We have little information on the value of θ. In order to characterize θ , we estimate econometrically
the linkage between the decision to plant L hectares in sugar beet in one hand, and sugar prices and
quotas on the other hand. We assume that Cm is a linear (increasing) function of L and we include a
trend t to account for technical change, i.e. Cm=W(a+brL+ct), where a, b and c are coefficients to be
estimated and W is a price index of inputs. The variable θ is also assumed to depend in a linear way
on the in-quota and out-of quota sugar prices, i.e. θ = d+eQ+f(p1-p2), with Q being the level of quota,
d, e, f being coefficients to be estimated. Combining the expressions of Cm and θ , a synthetic
representation of the land acreage decision is therefore:
L = _1_I d. — aw — cWt + 1 p2 + L(pι — p2) + —Q I (7),
Wr I, b b b r2 b 1λ r2 b ^)
Econometric estimation of the coefficients of (7) makes it possible to estimate the cross subsidy
between in-quota sugar and C sugar, the production costs and the supply elasticities. In order to do so
we add an error term to equation (7), reflecting all other variables omitted in this specification. 2 We
use a Generalized Maximum Entropy (GME) estimation technique. This technique is robust for small
samples. It is also useful for integrating inequality constraints that are consistent with the theory (such
as b>0; θ ≥0, see the appendix). In addition, GME allows estimation of non linear functions, which
makes it possible to perform specification tests on a larger range of functional forms. The method
used is described in Golan et al (2001). We test the significance of estimates by the ratio of entropy
(Golan et al., 1999).
There is barely any literature on the properties of GME estimators under inequality constraints, but
there is little reason to believe the GME method solves the spurious regression problem if series are
non stationary and non cointegrated. We thus test for stationarity using three common tests. Results
are reported in the appendix. Because the EU sugar market organization has not changed over the last
years, there is only a limited variability in some of the observations. Even though the goodness of fit
looks satisfactory, the different stationarity tests are often inconsistent (see the appendix). That is,
econometric estimates are rather fragile. This is a limitation of the study, since the parameters d, e and
f play a role in the computation of production costs and rents. In each of the six countries producing
C sugar where (7) was estimated, at least one parameter entering in the expression of θ, i.e. f, and e, is
significantly different from zero. This suggests that there is indeed some form of cross subsidy
between C sugar production and the quota rent. The costs of production presented in Table 1 are
derived from the parameters estimates of equation (7). Estimates suggest low production costs in
Belgium, Germany and France, and high production costs in Italy and Spain. This is in line with the
2 The specification as in equation (7) performs poorly in the case of Italy. An alternative specification
is used θ=d+eQ+f(p1- p2)Q. In that case, e and f are not constrained.
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