A Cointegration Model of Age-Specific Fertility and Female Labor Supply in the United States

1. IntroductionModels of fertility based on economic theories of behavior have been subjected to rigorous conceptual and empirical scrutiny (for surveys, see Olsen 1994 and Macunovich 1996a; for critical reviews, see Murphy 1992 and Smith 1981). However, much empirical analysis of aggregate fertility patterns in the United States has relied on traditional regression methods, with little influence from recent developments in multiple time-series methods appropriate for nonstationary variables.Although important theoretical propositions are testable with individual data, understanding of trends and patterns in fertility behavior at the societal level requires aggregate analysis (Ryder 1980). The aggregation of individual effects to make statements about total fertility is problematic, as the composition of the population changes over time. Some effects that are measured at the individual level may reflect changes in individuals' positions within a society, and these effects will not be present at the societal level. Alternatively, social interaction may induce behavioral changes across a population that are not reflected in individual responses. As described by Kohler (2001), changes in societal norms and institutions can create feedback loops between aggregate variables and individual incentives toward childbearing, so that effects between aggregates may exceed substantially the responses measured at the level of the household.1Analysis of aggregate time-series data has its own considerable challenges. Fertility and its determinants are most likely nonstationary time series that trend or drift persistently away from their initial values. Such nonstationarity may undermine classical estimation and inference with traditional regression procedures, leading to spurious inferences about relations among variables. Furthermore, the principal determinants of fertility, for example, women's wages and education levels, female labor force participation, unemployment rates, and husband's incomes, are quite possibly endogenously determined in conjunction with fertility decisions. This problem of endogenous regressons can undermine the identifiability of the fertility model, rendering the relations unestimable. Even if the relations are identified, the problem of endogenous regressors leads to inconsistent least squares estimators of model parameters.The objective of this paper is to revisit a simple economic model of fertility, employing the cointegration model of Johansen (1995) that is appropriate for analyzing relations between nonstationary time series. Johansen's procedure allows the empirical determination of the number of stationary relations and produces maximum likelihood estimators of the parameters of these relations that are consistent and normally distributed, even in the presence of endogenous explanatory variables. Furthermore, to capture information on both the level and the timing of fertility, the analysis is applied to two age-specific fertility rates covering the prime childbearing years of U.S. women.2. Empirical Studies of Fertility with Aggregate DataEconomic models of fertility are grounded in either Easterlin's (1980a) relative income hypothesis or the New Home Economics (NHE) of Willis (1973) and Becker (1981). The former theory emphasizes the role of male incomes, relative to economic aspirations, as the driving force behind fertility and female labor force participation. Economic aspirations of young adults are determined by material conditions prevailing in their parental homes during their teenage years, when their parents would be close to their prime in earnings capacity. An increase in relative income shifts preferences in favor of childbearing and away from labor force activity by young adult women.In the full Easterlin model, relative income is determined by the size of the young adult cohort relative to that of prime aged adults, both measured contemporaneously (Easterlin 1980b). …