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Learning, career paths, and the distribution of wages

A large part of people’s wages rewards the knowledge embedded in them that they use in a production endeavour. Knowledgeable individuals specialise in hard, complicated tasks, while less knowledgeable ones specialise in simpler, more common tasks. This column uses a dynamic model of knowledge accumulation over time and career paths to find an underlying cause for wage inequality in the US over the last few decades. A good explanation for the wage inequality is the discrepancy between the rate of technological change and the rate at which the distribution of knowledge catches up.

Knowledge is an essential factor of production. A large part of the compensation of individuals rewards the knowledge embedded in them that they use in a production endeavour. So, as with any input, producing efficiently requires using the knowledge of individuals in a way that minimises its cost. Doing so requires assigning individuals with different levels of knowledge to play distinct roles in the production process. Knowledgeable individuals specialise in hard, complicated tasks, while less knowledgeable ones specialise in simpler, more common ones.  Rosen (1982), Garicano (2000), Garicano and Rossi-Hansberg (2004, 2006), and Caliendo and Rossi-Hansberg (2012) have formulated theories of the formation and characteristics of knowledge-based hierarchies that solve this optimisation and derive the resulting wages that individuals with different amount of knowledge receive in equilibrium. Furthermore, Caliendo et al. (2015) have shown that the implications of these theories hold well in the data.

Clearly, if individuals with different levels of knowledge play distinct roles in the production process, individual career paths will progress through these roles as agents acquire knowledge through schooling, experience, and other forms of learning. A worker that starts with little experience and knowledge will start at the bottom of the organisation. A variety of learning experiences over time will make him progress through the hierarchy and reach higher management layers, with more subordinates and higher wages. Part of the process of knowledge accumulation that determines the career paths of these individuals is probably the result of purposeful learning (Roys and Seshadri 2014, Lucas and Moll 2014). Another part, perhaps even more important, is the result of casual, more random interactions between individuals that lead to learning (Lucas 2009). Some individuals are lucky and find good mentors that help them develop quickly, while others have bad influences from whom they learn little. The fortunate ones move quickly up the hierarchy and earn more; others stay at the bottom jobs throughout their lives until retirement.

In a new paper, we model an economy that optimally forms an endogenous set of production hierarchies (Caicedo et al. 2016). In contrast to the knowledge-based hierarchy literature mentioned above, we aim to develop a dynamic model in which individuals progress through different jobs throughout their lives and where the distribution of knowledge evolves over time as agents learn from each other. To do so, we modify the theory of knowledge based-hierarchies to make production possibilities heterogeneous – projects that are harder and require more knowledge also provide higher returns. The resulting reward structure can be calibrated to match the distribution of wages in the US economy quite well. For example, the model can capture the high wages in the right tail of the distribution. The model also results in a distribution of agents across management layers that is roughly consistent with the US economy. As for individual career paths, the calibration of the model yields concave average wage-experience profiles that closely resemble the data.

With such a model in hand, it is natural to ask what type of changes in the economy could have led to the increases in wage inequality experienced in the US economy for the last few decades. We focus particularly on the period 1990-2010. Our theory can accommodate a variety of changes. For example, it accommodates increases in communication technology that allow managers to lead larger teams of subordinates (increases in the span-of-control). Another example is technological changes that increase the mass of very hard and profitable projects, as well as the availability of experts to solve them.  We show that none of these potential technological changes can yield wage distributions and age-earnings profiles that match the evolution of the US economy. Increases in communication technology that lead to larger spans-of-control have opposite effects on wage inequality, and increases in the quality and difficulty of projects together with the mass of experts to solve them results in small changes in the organisational structure and too much wage inequality at the top of the distribution.

The technological change that fits the data well is one in which the distribution of projects shifts relative to the distribution of knowledge; namely, a technological change rapid enough to make projects harder and more profitable without allowing the distribution of knowledge to catch up. Of course, in a balanced-growth path, the distribution of knowledge and the distribution of projects in the economy improve continuously as agents learn from each other. However, this is a change that goes beyond the evolution of these distributions in the balance growth path. Such a technological change opens new production possibilities that are highly profitable, but the economy has too few highly skilled agents to take full advantage of them. This type of increased scarcity of high skilled agents makes the individuals that possess such skills earn more, but it also leaves behind many agents with talents that are less useful for the new tasks required in production. Hence, this shift in technology increases wage inequality and makes wage-experience profiles steeper.  We show that such a technological change is able to match the US experience well. Furthermore, it results in an organisational structure that relies more on managers, resulting in thinner hierarchies with smaller spans-of-control – something we observe in the US data as well.

Taking this finding at face value causes one to inquire about the source of this technological change. As fascinating as such a question is, our work is not yet ready to answer it. The distribution of projects is an exogenous input in our theory, not an endogenous outcome. Of course, such a technological shift is reminiscent of the theories of biased-technological change of Acemoglu, and others. To obtain a balanced-growth path the distribution of production projects evolves in parallel with the endogenous distribution of knowledge resulting in a constant growth rate. These shifts could be easily rationalised with a standard theory of skill-biased technical change. However, the shift in the distribution of knowledge, which we identify as a potential culprit for the increases in wage inequality between 1990 and 2010, results in declines in output relative to trend. A benevolent planner would not choose such a technological change. It leads to winners and losers, but also to overall lower total output relative to trend. In our view, exploring the source of these specific potential changes in technology holds the key to understanding the evolution of wage inequality in a modern knowledge-based economy.   


Caicedo, S, R Lucas Jr, and E Rossi-Hansberg (2016), “Learning, Career Paths, and the Distribution of Wages”, CEPR Discussion Paper 11213

Caliendo, L, and E Rossi-Hansberg (2012), “The Impact of Trade on Organization and Productivity”, Quarterly Journal of Economics, 127:3, 1393-1467

Caliendo, L, F Monte, and E Rossi-Hansberg (2015), “The Anatomy of French Production Hierarchies”, Journal of Political Economy, 123:4, 809-852

Garicano, L, (2000), “Hierarchies and the Organization of Knowledge in Production”, Journal of Political Economy, 108:874-904

Garicano, L, and E Rossi-Hansberg (2006), “Organization and Inequality in a Knowledge Economy”, Quarterly Journal of Economics, 121:1383-435

Garicano, L, and E Rossi-Hansberg (2004), “Inequality and the Organization of Knowledge”, American Economic Review, 94:197-202

Lucas, R (2009), “Ideas and Growth”, Economica, 76:1-19. 11

Lucas, R, and B Moll (2014), “Knowledge Growth and the Allocation of Time”, Journal of Political Economy, 122:1-51

Rosen, S (1982), “Authority, Control, and the Distribution of Earnings”, The Bell Journal of Economics, 13:2, 311-323

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