تجربه در مقابل کهنگی: مدل یکپارچه سازی سرمایه انسانی

I introduce endogenous human-capital accumulation into an infinite-horizon version of Chari and Hopenhaynʼs (1991) [4] vintage-human-capital model. Returns to skill and tenure premia are highest in young vintages, where skill is scarcest and agents accumulate human capital fastest. As the vintage ages, the skill premium decreases and vanishes entirely upon vintage death. Workers run through cycles of human-capital accumulation: their wages rise as they accumulate skill, undergo downward pressure as the technology ages, and finally drop sharply when the worker switches to a new technology. The results are in line with German linked employer–employee data: tenure premia are highest in young establishments, as well as in fast-growing industries, occupations and establishments. A calibration exercise suggests that human-capital accumulation is the most important determinant of workersʼ wage profiles, whereas changes to the price of skill and vintage productivity gains play a smaller quantitative role.

Returns to skill vary substantially across industries, occupations and firms. This paper argues that this is what we should expect when skill is specific to technologies. The basic mechanism I propose is as follows. New technologies, in which skill is scarce, offer high returns to skill in order to provide incentives for rapid skill accumulation. In old technologies, however, there is an abundance of skilled workers, but firms in these technologies face problems filling vacancies at the entry level. Workers know that the technology is at risk of becoming obsolete and are thus reluctant to enter. In order to lure workers into these old technologies, firms have to compensate workers with higher entry wages. To develop these ideas, I build a vintage-human-capital model with endogenous human-capital accumulation. As in Chari & Hopenhayn [4], human capital is tied to a technology and is lost when the technology is phased out. In each vintage, different levels of human capital are used in production. Unlike in Chari & Hopenhaynʼs [4] two-period overlapping-generations model, however, human-capital accumulation is endogenous and the possibly infinite lives of individuals allow for rich patterns in tenure-wage profiles (shown in Fig. 1). Full-size image (7 K) Fig. 1. Tenure-earnings profiles over career. Figure options In the model, workers run through cycles of skill formation. They enter into a vintage, accumulate skills and finally re-locate to a new vintage once the technology becomes obsolete. If different skill levels are complementary, then workers enter all active vintages. This is true even for the oldest technologies because firms need to fill vacancies of low-skill workers. Since workers are ex-ante homogeneous, all technologies have to be equally attractive for workers at entry. This requires old technologies to pay higher entry wages in order to make up for the shorter duration of the career. This is apparent in the shortest earnings profiles in Fig. 1, which pertain to workers entering old technologies. Skill accumulation is fastest in the newest vintages, in which skilled labor is scarce. For these workers earnings growth is fastest, as we see in the longer profiles in Fig. 1. Entrants into frontier technologies have the lowest entry wages. They can reap the benefits from their skills over a long time, which makes these careers especially attractive. In equilibrium, entry into young technologies increases until the return of the career is equal to that of old technologies. Since skill is abundant in old technologies, human-capital accumulation is slowest and earnings profiles are flattest in old vintages. We also see in Fig. 1 that many workers experience wage losses towards the end of their career. These are driven by obsolescence, the fact that the relative price of skill falls as the vintage ages. Upon re-locating to new technologies, workers again experience sharp drops in wages as they lose their vintage-specific human capital. I find evidence supporting the model in a German matched employer–employee dataset when interpreting vintage age (in the model) as establishment age (in the data): young establishments have higher tenure premia, but pay lower average wages than old establishments. The model is also successful in predicting correlations of growth measures and the earnings structure: fast-growing industries, occupations and establishments display higher tenure premia than slow-growing ones, but pay lower wages on average.1 Finally, I calibrate the model to the cross-sectional tenure-earnings structure and the employment distribution across establishments. I find that there is complementarity between skills, but that this complementarity is weak. Workersʼ earnings growth is estimated to be due mainly to human-capital accumulation, whereas the relative scarcity of skill and productivity gains in their technology play quantitatively minor roles. The calibration results indicate that an acceleration in the pace of technological change – as has been measured over recent decades by Cummins & Violante [5] based on work by Gordon [8] – leads to an intensification in skill accumulation and a rise in the premium on skill. In relation to the previous literature, the model presented here is closest to Chari & Hopenhayn [4], but differentiates itself by endogenous human-capital accumulation, workersʼ infinite life time and the resulting detailed predictions on tenure-wage profiles. In terms of predictions, a key difference is that workers in my setting experience wage losses both during their tenure in a vintage and upon switching between vintages, whereas workersʼ wages are always an increasing function of time in their setting. Furthermore, since human-capital accumulation is exogenous in Chari & Hopenhayn [4], their setting cannot tell apart how much of wage growth is due to skill accumulation and how much is due to the scarcity of skill. The paper is also related to the wider literature on vintage capital (see [2] for an overview). Many issues, such as the incentives for the optimal scrapping time of a technology and the possibility of replacement echoes, are common to vintage capital and vintage human capital. Similar to vintage models are ladder models of technology. In these, all technologies are in principle available at all times, but firms choose to push the frontier only little by little because they face high switching cost when jumping to technologies that are much more advanced than the one they are currently using. Parente [16] studies a ladder model where agents face a trade-off between experience accumulation (following an exogenous learning curve) and obsolescence. In Violanteʼs [18] model, workers and machines of different vintages are matched in a frictional process. Again, workers accumulate skill according to a learning curve and experience skill losses that are increasing in the technological distance between machines. These human-capital losses induce wage losses upon job switches as in my model, but there is no obsolescence of skill: wages always increase during a workerʼs tenure in a vintage. Furthermore, these models do not predict that the premium on experience is higher in young technologies. Nelson & Phelps [15] have a view of human capital that is entirely different from, if not opposite to, vintage human capital. These authors posit that human capital facilitates the transmission and adoption of new ideas. Under this hypothesis, a high stock of human capital gives rise to frequent adoption of new technologies. Vintage-human-capital models take the opposite view: all skills are specific to a technology, so the adoption of new technologies destroys human capital. The Nelson–Phelps view suggests that an economy which adopts new technologies possesses high levels of human capital and workers experience steady wage growth. The vintage-human-capital model in this paper, however, tells us that fast technological growth is disruptive in the sense that workers experience abrupt wage losses and an ensuing spell of steep wage growth when they re-locate to new vintages.2 Some theoretical studies on the dynamics of organizations are also related to my model. Prescott & Boyd [17] develop an overlapping-generations model of coalitions, where experienced and inexperienced workers face a trade-off between production of output and training of young workers. An important difference between their model and mine is that no reallocation of workers from obsolete technologies to new ones occurs in their model. In a more recent contribution, Garicano & Rossi-Hansberg [7] model explicitly how tasks are shared within an organization and how organizations grow more complex over time. In my framework, however, technologies maintain the same structure over time; it is only the assignment of workers to tasks that changes. An entirely different class of models that is able to generate increasing earnings profiles are search-and-matching models. Burdett & Coles [3] show that firms in a frictional labor market optimally offer increasing wage schedules in order to prevent costly turnover. The predictions of the model presented here are different, however: in Burdett & Coles [3] changes in employer are crucial, whereas changes in the technology are what matters in my setting. The remainder of the paper is organized as follows: Section 2 presents the model, characterizes the competitive equilibrium and shows equivalence to a plannerʼs problem. Section 3 presents quantitative results from a calibrated version of the model. Section 4 concludes and discusses potential further applications of the framework.

This paper has studied a model of vintage-human-capital accumulation that matches key facts on the tenure-earnings distribution in a German data set. It provides a promising avenue for understanding the systematic variation in the earnings structure across establishments, industries and occupations. In the following, some potential applications of the framework are briefly discussed. A first proposed application is a macroeconomic one: the model relates the rate of embodied technological growth to the earnings structure, both at the industry and the economy-wide level. Previous versions of the paper had focused on this point, arguing that the steepening of age-earnings profiles and the concomitant rise in cross-sectional and time-series variance of earnings in many industrialized countries over the last decades could have been caused by a technological acceleration. A second aspect worth mentioning, which has only been touched upon in the previous discussion, is the productivity profile of a vintage over time (see the lower-right panel of Fig. 4). It displays the typical back-loaded shape that is often posited in an ad-hoc fashion for organization capital (see [1], for example). In fact, the model presented here can be construed as a micro-foundation for the way an organization increases its productivity over time and how it shares these productivity gains among its members. Finally, one could study the riskiness of human capital and technology choice for workers by introducing a stochastic component into the framework.