An Economic Assessment of Banana Genetic Improvement and ...

MODEL OF POTENTIAL DEMAND FOR CULTIVARS IN UGANDA 77
!
i ! Y vu
vi
= 0.
(6)
Corner (zero) solutions are possible for
specific cultivars, because the set of planted
cultivars need not be the same across households.
The scale constraint circumscribes
the size of the banana grove, where v - denotes
the total number of mats, measured in
the same units as:
vr
$ ! vi .
(7)
i ! vu
A set of non-negativity restrictions are
imposed:
xi $ 0, qi $ 0, vi
$ 0.
(8)
Kuhn-Tucker conditions are used to
solve for v i , the demand for planting material
from cultivar i = 1, . . ., N:
v v zC, z
P G
i = i]
, p, p , I, Tv , r,
vu
XHH, XF, XMh , (9)
where v i = 0 ∀i ∉ ṽ, and v i = v i ( .) ∀i ∈ ṽ such
that ω ⊂ ṽ : v i > 0 ∀i ∈ ω and s ⊂ ṽ : v i = 0
∀i ∈ s, where ω denotes the subset of cultivars
from the feasible set ṽ that the household
chooses to grow in positive numbers,
and s depicts a subset of cultivars available
but not grown by the household.
The demand for planting material of a
cultivar (v i ) is defined as the number of
banana mats of cultivar i grown by the
household. Bananas are grown in a mat
consisting of the mother plant and plantlets
and are vegetatively propagated from a
plantlet. Thus, the demand for a cultivar is
expressed as a count of plants rather than
as a share of crop area, as has often been
the case in the literature about adoption of
improved cereal cultivars. The demand for
a cultivar is determined by the bundle and
levels of consumption attributes and agronomic
traits it provides (z C ,z P ), household
characteristics (Ω HH , T,I), farm characteristics
(Ω F ,ˉv,ṽ), and market characteristics
(p B , p G , Ω M ), where p B are banana bunch
prices.
Observed outcomes are a combination of
interior and corner solutions. Corner solutions
arise for two reasons. One occurs when
cultivars are not locally available to households,
and it is exogenous (∀i ∉ ṽ). A second
reason is endogenous, occurring when cultivars
are available in the village, but households
choose not to grow them (∀i ∈ s). Each
household chooses to grow a subset of available
cultivars (∀i ∈ ω) in positive numbers
and at different levels. The solution to the
optimization problem consists of two components:
the choice to grow a subset of available
cultivars and their scale of cultivation, or mat
count. Because households often grow several
cultivars simultaneously to meet their
demand for attributes and traits, the empirical
analysis is based on a system of censored
equations, as defined in equation (9).
Econometric Approach
A limitation of most adoption studies is that
the censored dependent variable is defined
over actual choices only for cultivars that
are currently grown, creating a potential for
selection bias. This limitation is generally
imposed by the underlying data. The data
collected in Uganda allow for the recovery
of a more complete choice set of banana
cultivars by combining both revealed and
stated preferences for the attributes of cultivars
that are currently grown and no longer
grown, but known to the farmer.
The count of banana mats is zero for cultivars
not in the feasible set (∀i ∉ ṽ). Cultivars
not in the feasible set are those to which
farmers have never been exposed: they
have neither observed nor grown such cultivars.
The lack of exposure to these cultivars
precludes household awareness of
their attributes. Farmers are aware of the
attributes of the cultivars they currently
grow in positive numbers (ω ⊂ ṽ : v i > 0).
Farmers are also familiar with the attributes
of cultivars they do not currently