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

In order to answer the first question, do dairy firms in the largest size cohorts grow at
least as rapidly as firms in medium size cohorts, we classified cohorts 4-9 as medium-
sized firms. These firms received agricultural revenue in 1992 ranging from $95,000 to
$330,000. Only firms in cohort 10 received more than $330,000 so this cohort was
classified as the larger firms. The mean size of the largest cohort grew more rapidly over
the 10-year period and over each 5-year period than the mean size of all other cohorts
except the smallest cohort. Thus, the answer to the first question is clearly yes.

The estimated parameters for the LSDV model, equation (1), are reported in Table 3.
From these parameter estimates, both of the hypotheses from the dynamic firm growth
literature can be tested. Support for Gibrat’s law (i.e., firm growth follows a random
walk) would be implied by the parameter on r being zero. Support for mean reversion
(i.e., firm growth is inversely related to initial size) would be implied by a significantly
negative parameter on r. The estimated parameter on this variable was both positive and
significant at the 1% level. Although its magnitude is small, both of the dynamic firm
growth hypotheses are rejected for the U.S. dairy industry in favor of the alternate
hypothesis that firm growth is positively related to initial firm size. The size distribution
is not converging to a stable steady state equilibrium.

Consequently, the nonparametric examination of rates of growth by cohort and the
results of the statistical hypothesis tests both render support to the alternative view that an
equilibrium firm size (i.e., one operating at the minimum point on the average cost curve)
has not yet been reached in the dairy industry.

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