Contribution of Economics to Design of Sustainable Cattle Breeding Programs in Eastern Africa: A Choice Experiment Approach

Pn (θ) = ∫ Ln (β) g (βθ) dβ                                                         (4)

Since there is no closed form solution for equation 4 in the estimation, P_n (θ) is approximated
by simulations by summing over values of β generated by Halton draws. Halton draws are
superior to random draws in simulations. 100 Halton draws produce the same approximation
as 1000 pseudo-random draws (Train, 2003). The simulated probability is presented thus;

Pn (θ) =¹ ∑ Sn (β^{r θ} )                                                                 (5)

r r =1,..,R

Where r is the number of draws of β from g(β_n | θ) and P^~_n is the simulated probability of
person n’s choices. The simulated log-likelihood function is SLL(θ) = ∑_n ln(P^~_n (θ)) and the
estimated parameters are those that maximize the function. Various population distributions
from which β is drawn can be assumed; this includes normal, lognormal, triangular and
uniform distributions. In this paper, we assume normally distributed random parameters apart
from purchase price which is drawn from triangular distributions.

3.3 Production Systems and Preference Heterogeneity

Producers from different production systems and countries, may face different
constraints and opportunities in terms of livestock production activities, and may exhibit
different preferences for cattle traits. We therefore tested for preference stability in the two
cattle production systems in our study sites; crop-livestock in Kenya and Ethiopia and
pastoral systems in Kenya using likelihood ratio tests. This was done by checking if the log-
likelihood function from the multinomial logit (MNL) estimation from the different sub-
samples is significantly larger than the pooled sample log-likelihood. The hypotheses to be
tested were:

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