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Small Business Economics

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04.05.2018

Firm size and productivity from occupational choices

verfasst von: Luis Medrano-Adán, Vicente Salas-Fumás, J. Javier Sanchez-Asin

Erschienen in: Small Business Economics | Ausgabe 1/2019

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Abstract

We model the distributions of firm sizes and of firms’ total factor productivity (TFP) as outcomes of a market equilibrium from the occupational decisions of individuals with different entrepreneurial skills, of working as employees, employers, or solo entrepreneurs. The model explains empirical regularities such as (i) the positive cross-section correlation between average size of firms and average labor productivity of countries, (ii) the positive association between size and TFP of firms in an economy, and (iii) the power law distribution of firm sizes. Two parameters of the model, one that measures the organizational size diseconomies and other related to the dispersion of the distribution of entrepreneurial skills in the population, appear as main determinants of the differences in firm sizes and in productivity, across economies and among firms within an economy. The results of the paper should be of interest for the design and evaluation of firm-size-dependent policies.

Vorheriger Artikel What keeps them going? Socio-cognitive entrepreneurial career continuance

Nächster Artikel Family-centered goals, family board representation, and debt financing

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The model assumes complete and symmetric information. The occupation choice between entrepreneurs and employees has also been explained by the different degree of risk aversion of individuals and uncertain pay-offs from entrepreneurship (Kihlstrom and Laffont 1979). When individuals learn their entrepreneurial skills from experience, then the occupational choice equilibrium is the convergence point of a dynamic process (Jovanovic 1982; Hopenhayn 1992).

In Garicano (2000) and Garicano and Rossi-Hansberg (2006), entrepreneur-managers contribute to production using their specialized knowledge to help employees solve complex problems. In the market equilibrium, there is an optimal matching of employees and managers, while in Rosen (1982), all employees can be perfectly exchanged among employers.

In Lucas (1978), the cost of capital c is equal to the shadow price of the constraint on total capital available. Rosen (1982) does not include capital as a production input. Other papers, Gollin (2008) and Guner et al. (2008), solve endogenously for the discount factor in a market equilibrium where consumers make saving decisions and producers make investment decision. We assume that financial markets optimally separate consumption from production decisions, and the users’ cost of capital is the slope of the separating line.

The proof is not reported to save space but is available from the authors on request.

In general, if θ ≠ 1 and g(e) ≠ e, the distribution of TFP will be an increasing non-linear transformation of the left-truncated distribution of entrepreneurial skills.

Suppose, for example, that we want to analyze the effect of parameter β on total output, TY_T^*. The analytical expression of the derivative of TY_T^*with respect to β (computed with the software Wolfram Mathematica) has thousands of terms, which have different signs and depend on seven exogenous parameters and three endogenous variables. It is humanly impossible to prove whether the sign of this derivative is positive or negative.

Hsieh and Klenow (2009) find that their estimated TFP for the firm in the 90th percentile of the size distribution of plants in the USA is 8.8 times the TFP estimated for the plant in the 10th percentile (22.4 for India and 11.5 for China). It is much higher than the ratio estimated here, 1.7, although in the calculations they assume constant returns to scale, while in our model, returns to scale are decreasing.

The proof is available upon request.

In general, this equation has two positive solutions, but the largest one is not an equilibrium since the corresponding values of e₂ and w do not satisfy the necessary conditions b ≤ e₁ ≤ e₂, and w ≥ 0.

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Titel: Firm size and productivity from occupational choices
verfasst von: Luis Medrano-Adán
Vicente Salas-Fumás
J. Javier Sanchez-Asin
Publikationsdatum: 04.05.2018
Verlag: Springer US
Erschienen in: Small Business Economics / Ausgabe 1/2019
Print ISSN: 0921-898X
Elektronische ISSN: 1573-0913
DOI: https://doi.org/10.1007/s11187-018-0048-y

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