Qi has now become a function of the prices of the quasi-fixed inputs capital and (family) labor,
whereas also the intercept term (see the second right hand side term between brackets) and the
coefficients for the exogenous factors (see the term associated with Wk ) have been changed in
comparison with the short-run equations (3).
A complication in the model discussed above is how to handle the introduction of the milk
quota in 1984. Within the theoretical framework the rationing of milk output implies that that instead
of the price of milk the quota restriction becomes an explanatory variable. Moreover, microeconomic
theory indicates that imposing a constraint on one output in a multiple output technology will lower
the supply elasticities of the unregulated outputs (Le Chatelier/Samuelson effect). Bouchet et al (1989)
simply ignore the introduction of the milk quota, whereas Oskam (1992) based his empirical estimates
on the pre-quota period only. Jongeneel (2000, 167-188) took the after 1984-period as a starting point
and assumed a cost minimization approach with milk quantity as a quasi-fixed output variable,
whereas the endogeneity of milk output in the pre-quota period is accounted for by relying on an
instrumental variable estimator. The ideal approach would be to combine a profit maximization and
cost minimization model, taking into account the relationships between the two models (cf. Fulginiti
and Perrin, 1993). Although in theory possible, following this procedure one ends up with a highly
non-linear model which is difficult to estimate. In this study we choose a relatively simple ‘solution’
by respecifying the milk output supply equation (3) in an ad hoc way as
Q ≈ α + У λ...P + DUMquota λ рР + + +
i i i'≠milk ii' i' i,milk milk
i=milk
(3’)
У ηZ. + (1 - DUMquooa)0Qmil.+ У ФWk
j ij j milk k ik k
where DUM quota represents a dummy variable which has the value of 1 in the pre-quota period and
the value 0 from 1984 and onward. Qmilk is the quota level, and $ the parameter associated with the
quota variable.
Estimation
Data series and stationarity
In our analysis, outputs are real value of gross arable production and real value of milk and meat
production. Hired labor, fertilizer, and feed are variable inputs, the quantity of which is represented by
its real value. Family labor is seen as quasi-fixed inputs, as well as capital investments (buildings and
equipment). “Quasi-fixed” means they are fixed inputs in the short-run but variable and chosen
optimally in the long run. Investment in land consolidation and total expenditure on agricultural R&D
are defined as fixed inputs as they are exogenously given. To take into account of the accumulation
and depreciation effect of the R&D expenditure, we use the lagged sum of annual expenditure and the
discounted total expenditure from year 1949 until the previous year as a proxy. The variables used in
the estimation are listed in Annex A, which also provides some descriptive properties. To impose
homogeneity, prices are normalized with fertilizer price, and consequently the equation for fertilizer
was dropped out. A big event that is likely to have had an impact on agricultural production was the
introduction of (binding) milk quota in 1984.
In order to investigate the time series properties of the data, the Augmented Dickey Fuller test
was performed to identify the order of integration of the (individual) variables involved in the
postulated long run relationships. As is shown in Table 2 all series appear to be non-stationary and
integrated of order 1. As such this emphasizes that it is highly relevant to take the time series
properties into account in long term growth of agricultural output analysis2.