An Economic Assessment of Banana Genetic Improvement and ...

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92 CHAPTER 7
Table 7.1 Results of the likelihood ratio test for the null hypothesis that the
coefficients on the two management decisions are equal
Management practice
Tobit
model
Value of the log likelihood function
Probit
model
Truncated
regression
Likelihood
ratio test
p-value
Mulching –90.358 –147.68 134.69 0.000
Manure –110.90 –163.50 91.90 0.000
general structure of the demand equation
can be expressed as:
y* = a' Z + m m | Z~N (0,1). (7)
Z represents a vector of explanatory variables
cast on the right hand side of equation
(6), m is a vector of unobserved heterogeneity
and a is a vector of parameters to be
estimated. At the time of the survey, demand
was not observed for some households,
and hence we cannot estimate the
structural equation. Instead we estimate a
reduced form and focus on two management
decisions, the discrete decision (to use
or not to use) and the extent of use.
Several problems were encountered
when estimating the demand of soil fertility
management technology. First, the extent of
use decision (δ*) is observed only when the
outcome from the decision to use or not to
use the technology is positive. Missing data
for a set of explanatory variables lead to a
censoring of the demand for the management
practices for which the discrete decision
is nonpositive (Maddala 1983; Greene
2000; Wooldridge 2002).
A tobit regression model has been widely
used in estimation when the dependent variable
is observed within a limited range
(Greene 2000). Underlying the tobit model
is the assumption that the coefficients on the
probability and extent of adoption are the
same (Greene 2000). Thus, the tobit model
fails to separate the two decisions that characterize
the adoption of a divisible technology.
The decision to use and the extent of
use are also likely to be influenced by different
factors (Wooldridge 2002).
To test whether the tobit model is a suitable
representation of the processes affecting
the use of mulching or manure technology,
probit, tobit, and truncated regressions
were estimated for each of the two technologies.
The null hypothesis of equal coefficients
was tested using the likelihood ratio
statistic, where the restricted regression is
the tobit model and the unrestricted regression
is the combined probit and truncated
regression. Results are summarized in Table
7.1. For both manuring and mulching, the
statistical significance of the test-statistic
leads to rejection of the null hypothesis that
the coefficients are equal. The data therefore
support separate estimation of the use
and extent of use decisions. 0 (8)
y = 0 otherwise.
As defined above, d* is the optimal observed
area share of the bananas under the
technology, X is a vector of explanatory
variables, and E(e⏐X) = 0; it is assumed
that the unobserved heterogeneity in the
vector e is uncorrelated with the exogenous
variables.
The second problem is that the soil fertility
management decisions are also conditioned
on the farmers’ perceptions of the soil
fertility problems, a random variable. Farm-