The methodologies of the studies - Institutional Constraints to Small Farmer Development in Southern Africa - page 300

In a similar analysis, Sanchez (2005) proposes that labour supply is a function of returns
and risks in an activity, capital available to the household and household characteristics.
Returns and risks explain the incentives to participate in a given activity and both capital
available to a household and household characteristics reflect the capacities to participate
in a certain activity.

The household utility function can be solved by specifying a model of the form:

U ij = β j X i + µ ij (A.2)

where:
U ij = the utility associated with the i th household choice of activity j ;
X i = a vector of parameters of the i th household;
µ ij = the error term.

But utility U ij is not observable (Alvarez and Nagler, 1995). What we observe is decision to
participate, which is represented by a dummy and can be expressed as a probability function
employing the binary linear model (BLM) that allows for choices between a set of two
alternatives to be analyzed:

ρ (Y=1) = e β 'χ / 1 + e β 'χ (A.3)

ρ (Y=0) = 1 - e β 'χ / 1 + e β 'χ = 1 / 1 + e β 'χ

(A.4)

which for market participation choices can be expressed as a logit transformation of the
type:

Logit (Pi i ) = ln (P i / 1 - P i ) = α + β 1 X 1 + …+ β n X n + U t (A.5)

Where:
ln (P i / 1 - P i ) = logit for market participation choices;
P i = not participating in markets;
1-P i = participating in markets;
β = coefficient;
X represents covariates;
U t = error term.

For the baseline status study, the dominant model applied sequentially introduced
dependent variables that represented the probability of participating in own business, own
agriculture, wage employment and remittances. This decision is explained by a set of socio-
economic factors that distinguished the households into categories.