Do the Largest Firms Grow the Fastest? The Case of U.S. Dairies

state equilibrium size occurs. Under mean reversion, growth rates are hypothesized to be
inversely related to firm size. In this case, larger firms grow relatively slower than
smaller firms, which implies that firms converge to a stable steady state equilibrium. The
remaining alternative is that cost economies are sufficiently great that larger firms grow
relatively faster than smaller firms. Similar to Gibrat’s law, this case implies that no
convergence to a steady state equilibrium occurs.

The bulk of prior empirical evidence, based mainly on corporate firm growth, has
failed to reject the random walk assumption of growth and has supported Gibrat’s law
(Geroski, 1998). The empirical evidence on the growth of farms, however, has been
inconclusive. For example, although several of the previously cited studies found
evidence of increasing returns to scale for larger farms, Kostov et. al. (2005) implicitly
rejected that hypothesis as well as explicitly rejecting Gibrat’s law in favor of the mean
reversion hypothesis for a sample of Irish dairy farms. Smaller farms grew at faster rates
than larger farms which suggested greater potential for extracting additional cost
economies among smaller farms.

We test whether incumbent dairy farms have grown in accordance with Gibrat’s law
or mean reversion hypotheses using a linear, fixed-time-effects regression between the
initial cohort sizes and their respective annual growth rates. The least squares dummy
variable (LSDV) model is specified as follows:

(1)     y_ι = βιD   + β2D1997 + β3_ζ + ^. ,             i = 1, . . ., 20

where yi is the annual compound growth rate of the cohort mean between its census and
the subsequent census, D1992 and D1997 are census dummy variables, r. is the mean size of

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