cohort i in the respective census, 1992 or 1997, andεi is independently and identically
distributed white noise.
The hypothesis tests are equivalent to a t-test of the significance ofβ3 . If this
parameter is significantly different from zero, the null hypothesis that cohorts grow in
accordance with Gibrat’s law is rejected. If it is not significantly negative, the null
hypothesis that cohorts grow in accordance with the mean reversion hypothesis is
rejected. If both hypotheses are rejected in favor of a significantly positive β3 , the
hypothesis that cost economies are sufficiently great that larger firms grow relatively
faster than smaller firms is not rejected.
To address the second and third questions about increasing diversification, farms are
separated into four sales categories in each census. The sales categories differ only by
the contribution of the farm’s milk and dairy product sales to its total agricultural sales:
90% or greater, 75-89.9%, 50-74.9%, and less than 50%. The sales category of each
incumbent and new entrant farm is determined for each census. Evidence of increasing
diversification over time and inferential evidence of economies of scope would occur if
subsequent censuses reveal increasing portions of farms in the lower sales categories and
decreasing portions in the higher sales categories. Positively correlated rates of increase
in lower sales categories with cohort size would provide evidence that larger farms
experience relatively greater economies of scope.
Data
Longitudinal data from the Census of Agriculture in 1992, 1997, and 2002 are used in
this study. Except for retired and residential/lifestyle farmers, the incumbent sample
includes all farms classified as dairy farms in the 1992 Census of Agriculture. It includes