سرمایه انسانی و پویایی های توزیع درآمد

Earnings heterogeneity plays a crucial role in modern macroeconomics. We document that mean earnings and measures of earnings dispersion and skewness all increase in US data over most of the working life-cycle for a typical cohort as the cohort ages. We show that (i) a human capital model can replicate these properties from the right distribution of initial human capital and learning ability, (ii) differences in learning ability are essential to produce an increase in earnings dispersion over the life cycle and (iii) differences in learning ability account for the bulk of the variation in the present value of earnings across agents. These findings emphasize the need to further understand the role and origins of initial conditions.

Recent work in macroeconomics has explored the quantitative implications of dynamic models for the distribution of consumption, income and wealth. This work takes earnings or wages as an exogenous random process and then proceeds to characterize the distributional implications of optimal consumption-savings and labor-leisure behavior. 1 These models would appear to be attractive for assessing the distributional effects of changes in government policy since they are able to produce many of the quantitative features of the actual distribution of consumption, income and wealth. 2 A critical issue for this research agenda is to integrate deeper foundations for the determinants of earnings and wages into these models by allowing earnings to be endogenous. We list two reasons for why this is important. First, we note that when earnings are exogenous there is no channel for policy to affect consumption and welfare through earnings. This channel is arguably of first order importance. In fact, a dominant theme in the earnings distribution literature is that earnings profiles are determined by the optimal investment of time and resources into the accumulation of skills. As a result, these investment decisions will not be invariant to changes in government policies. Second, a key issue for the purposes of assessing many government policies is the degree to which the variation in the present value of earnings is due to differences established early in life versus shocks received over the life cycle. If the former is responsible for the bulk of the variation in earnings, then policies directed towards these initial differences are of first-order importance. This paper takes a first step towards developing deeper foundations by examining, at a quantitative level, the earnings distribution dynamics of a well-known and widely-used human capital model. More specifically, we document properties of how the US earnings distribution evolves for a typical cohort of individuals as the cohort ages. We then assess the ability of the model to replicate these properties. This assessment serves to highlight the potential role and importance of differences in initial conditions for understanding the dynamics of the earnings distribution. The specific properties of the US earnings distribution that we focus on relate to how average earnings, and measures of earnings dispersion and skewness change for a typical cohort as the cohort ages. To characterize these age effects, we use earnings data for US males and employ a methodology, described later in the paper, for separating age, time and cohort effects in a consistent way for a variety of earnings statistics. Our findings, summarized in Fig. 1, are that average earnings, earnings dispersion and earnings skewness increase with age over most of the working life-cycle. Full-size image (38 K) Fig. 1. Earnings distribution dynamics—PSID data. This figure plots mean, dispersion, and skewness in earnings by age using PSID data. The age-profiles are based on the percentile estimation procedure described in Section 2.2. Figure options We assess the ability of the Ben-Porath (1967) human capital model to replicate the patterns in Fig. 1. This framework is the natural candidate for our study. The Ben-Porath model is well-known and widely-used, and has been the basis for both theoretical and empirical analyses of human capital. Its prominence in the literature is reflected in recent surveys, such as Mincer (1997) and Neal and Rosen (2000).3 In our version of this model, each agent is endowed with some immutable learning ability and some initial human capital. Each period an agent divides available time between market work and human capital production. Human capital production is increasing in learning ability, current human capital and time allocated to human capital production. An agent maximizes the present value of earnings, where earnings in any period is the product of a rental rate, human capital and time allocated to market work. Our assessment focuses on the dynamics of the cohort earnings distribution produced by the model from different initial joint distributions of human capital and learning ability across agents. Our findings are striking. We establish that the earnings distribution dynamics documented in Fig. 1 can be replicated quite well by the model from the right initial distribution. In addition, the model produces the key properties of the cross-sectional earnings distribution. These conclusions are not sensitive to the precise value of the elasticity parameter in the human capital production function, nor are they sensitive to the age at which human capital accumulation process articulated by the model begins. The initial distributions which replicate the patterns in Fig. 1 rely crucially on differences in learning ability across agents. Age-earnings profiles for agents with high learning ability are steeper than the profiles for agents with low learning ability. This is the key mechanism for how the model produces increases in earnings dispersion and skewness for a cohort as the cohort ages. Earnings profiles are steeper for high ability agents since early in life they allocate a relatively larger fraction of their time to human capital production and thus have low earnings, while their time allocation decisions and high learning ability imply that later in the life-cycle they have higher levels of human capital and, hence, earnings. This mechanism is consistent with regularities long discussed in the human capital literature such as the fact that time allocated to skill acquisition is concentrated at young ages, that age-earnings profiles are steeper for people who choose high amounts of schooling and that the present value of earnings increases in a measure of learning ability.4 It is important to mention that it is not the case that the model can always match a set of life-cycle earnings distribution facts, provided that one can choose an infinite number of parameters characterizing the initial distribution. Proposition 1 in Section 3 shows that when all agents are born with the same learning ability, but different initial human capital, the model always generates a counterfactual pattern of decreasing earnings dispersion no matter how one chooses the distribution of human capital across agents. Intuitively, one can always exactly match any distribution of earnings at the end of the working life-cycle provided one can choose the distribution of initial human capital freely. However, the ability to match the facts documented in Fig. 1 requires that one exactly matches the earnings distribution in the end of the working life cycle as well as in all previous periods. Thus, having an infinite number of parameters to choose in the form of an unrestricted initial distribution does not guarantee that one can match the patterns in Fig. 1. We close the paper by contrasting the implications of the model with some evidence on persistence in individual earnings. The model implies that over time both individual earnings levels and earnings growth rates are strongly positively correlated. Evidence from US data shows that earnings levels are positively correlated but that earnings growth rates one year apart are negatively correlated. This and related evidence suggests that there is potentially an important role for idiosyncratic shocks that lead to mean reversion in earnings. These shocks are by construction absent from the benchmark model. A critical issue for future work is to determine the importance of both initial conditions and shocks over the life-cycle in models in which the earnings distribution is endogenous.5 We believe that this issue can be usefully pursued by investigating both the distributional dynamics of earnings and consumption over the life cycle. The paper is organized as follows. Section 2 describes the data and our empirical methodology. Section 3 presents the model. Section 4 discusses parameter values. Section 5 presents the central findings of the paper. Section 6 concludes.

We assess the degree to which a widely-used, human-capital model is able to replicate the age dynamics of the US earnings distribution documented in Fig. 1. We find that the model can account quite well for these age-earnings dynamics. In addition, we find that the model produces a cross-sectional earnings distribution closely resembling that implied by the age-earnings dynamics documented in Fig. 2. Our findings indicate that differences in learning ability across agents are key. In particular, in the model high ability agents have more steeply sloped age-earnings profiles than low ability agents. These differences in earnings profiles in turn produce the increases in earnings dispersion and skewness with age that are documented in Figs. 1 and 2. These findings are robust to the age at which the human capital accumulation mechanism described by the model begins and to different values of the elasticity parameter of the human capital production function. We also find that, despite its relative success in replicating these facts, the model is inconsistent with evidence related to the persistence of individual earnings. We mention two areas in which future work seems promising. The first has to do with the fact that the distribution of agents by initial human capital and ability is unrestricted by the model. Models of the family can provide restrictions on this initial distribution. For this class of models, an assessment of the ability to replicate the facts of age-earnings dynamics and intergenerational earnings correlations is a natural next step. The second area for future work deals with the fact that the model examined here abstracts from many seemingly important features. Three such features are the absence of a leisure decision, an occupational choice decision and shocks that make human capital risky. We comment on this last feature. First, allowing for risky human capital would be one way of integrating deeper foundations for earnings risk into the standard consumption-savings problem considered by the literature on the life-cycle, permanent-income hypothesis. This literature has examined in detail the determinants of consumption and financial asset holdings over the life cycle, but no comparable effort has been put into investigating the accumulation of human capital. Second, while there seems to be agreement that human capital is risky there is relatively little work that analyzes different sources of risk and then determines their quantitative importance.23 It is clear from this paper that a richer set of facts is needed to identify both initial conditions and shocks in a model with risky human capital, given that human capital theory can explain the patterns in Fig. 1 without shocks. Two interesting questions for a theory with risky human capital are (i) can such a model account for both the distributional dynamics of earnings and consumption over the life cycle? and (ii) what fraction of the dispersion in lifetime earnings is accounted for by initial conditions versus shocks? We plan to explore these questions in future work.