Obstacles to the profitable production and marketing of horticulture products in Lesotho: an offset-constrained probit modelling of farmers’ perception - Institutional Constraints to Small Farmer Development in Southern Africa - page 160

possession or otherwise of title deeds to land cultivated, extension services, and availability
of markets. The hypothesis to be tested is that the probability that farmers will be satisfied
with the outcome of their production activities will depend on several elements in the
environment of the farmer. For instance, where the farmer has access to land and other
productive resources, extension services, title deeds, etc., the chances are that the farmer
is likely to perform at levels that he/she finds satisfactory. But this attribute as well as the
possible other factors influencing it are unobservable which makes the problem one that
is amenable by any of the qualitative choice models such as probit, logit or tobit models
(Greene, 2000). The probit model is chosen in this particular study. The probit model was
necessary to avoid selection bias in the sample (Yúnez-Naude and Taylor, 2001).

To proceed, the model of production satisfaction can be stated in general terms as follows:

Y = PS = ƒ( X 1 , X 2 , … X n ) (1)

Where:

Y is the dependent variable that captures what the small producers think about the results
they are achieving in their horticultural production, and the X's in the model represent the
set of institutional factors already mentioned above.

Such a model can be specified as follows:

y * i = β 1 + β 2 x 2i + … + β k x k + μ i (2)

But the handicap is that y * i cannot be observed in reality but can only be inferred. This
means also that its exact determinants can only be estimated on the basis of the dummy
variables constructed for this purpose which can be defined as:

y i =0 if y * i < 0 and (3)

y i = 1 if y * i ≥ 0

(4)

From the foregoing equations, it can be deduced that:

Prob ( y =1) = Prob ( u i > -β ' x i ) = 1-F(-β ' x i ) (5)

which assumes that F is the cumulative distribution function for the error term u. Under
the assumption that the error term, u , is normally and independently distributed, i.e. ( IN(0,
σ 2 ), we can define a probit model as: