(O'Neill and Polachek, 1993, Blau and Kahn, 1997) provide evidence that over the past decades returns to .... u(cit) + v (1 â nit) + Rtθitnit + βE [Vt+1 (H (θit,nit) exp (εit+1))\Jt] ) where u() ...... Phillips, a white woman, was not hired because she.
Measuring Changes in Returns to Experience: Learning-by-doing and Gender Differentials∗ Claudia Olivetti Boston University February 2006
Abstract This paper studies the evolution of gender differentials in rates of return to labor market experience between the 1970s and the 1990s. In particular, it formulates a dynamic model with learning-by-doing human capital accumulation where individuals choose both their labor force participation and their labor supply. Both decisions depend upon individual-specific productivity. This generates a selection and a simultaneity problem in estimating the parameters of the human capital production function that are dealt with by using the methodology in Olley and Pakes (1996). The production function is estimated separately by gender for the 1970s and for the 1990s using data from the PSID. I find that, over this time period, returns to experience increased within gender groups. The increase was relatively larger for women than for men. As a byproduct, I also find that correcting for the two biases is important. Indeed, failing to take them into account would always generate larger estimated rates of return to experience for women than for men.
∗
Preliminary draft. I want to thank Victor Augurregabiria for insightful comments and suggestions. I also thank Petra Todd and Kenneth Wolpin for their comments on an earlier version of this paper.
1
Introduction
Returns to experience have been rising both for men and women since the 1970s. Prior studies (O’Neill and Polachek, 1993, Blau and Kahn, 1997) provide evidence that over the past decades returns to experience have increased relatively more for women than for men. Another finding that has been documented in several empirical papers, is that current wages are affected by past labor supply choices1 . This finding is robust to the particular specification chosen for the process of human capital accumulation and to the subset of the population considered (males vs. females). In this paper, I use panel data to explore how the relationship between past wages, hours worked and current wages through learning-by-doing evolved between the 1970s and 1990s both for men and for women. I build a dynamic model with learning-by-doing human capital accumulation where individuals, after observing the realizations of their individual-specific productivity shock, choose both their labor force participation and their labor supply, taking the rental rate of human capital as given. An individual’s wages are observed only if he/she works on the labor market and the labor supply decision is also an input in the production of human capital. Both decisions depend upon the individual-specific unobserved productivity and produce two different types of problems in the estimation of the production function. The labor force participation decision generates a bias due to the problem of selection into the sample. The labor supply decision induces a simultaneity bias in the estimates of the production function. Following the estimation methodology developed in Olley and Pakes (1996), I implement a semiparametric estimator for the human capital production function parameters that corrects for the sample selection and simultaneity bias that arise in this dynamic context. The parameters of the production function are estimated separately by gender for the 1970s and for the 1990s using PSID data. I find that returns to experience increased over the time period considered for both men and women. Moreover, women’s returns to experience increased more than twice as much as men’s did. As for the 1990s, returns are still larger for men than for women, although the gap shrank considerably. The same type of behavior is observed within education groups. I also find that correcting for the two biases is important. Indeed, failing to take them into account would always generate larger estimated rates of return to experience for women than for men. This is due to the fact that women’s estimates are more affected by the sample selection bias (especially in the 1970s when their labor force participation is very low) whereas men’s estimates are not. The corrected estimates produce results that are in line with the empirical observation. I also find that human capital depreciates at a faster rate in the 1990s than in the 1970s, and that the human capital 1
For instance, Altug and Miller (1998), Chang, Gomes and Schorfheide (2002), Eckstein and Wolpin (1989), Imai and Keane (2004), and Shaw (1989).
2
accumulation profile is steeper in the 1990s than in the 1970s. The structure of the paper is as follows. The second section briefly summarizes previous empirical work. Section 3 presents the dynamic model. Section 4 discusses the estimation strategy adopted. Section 5 provides a description of the data set. Section 6 reports estimates of the parameters of the model and provides a discussion of the estimation results. Section 7 discusses the alternative dynamic model that I plan to estimate. Finally, concluding remarks are provided in Section 8.
2
Related Literature
Beginning with the work of Katz and Murphy (1992), several researchers have documented an increase in the returns to labor market experience within gender, education, and experience group over the past few decades. Prior studies, Blau and Kahn (1997) and O’Neill and Polachek (1993), provide evidence that, over this period, returns to experience have been increasing more for women than for men.2 In particular, Blau and Kahn (1997) present estimates of female and male Mincer earnings equations for 1979 and 1988 using PSID data. Their results show that, although both female and male returns to experience increased over this time period, women’s return to full time experience increased more than men’s. These estimates, however, do not take into account the problem of non-random selection into the sample. As it is well known in the literature, this problem introduces an upward bias in the estimates of earnings equations for women. In fact, they find that women’s returns to full time experience are 25% higher than men’s in 1989. O’Neill and Polachek (1993) use PSID data for the period 1976 to 1987 to investigate the main factors contributing to the one percent yearly decrease in the gender wage gap experienced in the US since 1976.3 They disentangle the contribution of changes in actual experience from the contribution of changes in returns to experience to the decrease in the gender wage gap. Their estimates show that the average annual change in return to experience over this time interval has been positive both for men and for women. Furthermore, the average change in return for women of all experience levels was more than twice as much as the average change for men. For younger workers (i.e. workers with less than 15 years of experience), the relative increase in women’s returns to experience was four times as big as it was for men. 2
These studies show that the increase in return to experience and the increase in actual experience for women explained a large portion of the decreasing gender wage gap. In particular, they show that convergence in work-related characteristics (schooling and experience) may account for one third to a half of the drop in the gender gap, whereas the relative increase in women’s returns to experience explains part of the rest. 3
PSID data are used in both studies. This data set includes retrospective data on actual number of years of work experience. In fact, given women’s segmented labor force participation, potential experience does not provide an accurate measure of the actual number of years worked by female workers.
3
These studies do not take into account dynamic aspects of the working decision such as the strong complementarity existing between current hours of work and wages in determining future wages over the life cycle. Several papers finds that current wages are affected by past labor supply choices (Altug and Miller (1998), Eckstein and Wolpin (1989), Imai and Keane (2004), and Shaw (1989)). The result is robust to differences about how the human capital accumulation is modeled and the data used (male vs. female). For example, some of these papers model investments in human capital through labor market participation (Eckstein and Wolpin (1989)), some others model it through labor supply (Imai and Keane (2004), and Shaw (1989)), and some allow for both labor supply and labor force participation decisions to influence the investment in human capital (Altug and Miller (1998)). Moreover, whereas Eckstein and Wolpin (1989) and Altug and Miller (1998) focus on the behavior of married women, Imai and Keane (2004) and Shaw (1989) consider prime-age men. In all these studies the measurement of the parameters of the human capital production function is not the main objective of the analysis and they do not discuss how these estimates change over time. The goal of this paper is to explore how the learning-by-doing relationship that describes how past wages and hours worked affect current wages evolved over the past decades for each gender. In particular, I focus on how gender differentials in the rate of returns to labor market experience changed between the 1970s and the 1990s.
3
A dynamic model with learning-by-doing
I develop a dynamic life-cycle model with learning-by-doing human capital accumulation where individuals, after observing the realizations of their individual-specific productivity shock, choose both their labor force participation and their labor supply, taking the rental rate of human capital as given. Individuals differ by age, sex, stock of human capital and current productivity shock. The timing of the workers’ decisions is as follows. At the beginning of each period an agent observes the individual realization of the shock. Based on this information and on his past history, he/she chooses whether to participate to the labor market and how many hours to work. Agents are assumed to form rational expectations. Hence, they take into account the fact that their current labor supply not only determines current earnings but also affects their productivity and wages.4 Future wages will in turn affect future labor force participation decisions. The individual state variables are given by θit , the human capital stock of an individual i at time t, and εit , the individual-specific productivity at time t. The accumulation equation for human capital is given by: 4
This is a model where no borrowing/savings are allowed (there are no assets). Alternatively, we can think about it as to a model with complete markets. This is assumed to avoid to take into account the interaction between savings and working decision in the estimation (since PSID data do not include the information on household’s assets).
4
θit+1 = H (θit , nit ) exp (εit+1 )
(1)
where H(., .) is the learning-by-doing human capital production function, which is continuous and differentiable in all its arguments, strictly concave in current hours worked nit , and concave in the current stock of human capital, θit . According to this specification, the stock of human capital at time t + 1 is determined by the individual’s capital stock at the beginning of time t plus the investment at time t. The productivity index εit+1 is assumed to evolve over time according to a generic conditional distribution F (.|εit ) , where εit summarizes all the information known at time t. The individual-specific productivity shock can be interpreted as a health shock, or as a jobrelated shock that changes an individual’s chances to accumulate skills while working. That is, the effect of the individual specific productivity shock is to change stochastically the slope of the human capital production function. The productivity index is assumed to be correlated over time although I do not make any specific assumption on the functional form of the distribution Fε , and thus on the structure of the correlation matrix. Each individual has preferences over consumption and leisure. The instantaneous utility function is assumed to be additively separable in consumption and leisure, concave in consumption and strictly concave in leisure. As is standard in the literature on human capital, wages are defined as the product of the individual’s human capital stock and the rental rate of human capital in the economy (i.e. the efficiency wage). That is, the wage rate for the i-th individual at time t is given by: wit = Rt θit , where the rental rate to human capital, Rt , is common across all agents. Note that the wage rate at time t does not depend on hours worked in that period. As we will see in the next section, this one-period “time-to-build” assumption is relevant for the estimation of the model. An individual maximizes the expected discounted value of future income taking the series of rental rates of human capital as given. Since agents are price-takers, rental rates are omitted from the notation, but the value functions are indexed by time. Thus an individual solves the following maximization problem (in recursive form):
Vt (θit , εit ) = max
(
u (cit ) + v (1) + βE [Vt+1 (H (θit , 0) exp (εit+1 ) , εit+1 ) |Jt ] , supnt ≥0 u (cit ) + v (1 − nit ) + Rt θit nit + βE [Vt+1 (H (θit , nit ) exp (εit+1 )) |Jt ]
)
where u () represents preferences for consumption, v () preferences for leisure, β is the discount factor, Jt is the information set at time t. Note that, if an individual works zero hours at time t, then the next period human capital stock, θit+1 , simply equals the stock of human capital at time t minus depreciation. A worker compares the payoff from participating in the market to the payoff obtained from nonparticipation. If he/she participates, then he/she optimally chooses the number of hours worked. 5
Thus the solution to this control problem produces an individual labor force participation rule and a labor supply function. The participation rule and the labor supply function are given by: χit =
(
1 0
if εit ≥ εt (θit ) otherwise
(2)
and nit = nt (θit , εit )
(3)
where χt is an indicator function that is equal to zero if the individual does not work on the market. The functions εt (.) and nt (.) describe the optimal behavior of an individual. In particular, εt (.) is a threshold productivity level. That is, given the rental rate of an efficiency unit of labor and the individual stock of human capital, individuals will participate in the labor market only if their realization of the shock at time t is higher than the threshold. These functions are indexed by calendar time t since they depend on the aggregate factor prices that prevail on the market at the time these decisions are made. It is important to discuss here the assumptions on the transitional density of εit that are required in order for the optimal decision rule for participation to have this threshold structure. In this model given θit , εit does not enter in the one-period utility function. Moreover, εit enters in the intertemporal utility function only through the expected value function. Hence, in order to ensure that the expected value function is monotonic in εit and that the threshold structure obtains, I need to assume that the individual-specific productivity shock, εit , is not i.i.d..5
4
The estimation strategy
The following specification for the human capital production function is chosen: ´ ³ θit+1 = (1 − δ) + η t nψ it θ it exp (εit+1 )
(4)
where δ is the human capital depreciation rate. According to this specification, the stock of human capital at time t + 1 is equal to the current capital stock minus depreciation, plus investment. As I mentioned previously, this functional form implies that current human capital is a sufficient statistics for an individual’s past history on the labor market.6 I assume the human capital pro5
Note that this is a stronger assumption than the one required in Olley and Pakes (1996). In section 7 I present an alternative, more general, model where this assumption is relaxed. 6
Alternatively, as in Altug and Miller (1998), it could also be assumed that today’s human capital is determined by the individual’s entire past history of hours worked on the market. Unfortunately, the data available do not allow to follow an individual over his/her entire life time thus the specification I choose seems to be more accurate.
6
duction function to be linear in θit . Under this assumption, the rate of growth of human capital is independent on the level of human capital stock at time t. As discussed by Weiss and Gronau (1981), this assumption makes it possible to separate the effect of labor supply on the level and on the rate of growth of human capital.7 I assume the functional form to be identical for men and women, but I allow for the parameters of the production function to differ by gender.8 The marginal rate of return to an extra hour of work is given by the first derivative of this function, and is proportional to ηψ. The parameter η can also be generalized to include a pure age-effect. That is, it can be allowed to be a polynomial linear or quadratic in the age of the individual at time t. This assumption would capture the fact that, as an individual ages, extra hours of work are less effective in the production of human capital, i.e. the learning-by-doing effect is weaker. The parameters of equation (4) cannot be identified directly since the human capital stock is not observed. However, we observe wages. As discussed above, the wage of the i-th individual is given by: wit = θit Rt , where Rt is the efficiency wage at time t which is allowed to differ by gender and/or education. Multiplying both sides of equation (1) by the rental rate Rt+1 , multiplying and dividing the right hand side of the equation by Rt , and taking logs gives the equation that is estimated: ³ ´ ln wit+1 − ln wit = ln (1 − δ) + η (ait ) nψ it + π t+1 + εit+1 + vit+1 , if {χit = 1; χi,t+1 = 1}
(5)
where wit is the observed wage at time t, εit+1 is the individual-specific productivity shock, ν it+1 can be interpreted as i.i.d. measurement error and π t+1 = ln RRt+1 is the rate of growth of rental t rates to human capital. Note that both εit+1 and vit+1 are unobserved, though εit+1 is a state variable in the individual’s decision problem, hence a determinant of both the participation and the labor supply decisions, whereas vit+1 is not. The least square estimates of equation (5) are biased due to the presence of the self-selection problem caused by the individual’s labor participation decision and the endogeneity induced by the labor supply decision. The sample selection bias arises because we only observe wages for individuals who chose to participate to the labor market. In particular, in my framework an individual is included in the sample only if he/she worked for two consecutive periods. Hence, the conditional expectation of ln ω it+1 − ln ωit (conditional on past and current labor force participation decisions and on 7
An analogous human capital production function is estimated by Imai and Keane (2004) in the context of a structural dynamic model that allows for both human capital accumulation and savings. Altug and Miller (1998) also make a similar assumption. 8
Heckman, Lochner and Taber (1998) estimate a human capital production function with on-the-job training. They do not find evidence that the shape of the production function differs by gender.
7
£ ¤ information available at time t + 1) will include the term E εit+1 |χit = 1, χit+1 = 1 where χi,t+1 = I(εi,t+1 > ¯εt+1 (θi,t+1 )). That is, in this context the “control function” depends on two indexes of the individual-specific state variables, as opposed to the single index models dating back to Gronau (1974) and Heckman (1974).9 Note that in this dynamic framework the process of selection into the labor force generates two sources of bias that might affect the parameter estimates of the human capital production function in opposite directions. On the one hand, in each period only individuals characterized by higher level of productivity will be on the labor market - this would induce an upward bias in the estimates. On the other hand, we expect the threshold level of productivity ¯εt+1 (.) to be a decreasing function of θi,t+1 . That is, individuals with high θi,t+1 tend to work even if the realization of the productivity shock, εi,t+1 , in that period is relatively small - this would induce a downward bias in the estimates. Which of these two effects prevail depends on how persistent the individual-productivity shock is. The simultaneity bias arise because the individual-specific productivity shock is persistent and an individual beliefs about future realization of this shock will partly affect today’s labor supply decisions. More precisely, conditional on their choice to work, more productive individuals will invest more in their human capital, that is, they will work more hours. To the extent that workers know their productivity when deciding their labor supply and that the individual-specific productivity is correlated over time, this generates a simultaneity (upward) bias. Note that given my one-period “time-to-build” assumption for the process of human capital accumulation, nit is positively correlated with εi,t+1 only if εi,t+1 is positively correlated with εit . Hence, if the individual-specific productivity shock εit were i.i.d. there would be not simultaneity bias. Following the estimation methodology developed in Olley and Pakes (1996), I use the optimal participation and labor supply decisions from the model to implement a semiparametric estimator for the human capital production function parameters that corrects for the sample selection and simultaneity bias. In Olley and Pakes (1996) this methodology is developed in order to study the dynamic of the productivity in the telecommunications equipment industry. In particular, in their environment firms’ entry/exit decision produce the sample selection bias whereas the firms’ input demand generates the simultaneity bias. In my environment individuals’ labor force participation decisions correspond to firms’ entry/exit decision in the industry and, given the learning-by-doing human capital accumulation assumption, individuals’ labor supply decisions correspond to firms’ investment decisions in capital inputs. Moreover, in the Olley and Pakes’s framework the control function associated with the main equation that is estimated has the double-index structure that also characterizes my problem. Following their methodology I can use the decision rule for labor supply derived from the dynamic model in order to express the unobserved individual-specific 9
See Vella (1998) for an extensive discussion of alternative estimators that can be used to address the sample selection bias.
8
productivity at a given time as a function of the observable market hours and wages in the same period.10 Note that in contrast to the Olley and Pakes framework, in my model the ‘no investment’ decisions (zero hours worked) coincides with the ‘exit from the market’ decision (do not participate to the labor market). This implies that I do not need to “recover” the individual-specific productivity shock for those individuals that work zero hours. More in details, the solution to the individual’s decision problem results in equation (3) for the labor supply decision. That is, provided that an individual chooses to participate to the labor market, he/she will work nit+1 = nt+1 (θit+1 , εit+1 ) hours. Under regularity condition for the functional forms of the problem, the labor supply decision rule is continuous. Moreover, under the assumption that preferences are such that the labor supply function is not backward bending, this function is also monotonically increasing in the unobserved productivity εit+1 (for every θit+1 ). This assumption is important because, given that individual productivity is assumed to be correlated over time, permanent productivity shocks could result in individuals decreasing their hours worked if the shock in one period is very positive. Under this assumptions, equation (6) can be inverted for the subsample of (θit+1 , nit+1 ) such that nit+1 is strictly positive. That is we can write: εit+1 = ht+1 (θit+1 , nit+1 )
(6)
This equation implies that we can express the unobservable productivity variable εit+1 only as a function of observables because human capital stock θit+1 can be written as a function of the individual’s wage divided by the rental rate of human capital prevailing on the market at time t + 1. That is, we can rewrite (6) as: εit+1 = ht+1
µ
ω it+1 , nit+1 Rt+1
¶
(7)
where nit+1 is hours worked by individual i at time t+1, and ωit+1 is the wage earned by individual i at time t + 1. Equation (7) is based on the assumption that there is only one unobserved individualspecific state variable, εit+1 , and that the labor supply function is strictly increasing in εit+1 . Moreover, the fact that human capital at time t + 1 can be expressed as a function of current ) allows for the identification of the parameters of the learning-by-doing wages ( θit+1 = ωRit+1 t+1 technology for the accumulation of human capital in one-step, as opposed to the tree-step procedure in ³Olley and Pakes ´ (1996). This is possible because the learning-by-doing part of the equation (i.e. ψ ln (1 − δ) + ηnit ) is a function of lagged observables, whereas ht+1 (.) can be written solely as a function of current observables. In Olley and Pakes (1996) the equation includes contemporaneous 10
This is a way to capture heterogeneity throughout the population. See, MaCurdy (1981) and Altug and Miller (1998) for a discussion. This approach is more general than a fixed effect framework since it allows for an individual’s unobservable characteristics to vary over time.
9
observables in both terms, and thus not all the parameters of the production function can be identified in the first step. Substituting equation (7) into (5) gives the function that is actually estimated: µ ¶ ´ ³ ω it+1 ψ , nit+1 + ν it+1 ln ωit+1 − ln ω it = ln (1 − δ) + ηnit + π t+1 + ht+1 Rt+1
(8)
In the estimation, I use a polynomial series estimator ³ for ht+1 (.)´. That is, I write ht+1 (.) as a , nit+1 with a full set of interactions. second order orthogonal polynomial series in the duplet ωRit+1 t+1 Moreover, I assume that the errors ν it+1 are i.i.d. random variables. In order to capture the yearto-year variation in wages linked to the performance of the aggregate economy (i.e. the rate of growth of rental rates π t+1 ), I introduce time dummies in the equation. Equation (8) is estimated by least square.11 I use PSID data to estimate the parameters of the human capital production function by gender for each of the two decades, 1970s and 1990s. Hence, although the function ht+1 (., .) is assumed to be time-invariant for men and women within every decade, i.e. the 1970s and the 1990s, the function is allowed to vary across decades and by gender. In what follows, I describe the data set and present the estimation results.
5
Data
I build four longitudinal data sets using PSID data. The first sample includes males aged 20 to 65 for the time period 1969 to 1977. The second sample includes male in the same age group for the period 1989 to 1997.12 The third and fourth samples include 20 to 65 year old women for the same two time periods. The actual calendar years for the data are 1970 to 1976, and 1990 to 1996. The first time period will be referred to as the 1970s, the second time period as the 1990s. Results are presented in terms of calendar years. An individual is included in the estimation sample as long as he/she has non-missing data on hours worked and earnings for at least two consecutive years. The labor supply variable is annual hours worked, and the income variable is the natural logarithm of hourly wages. Hourly wages are constructed by dividing real annual earnings by annual hours worked. Reported earnings are deflated deflated using the CPI with base 2000 from the Bureau of Labor Statistics. Table 1 reports the sample means for hourly wages and annual hours worked. The statistics are reported separately for women and men in the 1970s and in the 1990s samples. Values are reported 11
The series expansion of ht+1 (.) also includes terms in current wage (in levels) that is also on the left hand side of the equation. Least square estimation solves this simultaneity problem since it minimizes the sum of the squared errors. Moreover, rental rates are also included in the series expansion and thus the series of rental rates cannot be identified. 12
For the period 1994-1997 I use PSID early release data.
10
by year. I also report the number of observations available for every year. Note that, in the raw data the fraction of women working zero hours in the 1970s is around 42% for all the years composing the sample. This percentage drops to 20% in the 1990s. For men the corresponding percentage is around 6% both for the 1970s panel and for the 1990s panel. This fact is not surprising but it clearly shows that the problem of sample selection is particularly strong for women in the 1970s. Table 2 and 3 describe the average age profiles of mean hourly wages for men and for women in the age group 25 to 40 in the 1970s and in the 1990s. The life-cycle earnings profiles become steeper in the 1990s for both male and female workers. I estimate the production function both for part-time and full-time workers. I adopt the standard definition of full-time workers and include only individuals who worked at least 1500 hours a year in the second sample. In what follows, I will also include schooling in the human capital production function under different assumptions (see below). The education variable chosen corresponds to the PSID variable “years of completed education”. The information is aggregated into three different categories. Individuals with less than a high school diploma, individuals with a high school diploma and those who had at least some years of college. The next section presents the estimation results and discusses the main findings for the main statistics of interest - the change in relative rates of return to labor market experience.
6
Results
I report the estimation results for two cases. In the first case, I simply estimate equation (5) by least squares without correcting for the two biases. In the second case, I estimate equation (8) which includes correction terms for both the sample selection and the simultaneity bias. The results are presented for men and women separately. That is, I assume the functional form to be identical for men and women, but I allow for parameters to differ by gender and by decades (i.e. the 1970s and the 1990s). I compare the relative rates of return to experience implied by these two sets of estimates. The uncorrected estimates generate larger returns to experience for women than for men in both periods. Once I correct for the sample selection and the simultaneity bias, men’s estimated returns to experience are larger than women’s returns both for the 1970s and 1990s. Moreover, women’s returns to experience increase relatively more than men’s did. The last result is comparable with the results obtained by Blau and Kahn (1997) and O’Neil and Polachek (1993) using the same definition of full time work experience but based on standard Mincer wage regressions.13 13
I also run a set of regression for part time workers, where we define part time as working less than 1500 hour a year. The estimation results obtained for part time workers provide mixed evidence about changes in returns to experience by gender. Blau and Kahn (1997) also find similarly mixed evidence.
11
Since the process of human capital accumulation can be more or less effective depending on educational attainment, the human capital production function is allowed to include education. I run the estimation for two different specifications of the production function: ´ ³ (1) ln ω it+1 − ln ωit = ln (1 − δ) + ηnψ it + π t+1 + αEit+1 + εit+1 + η it+1 ´ ³ (2) ln ω it+1 − ln ωit = ln (1 − δ) + ηnψ it + π t+1 Eit+1 + εit+1 + η it+1
where Eit represents the i-th individual’s education at time t.14 In the second specification individuals with different schooling face different rental rates to human capital. I also estimate the equation allowing for a quadratic pure-age effect in the parameter η (that is, considering η (ait ) = η 0 + η 1 ait + η 2 a2it ) and compare the results obtained when there is no age effect to the ones obtained under this assumption. In this case, age becomes one of the state variables in the model. Thus, Equation (10) is modified to ³ allow the correction term ht+1 (.) to be a second ´ ω it order orthogonal polynomial series in the triple Rt , nit , ait with a full set of interactions. I use time dummies to capture the year-to-year variation in the returns to human capital investment. Table 4 presents the results obtained when I estimate equation (5). Standard errors are reported in parentheses. The results are very similar for both schooling specifications. The estimates of the depreciation rates show how human capital depreciates at a faster rate in the 1990s than in 1970s for both men and women. Moreover, female’s human capital seems to depreciate at a faster rate than men’s returns in the 1970s. The estimated parameters for the specification that corrects for simultaneity and sample selection, equation (8), are described in Table 5. Also in this case the depreciation rates are higher for women than for men both in the 1990s and in the 1970s. At the same time, depreciation rates increase in the 1990s for both gender groups. This is consistent with some form of skill-biased technological change. Note that for all the different specifications, the estimates of the exponent ψ are always smaller than one. This implies that additional hours of work increase the human capital stock at a decreasing rate. Figure 2 draws the rates of return to experience corresponding to the estimates in Table 4 and 5. Given the specification of the human capital production function adopted in this paper, my definition of returns to labor market experience refers to the impact of additional working hours d
θ it+1 θ it
on the rate of growth of earnings. That is, the figure plots the function: dnit = ψηnψ−1 it . This function is plotted for values of annual hours worked in the interval [1500, 2000]. The numbers on the vertical axis then represent the log hourly wage growth when an individual (who is already 14
Another alternative would be to allow V () and h () to also differ by education and, therefore, to estimate the human capital production function for each education group. I plan to consider this strategy in the future version of the paper.
12
working 1500 hours a year) works an additional 10, 20 or more market hours during the year. Before I discuss the results of the estimation it is useful to give a sense of the magnitude of my estimates of the rates of return to extra hours of work as compared to the standard estimates of the returns to labor market experience obtained from Mincer log-earnings equations that include experience and its square.15 Simple calculations show that my estimates of the human capital production function parameters imply returns to one extra year of full-time work experience ranging from 3% to 5%. These values are of the same order of magnitude as the estimates reported in Blau and Kahn (1997) based on a Mincer log-earnings specification.16 Panel A of Figure 2 displays the rates of return to experience obtained using the ‘uncorrected’ estimates of the human capital production function from Table 4. In this case the return to experience are substantially higher for women than for men over the two time periods. In particular, women’s returns to full time experience are 11% higher than men’s in the 1970s and 13% higher than men’s in the 1990s. Returns to experience increase between the 1970s and the 1990s for both genders, although women’s returns increase at a faster rate. In particular, they increase by 19% for men and by 23% for women. The fact that women’s returns are higher than men’s returns is not very realistic and it is mainly due to the fact that the estimates are not corrected for the sample selection bias.17 The problem of non-random selectivity is extremely important in this context since this bias affects women’s and men’s estimates to a different extent. In fact, the fraction of men not working on the market is very small, and the problem of selection into the sample negligible. On the other hand, women’s estimates are strongly affected by sample selection since their labor force participation is low, particularly in the 1970s.18 The effects of the simultaneity bias uniformly affect men’s and women’s estimates of the production function parameters, and thus do not create a distortion in the relative change in the male/female returns to experience differential. Panel B of Figure 2 displays the rates of return to experience obtained using the ‘corrected’ estimates of the human capital production function from Table 5. In this case, men’s returns to experience are always larger than women’s. In fact, for specification (1) the female returns to experience are now 2 0 Given the earnings equation ln wit = α0 + α1 Xit + α2 Xit + α3 Zit + εit , where Xit is year of experience and Zit ln wit is a vector of additional controls, the returns to labor market experience are given by: ∂∂X = α1 + 2α2 Xit . it 15
16
The following transformation can be used to compare the estimated coefficients. Based on the Mincer specification ∂ ln
wit+1
wit for the wage regression we can obtain: = α1 + 2α2 (Xit + Pit+1 ) where Xit represents accumulated labor ∂Pit+1 market experience at time t and Pit+1 is an indicator function that is equal to 1 if the individual worked full-time between time t and time t + 1. Roughly speaking, this corresponds to my measure of the returns to labor market experience.
17
Similarly, Blau and Kahn (1997) estimates would imply 25% higher returns to experience for women than for men in 1989. 18
40% of the women are never observed working in the 1970s sample. This fraction drops to 20% in the 1990s sample.
13
65% of those of men in the 1970s, but they increase to 82% of the male returns in the 1990s. For specification (2) the female/male ratio increases from 50% in the 1970s to 82% in the 1990s. The second panel of Figure 2 clearly shows that returns to experience increased within gender categories over this time period. Furthermore, women’s returns to experience increased relatively more than men’s across decades, 38% and 9%, respectively. Thus the correction amplifies the magnitude of women’s increase in returns to experience between 1970s and 1990s. It is important to note that men’s estimated rates of return to experience are only slightly affected by the correction for the sample selection bias.19 Table 6 and 7 present the estimation results when η () depends on age. I only present the results obtained under the first specification for schooling. The age effect is estimated to be negative for all gender groups in both decades. That is, the learning-by-doing effect of extra hours of work is weaker as an individual ages.20 As opposed to the previous case, when the age effect is taken into account depreciation rates are higher for men than for women both in the 1990s and in the 1970s. Yet, human capital depreciates at a faster rate in the 1990s than in the 1970s for both gender groups. Figure 3 (panel A and B) shows the marginal returns to experience obtained under this specification. In this case, women in the 1990s display the same returns as men in the 1970s. The correction for the two biases has the same effect on returns to experience than in the previous case. The pattern emerging for the change in relative returns to experience is also similar to the one observed in Figure 2.21 In particular, women’s returns to experience more than double between the 1970s and the 1990s, whereas men’s returns to experience increase by 44%. Moreover, the female/male returns to experience ratio increases from 50% in the 1970s to around 80% in the 1990s. These values are very similar to the ones I find for the case with no age effect. To summarize, the estimations show that, over this time period, returns to experience increased within both gender groups, and that the increase was relatively larger for women than for men. Although my estimation procedure is different, the estimations for returns to experience are consistent with those documented by Blau and Kahn (1997) and O’Neil and Polachek (1993). I also find that correcting for the sample selection bias, is extremely important in this context. Indeed, failing to take it into account would always generate larger estimated rates of return to experience for women than for men. 19
I also run a set of estimates where I correct for the sample selection bias by approximating the control function with a fully interacted second order polynomial in the propensity scores for time t and time t + 1. In this case, men’s estimated returns to experience are almost unaffected, whereas women’s estimated returns are significantly lower with respect to the case with no correction. 20
This implies that human capital accumulation profiles are concave in age. Although the estimation procedure is different, Imai and Keane [2004] also find a negative age effect for a similar specification of the human capital production function. 21
The results are presented for 30 years old individuals.
14
7
An Alternative Model
The model considered so far makes a fairly restrictive assumption on the transitional density of the individual-specific productivity shock. That is, εit cannot be i.i.d. otherwise the decision rule for labor participation does not have the threshold structure that is used in the estimation procedure. In order to circumvent this problem I plan to estimate the following alternative model: (1) (2) (3) (4)
wit θi,t+1 ωit εi,t+1
= = ∼ ∼
Rt θit exp(ω it ) H(θit , nit ) exp(εi,t+1 ) Fω (ω i,t+1 |ω it ) iid
In this model εit is no longer a state variable, but ωit is a state variable even if it is i.i.d. Of course, the interpretation of ωit in this model is different than the interpretation of εit . The productivy shock now does not directly impact the individual’s ability to learn while on-the-job and therefore the human capital accumulation process as before. Rather it is a shock to the individual’s earnings that only affect the human capital production function indirectly through its impact on labor force participation and labor supply decisions. This model is more closely related to the production function model in Olley and Pakes, and it is straightforward to prove that it has the threshold structure proposed in equation (2). In particular, in this alternative model the state variables are ω it and θit and one does not need to assume that ω it is not i.i.d. in order to obtain such threshold structure. The optimal decision rules in this case would be given by: nit = nt (θit , ω it ) ¯ t [θit ]) χit = I{ω it > ω The equation for wages to be estimated now becomes: i h ∆ ln wi,t+1 = π t+1 + ln (1 − δ) + ηnψ it + ∆ω it + εi,t+1 ,
if {χit = 1; χi,t+1 = 1}.
By using the inverse functions for both nt (.) and nt+1 (.) we can rewrite the expression above
as: i h ∆ ln wi,t+1 = π t+1 + ln (1 − δ) + ηnψ it + ht+1 (θ i,t+1 , ni,t+1 ) − ht (θ it , nit ) + εi,t+1 , if {χit = 1; χi,t+1 = 1}.
Hence, the following equation would be estimated: ∆ ln wi,t+1 if {χit
µ ¶ µ ¶ i h wi,t+1 wit ψ = π t+1 + ln (1 − δ) + ηnit + ht+1 , ni,t+1 − ht , nit + εi,t+1 , Rt+1 Rt = 1; χi,t+1 = 1} 15
Note that a relatively “small” change in the model leads to an important difference in the econometric specification and, perhaps, to very different estimates of δ, η, and ψ. In this model an endogeneity bias can arise because wi,t+1 is correlated with εi,t+1 . This is a problem that also affect the estimates of the previous model. However, since in this case εit is i.i.d. consistent estimates of the relevant parameters of the human capital production function can be obtained by using lagged values of wages and hours as instruments. The next draft of the paper will replace the current model with this alternative specification and will discuss the estimates of the parameters of the human capital production function obtained in this case. I will also consider alternative functional forms for the human capital production function and will provide estimates of the returns to labor market experience experience for the overall period 1970 to 1997 period and for each of the three decades: 1970s, 1980s and 1990s.
8
Concluding Remarks
This paper documents that the rates of return to labor market experience grew at a faster rate for women than for men between the 1970s and the 1990s. However, the underlying changes in the technology for human capital accumulation that might have produced this outcome are taken as given. What factors are more likely to have contributed to this relatively larger increase in women’s returns to experience? In general the increase in returns to experience can be attributed to technological change that favors more skilled workers. Technological progress favorable to women’s characteristics can contribute to the relative increase in women’s returns to experience. Other possible explanations are the change in the distribution of female workers by occupation, the increase in women’s labor market experience and the decline in discrimination against women, in particularly against married women and married mothers. Regarding the first explanation, as documented by many researcher, women earned access to jobs where labor experience is more important over this period. For example, data from the Current Population Sirvey show that, whereas in 1975 only 7.5% of all working women had executives, administrative or managerial occupation, the same percentage increased to 12% in 1995. This shift is even more striking when we consider married women (in this case the fraction more than doubled), married mothers with children in preschool age (3% to 11.5%), and married mothers with children less than 18 years old (3.7% to 14%). This increase took place at the expense of less skill intensive occupations (laborers, operators etc.). The fraction of women working in the service sector or in traditionally female occupations, such as secretarial, teaching, and nursing jobs, did not change substantially between the 1970s and the 1990s. Moreover, women’s years of labor market experience increased substantially across the two decades. As for the second explanation, a reduction in discrimination could have occurred as a direct result of the activity of government agencies (e.g. the Equal Employment Opportunity Commission).
16
Although studies of government antidiscrimination activities do not find that they had any impact before the mid-1980s.22 The evidence on the decline of the residual gender earnings differential over this period is also consistent with these explanations. Further work on the determinants of the relative increase in returns to labor market experience is warranted.
References [1] Altug S. and Miller R.A. “The Effect of Work Experience in Female Wages and Labor Supply,” The Review of Economic Studies 65: 45-85, 1998. [2] Blau F. and Kahn L. “Swimming Upstream: Trends in the Gender Wage Differential in the 1980,” Journal of Labor Economics, 15: 1-42, 1997. [3] Chang Y., Gomes J. and Schorfheide F. “Learning-by-Doing as Propagation Mechanism,” American Economic Review, 92: 1498-1520, 2002. [4] Eckstein Z. and Wolpin K. “Dynamic Labor Force Participation of Married Women with Endogenous Work Experience,” The Review of Economic Studies 56: 375-390, 1989. [5] Gronau, R. “Wage Comparison - A Selectivity Bias,” Journal of Political Economy, 82: 11191143, 1974. [6] Heckman J. J., Lochner L. and Taber C. “Explaining Rising Wage Inequality: Exploration with a Dynamic General Equilibrium Model of Labor Earnings with Heterogeneous Agents,” Review of Economic Dynamics, 1: 1-58, 1998. [7] Heckman, J. (1974), “Shadow Prices, Gender Differences and Labor Supply,” Econometrica 42, 679-694. [8] Ichimura H. and Todd P. “Implementing Nonparametric and Semiparametric Estimation” forthcoming Handbook of Econometrics V [9] Imai S. and Keane M. P. “Intertemporal Labor Supply and Human Capital Accumulation,” International Economic Review 45: 601-641, 2004. 22
The study of the legal suit against sexual discrimination brought (and won) before the Supreme Court indicates that such activities became more effective in the mid-Eighties. The first female discrimination case before the Supreme Court was ”Phillips v. Martin Marietta Corp” in 1971. Phillips, a white woman, was not hired because she had preschool-age children, yet men in the same situation were hired ( source EEOC, annual report 1972). The court ruled definitely on this case at the end of the seventies. Several similar cases were brought to the attention of the court by the mid eighties.
17
[10] Katz L. and Murphy K. “Changes in Relative Wages, 1963-1987: Supply and Demand Factors,” Quarterly Journal of Economics pp. 35-78, 1992. [11] MaCurdy T. “An Empirical Model of Labor Supply in a Life-Cycle Setting,” Journal of Political Economy, 89: 1059-1085, 1981. [12] Mincer J. Schooling, Experience, and Earnings. Columbia University Press 1974 [13] Mincer J. and Polachek S. “Family Investments in Human Capital: Earnings of Women,” Journal of Political Economy 82: 76-108, 1974. [14] Olley G.S. and Pakes A. “The Dynamics of Productivity in the Telecommunications Equipment Industry,” Econometrica, Vol. 64 6: 1263-1297, 1996. [15] O’Neill J. and Polachek S. “Why the Gender Gap in Wages Narrowed in the 1980,” Journal of Labor Economics, 11: 205-228, 1993. [16] Shaw K. “Life-cycle labor supply with human capital accumulation,” International Economic Review 30: 431-456, 1989. [17] Vella, F. “Estimating Models with Sample Selection Bias: A Survey,” Journal of Human Resources 33: 127-169, 1998. [18] Weiss Y. and R. Gronau “Expected Interruptions in Labor Force Participation and Sex-related Differences in Earnings Growth,” Review of Economic Studies 48: 607-619, 1981.
18
Table 1. Average hourly wage and annual hours worked by year 1970s: men
women
wage
hours
obs
wage
hours
obs
1970
15.4
2275
2042
9.37
1422
1078
1971
15.69
2271
2062
9.54
1399
1138
1972
16.17
2300
2061
9.7
1427
1021
1973
16.75
2301
2066
9.9
1412
1135
1974
16.85
2240
2026
10
1406
1132
1975
16.61
2191
1998
10.1
1379
1145
1976
17.2
2202
1971
10.5
1395
1113
1990s men
women
wage
hours
obs
wage
hours
obs
1990
17.55
2263
2235
12.45
1705
1774
1991
17.99
2219
2262
12.25
1674
1825
1992
18.8
2180
2233
14.03
1646
1809
1993
22.45
2178
2112
16.13
1689
1745
1994
21.34
2229
2041
14.83
1679
1835
1995
20.35
2235
2090
15.01
1709
1834
1996
20.1
2218
2058
14.5
1712
1812
19
Table 2: Life-cycle wage profiles, 1970s women 1970
1971
1972
1973
1974
1975
1976
25
9.67
9.78
11.71
9.27
9.01
9.97
8.97
26
5.64
10.44
8.64
7.27
10.05
9.54
9.93
27
10.61
7.53
6.65
10.03
8.60
9.78
5.63
28
8.47
11.28
9.33
9.51
10.98
7.35
9.43
29
9.45
9.15
8.97
7.67
11.23
12.01
6.99
30
11.60
7.56
7.60
12.06
8.40
9.14
11.14
31
10.34
12.95
11.33
8.95
10.19
8.18
11.14
32
10.74
10.20
8.24
8.00
11.89
16.99
9.63
33
10.95
11.02
11.27
11.79
8.22
8.63
14.46
34
7.39
8.83
8.08
11.41
12.63
8.48
8.92
35
8.66
8.56
9.36
10.52
8.65
14.32
8.65
36
8.14
7.52
8.81
10.67
12.27
10.66
14.12
37
6.44
6.85
7.17
8.58
10.35
12.18
7.92
38
9.72
8.75
4.30
7.86
8.00
8.30
11.60
39
7.37
8.54
10.45
7.10
9.15
7.55
10.94
40
8.15
8.18
7.66
6.87
6.48
8.88
8.89
men 25
15.01
11.46
13.46
12.43
11.21
12.46
13.43
26
13.30
13.59
12.46
14.73
13.72
11.29
17.95
27
13.68
13.00
14.18
11.89
14.20
12.74
15.96
28
13.60
14.51
14.28
14.75
13.93
14.60
14.19
29
13.46
13.72
14.48
14.10
13.94
13.37
16.19
30
14.52
13.53
15.08
16.04
14.85
13.72
13.40
31
14.46
14.72
14.67
15.82
15.09
15.11
14.83
32
14.26
15.10
14.50
17.28
14.94
14.86
14.43
33
16.19
13.91
15.43
15.88
17.46
15.18
18.71
34
13.87
17.93
15.54
15.21
17.34
16.48
17.46
35
17.87
14.42
17.57
17.70
16.24
14.57
18.07
36
16.90
15.43
14.75
16.02
19.20
16.94
14.62
37
16.30
17.43
13.69
17.20
18.37
17.78
18.19
38
18.31
16.35
19.15
14.52
14.91
18.02
16.15
39
15.86
17.25
17.46
20.89
20.47
16.16
19.90
40
16.08
18.14
18.78
17.13
14.52
16.09
16.13
20
Table 3: Life-cycle wage profiles, 1990s women 1990
1991
1992
1993
1994
1995
1996
25
10.72
9.34
12.42
10.04
12.26
8.52
6.80
26
10.20
10.02
13.79
19.60
11.17
7.86
7.92
27
10.48
10.80
11.77
22.69
14.23
9.95
9.93
28
9.90
10.51
12.68
13.47
16.17
14.91
9.54
29
13.73
10.46
11.11
13.18
12.84
15.42
21.31
30
11.19
13.43
11.94
14.17
11.79
22.14
10.28
31
11.49
10.02
16.34
15.48
11.74
13.78
13.75
32
11.61
13.98
11.93
13.21
12.48
13.12
14.37
33
9.87
9.95
10.60
14.44
14.18
21.40
13.62
34
12.18
11.46
12.96
12.95
11.73
14.26
15.38
35
15.39
12.96
10.91
21.35
15.29
12.85
14.29
36
12.84
13.78
14.32
13.05
14.60
13.96
14.64
37
21.32
12.74
14.78
28.65
19.19
12.37
15.38
38
12.46
14.27
20.23
16.04
20.46
13.03
13.53
39
10.37
10.87
16.46
16.07
15.51
15.20
9.87
40
12.86
12.75
18.46
15.61
14.98
15.18
14.52
men 25
11.41
8.92
11.44
12.39
13.42
9.34
11.30
26
11.89
13.18
12.07
14.25
9.97
12.02
9.64
27
12.57
11.97
14.69
13.97
13.48
16.75
11.29
28
13.65
13.76
13.29
17.85
19.58
14.65
15.41
29
14.95
14.12
15.19
18.00
20.78
17.27
11.50
30
15.37
15.41
14.28
15.86
16.95
15.00
12.90
31
14.92
15.67
17.69
21.57
15.20
15.40
16.40
32
15.58
16.41
15.85
18.70
27.11
14.57
16.32
33
16.18
16.61
16.67
20.84
19.38
20.92
16.59
34
16.14
16.54
16.28
17.62
19.34
18.94
22.29
35
16.62
16.78
19.28
20.77
18.72
18.61
19.42
36
17.21
17.52
16.94
19.69
19.39
18.18
19.63
37
19.53
19.45
17.71
24.17
18.30
19.57
18.06
38
18.91
17.30
21.34
20.51
18.92
19.15
18.87
39
19.47
20.26
21.87
20.23
20.27
19.57
21.61
40
22.67
27.68
20.64
19.66
19.61
20.52
22.98
21
Table 4: Human capital production parameters (no correction) 1970s men
women
men
0.546 (.050)
0.448 (.062)
0.290 (.090)
0.40 (.090)
0.002 (.001)
0.009 (.006)
0.013 (.008)
0.012 (.009)
0.7 (.090)
0.55 (.095)
0.524 (.090)
0.54 (.114)
0.547 (.055)
0.469 (.065)
0.290 (.09)
0.330 (.10)
0.002 (.001)
0.009 (.007)
0.013 (.01)
0.012 (.01)
0.710 (.090)
0.548 (.094)
0.524 (.09)
0.543 (.115)
ln ω it − ln ω it−1 (1 − δ) η ψ
ln ω it − ln ω it−1 (1 − δ) η ψ
1990s women
´ ³ = ln (1 − δ) + ηnψ it−1 + π t + αEit + εit + η it
´ ³ = ln (1 − δ) + ηnψ it−1 + π t Eit + εit + η it
Table 5: Human capital production parameters (correction) 1970s men
ln ω it − ln ω it−1 (1 − δ) η ψ
women
men
women
³ ´ = ln (1 − δ) + η (ait−1 ) nψ it−1 + π t + αEit + εit + η it
0.723 (0.070)
0.500 (0.060)
0.650 (0.070)
0.004 (0.002)
2.0e-05 (0.008)
6.0e-04 (3.0e-04)
0.640 (0.110)
0.920 (0.090)
0.855 (0.260)
0.730 (0.320)
0.770 (0.060)
0.480 (0.090)
0.760 (0.080)
0.430 (0.073)
0.003 (0.002)
.0001 (4.0e-05)
0.001 (4.0e-04)
0.0098 (3.5e-04)
0.650 (0.120)
0.980 (0.120)
0.860 (0.270)
0.750 (0.330)
ln ω it − ln ω it−1 (1 − δ) η ψ
1990s
0.480 (0.140)
0.002 (5.0e-04)
´ ³ = ln (1 − δ) + η (ait−1 ) nψ it−1 + π t Eit + εit + η it
22
Table 6: Human capital production with age effect (no correction) 1970s men
(1 − δ) η0 η1 η2 ψ
1990s women
men
women
0.460 (0.078)
0.450 (0.091)
0.2746 (0.093)
0.388 (0.1)
0.005 (0.002)
0.014 (0.010)
0.01498 (0.007)
0.017 (0.009)
-5.9e-05 (2.7e-05)
-5.5e-05 (1.2e-05)
-1.4e-04 (8.0e-05)
-5.3e-05 (2.0e-05)
1.1e-06 (6.05e-07)
2.5e-07 (1.5e-06)
2.5e-06 (1.1e-06)
-2.45e-07 (1.7e-06)
0.621 (0.098)
0.497 (0.120)
0.517 (0.089)
0.492 (0.110)
Table 7: Human capital production with age effect (correction) 1970s men
(1 − δ) η0 η1 η2 ψ
1990s women
men
women
0.30 (0.093)
0.340 (0.074)
0.230 (0.042)
0.314 (0.07)
5.0e-04 (1.0e-04)
2.0e-04 (2.23e-05)
0.0026 (9.0e-04)
0.001 (5.0e-04)
2.2e-06 (4.1e-07)
5.0e-05 (1.6e-06)
1.6e-04 (8.4e-05)
1.4e-05 (-1.2e-07)
-1.0e-07 (3.3e-08)
-1.0e-06 (2.3e-07)
-3.2e-07 (4.9e-08)
-7.5e-07 (7.5e-08)
0.770 (0.200)
0.680 (0.133)
0.580 (0.183)
0.690 (0.170)
23
Figure 1: Marginal returns to experience
m en70s
m en90s
wo m en70s
wo m en90s
0.025
0.02
0.015
0.01
0.005
0
Panel A: No correction
0 .0 2 5 m en70s
m e n9 0 s
0.0 2
0 .0 1 5
0.0 1
0 .0 0 5
0
Panel B: Corrected estimates
24
wo m e n 7 0 s
wo m e n9 0 s
Figure 2: Marginal returns to experience (age-effect)
0.025
m en70s
m en90s
wo m en70s
wo m en90s
0.02
0.015
0.01
0.005
0
Panel A: No correction
0.025 m en70s
m en90s
0.02
0.015
0.01
0.005
0
Panel B: Corrected estimates 25
wo m en70s
wo m en90s
