Managers and productivity differences

Abstract

We document that for a group of high-income countries the life-cycle earnings growth of managers relative to non-managers is positively correlated with output per worker. We interpret this evidence through the lens of an equilibrium life-cycle, span-of-control model where managers invest in their skills. We use the model to quantify the importance of exogenous productivity differences and the size-dependent distortions emphasized in the misallocation literature. Our findings indicate that such distortions are critical to generate the observed differences in the growth of relative managerial earnings across countries. Distortions that halve the growth of relative managerial earnings, a move from the U.S. to Italy in our data, lead to a reduction in managerial quality of 27% and to a reduction in output of about nearly 7% – more than half of the observed gap between the U.S. and Italy. Cross-country variation in distortions accounts for about 42% of the cross-country variation in output per worker gap with the U.S.

Introduction

Development accounting exercises conclude that productivity differences are central in understanding why some countries are richer than others (Klenow and Rodriguez-Clare, 1997; Prescott, 1998, Hall and Jones, 1999, Caselli, 2005). What does determine cross country productivity differences?

A growing literature emphasizes differences in management practices as a source of productivity differences; see Bloom and Van Reenen (2011) and Bloom et al. (2016), among others. Management practices differ greatly, both across countries and across firms within a given country, and better management practices are associated with better performance (total factor productivity, profitability, survival etc.). U.S. firms on average have the best management practices, and the quality of management declines rather sharply as one moves to poorer countries.

In this paper, we present novel evidence on the earnings of managers and their relation with output per worker. We first document that age-earnings profiles of managers differ non-trivially across countries. Using microdata for a set of high-income countries, we show that earnings of managers grow much faster than the earnings of individuals who have non-managerial occupations in most countries. In the United States, the earnings of managers grow by about 75% during prime working ages (between ages 25–29 to 50–54), while the earnings growth for non-managers is about 40%. This gap is weaker in other countries in our sample. In Belgium, for instance, earnings growth of managers in prime working years is about 65% whereas earnings growth of non-managers is similar to the U.S. On the other extreme, we find that in Spain the earnings of non-managers grow more than those of managers over the life-cycle.

We subsequently document that there is a strong positive relation between the relative steepness of age-earnings profiles and GDP per worker: managerial earnings grow faster than non-managerial earnings in countries with higher GDP per worker. The correlation coefficient between the log of relative earnings and log-GDP per worker is 0.49, and stable across several robustness checks on our data. Since better management practices and the GDP per worker are positively correlated in the data, there is also a very strong positive relation between the earnings growth of managers relative to the earnings growth of non-managers and the quality of management practices across countries. The relation between the relative steepness of age-earnings profiles and GDP per worker remains robust when we control for individuals' educational attainment, sector of employment and self-employment status. Furthermore, these cross-country relations hold only when we look at the relative earnings growth of managers vs. non-managers (workers). There is no systematic relation between GDP per worker and the relative earnings growths of professionals (lawyers, engineers, doctors etc.) vs. workers, self-employed vs. workers, or college-educated versus non-college educated.

It is, of course, an open question how to interpret the differences in managerial practices and quality across countries. In this paper, we offer a natural interpretation. 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 and their incomes at the center of income and productivity differences across countries.

We study a span-of-control model with a life-cycle structure along a balanced growth path. Every period, a large number of finitely-lived agents is born. These agents are heterogeneous in terms of their initial endowment of managerial skills. The objective of each agent is to maximize the lifetime utility from consumption. In the first period of their lives, agents make an irreversible decision to be either workers or managers. If an agent chooses to be a worker, her managerial skills are of no use and she earns the market wage in every period until retirement. If an agent chooses to be a manager, she can use her managerial skills to operate a plant by employing labor and capital to produce output and collect the net proceeds (after paying labor and capital) as managerial income. Moreover, managers invest resources in skill formation and, as a result, managerial skills grow over the life cycle. This implies that a manager can grow the size of her production unit and managerial income by investing a part of her current income in skill formation each period.

Skill investment decisions in the model reflect the costs (resources that have to be invested rather than 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. We assume that economy-wide productivity grows at a constant rate. In this scenario, we show that the model economy exhibits a balanced growth path as long as the managerial ability of successive generations grows at a constant rate.

A central component of our model is the complementarity between available skills and investments in the production of new managerial skills. More skilled managers at a given age invest more in their skills, which propagates and amplifies initial differences in skills over the life cycle. This allows the model to endogenously generate a concentrated distribution of managerial skills. As in equilibrium more skilled managers operate larger production units, the model has the potential to account for the highly concentrated distribution of plant size in data.

We calibrate the model to match a host of facts from the U.S. economy: macroeconomic statistics, cross sectional features of establishment data as well as the age-earnings profiles of managers. We assume for these purposes that the U.S. economy is relatively free of distortions. We find that the model can indeed capture central features of the U.S. plant size distribution, including the upper and lower tails. It also does an excellent job in generating the age-earnings profiles of managers relative to non-managers that we document from the data.

We then proceed to introduce 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, which was proposed originally by Benabou (2002). Size-dependent distortions have two effects in our setup. First, a standard reallocation effect, as the enactment of distortions implies that capital and labor 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, the model provides us with a natural framework to study how differences among countries in aggregate exogenous productivity and distortions can account not only for differences in output per worker but also for differences in managerial quality, size distribution of establishments and age-earnings profiles of managers. In particular, observations on the relative earnings growth of managers allows us to discipline the level of distortions.

In consistency with the facts documented above, our model implies that lower levels of economy-wide productivity result both in lower managerial ability as well as in flatter relative age-earnings profiles. A 20% decline in aggregate productivity lowers investment in skills by managers by nearly 47%, leading to a decline in the average quality of managers of about 10%. With less investment, managerial incomes grow at a slower rate over the life cycle, generating the positive relation between output per worker and steepness of age-income profiles that we observe in the data. Lower investment by managers magnifies the effects of lower aggregate productivity, and output per worker declines by about 30%.

We then consider a menu of distortions and evaluate their effects on output, plant size, notions of productivity, and age-earnings profiles of managers. When we introduce the size-dependent distortions into the benchmark economy, we find substantial effects on output, the size distribution of plants and the relative steepness of managerial earnings. We show that such steepness is critically affected by distortions, and that distortions can eliminate all differences in the earnings growth of managers to non-managers. We find that distortions that halve the growth of relative managerial earnings (which would correspond to a move from the U.S. to Italy in our data), lead to a reduction in output per worker of about 6.9% – corresponding to more than half of the observed output gap between the U.S. and Italy. As a result of both misallocation and skill investment effects, managerial quality declines significantly by nearly 27%.

We find that these results are robust to the consideration of transitions between managerial and non-managerial work over the life cycle. We do this in detail in the Online Appendix, where we present an extension of the benchmark model with transitions between occupations.

We finally use the benchmark model to assess the combined effects of distortions and exogenous variation in economy-wide productivity. For these purposes, we force the model economy to reproduce jointly the level of output per worker in each country and the relative earnings growth of managers. We do so by choosing economy-wide productivity levels and the level of size dependency of distortions in each country to hit these two observations. We find that distortions are critical in generating relative earnings growth across countries. As a result, observations on relative earnings growth provide us with natural targets to discipline the level of distortions. Once we are able to reproduce both the level of GDP per worker and the relative earnings growth of managers within our model, we can assess the contribution of economy-wide productivity and distortions to cross-country differences in output per worker. To this end, we first allow economy-wide productivity to differ across countries and shut down the distortion channel, and then do the reverse (i.e. we allow distortions to vary and shut down differences in economy-wide productivity). We find that distortions alone account for about 42% of variation in GDP per worker gap with the U.S. across countries, while the rest of the variation is accounted for by differences in exogenous economy-wide productivity and interaction effects. The level of distortions that reproduce the relative earnings growth of managers in Italy (about half of the relative earnings growth in the US) are able to generate about 43% of the observed output gap with the US.

The current paper builds on recent literature that studies how misallocation of resources at the micro level can lead to aggregate income and productivity differences; see Hopenhayn (2014), Restuccia and Rogerson (2013) and Restuccia (2013) for recent reviews. Following Guner et al. (2008) and Restuccia and Rogerson (2008), we focus in this paper on implicit, size-dependent distortions as a source of misallocation.¹ Unlike these papers, we model explicitly how distortions and economy-wide productivity differences affect managers' incentives to invest in their skills and generate an endogenous distribution of skills. As a result, we show how data on relative earnings growth of managers can be used to infer the degree of distortions within our model.

Our emphasis on age-earnings profiles of managers naturally links our paper to the empirical literature on differences in management practices – see Bloom and Van Reenen (2011), and Bloom et al. (2014) for recent surveys – as well as to the recent development and trade literature that considers amplification effects of productivity differences or distortions due to investments in skills and R&D. Examples of these papers are Erosa et al. (2010), Rubini (2014), Atkeson and Burstein, 2010, Atkeson and Burstein, 2015, Gabler and Poschke (2013), Manuelli and Seshadri (2014), and Cubas et al. (2016), among others. Guvenen et al. (2014) study how progressive taxation affects the incentives to accumulate general human capital and, as a result, output for a group of high-income countries.

The importance of management and managerial quality for cross-country income differences have been emphasized by others before. Caselli and Gennaioli (2013) was possibly the first paper that highlighted the importance of managers for cross-country income differences. Caliendo and Rossi-Hansberg (2012) analyze how the internal organization of exporting firms changes in response to trade liberalization and the ensuing effects on average productivity. Gennaioli et al. (2013) build a span-of-control model of occupational choice with human capital externalities to study income differences across regions. Recent work by Bhattacharya et al. (2013), Roys and Seshadri (2014), Akcigit et al. (2016), and Alder (2016), among others, also study how managers and their incentives matter for aggregate productivity and the size distribution of plants and firms. Differently from these papers, we document novel facts on managerial earnings and use these facts to discipline our model economy. Our emphasis on cross-country differences in managerial earnings also relates our paper to Lagakos et al. (2016), who study differences in experience-wage profiles across countries and show that they are flatter in poorer countries. Similar to our findings, they highlight the fact that experience-wage profiles are steeper in cognitive occupations relative to non-cognitive ones. We focus on the relation between relative earnings growth of a particular group (managers) and the GDP per capita across countries, and interpret this relation within a quantitative model.

Our paper is also connected to work that documents cross-country differences in plant and firm-level productivity and size. Hsieh and Klenow (2009), Bartelsman et al. (2013), Hsieh and Klenow (2014) and Garcia-Santana and Ramos (2015) are examples of this line of work. Poschke (2017) builds a model of occupational choice with skill-biased change in managerial technology – managers with better skills benefit more from technological change – to account for cross-country differences in firm size distribution. Bento and Restuccia (2017) document cross-country differences in plant size in manufacturing and develop a model where distortions affect investments in plant-level productivity. In both their model and ours, distortions are amplified by endogenous investment decisions. They use this model to draw a mapping from plant size to aggregate productivity differences. Gomes and Kuehn (2017), like our paper, emphasize the importance of human capital for occupational choice, and use a span-of-control model to study how differences in educational attainments can account for cross-country differences in average firm size.

Finally, our paper is related to recent papers that emphasize the link between managerial incentives, allocation of talent and income inequality. Celik (2017) studies how income inequality can affect the allocation of talent between routine production and innovation in an overlapping generations models in which agents can spend resources productively to enhance their skills, or unproductively to create signals about their skills. More closely related to our paper, Jones and Kim (2017) study a model in which heterogeneous entrepreneurs exert effort to generate growth in their incomes and how such effort can create a Pareto-tail for top incomes.

Our paper is organized as follows. Section 2 documents facts on age-earnings profiles for a set of high income countries. Section 3 presents the model and the modeling of distortions. Section 4 discusses the calibration of the benchmark model. Section 5 presents the findings associated to the introduction of differences in exogenous economy-wide productivity and size-dependent distortions. In section 6, we evaluate the importance of skill investments and transitions between managerial and non-managerial work over the life cycle for our findings. Section 7 quantifies the relative importance of distortions vis-a-vis exogenous productivity differences in accounting for relative managerial earnings growth and output differences across countries. Finally, section 8 concludes.