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The role of scale economies in determining firm size in modern economies

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Abstract

Some three to four decades ago, it was generally accepted in economic literature that the average size of firms would continue to increase with progressive economic development. This would be the result of an ever increasing importance of exploitation of scale economies. However, since that time, small-scale self-employment rates have increased in many industrialized countries. This raises the question to what extent scale economies are still important in modern economies. Using data for 23 OECD countries over the period 1972–2008, we test the importance of scale economies in determining average firm size as proxied by the employment to self-employment ratio. We control for several other determinants of firm size, including the rate of urbanization. We also allow the relation to differ across levels of economic development. Our results suggest that notwithstanding the rise of small-scale self-employment observed in many countries over the last few decades, economies of scale and scope continue to play an important role in advanced economies.

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Notes

  1. Lucas’ theoretical model makes two plausible assumptions. First, it is assumed that the elasticity of factor substitution between capital and labor is less than unity, which is generally found to hold in empirical work (Hamermesh 1993). The second assumption is that Gibrat’s Law holds, which states that firm growth is independent of firm size. This condition is generally found to hold in practice, except for firms below the minimum efficient scale (MES): For this subset of firms, smaller firms are generally found to grow faster than larger firms, conditional on survival (Teruel-Carrizosa 2010). But even for this subset of firms, Gibrat’s Law may also hold once firm age is controlled for (Haltiwanger et al. 2013).

  2. Lucas provided evidence on the positive relationship between average firm size and the per capita capital stock by using employees per firm and per capita GNP as proxies. Indeed, the Lucas proposition refers to the effects of increases in per capita capital on the equilibrium number of entrepreneurs and then on the average number of employees per entrepreneur. For this reason, the more appropriate proxy for average firm size is the employment to self-employment ratio.

  3. Reasoning from self-employment prevalence, several scholars hypothesize that the size of the self-employment sector is related to a country’s stage of development (see, e.g., Acs 2006; Acs and Amorós 2008). In particular, countries with lower incomes tend to face high rates of necessity-based entrepreneurial activity, with limited capacity to create jobs. The predominance of this type of entrepreneurs in countries with lower incomes is associated with lower firm sizes.

  4. For the role of networks, see also Nijkamp (2003).

  5. Since in general the self-employment rate and average firm size are negatively related, a U-shape in terms of the relation between self-employment and economic development may be thought of as an inverse U-shape between average firm size and economic development, implying a decreasing average firm size for the most highly developed economies (contradicting the Lucas proposition). On the other hand, an L-shaped relation between self-employment and economic development implies a positive relation between average firm size and economic development (consistent with Lucas) but with an elasticity decreasing in value.

  6. Following the usual convention in macroeconomic studies of self-employment, we exclude the agricultural sector from the analysis. Agriculture is structurally different from the rest of the economy in that self-employment is the natural labor force status in this sector. Also, the sector is characterized by heavy subsidies and a relatively high proportion of unpaid family workers (Parker and Robson 2004).

  7. Average firm size is defined as total employment divided by number of firms. For reasons explained before, we use total employment divided by self-employment as a proxy, hence the denominator differs. However, since self-employment and number of firms are strongly positively correlated (as most active firms are run by only one entrepreneur and most entrepreneurs run only one firm), we consider the employment to self-employment ratio an accurate proxy of average firm size.

  8. In particular, in their model, it is assumed that investment in human capital accumulation ‘is denominated in terms of the output of the particular industry, in order to capture the idea that industry-specific learning requires some industry-specific inputs’ (Rossi-Hansberg and Wright 2007, p. 1642).

  9. Other factors such as business cultures and management styles could be also explored (Hofstede 1994). We do not include these variables in our model because of the lack of an adequate proxy.

  10. First, total employment is computed by subtracting the number of unemployed from the number of persons in the total labor force. Data on total labor force are taken from OECD Labour Force Statistics, while the number of unemployed is calculated using the standardized unemployment rate published in OECD Main Economic Indicators. Some missing values in the unemployment series are estimated using data from OECD Labour Force Statistics. Second, based on employment data by sector from OECD National Accounts, government employment and employment in the primary sectors of economy are excluded from total employment to arrive at private sector employment outside the agriculture, hunting, forestry and fishing industries.

  11. COMPENDIA is an acronym for COMParative ENtrepreneurship Data for International Analysis. It is one of the few cross-country databases on entrepreneurship rates that exist to date, next to the Global Entrepreneurship Monitor and the World Bank Group Entrepreneurship Survey (Marcotte 2013). See http://www.entrepreneurship-sme.eu/ for the data and Van Stel (2005) for a justification of the harmonization methods. This database has been used and acknowledged widely (see, among other studies, Armour and Cumming 2008; Carree et al. 2002, 2007; Davis 2008, p. 54; Koellinger and Thurik 2012; Nyström 2008; Parker et al. 2012; Praag and Stel 2013).

  12. Data taken directly from the OECD Labour Force Statistics suffer from a lack of comparability across countries and over time. In particular, owner–managers of incorporated businesses (OMIBs) are counted as self-employed in some countries and as employees in other countries. Also, the raw OECD data suffer from many trend breaks relating to changes in self-employment definitions (Van Stel 2005).

  13. The EPL index is only available from 1985 onward.

  14. For each country, the EPL index is calculated using 18 items, which can be grouped in the following areas: (i) employment protection against individual dismissal; (ii) requirements for collective dismissals; and (iii) regulation of temporary forms of employment.

  15. In general, the majority of the conventional unit root tests such as the Dickey-Fuller tests and the Phillips–Perron tests suffers from three problems. First, many tests have low power when the root of the autoregressive polynomial is close to but less than unity (DeJong et al. 1992). Second, most tests suffer from severe size distortions when the moving-average polynomial of the first-differenced series has a large negative autoregressive root (Schwert 1989; Perron and Ng 1996). Third, the implementation of unit root tests often requires the selection of an autoregressive truncation lag \(k\); however, as discussed in Ng and Perron (1995), there is a strong association between \(k\) and the severity of size distortions and/or the extent of power loss. Ng and Perron (2001) solved these problems and we refer to their article for further details.

  16. For Sweden, we find mixed evidence as three out of four Ng–Perron tests reject the null hypothesis of nonstationarity at the 5 % significance level but one test does not reject the null hypothesis, not even at 10 % level.

  17. Looking for cointegration relationships between GDP and macroeconomic variables is a common practice in some fields such us energy economics—Ozturk (2010) and Payne (2010) recently surveyed this body of empirical literature, environmental economics, with Esteve and Tamarit (2012a, b) as examples of recent works—applied macroeconomics—Magazzino (2012); Kumar et al. (2012) and Facchini and Melki (2013) among others—and the economics of self-employment—Carmona et al. (2010, 2012) or Congregado et al. (2012) among others.

  18. For 16 countries, the null hypothesis of zero cointegration relations is rejected at the 5 % significance level. In addition, for Denmark, Sweden, Switzerland, the UK and Canada, the null hypothesis is rejected at the 10 % level only.

  19. The problem of reverse causality is extremely important in this context, as the recent and fast growing body of literature on the effects of firm size on aggregate output shows—see, Gabaix (2011), Di Giovanni and Levchenko (2012) and Acemoglu et al. (2012), among others.

  20. Test results are available on request from the authors.

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Acknowledgments

The paper has been written in the framework of the research program SCALES carried out by Panteia/EIM and financed by the Dutch Ministry of Economic Affairs. We are grateful to Simon Parker for providing us with helpful comments on an earlier draft.

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Authors and Affiliations

  1. University of Huelva, Huelva, Spain

    Emilio Congregado & Antonio A. Golpe

  2. Panteia/EIM, Zoetermeer, The Netherlands

    André van Stel

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  1. Emilio Congregado
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Correspondence to Emilio Congregado.

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Congregado, E., Golpe, A.A. & van Stel, A. The role of scale economies in determining firm size in modern economies. Ann Reg Sci 52, 431–455 (2014). https://doi.org/10.1007/s00168-014-0593-5

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