Unemployment and the Labor Force Participation of Married Men and Women: A Simultaneous Model

R ECENT research on labor supply reIt sponses to labor market unemployment has identified a puzzle with definite labor policy implications. Aggregate cross-section estimates indicate that the labor supply response to unemployment is negative, large and statistically significant, while economy-wide time series estimates suggest that the response is small, may be positive or negative and often statistically insignificant. ' Research reported here suggests a resolution for this contradiction and suggests that more attention be given to the simultaneous nature of labor market variables. Using Census data of 99 SMSAs with populations over 250,000 in 1970, we find substantial evidence in favor of the hypothesis that previous OLS estimates using cross-section data are too large the result of simultaneous equations bias. The principal source of bias in cross-section studies is failure to recognize that unemployment rates in local labor markets are determined simultaneously with labor force participation rates. Local unemployment rates appear to be remarkably stable over time2 and systematically related to several forces besides changes in overall labor demand; i.e., there is a "normal" rate of unemployment for each local labor market determined by the peculiar characteristics of its labor force and industrial environment. These characteristics of the local economy also determine normal labor force participation. When the interdependent relationship of labor force participation and unemployment in local labor markets is explicitly included in a model of labor force participation, simultaneous equations bias in estimating the labor force participation-unemployment relationship is removed. By contrast, it seems that the principal source of variation in economy-wide unemployment from quarter to quarter or even from year to year is aggregate demand rather than the nature and composition of the labor force. Therefore, simultaneous determination of labor force participation and unemployment would not appear to be a source of bias in OLS estimates of the time series relationship between labor force participation and unemployment. An alternative interpretation is found in Bowen and Finegan (1969), however. They claim that the smaller magnitude of the relationship in the time series data as compared to the cross-section SMSA data is caused by a lagged response of labor force participation more accurately reflected in the cross-section results. Nevertheless, their work with a distributed lag model (pp. 522-529 Received for publication June 4, 1975. Revision accepted for publication January 28, 1976. * Part of the material in this project was prepared under Grant No. 91-39-74-02 from the Manpower Administration, U.S. Department of Labor, under the authority of Title I of the Manpower Development and Training Act of 1962, as amended. Researchers undertaking such projects under government sponsorship are encouraged to express freely their professional judgment. Therefore, points of view or opinions stated in this document do not necessarily represent the official position or policy of the Department of Labor. Support of the Instruction and Research Computer Center, Ohio State University, is gratefully acknowledged. We acknowledge the helpful comments of Donald Parsons, A. V. Adams, Jan Kmenta, Ronald Oaxaca, and T. Paul Schultz, and the assistance of Edward Honton, Esen Mutluay, Daniel Westbrook, and Ronald Williamson. 1 A well-known summary of the literature through 1966 is contained in Mincer (1966). Previous research bearing on the relation between unemployment and labor force participation is found in the following sources: Woytinsky (1940), Long (1953, 1958), Mincer (1962, 1966), Hansen (1961), Altman (1963), Cain (1966), Reder (1964, 1969), Tella (1964), Dernburg and Strand (1964), Cooper and Johnston (1965), Bowen and Finegan (1965, 1969), Barth (1968), Doeringer and Piore (1971), Wachter (1972), Baer (1972), and Goodman (1974). We accept Mincer's contention that the relatively large estimates of the effect of unemployment on labor force participation based on time series data and reported by Tella, Dernburg and Strand, and Cooper and Johnston are based on incorrect specifications of the underlying models of labor force participation. Bowen and Finegan (1969, ch. 16 and appendix) also discuss defects in the Dernburg-Strand and Tella studies. 2 The simple correlation between unemployment rates in the 99 largest SMSAs between 1970 and 1960 is 0.6; between 1960 and 1950 it is 0.56.