A Labor Supply Model for Secondary Workers

T HE purpose of this paper is to estimate a labor supply or participation rate function for period 1948 through 1968, for various age-sex groups that comprise secondary labor force.' There are three major findings of paper. First, participation behavior is primarily explained by real wages. There are, however, two hypotheses, relative and permanent wage models that may underlie wage variables. The relative wage variable is adapted from recent research in demography and is found to predominate over more traditional permanent wage effect for a number of female age groups. (As will be seen, in labor force equations, permanent and relative wage theories predict opposite signs for a wage variable so that a test of two hypotheses is possible.) Secondly, supply of labor responds positively to a variable that reflects rate of inflation. The inclusion of this variable follows a formulation proposed by Friedman (1968). He conjectures that a form of money illusion in supply function of labor is foundation of an empirically observable, short-run Phillips curve. Thirdly, labor supply is found to respond to changes in excess demand conditions in labor market only during period of chronic, high 1958-1966 and even during that period, effect observed is considerably smaller than that noted in earlier studies. The model is compared with more traditional labor force equation that contains rate and a time trend. Both equations are fitted for period 1948-1968 and are then used to forecast most recent data for quarters 1969.1 through 1970.3. The equation presented in this paper dominates alternative model in terms of adjusted R 2's and Durbin-Watson statistics (in estimated period) and it uniformly forecasts better. Finally, implications of labor force equation are explored. It is suggested that recently adopted concepts such as unemployment, the labor force, and potential need redefinition in light of findings presented here. There are, at present, two basic approaches to study of labor force participation. The first is generally associated with Tella (1965) and Dernburg and Strand (1966) (and will hereafter be referred to as unemployment model). They found that labor force participation rate varied inversely with rate. This finding was identified with worker effect. The model may be estimated in form (LIP)i = a( + a, U + a9T'a1 < 0 (1) where (LFP)i is labor force participation rate of subgroup i, and U is aggregate rate. The time trend, T, may be interpreted as representing gradual, sociological change of preferences which is sending women from home into labor force and older workers from labor force into home. This equation has gained wide acceptance in literature, and its results have had an important impact on public policy discussions. Thus finding that discouraged workers leave labor force when (measured) is high is used to adjust rate and level of output to take account of hidden unemployed. The adjusted series has become an independent variable in empirical wage equations since work of Simler and Tella (1968). The adjusted output series and resulting measure of GNP gap are used in planning fiscal and monetary policy. Clearly to extent, however, that equation (1) does not describe labor force behavior and overstates Received for publication May 17, 1971. Revision accepted for publication July 23, 1971. * The author thanks Richard A. Easterlin, Benjamin M. Friedman, Robert J. Gordon, Lawrence R. Klein, Thomas Sargent and Susan M. Wachter for helpful suggestions. ' The secondary labor force is defined here to include males 16-19 and 65+ and females 16 through 65+. The dependent variable is a form of participation rate and hours worked are not included. 2See, for example, Tella (1965), Dernburg and Strand (1966) and Bowen and Finegan (1969). Models of Barth (1968) and Vroman (1970) also found a low elasticity for labor force in terms of participation rate.