Explaining Changes in Female Labour Supply in a Life-Cycle Model

Female labour force participation and labour supply, in the US, as in many other developed countries, has changed dramatically over the last 30 years. If one compares cohorts of women born in the 1930s (such as Elizabeth Dole), 1940s (Hillary Clinton) and 1950s (Oprah Winfrey), two main features emerge when considering labour supply in its various dimensions. First, comparing the Elizabeth Dole cohort to the Hillary Clinton one, we can see a substantial shift of the age profile of labour supply. However, the shape of the profile does not change much. In particular, in both profiles we observe a low participation corresponding to child rearing years. When comparing the Hillary Clinton cohort with the Oprah Winfrey one, we see that the low participation rates associated with the 'fertility years' are no longer present. The aim of this paper is to propose a life cycle model of saving and labour supply that could account for these dramatic changes. We explore whether changes to some specific parameters and exogenous variables of this model can generate the patterns observed in the data. Or, to use a different perspective, we want to quantify the size of changes in unobservable factors needed to explain the observed patterns. The main change in labour supply behaviour in the data is on the extensive margin. We consider a number of possible determinants of these changes in participation. First, wages may have increased relative to the fixed cost of participation. For example, the costs of child-care may have fallen. This would lead to greater participation at all ages and especially among mothers of infants. Second, on-the-job learning or the return to experience may have increased. As argued by Olivetti (2001), this increases the opportunity cost of reduced labor supply. Third, the depreciation of skills that occurs if an individual is not participating may have increased. Finally, we look at other possible explanations, such as a delay in the arrival of the first child and an increase in uncertainty over husband's income. Our structural model of life-cycle behaviour attempts to evaluate these alternative explanations. Obviously, wages are likely to be an important determinant of female labour supply. However, by looking at the dynamics of wages alone, it is difficult to disentangle the return to experience, the depreciation rate of human capital and the extent of participation bias (selection). Moreover, the interactions of these effects with other important determinants (such as fertility patterns, the cost of children, uncertainty, and so on) even in a simple life cycle model can be quite complex and difficult to quantify. Furthermore, a simple analysis that relates wages to labour supply, neglects general equilibrium effects that also imply an effect running from labour supply to wages. The main purpose of this paper is to build a realistic life-cycle environment in which we can explicitly model the participation choice. We can then calibrate the model to fit the behaviour of a given cohort and experiment with changes in the basic determinants of labour supply to determine which are more likely to yield the profiles of other cohorts. In our life cycle model households face uncertainty about the wages of the husband and the wife; maternity is exogenously given and children impose some monetary fixed cost when mothers decide to work. Decisions are taken at an annual frequency. The model takes into account returns to experience as a result of participation and depreciation of human capital when labor market interruptions are made. Households are able to save and borrow and women choose whether or not to work. This makes our model different from Keane and Wolpin (1989) and van Der Klaauw (1996), who estimate structural models of females' employment decision in the first case and females' employment and marital status decisions in the second case imposing that consumption coincides with income. Without the saving choice, the only way to intertemporally substitute consumption would be through changing labor supply and hence, in a model with returns to experience, the future wage rate. Saving is potentially a more flexible means of intertemporal substitution and so ignoring savings overstates the importance of the labor supply choice in life-cycle smoothing. We calibrate our model by matching observed participation profiles to simulated participation and observed wage profiles to the simulated wages of those who choose to work. Wage profiles in both the data and in the simulations are subject to selection; that is we only observe the wages of the women who choose to participate. Our selection model enables us to identify the depreciation effect separately from the return to experience. We use observed profiles from the cohort born at the start of the '40s for our calibration. We then explore the role of different factors in shaping changes of the life-cycle wage profile and participation profile. Pencavel (1998) and Coleman and Pencavel (1993) report similar paths for participation to the paths we report. The facts on employment are not in dispute. More controversial is understanding the data on wage profiles, on depreciation of human capital and on the underlying question of why participation has changed. Mincer and Pollachek (1974) and Mincer and Olfek (1982) discuss the extent of human capital depreciation under different assumptions on the permanence of depreciation. We report some statistics on depreciation but without a structural model of participation it is hard to identify the depreciation rate. Olivetti (2000) suggests that changes in wage profiles across cohorts reflect a change in the return to experience. The evidence we present is somewhat weaker: first, the cohort effect which leads to an increase in the return to experience can plausibly be interpreted as a year effect with wages in the 1980s growing faster than in previous periods. Second, wage growth seems to have benefited those who have worked only intermittently as well as those who have worked full time. There is now a substantial literature addressing the underlying question of why participation has changed. For example, Olivetti (2001) uses a four period model and the estimates of the returns to experience in Olivetti (2000) to show the effect that increase in the returns to experience has on hours worked by women. Greenwood and Seshadri (2002) measure the impact of technological progress on the increase in women's participation. Caucutt, Guner and Knowles (2001) explore the interaction between wage inequality and the marriage, fertility and labour supply decisions. The contribution of the current paper is primarily to use a realistic life-cycle model of saving and participation to compare alternative explanations.