Agriculture Reference
In-Depth Information
2
at the contract level, one that is not contaminated
with endogenous variability.
18
Finding such measures in studies of franchising and other
areas has proved difficult (Lafontaine and Bhattacharyya 1995), so most scholars have ei-
ther ignored them or relied on proxies that seem reasonable, but are not often clearly linked
to the underlying theoretical model and may be highly endogenous to the firm's behavior.
19
In order to purge completely the endogenous variability in farm production, a true mea-
sure of variability in the random input would require daily time series data on a composite
variable for each crop that included all natural factors from rainfall and temperature to sun-
light and insect populations. Such a composite variable would be a proxy for
reasonable empirical counterpart for
σ
and would
require measures of the quantities of these natural parameters. More important, it would
also require measures of the timeliness of these parameters. Such data are simply not avail-
able on a crop-by-crop basis. Timeliness is of particular importance for weather variables
such as rainfall.
20
Simple measures of rainfall would not, for example, provide information
about hail- or rainstorms during the middle of a harvest. It is entirely possible, for instance,
that a late August rainfall in South Dakota can severely harm a swathed wheat crop ready to
be combined and simultaneously aid a standing crop of corn or sunflowers to be harvested
later.
In lieu of this measurement problem, we use data on crop yield variability for the region
in which a plot of farmland is located, to approximate this ideal measure of exogenous
variability when there are large numbers of farmers in a relatively homogeneous region. To
illustrate, define a “region” as an area where
θ
farmers produce the same crop and face the
same exogenous forces of nature and use the same technology each year. For any individual
farmer producing crop
n
j
, the output or yield (per acre) for period
t
will be
Y
ijt
=
e
ijt
+
θ
jt
i
=
...
n
j
=
...
k
t
=
...
T
1,
,
;
1,
,
; and
1,
,
;
(6.6)
2
j
where
θ
jt
is distributed with mean 0 and intertemporal variance
σ
as in the theoret-
ical model. The random input
θ
jt
varies across time and crops but not across farms
Y
jt
=
within a region. Aggregating across
n
farmers, average per-period regional yield is
(
i
=
1
Y
ijt
)/n
, which simplifies to
n
e
ijt
n
Y
jt
=
+
θ
jt
(6.7)
i
=
1
The first term on the right-hand side of equation (6.7) approaches a time-independent
constant as
becomes
21
n
j
gets “large,” so the variance of average regional yield for crop
Var(Y
jt
)
=
Var(θ
jt
)
=
σ
2
j
.
(6.8)
