Misallocation is a key determinant of average establishment size and aggregate productivity across rich and developing countries
The enormous disparity in average incomes across countries has been the primary empirical fact motivating the study of economics for two centuries. In recent decades, a consensus has emerged that differences in productivity are the main proximate cause of this disparity (e.g. Jones 2016, Klenow and Rodriguez-Clare 1997). A number of theories have been proposed to account for productivity differences, with testable implications contrasted with available data. An important implication of recent theories of aggregate productivity with production heterogeneity or firm turnover is a prediction for how the average employment size of business establishments (or a related outcome, the rate of new business formation) varies across levels of development. But empirical cross-country observations about establishment size have been hindered by limited and ill-comparable data across countries.
Establishment size and development
A complete analysis of the determinants of average establishment size, along with their relevance for theories of development, requires comprehensive and internationally comparable data. To this end, in a recent paper (Bento and Restuccia 2018) we constructed a new dataset of average establishment size for multiple service-sector industries using hundreds of census reports and registries from 127 countries. We combined this data with comparable data for the manufacturing sector from Bento and Restuccia (2017) to provide a comprehensive picture of average establishment size in the non-agricultural sector across countries. Our measure of establishment size is the average number of persons engaged per establishment, where an establishment is defined as a physical location in which commercial activity takes place. A critical element in the construction of our dataset for international comparisons is the inclusion of all establishments regardless of whether they are registered or informal, have paid employees or are self-account businesses, as there is systematic variation in these categorisations across countries that can bias the measured relationship between establishment size and development.
A number of broad stylised facts emerge from these data.
- First, average establishment size in both manufacturing and services increases with average incomes across countries, measured by GDP per capita (Figure 1).
- Second, average establishment size tends to be larger in manufacturing than in services by a factor of three.
- Third, the income elasticity of average establishment size is similar in both sectors, about 0.3.
As a result, the ratio of average establishment size in manufacturing relative to services does not differ systematically between rich and poor countries.1
Figure 1 Average establishment size in manufacturing and services
Determinants of establishment size
To study the empirical determinants of average establishment size and the link with theories of development, we use data from a number of sources on country-specific variables such as population, sectoral employment, external financing to GDP, and a measure of misallocation, among others.2 Misallocation generically refers to a situation where factors of production are not allocated efficiently across heterogeneous producers. The specific measure we focus on is the productivity elasticity of distortions, that is, the gradient of distortions with respect to establishment productivity. We construct this measure for each sector using firm-level data for a large number of countries from the World Bank’s Enterprise Surveys. The higher the productivity elasticity of distortions, the more inefficiently factors are allocated across establishments in a sector-country which makes productive establishments relatively small and less-productive establishments relatively large. The data show that poor countries feature systematically larger productivity elasticity of distortions in both the manufacturing and service sectors than more developed countries (Figure 2).
Figure 2 Productivity elasticity of distortions and GDP per capita
The data indicate that average establishment size is unrelated to population and to sectoral employment, in both manufacturing and services. This finding is consistent with workhorse models of firm dynamics such as Hopenhayn (1992), which predict that higher population is associated with a proportionately higher number of establishments. It is inconsistent with models featuring variable markups of price over marginal cost, where markups are decreasing in the number of competitors. In these models, the number of establishments increases less than proportionately with population.3
The ratio of external financing to GDP is often used as an inverted proxy for the extent of financial frictions. Theory predicts that financial frictions should lead establishments to finance capital internally and the constraints should bite harder in manufacturing where setup costs are higher than in services, so that countries with more severe frictions should feature smaller establishments in each sector but relatively larger establishments in manufacturing relative to services, compared to more financially developed countries. The data do not support this prediction. In the data, while external finance is associated with larger establishments in both manufacturing and services, it does not relate with the size ratio across sectors. One theory we cannot directly assess due to the lack of specific data concerning cross-country differences in barriers to establishment entry. Several papers have argued that businesses in poor countries face high entry costs, which are predicted to lower the number of establishments and increase average establishment size. The data are not consistent with this theory, as establishments are smaller and more numerous in poor countries. This suggests the possibility that the cost of establishment entry is not in fact higher in poor countries, or at least that this is not a significant source of systematic variation of establishment size across countries.
Misallocation, productivity, and establishment size
A robust determinant of average establishment size that is consistent with theory is our constructed measure of misallocation. In both manufacturing and services, a greater productivity elasticity of distortions is associated with smaller establishments. Further, a larger gap between the observed elasticity in manufacturing relative to services is associated with a lower ratio of average size in manufacturing relative to services. Hsieh and Klenow (2014) and Bento and Restuccia (2017) theorise that when more productive establishments face larger distortions than less productive establishments, all establishments have less incentive to invest in productivity. Investment is predicted to decrease, both in absolute terms and relative to revenue, and as a result there is more entry and smaller average establishment sizes. A key insight from these theories is that the larger distortions faced by productive establishments effectively discourage productivity-enhancing investments, holding back the size of establishments. In Bento and Restuccia (2018), we incorporate this mechanism into a quantitative two-sector model of structural transformation. Consistent with the data, population in the model does not affect average size, while barriers to entry have the usual effect of increasing average establishment size. Although changes in average establishment size affect sectoral productivity and therefore relative sectoral employment shares, there is no feedback effect of sectoral employment on average establishment size.
We calibrate the model to match moments of aggregate and sectoral data for the US. We then posit that countries differ only in sector-specific distortions, which are restricted to the observed productivity elasticity of distortions for each sector in each country. We then calculate the impact of sectoral misallocation on each country’s average income, as well as aggregate productivity, employment, and average establishment size in each sector. As the productivity elasticity of distortions increases, the theory predicts less investment in productivity by establishments, more (smaller) establishments, greater misallocation of factor inputs across establishments, and lower GDP per capita. The variation in average establishment size generated by the model is quite close to the differences between rich and poor countries observed in the data. For example, using the average elasticity of distortions in poorer countries of 0.78 in manufacturing and 0.87 in services in the model implies that average establishment size is eight persons engaged per establishment in manufacturing and 1.5 persons in services, close to the data for the average in poorer countries of nine persons engaged in manufacturing and three in services. Moreover, the differences in per-capita income in the model that are driven by differences in misallocation account for about half of the observed variation in non-agricultural incomes between rich and poor countries (Figure 3).
Figure 3 GDP per capita in the model and in the data
We also use the model to infer the magnitude of entry costs in each sector and country from residual variation in average establishment size between the model and the data. Our finding is that entry costs are not systematically higher in poor countries – if anything, they are lower (Figure 4).
Figure 4 Implied establishment entry costs across countries
Average establishment size increases with the level of development across countries, although the ratio of size between manufacturing and services does not vary systematically with income per capita. These findings point to misallocation in the context of models with productivity investment by establishments as an important driver of establishment size and aggregate productivity differences between rich and poor countries. Understanding the specific policies and institutions driving misallocation in poor and developing countries is an essential task for future research (Restuccia and Rogerson 2017). Given the significance of misallocation in accounting for the large gap in non-agricultural incomes between rich and poor countries, our findings suggest enormous potential for future policy and institutional reform.
Bento, P and D Restuccia (2017), “Misallocation, establishment size, and productivity”, American Economic Journal: Macroeconomics 9(3): 267-303.
Bento, P and D Restuccia (2018), “On average establishment size across sectors and countries”, NBER Working Paper 24968.
Buera, F J, J P Kaboski and Y Shin (2011), “Finance and development: A tale of two sectors”, American Economic Review 101(5): 1964-2002.
Duarte, M and D Restuccia (2017), “Relative prices and sectoral productivity”, NBER Working Paper 23979.
Hopenhayn, H A (1992), “Entry, exit, and firm dynamics in long-run equilibrium”, Econometrica 60(5): 1127-1150.
Hsieh, C-T and P J Klenow (2014), “The life cycle of plants in India and Mexico”, Quarterly Journal of Economics 129(3): 1035-1084.
Jones, C I (2016), “The facts of economic growth”, p. 3-69, in Taylor, J B and H Uhlig (eds), Handbook of Macroeconomics, Vol. 2. Amsterdam: Elsevier.
Klenow, P J and A Rodriguez-Clare (1997), “The neoclassical revival in growth economics: Has it gone too far?”, NBER Macroeconomics Annual 12: 73-103.
Restuccia, D and R Rogerson (2017), “The causes and costs of misallocation”, Journal of Economic Perspectives 31(3): 151-74.
 The first two facts hold at a more disaggregated level for individual service-sector industries. But across industries the income elasticity of average establishment size varies substantially, for instance the elasticity is 0.13 in Wholesale Trade and 0.44 in Information and Communication.
 Population, sectoral employment, GDP, and external financing are from Penn World Tables v8.0, Duarte and Restuccia (2017), and Buera et al. (2011).
 As the number of establishments increases with population, markups shrink. The resulting drop in profit rates discourages entry and reduces the number of establishments relative to population.