Testing our predictions

In this Chapter, we test the propositions derived from the stochastic Generalized Proportional Growth (GPG) model described in Chapter 3, along four dimensions: the size distribution of firms, the growth rate distribution, the relationships between firm size, and both mean and the variance of the growth rates. We take advantage of PHID, a unique dataset that decomposes sales figures at the firm level into its constituent products, a crucial property for the multi-level structure of our model, where firm’s growth is the outcome of product-level dynamics. The version of PHID used for this book covers sales figures of over 130,000 pharmaceutical products marketed by 4,921 companies in 21 countries over 1998-2008. In addition to PHID, we use alternative datasets to assess robustness of results across various industrial sectors and national economies: manufacturing firms in OECD countries (ORBIS); publicly-traded manufacturing firms in the U.S. (Compustat); the universe of French firms (FICUS); the Gross Domestic Product (GDP) of 195 countries from 1960 to 2011 (World Bank). We combine two different approaches, commonly used in the literature, to challenge the consistency of a theoretical stochastic model. The first approach compares the theoretical distribution with the empirical distribution of a variable, with particular focus on the tails of the distribution. The second approach makes use of econometric techniques to model the relation between firm’s growth and relevant variables such as size, age, innovation, diversification and others. Results show that the hypothesis of lognormal distribution for firm’s size is rejected for all the datasets analyzed, and that size distribution generally flows a power law with exponents in agreement with the GPG model. Moreover, the best fit for the distribution of growth rates is achieved with the GPG model with two-levels of aggregation. The standard deviation of growth rates is found to decrease with firm’s size, with approximate power law dependence in line with GPS predictions. Finally, findings from the econometrics analysis show that the average growth rate decreases with firm size, even after controlling for firm’s survival, and that innovation is crucial to explain such departure from Gibrat’s Law.