  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.
