We study firm responses to a large-scale change in apprenticeship regulation in Colombia. The reform requires firms to train, setting apprentice quotas that vary discontinuously in firm size. We document strong heterogeneity in responses across sectors, where firms in sectors with high skill requirements tend to avoid training apprentices, while firms in low-skill sectors seek apprentices. Guided by these reduced-form findings, we structurally estimate firms' training costs. Especially in high-skill sectors, many firms face large training costs, limiting their willingness to train apprentices. Yet, we find substantial overall benefits of expanding apprenticeship training, in particular when the supply of trained workers increases in general equilibrium. Finally, we show that counterfactual policies that take into account heterogeneity across sectors can deliver similar benefits from training while inducing fewer distortions in the firm-size distribution and in the allocation of resources across sectors.
We develop a theory of career paths and earnings where agents organize in production hierarchies. Agents climb these hierarchies as they learn stochastically from others. Earnings grow as agents acquire knowledge and occupy positions with more subordinates. We contrast these and other implications with U.S. census data for the period 1990 to 2010, matching the Lorenz curve of earnings and the observed mean experience-earnings profiles. We show the increase in wage inequality over this period can be rationalized with a shift in the level of the complexity and profitability of technologies relative to the distribution of knowledge in the population.
In this note, I propose two alternative frameworks to study idea diffusion models with cohort structures. Both frameworks fix Lucas (2009) aggregation mistake while keeping the analytical tractability of the model and its insights. The frameworks differ in their assumptions on the meeting process. First I study a continuous arrival process where agents meet others at each point in time, and then a more commonly used Poisson process where meeting opportunities arrive stochastically at some given Poisson rate. I generalize the growth formula in Lucas (2009) and show both models yield the same growth rate on a balanced growth path. Moreover, I show the continuous arrival process can be viewed as the limit of Poisson processes where the meeting rate increases but the quality of meetings decreases.
An inventor’s own knowledge is a key input in the innovation process. This knowledge can be built by interacting with and learning from others. This paper uses a new large-scale panel dataset on European inventors matched to their employers and patents. We document key empirical facts on inventors’ productivity over the life cycle, inventors’ research teams, and interactions with other inventors. Among others, most patents are the result of collaborative work. Interactions with better inventors are very strongly correlated with higher subsequent productivity. These facts motivate the main ingredients of our new innovation-led endogenous growth model, in which innovations are produced by heterogeneous research teams of inventors using inventor knowledge. The evolution of an inventor’s knowledge is explained through the lens of a diffusion model in which inventors can learn in two ways: By interacting with others at an endogenously chosen rate; and from an external, age-dependent source that captures alternative learning channels, such as learning-by-doing. Thus, our knowledge diffusion model nests inside the innovation-based endogenous growth model. We estimate the model, which fits the data very closely, and use it to perform several policy exercises, such as quantifying the large importance of interactions for growth, studying the effects of reducing interaction costs (e.g., through IT or infrastructure), and comparing the learning and innovation processes of different countries.
In this paper, I study the convergence of the wage distribution between the South and the Non-South of the US. I focus on workers inside metropolitan areas and show that in 1940 the South not only had lower average wages but also a more disperse log wage distribution. After 1940, there was a remarkable convergence in the entire wage distribution between the two regions, and by 2010 they were almost identical. I propose a spatial model with a continuum of heterogeneous agents to account for the initial differences in the wage distribution. In the model, technological differences across regions made low skilled workers relatively less productive in the South, leading to lower average wages and more dispersion in the wage distribution. I calibrate the model splitting data into low-skill services, manufacturing, and high-skill services. The calibration suggests differences in low-skill services and manufacturing technology account for most of the initial disparities in the wage distribution. The spatial model also predicts high skilled workers sorted into the Southern cities, as observed in 1940's data.