A cross-sectional analysis of growth and profit rate distribution: the Spanish case

Vidal-Tomás, David and Ruiz-Buforn, Aba and Blanco-Arroyo, Omar and Alfarano, Simone (2020): A cross-sectional analysis of growth and profit rate distribution: the Spanish case.

Abstract

We analyse the time evolution of the empirical cross-sectional distribution of firms profit and growth rates. In particular, we analyse the conditional properties of the empirical distributions depending on the size of the firms and business cycle phase. In order to do so, we employ the Laplace distribution as a benchmark, further considering the Subbotin and Asymmetric Exponential Power (AEP hereafter) distributions, to capture the potential asymmetry and leptokurtosis of the empirical distribution. Our results show that the profit rates of large firms are characterised by an asymmetric Laplace distribution with parameters largely independent of the business cycle phase. Small firms, instead, are characterised by the AEP distribution, which accounts for the conditional dependence of distribution on the phase of the business cycle. We observe that the largest firms are more robust to downturns compared to the small firms, given their invariant distributional characteristics during crisis periods.

• Item Type: MPRA Paper
• Language: English
• Keywords: Profit rates ; Growth rates ; Firm size ; Business cycle ; Laplace distribution ; Asymmetric Exponential Power distribution
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General; D - Microeconomics > D2 - Production and Organizations > D21 - Firm Behavior: Theory; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E10 - General; L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L10 - General

References

Alfarano, S. and Milakovic, M. (2008). Does classical competition explain the statistical features of firm growth? Economics Letters, 101(3):272–274.

Alfarano, S., Milakovic, M., Albrecht, I., and Kauschke, J. (2012). A statistical equilibrium model of competitive firms. Journal of Economics Dynamics and Control, 36(1):136–149.

Amaral, N., L.A. Buldyrev, S., Havlin, S., Maass, P., Salinger, M., Stanley, H., and Stanley, M. (1997). Scaling behavior in economics: the problem of quantifying company growth. Physica A, 244(1):1–24.

Axtell, R. L. (2001). Zipf distribution of us firm sizes. Science, 293(5536):1818–1820.

Bachmann, R. and Bayer, C. (2014). Investment dispersion and the business cycle. The American Economic Review, 104(4):1392–1416.

Blanco-Arroyo, O., Ruiz-Buforn, A., Vidal-Tomas, D., and Alfarano, S. (2018). On the determination of the granular size of the economy. Economics Letters, 173:35–38.

Blanco-Arroyo, O., Ruiz-Buforn, A., Vidal-Tomas, D., and Alfarano, S. (2019). Granular companies and regional breakdown: An analysis of the spanish case. Studies of Applied Economics, 37(2):109–124.

Bottazzi, G. (2004). Subbotools user’s manual: For version 0.9. 7.1, 8 september 2004. Technical report, LEM Working Paper Series.

Bottazzi, G., Dosi, G., Lippi, M., Pammolli, F., and Riccaboni, M. (2001). Innovation and corporate growth in the evolution of the drug industry. International Journal of Industrial Organization, 19(7):1161–1187.

Bottazzi, G., Li, L., and Secchi, A. (2019). Aggregate fluctuations and the distribution of firm growth rates. Industrial and Corporate Change, 28(3):635–656.

Bottazzi, G. and Secchi, A. (2003). Why are distributions of firm growth rates tent-shaped? Economics Letters, 80(3):415–420.

Bottazzi, G. and Secchi, A. (2006). Explaining the distribution of firm growth rates. The RAND Journal of Economics, 37(2):235–256.

Bottazzi, G. and Secchi, A. (2011). A new class of asymmetric exponential power densities with applications to economics and finance. Industrial and Corporate Change, 20(4):991–1030.

Bottazzi, G., Secchi, A., and Tamagni, F. (2014). Financial constraints and firm dynamics. Small Business Economics, 42(1):99–116.

Buldyrev, S. V., Growiec, J., Pammolli, F., Riccaboni, M., and Stanley, H. E. (2007). The growth of business firms: facts and theory. The Journal of the European Economic Association, 5(2-3):574–584.

Coad, A. and Planck, M. (2012). Firms as bundles of discrete resources–towards an explanation of the exponential distribution of firm growth rates. Eastern Economic Journal, 38(2):189–209.

Coad, A., Segarra, A., and Teruel, M. (2013). Like milk or wine: Does firm performance improve with age? Structural Change and Economic Dynamics, 24:173–189.

De Veirman, E. and Levin, A. (2011). Cyclical changes in firm volatility. Technical report, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.

Dosi, G. and Nelson, R. R. (2010). Technical change and industrial dynamics as evolutionary processes. Handbook of the Economics of Innovation, 1:51–127.

Erlingsson, E. J., Alfarano, S., Raberto, M., and Stef´ansson, H. (2013). On the distributional properties of size, profit and growth of icelandic firms. Journal of Economic Interaction and Coordination, 8(1):57–74.

Fu, D., Pammolli, F., Buldyrev, S. V., Riccaboni, M., Matia, K., Yamasaki, K., and Stanley, H. E. (2005). The growth of business firms: Theoretical framework and empirical evidence. Proceedings of the National Academy of Sciences of the United States of America, 102(52):18801–18806.

Gabaix, X. (2011). The granular origins of aggregate fluctuation. Econometrica, 79(3):733–772.

Gaffeo, E., Gallegati, M., and Palestrini, A. (2003). On the size distribution of firms. additional evidence from the g7 countries. Physica A, 324:117–123.

Geroski, P. A. and Gregg, P. (1997). Coping with recession: UK company performance in adversity, volume 38. Cambridge University Press.

Gibrat, R. (1931). Les in´egalit´es ´economiques. Recueil Sirey.

Haltiwanger, J. C. (1997). Measuring and analyzing aggregate fluctuations: the importance of building from microeconomic evidence. Federal Reserve Bank of St. Louis Review, 79(3):55.

Higson, C., Holly, S., and Kattuman, P. (2002). The cross-sectional dynamics of the us business cycle: 1950–1999. Journal of Economic Dynamics and Control, 26(9):1539–1555.

Higson, C., Holly, S., Kattuman, P., and Platis, S. (2004). The business cycle, macroeconomic shocks and the cross-section: The growth of uk quoted companies. Economica, 71(282):299–318.

Holly, S., Petrella, I., and Santoro, E. (2013). Aggregate fluctuations and the cross-sectional dynamics of firm growth. Journal of the Royal Statistical Society: Series A (Statistics in Society), 176(2):459–479.

Jaynes, E. T. (1978). Where do we stand on maximum entropy? Roger D. Rosenkrantz (Ed.), E.T. Jaynes: Papers on Probability, Statistics and Statistical Physics, Kluwer Academic Publishers, Dordrecht, Netherlands.

Mundt, P., Alfarano, S., and Milakovi´c, M. (2016). Gibrat’s law redux: think profitability instead of growth. Industrial and Corporate Change, 25(4):549–571.

Mundt, P., F¨orster, N., Alfarano, S., and Milakovic, M. (2014). The real versus the financial economy: A global tale of stability versus volatility. Economics: The Open-Access, Open-Assessment E-Journal, 8(2014-17):1–26.

Mundt, P. and Oh, I. (2019). Asymmetric competition, risk, and return distribution. Economics Letters, 179:29–32.

Penrose, E. and Penrose, E. T. (2009). The Theory of the Growth of the Firm. Oxford university press.

Riccaboni, M., Growiec, J., and Pammolli, F. (2011). Innovation and corporate dynamics: a theoretical framework. University Library of Munich.

SABI (2020). Data from System of Analysis of Iberian Balance Sheets, https://sabi.bvdinfo.com/.

Smith, A. (1776). An Inquiry into the Nature and Causes of The Wealth of Nations. Petersfield: Harriman House.

Stanley, M., Amaral, L., Buldyrev, S., Havlin, S., Leschhorn, H., P., M., Salinger, M., and Stanley, H. (1996). Scaling behaviour in the growth of companies. Nature, 379:804–806.

Subbotin, M. (1923). On the law of frequency of errors. Matematicheskii Sbornik, 31:296–301.

Sutton, J. (1997). Gibrat’s legacy. Journal of Economic Literature, 35:40–59.