lower than estimates by Houck et al. (p. 86, OLS
= -0.53,2SLS = -0.54,3SLS = -0.67, -0.68), who
used annual data for 1946-1966 (price variable =
soybean price∕soybean meal price). Our 2SLS
estimate of -0.10 is lower than Chambers and
Just’s 3SLS estimate of -0.20 (quarterly data,
1969:1-1977:2, deflated prices), close to
Helmberger and Akinyosoye’s 3SLS estimate
of -0.14 (annual data, 1948/49-1977/78, deflated
prices), but lower than Houck and Mann’s 2SLS
estimate of-0.32 (annual data, 1946-1964, nomi-
nal prices). Conway, using a stochastic coeffi-
cients approach to reestimate Chambers and
Just’s quarterly model (omitting the seasonal
variables), confirmed their estimated soybean
price elasticity of -0.20. All of these other pub-
lished estimates were from single-equation
estimations, which were subject to aggregation
bias, as are our OLS and 2SLS estimates.
Our -0.30 deflated soybean price elasticity
estimate for U.S. exports to Japan is lower than
Greenshields’ -0.65 (annual data, 1955-73, de-
flated import price index), but close to the -0.35
estimate by Meyers et al. (annual data, 1960/
61-1976/77; elasticities for 1973/74-1976/77,
price variable = soybean wholesale price index
in Japan).
Our soybean price elasticity estimate of -0.29
for the EC exceeds the -0.23 estimate by
Knipscheer et al. (semi-annual data, 1961-1976,
price variable = soybean meal price∕com price).
We would expect our elasticity estimate to
exceed theirs because their dependent variable
was total EC imports of both soybeans and
soybean meal (per animal feed unit), the de-
mand for which would be less elastic than for
total soybeans alone, which would be less elastic
than the EC demand for U.S. soybeans. (U.S.
soybeans constituted 77 percent of EC soybean
imports, 1974-1985 [Davison]). Also, we would
expect a one-year elasticity to exceed a six-
month elasticity.
CONCLUSIONS
Estimating export demand for U.S. soybeans
in a single equation using data aggregated across
all markets subjects the estimates to both ag-
gregation and simultaneous equation bias. The
prevalence of import equations estimated by
2SLS or 3SLS in the literature indicates aware-
ness of and correction for simultaneous equa-
tion bias. However, across-country aggrega-
tion bias seems to have attracted less attention.
If the aggregated variables and their para-
meters, plus the other exogenous variables, are
the same across the individual markets in the
correct specification, single-equation estima-
tion is the quickest and easiest way of estimat-
ing the elasticities. If the parameters on the
aggregated variables are not the same across
the markets, as this study suggests, then aggre-
gating individual-market data to estimate a
single OLS or 2SLS import equation imposes
unrealistic assumptions that may distort the
estimates of the true elasticities.
Testing for evidence of simultaneous equa-
tion bias before accepting 2SLS estimates could
obviate 2SLS distortions, which in this example
appear to exceed those from aggregation bias.
The multiple-equation weighted-market-
share approach, which reduces the problems of
aggregation and simultaneous equation bias
intrinsic to a single equation, requires more
databuthasthe advantage of providing market-
specific elasticity estimates that can be eval-
uated individually. Questionable equations or
estimates can be identified and isolated. Re-
searchers can then reestimate weak equations
or use market-specific elasticities judged more
appropriate.
135