A new perspective on the firm size-growth relationship: shape of profits, investment and heterogeneous credit constraints

This paper shows that the diverging results obtained in the literature on the firm size-growth relationship can be reconciled in a very general theoretical framework featuring firm-level heterogeneity and investment decision. Three main elements determine the nature and the intensity of the relationship between firm-level size and investment: the shape of operating profits with respect to size, the shape of marginal returns to investment (in terms of size) with respect to initial size and the shape of marginal cost of investment with respect to size. Any difference across countries, industries or periods in one of these three dimensions can modify the sign and the intensity of the firm size-investment and the firm size-growth relationship at equilibrium. As an example, I show that in France, heterogeneous credit constraints, which affect the shape of the marginal cost of investment, can explain cross-sectoral variations in the firm size-investment and firm size-growth relationship over the 1996-2002 period. As a consequence, from a macroeconomic viewpoint, firm size distribution is, all else equal, more right-skewed in sectors where small firms are disproportionately credit constrained and small firms participate less to sectorial growth in these sectors. The analytical framework proposed in this paper is general enough to apply to the analysis of any heterogeneous response of economic agents.