The modelling approach taken in the column is described as
In order to understand and draw implications from our empirical findings, we study a span-of-control model with a life-cycle structure. Every period, a large number of finitely lived agents are born. These agents are heterogeneous in terms of their initial endowment of managerial skills. The objective of each agent is to maximise the lifetime utility from consumption. In the first period of their lives, agents make an irreversible decision to be either workers or managers. In the model economy, differences in managerial quality emerge from differences in selection into management work, along the lines of Lucas (1978), and differences in skill investments, as we allow for managerial abilities to change over time as managers invest in their skills. Hence, we place incentives of managers to invest in their skills and the resulting endogenous skill distribution of managers at the centre of income and productivity differences across countries.Figure 1. Cross-country relationship between output per worker and lifetime growth of managers’ earnings relative to non-managers
In the model economy, skill investment decisions reflect the costs (resources that have to be invested rather than being consumed) and the benefits (the future rewards associated with being endowed with better managerial skills). Since consumption goods are an input for skill investments, a lower level of aggregate productivity results in lower incentives for managers to invest in their skills. Furthermore, managers face potential size-dependent distortions as in the literature on misallocation in economic development. We model size-dependent distortions as progressive taxes on the output of a plant, and do so via a simple parametric function that was proposed originally by Benabou (2002).
Size-dependent distortions have two effects in our setup.
- First, a standard reallocation effect, as the introduction of distortions implies that capital and labour services flow from distorted (large) to undistorted (small) production units;
- Second, a skill accumulation effect, as distortions affect the incentives for skill accumulation and thus, the overall distribution of managerial skills – which manifests itself in the distribution of plant level productivity.
Overall, under higher exogenous productivity and smaller distortions, managers invest more in their skills in equilibrium and operate larger and more productive plants. As a result, both output per worker and the gap between the earnings of managers to non-managers become larger, in line with the cross-country evidence presented in Figure 1
[...] we contend that in order to understand why countries like Italy and others lag behind the US in terms of output per worker, we should take into account that in the US, the incentives to invest in managerial skills are not as distorted. A young person who contemplates a managerial career takes into account distortions (regulations and other factors that act as implicit size-dependent taxes) that he or she will face when earning a higher compensation as a manager. In economies with larger distortions, individuals will either invest less in their managerial skills or choose a non-managerial career. In equilibrium, these reactions lead to lower managerial quality and output per worker, and to lower earnings growth of managers relative to non-managers, as the data indicates.