An Economic Assessment of Banana Genetic Improvement and ...

78 CHAPTER 6
grow, but have grown in the past or currently
observe in the banana groves of their
neighbors (s ⊂ ṽ : v i = 0).
The definition of the dependent variable
imposes a unique shape on the underlying
distribution, which is strongly skewed to the
right. The concentration of the mass on the
corner (“excess zeros”) and the formulation
of the dependent variable in terms of integer
values (count of banana plants) dictate the
need for a count data approach (Cameron
and Trivedi 1998). One such approach is the
zero-inflated Poisson (ZIP) system, which
is used to predict the number of mats of
cooking banana cultivars grown, defined by
the set ṽ. 2
Zero inflated models, often employed to
jointly estimate censored systems of equations,
characterize the separate mechanisms
that generate corner solutions by assigning
different probabilities to the observed outcomes
based on a logit formulation:
exp_
ci
Zi
F_
ci
Zi
= .
1 + exp_
ci
Zi
The vector Z depicts the set of exogenous
characteristics explaining the probability
of each outcome, and γ i is the vector of
parameters to be estimated:
P[v i = 0] = F(γ i Z)
∀i ∉ ṽ
P[v i ∼ Poisson(μ i )] = 1 – F(γ i Z)
∀i ∉ ṽ
For all distinct cultivars (and attributes)
in the feasible set, the count of banana
plants is a non-negative integer distributed
Poisson with μ i = exp(β i X). The vector of
exogenous characteristics (X) includes the
consumption attributes and agronomic
traits of cultivars (which are not part of
Z), 3 with other household, farm, and market
characteristics. The ZIP formulation
accounts for the awareness of cultivar attributes,
as well as for levels of cultivar
demand.
Demand for planting material is estimated
jointly as a system of i = 1, . . . , N
independent censored count equations.
Models that treat correlated errors for large
systems of censored (count) demand equations
have not yet been sufficiently developed
for application (Englin, Boxall, and
Watson 1998; von Haefen, Phaneuf, and
Parsons 2004). In a nonstructural simultaneous
system, in any case, accounting for
error correlations would serve only to increase
estimation efficiency.
Dependent Variables
The spatial diversity of distinct banana cultivars
on farms and across the domain is
considerable (see Chapter 5 and Appendix
A). The dependent variable is defined as the
number of mats planted of seven candidate
host cultivars (ṽ for i = 1, . . . , 7), representing
the revealed demand for planting material
and almost half of the total mat numbers
of cooking cultivars in the survey domain.
A large number of cultivars are observed on
household farms in Uganda. No single cooking
cultivar occupies more than 9 percent of
the total number of banana plants grown by
all farmers surveyed. The vast majority of
cooking cultivars (75 percent) represent a
small share of all cooking banana plants in
the sample—each cultivar occupying less
than 1 percent. Because farmers grow on
average seven different cultivars per plantation,
a set of seven cultivars was taken as
representative.
The seven cultivars were selected from
among 67 potential host cooking cultivars
identified in the sample based on a combi-
2
The ZIP was found to perform better than the simple Poisson model. The Vuong statistic (distributed standard
normal) for the test of a ZIP model versus a standard Poisson model is 9.73, which favors the zero-inflated model
(Vuong 1989).
3
The difference in the composition of the sets represented by the vectors X and Z is data driven. Attribute
information is available for only the cultivars in the feasible set.