MODELLING ENERGY SAVING TECHNOLOGY CHOICES IN DUTCH GLASSHOUSE HORTICULTURE - Economics of Sustainable Energy in Agriculture - page 41

3. EMPIRICAL MODEL

The structural form estimation of (4.2), (4.3) and (4.5) would require a
solution for the technology specific value functions by, for example,
numerically iterating on the Bellman equations (4.3) conditional on some
functional specification for the one period returns and trial values for
the parameters The parameter values could then be updated estimating
the behavioural equations given by (4.5). The structural form estimation is
computationally very demanding since it requires numerical simulation of
the expected values for the next period's optimal value functions, i.e. for
expected maximums for the future revenue steams that are stochastic and
dependent on the technology choices 2 .
A computationally less demanding approach is to normalise the
boundaries of the distribution of the errors of the choice equations by the
value of one technology and approximate only the differences of the
technology specific value functions by a reduced form representation

( e.g.

Dorfman 1996).
In this study the farmer's choices are estimated in reduced form for
two reasons. First, given the small number of years in the panel data it
would be problematic to accurately simulate the dynamic structure of the
technology specific and stochastic returns processes. Large simulation
errors would bias the estimates for the expected next period optimal value
functions because the optimal value function is highly non-linear function
of the simulation errors (Keane and Wolpin 1994).
Second, because the choices are based on the differences of the
technology specific returns streams (not on the level of each returns
stream) the reduced form is empirically tractable. Approximation errors
between the structural optimal stopping model and the reduced form
models are found negligible (Provencher 1997) 3 . The results of Pietola and
Oude Lansink (2001) also indicate that the structural form simulation does
not significantly add information in estimating the conditional choice
probabilities. A reduced form specification has also been the standard in
the earlier studies on discrete technology choices ( e.g. Green et al. 1996).
The method that is used to estimate the reduced form model is
referred to as Simulated Maximum Likelihood (see Arias and Cox (1999)
for an introduction). In our application, at time t, firm i chooses
if

Where, is a vector of instruments, and is a

vector of parameters 4 . Similarly, is chosen if at