Revisiting Granular Models of Firm Growth

TL;DR

This paper revisits granular models of firm growth, linking firm size and growth rate statistics to diversification, and finds empirical patterns that challenge existing theoretical predictions.

Contribution

It introduces new theoretical insights into the relationship between firm size, diversification, and growth statistics, and identifies discrepancies between model predictions and empirical data.

Findings

Growth volatility conditioned on size is size-independent but has a thin tail.

Predicted Gaussian growth rate distribution remains fat-tailed across sizes.

Empirical patterns challenge the granularity hypothesis and suggest need for further research.

Abstract

We revisit granular models that represent the size of a firm as the sum of the sizes of multiple constituents or sub-units. Originally developed to address the unexpectedly slow reduction in volatility as firm size increases, these models also explain the shape of the distribution of firm growth rates. We introduce new theoretical insights regarding the relationship between firm size and growth rate statistics within this framework, directly linking the growth statistics of a firm to how diversified it is. The non-intuitive nature of our results arises from the fat-tailed distributions of the size and the number of sub-units, which suggest the categorization of firms into three distinct diversification types: well-diversified firms with sizes evenly distributed across many sub-units, firms with many sub-units but concentrated size in just a few, and poorly diversified firms consisting of only a small number of sub-units. Inspired by our theoretical findings, we identify new empirical patterns in firm growth. Our findings show that growth volatility, when adjusted by average size-conditioned volatility, has a size-independent distribution, but with a tail that is much too thin to be in agreement with the predictions of granular models. Furthermore, the predicted Gaussian distribution of growth rates, even when rescaled for firm-specific volatility, remains fat-tailed across all sizes. Such discrepancies not only challenge the granularity hypothesis but also underscore the need for deeper exploration into the mechanisms driving firm growth.