD)/S = 1 − (a/d)I°Xc-1. (3) Since the unemployment rate, U, is expressed in percentage terms, U = (SD)/S X 100 and (3) becomes U 100 100 (a/d) I°Xc-1. (4) For downward-sloping demand and upward-sloping supply functions, c < O and ƒ 0, so cƒ<0 and U/ǝX <0. Using new parameters, (4) > can be approximated by the following expression in log form: InU1 = a +ẞln/+ylnX, which is the basic form of the model.3 (5) 3 I have used seven classifications of teen-age monthly unemployment rates, seasonally adjusted, supplied by the Bureau of Labor Statistics for the time period January 1954-December 1965. They are for the following teen-age groups, age 16–19; (1) all teens, (2) all white teens, (3) all nonwhite teens, (4) male white teens, (5) female white teens, (6) male nonwhite teens, and (7) female nonwhite teens. The symbol U¡ COMMUNICATIONS The Extent of Unemployment Effects 4 437 The unemployment elasticities for the period January 1954 to December 1965 are listed in column 1 of table 1 with the standard errors in parentheses. The most striking feature of these elasticities is that they are all positive. This implies that increases in teen-age unemployment in every category are associated with increases in the real federal minimum wage. Except for male white teens, all unemployment elasticities are significant at the 5 percent level. It is interesting to compare the size of the elasticities for the different classifications of teen-agers, since they are intuitively consistent with each other. For instance, the unemployment elasticity for all teens is 0.362, so it is reasonable that the elasticity for white teens would be lower, and the elasticity for nonwhite teens higher, than 0.362. This is the case, as column 1 of table 1 indicates. The unemployment elasticity for white teens is 0.270 in table 1 while that for nonwhite teens is 0.914. This implies that changes in the federal minimum wage affect nonwhite teens more than white teens, which is to be expected. In fact, the impact on nonwhite teens is more than twice that on white teens. Also, it is reasonable that the unemployment elasticity for white teens would be between that for male white teens and female white teens, which it is. In fact, while the elasticity for white teens is 0.270, the elasticities for male and female white teens are 0.118 and 0.569, respectively. Similarly, the elasticity for nonwhite teens is between that for male and female nonwhite teens; more precisely, the elasticity for nonwhite teens is 0.914 while the elasticities for male and female nonwhite teens are 0.883 and 1.040, respectively. Another interesting feature of the estimates in column 1 of table 1 is that the unemployment elasticities for male white teens and male nonwhite teens are both lower than the elasticities for female white teens and female nonwhite teens, respectively. But the unemployment elasticities for male white teens and male nonwhite teens are closer to the aggregate unemployment coefficients than are the elasticities for female white teens and female is used to designate the ith classification of teen-age unemployment. Also, I have used the monthly consumer price and wholesale price indices supplied by the Bureau of Labor Statistics for the same period, designated P, and P, respectively. The seasonally adjusted total, manufacturing, and final product indices of industrial production were taken from Federal Reserve Bulletins, converted to a common base period, and detrended so as to measure only business fluctuations. They are designated It Im2. and I, respectively. The federal minimum wage designated Wm has been expressed as a monthly series with changes occurring only in the month the changes went into effect. The real minimum wage, X, is W„ divided by a price index. t' 4 The unemployment elasticity measures the percentage changes in the unemployment rate when the real federal minimum wage changes by 1 percent and is expressed in (5) by y. The model discussed in the text uses the total index of industrial production for I and the minimum wage divided by the wholesale price index for X. |