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Abstract

This paper demonstrates that heterogeneity in firms' promotion of human capital accumulation is an important determinant of life-cycle earnings inequality. I use administrative micro data from Germany to show that different establishments offer systematically different earnings growth rates for their workers. This observation suggests that that the increase in inequality over the life cycle reflects not only inherent worker variation, but also differences in the firms that workers happen to match with over their lifetimes. To quantify this channel, I develop a life-cycle search model with heterogeneous workers and firms. In the model, a worker's earnings can grow through both human capital accumulation and labor market competition channels. Human capital growth depends on both the worker's ability and the firm's learning environment. I find that heterogeneity in firm learning environments account for 40% of the increase in cross-sectional earnings variance over the life cycle, and that this mechanism is especially important for young workers. I then show that differences in labor market histories partially shape the worker-specific income profiles estimated by reduced-form statistical earnings processes. Finally, because young workers do not fully internalize the benefits of matching to high-growth firms, changes to the structure of unemployment insurance policies can incentivize these workers to search for better matches.

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Introduction

Earnings dispersion across workers rises over the life cycle: there is more inequality among older workers than among younger workers. Studying the life-cycle patterns of inequality provides clues about the sources of overall earnings dispersion. This paper argues that nearly half of the rise in inequality over the life cycle is caused by differences in the firms by which workers are employed. At some firms, earnings grow systematically faster, even controlling for the growth that is specific to their employees. As different workers spend different amounts of their lives in high wage-growth firms, earnings inequality rises over the life cycle. This finding shows that persistent earnings inequality is not purely a matter of intrinsic heterogeneity among workers, but also a matter of luck.

A long literature has studied the sources of earnings inequality. An important contributor is human capital disparities across workers. These differences between individuals may be present at labor market entry and develop further as workers gain job experience./1

Another source of earnings inequality comes from search frictions. Similar workers looking for jobs differ in the types of offers they receive. This determines whether they are able to match with high-paying firms and how much their earnings grow on the job. As a result, inequality in earnings arises due to luck in the search process./2

In this paper, I offer a new insight into the interactions between these two sources of inequality, and quantify how it contributes to the rise in earnings inequality over the life cycle. To do so, I delve into the sources of earnings growth. Motivated by the empirical finding that the growth rate of earnings differs across employers, I argue that luck of the draw in employer, due to search frictions, matters for a worker's growth rate of human capital. I build a search model of the labor market in which earnings can grow due to: differences in ability across workers, labor market competition, and differences in human capital promotion, or "learning environments," across firms. I use the model along with micro data to disentangle these channels and find that the firm component of human capital is a core contributor to the increase in cross-sectional earnings variance over the life cycle. I then show that these results matter for understanding the determinants of the labor income process, and for the role of policy in alleviating the inefficiencies induced by search frictions.

Using an administrative matched employer-employee data set from Germany, I show that establishments offer systematically different earnings growth rates to their workers. My data set allows me to observe the complete workforce of a subset of establishments and track workers through other jobs and through unemployment. I employ a two-way fixed effects specification to attribute growth in earnings to both worker and establishment effects. I document significant variation in earnings profiles between establishments. This finding suggests that similar workers, even workers who may have inherently similar earnings growth rates, will experience different earnings trajectories depending on the establishment they match with.

To understand the economic mechanisms that lead to this finding, I build a life-cycle search model of the labor market. The model features workers who search for jobs at firms that differ along two dimensions, productivity and learning environment./3

These firm attributes correspond to two reasons that can explain why earnings growth rates differ between firms. The first, productivity, affects a labor market competition channel. More productive firms are better able to raise wages to prevent workers from moving to competitor firms. The second, learning environment, governs the extent to which firms promote human capital accumulation. Some firms offer faster speeds of on-the-job learning, which increases productivity, and therefore wages in both the current job and subsequent jobs.

The key features of the model generate heterogeneity in earnings profiles across workers, even for similar workers employed at different firms. Workers in the model search on and off the job, accumulating human capital via learning-by-doing as they gain job experience. The speed of human capital growth for a given worker depends temporarily on the learning environment of the firm that the worker is matched with and permanently on the worker's level of learning ability. Apart from human capital growth, a worker's earnings growth is also impacted by labor market competition. Because workers can receive outside job offers while employed, they can also obtain earnings increases by moving to better paying firms or by using competing job offers to bargain for raises at their current firm.

The model implies that workers face trade-offs between a firm's productivity and learning environment. Because their ability to accumulate human capital declines over the life cycle, workers change how they value these two components between different ages. Learning environment is highly valued early in life, when human capital accumulation is highest. Workers who match to firms with better learning environments early in life receive permanently higher earnings throughout their lifetime. As human capital accumulation declines later in life, learning environment becomes irrelevant and workers only make decisions based on the firm's productivity. These changes in trade-offs drive the job search dynamics in the model and have quantitative impacts on the major sources of earnings dispersion across workers.

Identifying the parameters of this model is challenging because there are many distinct components to earnings growth: worker ability, firm productivity, and firm learning environment. In order to discipline the parameters, I construct new moments from the data that are separately informative about each of these growth components and use an indirect inference technique to match them in the model. The first set of moments disentangles firm productivity from learning environment and worker ability by comparing the earnings growth patterns of different-aged workers employed at the same firm. Assuming human capital accumulation is low for older workers, I construct an informative measure of human capital accumulation across firms by exploiting the differences in within-job earnings growth of older versus younger workers. The second set of moments disentangles the worker component from the firm components of growth. I use two-way (worker and firm) fixed effects models on earnings growth, while taking into account the biases associated with estimating these statistical models in both the data and structural model.

I use the model to decompose the life-cycle profile of the log earnings variance. I find that the increase in earnings variance is almost entirely driven by dispersion in human capital. This result comes from both the heterogeneity in worker learning ability and firm learning environment.

These two features mean that human capital grows at heterogeneous rates across workers. As a result, the dispersion in human capital increases as workers age. On the other hand, the dispersion in the components of earnings coming from labor market competition decreases. This is because workers settle into a more homogeneous set of higher paying firms and extract a larger share of the match surplus. These are the standard forces present in a textbook job ladder model. A version of this model without heterogeneity in the growth rates of human capital would miss the rise in the earnings variance.

I next assess the contribution of differences in firm learning environments and find that they account for 41% of the increase in the life-cycle earnings variance. This result comes from a counterfactual in which I turn off all heterogeneity in worker learning ability. In this setting, all human capital disparities arise solely due to luck in which firms workers meet. In addition, the impact of firms is is concentrated early on in workers' careers. For example, after the first 15 years in the labor market, about 85% of earnings dispersion is due to human capital differences. Of this, half of the additional variance relative to labor market entry comes from the long-term impacts of workers' previous matches. As workers are able to catch up to each other and move to better firms, the role of firms declines.

My findings imply that firms play an important role in the formation of workers' human capital. This result sheds light on the properties of reduced-form labor income processes. Statistical models of earnings estimated from panel data on workers find that individuals appear to face different earnings profiles. These tend to be attributed to permanent worker heterogeneity, like learning ability./4

Using the earnings "data" generated by the model, I estimate some of the commonly-used labor income processes from the literature. I found that the model is able to microfound these income processes. I also find that the income processes pick up profile heterogeneity, even in the version of the model without permanent differences in worker ability. This signifies that some of the heterogeneity in income profiles commonly attributed to worker effects come from the series of firms a worker matches with over their lifetime, which is not detectable in the panel data sets that are typically used in this context.

The model also has implications for worker welfare and the design of unemployment insurance (UI) policies. My findings also signify that some of the variation in earnings growth comes about due to search and matching frictions (or differences in luck), and not due to permanent, individual heterogeneity in skill. The jobs workers accept, particularly early on in life, have permanent impacts on human capital and hence lifetime inequality. When workers have limited bargaining power, they do not fully internalize the long-term impacts of human capital accumulation. As a result, the decentralized allocation of workers to firms is inefficient. The structure of UI in the model impacts workers' ranking of firms, which means it can be used to affect the allocation.

I find that age-dependent UI schedules can improve welfare and reduce lifetime inequality relative to the benchmark model. The best UI schedules offer the highest benefit levels to young workers and reduce them with age. This UI benefit pattern induces young workers to be selective in which jobs to accept early on, particularly along the learning environment dimension. Welfare improves since the matches formed result in persistently higher lifetime earnings. Inequality is reduced by giving all workers a chance to find jobs that will boost their earnings throughout their lives. This experiment offers an example in which UI policies impact long-term outcomes, in contrast to most other settings where they are used as insurance for short-term episodes like job loss.

1.1 Related literature

This paper is related to several strands of literature. Understanding the formation of human capital has been a longstanding research goal, going back to Becker (1962), Ben-Porath (1967), and Heckman (1976). A more recent complementary set of work, most notably, Herkenhoff et al. (2018) and Jarosch, Oberfield and Rossi-Hansberg (2019), explores how the quality of one's coworkers impacts human capital. This study, in contrast, views firm differences in earnings growth as coming from intrinsic firm characteristics. I also emphasize the ability of this channel to account for life-cycle features of earnings, and identify the model via establishment fixed effects. Luttmer (2014) also looks at a setting where people learn from others, but there is randomness in individual discovery. The resulting variation is likely similar to what I explore, but does not rely on search.

This work also relates to the long literature on the determinants of life-cycle earnings profiles (for a survey, see Rubinstein and Weiss (2006)). There has been more recent work, such as Bagger et al. (2014) and Bowlus and Liu (2013), that decomposes the contributions of human capital growth, labor market competition, and bargaining power to life cycle earnings growth. This work performs a similar decomposition, but emphasizes how heterogeneous firm learning environments shape the earnings variance profile. Another recent paper by Karahan, Ozkan and Song (2019) features worker-level heterogeneity in human capital and job ladder risk and assesses the contribution of each to lifetime earnings inequality. Here, I allow the human capital growth component of earnings to differ by firm as well.

Another paper that has explored the forces behind the earnings variance profile is Huggett, Ventura and Yaron (2011). They use exogenous human capital shocks and worker learning ability heterogeneity in a consumption/savings model to generate the increase in life-cycle variance. More broadly, the focus of the paper is to study the roles of initial conditions (level of human capital, learning ability, wealth) versus luck (shocks to human capital) in determining heterogeneity in lifetime income. In contrast, this work explores another "luck" channel that contributes to the rise in life-cycle earnings variance: the types of firms workers meet in a frictional labor market. Because my focus is only on forces that could explain the rise in variance, I only concentrate on a single initial condition, differences in learning ability./5

This paper also draws features from several prominent labor search models. The wage bargaining protocol adopts the sequential auction framework of Cahuc, Postel-Vinay and Robin (2006). Some of its features are also reminiscent of of Bagger et al. (2014) and Jarosch (2015). Like Bagger et al. (2014), I allow for deterministic human capital growth and adopt piece-rate wage contracts. As in Jarosch (2015), firms differ according to two dimensions: there, productivity and separation rate; here, productivity and learning environment. My model can also be cast as a special case of Lise and Postel-Vinay (2015). They allow workers and jobs to have multi-dimensional attributes, and workers can acquire skills at different rates that depend on the job they are matched with. I interpret my dimensions of worker and firm heterogeneity in different ways, which restricts how they enter output and human capital accumulation, compared with Lise and Postel-Vinay (2015)'s more general setup. In addition, Engbom (2020) features a model in which workers in some jobs endogenously choose more training than in others, in line with my empirical findings.

The results of this study also connect to the vast literature that estimates statistical models of the labor income process. Some classic examples are MaCurdy (1982), Abowd and Card (1989), and Meghir and Pistaferri (2004)./6

Other studies have explored the possibility of endogenizing this labor income risk. Two potential sources are human capital (Huggett, Ventura and Yaron (2011)) and job-to-job mobility (Low, Meghir and Pistaferri (2010), Lise, Meghir and Robin (2016)). These are both present in my model and enable it to generate the main characteristics of the stochastic labor income process.

This study also closely relates to the work of Hause (1980), Baker (1997), Guvenen (2009), and Guvenen (2007) on income profile heterogeneity. Using panel data on workers' income, this research finds evidence that individuals face heterogeneous income growth rates. Here, I propose a potential source of this variation, in which the earnings profiles of different firms partially piece together a given individual's life-cycle earnings path.

Finally, my work also represents an extension to the existing body of work relating firms and labor market outcomes (Abowd, Kramarz and Margolis (1999); Card, Heining and Kline (2013)). This strand of research documents dispersion in firm-specific wage premia that impact the level of wages for all employees within the firm. In many countries, this firm component of inequality is a major contributor to overall inequality./7

Here, I document a similar fact, but for wage growth. In addition, this literature has focused on the impacts of contemporaneous firm/worker relationships. This paper introduces one mechanism in which a worker's previous employers impacts his or her earnings in the future.

There have also been studies that link firms to earnings dynamics such as Friedrich et al. (2019) and Engbom and Moser (2020). Their goal is to quantify the transmission of firm-level shocks to workers' stochastic wage processes, finding a large contribution of firms to the variance of wages over the life cycle and throughout time. In contrast, I study the persistent impacts of firm-specific wage growth trends, yet also find a substantial role for firms in accounting for the cross-sectional life-cycle variance.

The remainder of this paper proceeds as follows. Section 2 presents some motivating evidence from the data that demonstrates the extent of the establishment heterogeneity in earnings profiles. Section 3 describes the search model that allows for sources of earnings growth to differ between firms. In Section 4, I discuss how I use the data to identify the new features that my model introduces. Section 5 discusses the parameter values and model fit. Section 6 presents the model's predictions and counterfactuals for the life-cycle variance of earnings. Section 7 estimates reduced-form earnings processes from the model's earnings outcomes. Section 8 shows how changes in unemployment benefits schedules affect worker outcomes in the model. Section 9 concludes.

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Conclusion

In this paper, I demonstrated that heterogeneity in learning environments between firms are major drivers of lifetime earnings inequality across workers. Motivated by the fact that firms offer systematically different earnings trajectories to the workers they employ, I developed a search model in order to disentangle the various sources of earnings growth heterogeneity. In the model, earnings can grow due to differences in worker ability, firm learning environment, and firm productivity.

In my setting, two similar workers can end up with very different levels of human capital due to differences in the firms by which they are employed over their lives. The model also introduced key trade-offs between jobs that drive workers' decisions over the life cycle. Because the ability to accumulate human capital is highest for the young, they highly value a match with a firm with a good learning environment; eventually this firm attribute becomes irrelevant and workers switch to climbing the ladder in productivity. I exploited these age differences in sources of earnings growth in the data to discipline the relevant sources of heterogeneity in the model.

I showed that heterogeneity in firm learning environments are responsible for 41% of the increase in the cross-sectional earnings variance over the life cycle. Over their lives, workers are exposed to different opportunities for human capital accumulation. In this way, search frictions have a direct impact on worker heterogeneity. This result signifies that firms play an important role for firms in shaping workers' human capital. Their effects are especially important for younger workers. Although workers do eventually catch up to each other by moving to better firms, early labor market experiences persistently impact lifetime earnings.

My results speak to the importance of initial conditions upon labor market entry and offer a channel through which firm/worker matches have long-term impacts. I explored two settings that illustrate the broader importance of these findings. I showed that firms shape some of the estimated profile heterogeneity across workers, suggesting that labor income processes should account more explicitly for temporary firm/worker matches and incorporate matched employer-employee data. The fact that firms matter also means that part of earnings growth is not driven by irreparable inherent worker heterogeneity. I demonstrated how unemployment insurance policy can balance the trade-offs between searching for good matches and human capital accumulation, and improve welfare at the same time.

This research points to several avenues for future work. Guvenen (2007) shows that imperfect knowledge of income growth rates has ramifications for the life-cycle profile of consumption. There, agents do not know their income growth rate when they enter the labor market but learn about it after seeing income realizations. I introduce a different type of uncertainty over income growth rates that stems from which firms a worker meets. Future work should further explore the significance of this kind of risk and how to distinguish it from the learning story.

There are other mechanisms in which firms may impact the earnings growth of their employees and have lasting effects. Some firms may offer better connections to other firms. Individuals at these firms may face higher arrival rates or be more likely to contact better employers. This explanation could point to another way in which search frictions impact the long-term outcomes of workers, without directly affecting workers' skills. To fully understand the long-term impacts of temporary matches, this story could be a worthwhile next step.

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