SOUTHERN JOURNAL OF AGRICULTURAL ECONOMICS
DECEMBER, 1989
testing Foraggregationand simultaneous
BIAS IN U.S. SOYBEAN EXPORT EQUATIONS
Carlos A. Arnade and Cecil W. Davison
Abstract
Most previous estimates of elasticities of
export demand for U.S. soybeans have ema-
nated from single import equations subject to
aggregation and simultaneous equation bias.
This analysis tests U.S. soybean export data for
aggregation and simultaneous equation bias and
divides the aggregate data into six market
equations to reduce these biases. Elasticity
estimates from the six equations are compared
with elasticity estimates from single equation
OLS and 2SLS estimations using the same
aggregate data. Results suggest that distor-
tions from unjustified 2SLS estimation may
exceed those from aggregation bias.
Key words: aggregation bias, simultaneous
equation bias, soybean exports,
price elasticity, market share.
Bilicymakers, exporters, and researchers
are interested in export elasticity estimates
that most accurately reflect importers’ re-
sponses to changes in important explanatory
variables, particularly price. Previous estimates
of the short-run price elasticity of demand for
U.S. soybean exports, reviewed by Gardiner
and Dixit, range from inelastic (-0.14) to elastic
(-2.00) with no consensus on the appropriate
range and are estimated from aggregate data
(summed across countries), which could distort
the estimates with bias from aggregation and
simultaneity.
This analysis tests for both aggregation bias
and simultaneous equation bias in import de-
mand equations. The article then presents elas-
ticity estimates compiled from specific mar-
kets, in order to reduce the effects of aggrega-
tion and simultaneous equation bias. Finally, it
compares a weighted sum of market specific
elasticity estimates with estimates from single
equation ordinary least squares (OLS) and two-
stage least squares (2SLS) estimations.
BACKGROUND
Typically, elasticity estimates vary because
of differences in: estimation methods, model
specification, the time period of estimation, the
type of data (quarterly or annual), and the quality
of data available to researchers. Variations in
specification, time periods, and data are ex-
pected among published elasticity estimates,
and can obscure variations due to methods
employed and data aggregation.
Research summarized by Gardiner and Dixit
used data aggregated across importing coun-
tries in one or a few equations (characterized as
a single equation approach in this article) to
obtain estimates of export demand elasticities.
For example, Houck et al. used aggregate data
in a single import demand equation and ob-
tained elasticity estimates by OLS, 2SLS, and
3SLS estimators. Chambers and Just used
aggregate data in single import demand equa-
tions as part of a 3SLS system of simultaneous
equations. Aggregate data are subject to inher-
ent problems that include the following:
(1) Simultaneous equation bias is likely when
U.S. exports are aggregated. Imports of
U.S. soybeans by one or two countries
may not influence U.S. prices, but imports
by all countries may.
(2) Aggregation bias -will occur if the parame-
ters on the linearly aggregated exogenous
variables are not the same across individ-
ual demand equations (Zellner).
(3) A single equation requires a broad ex-
change rate index, whereas country-
specific exchange rates can be used in indi-
vidual market equations. Thus, market-
Carlos A. Arnade and Ceeil W. Davison are Agricultural Economists, Agriculture and Trade Analysis Division and Commodity
Economics Division, ERS, U.S. Department of Agriculture.
Senior authorship is not assigned.
The authors thank Joe Glauber, Stephen Haley, Paul Johnston, Stephanie Mercier, Stephen Miller, and three anonymous Journal
referees for helpful comments and suggestions.
Copyright 1989, Southern Agricultural Economics Association.
129