Thesis Re-print: Does Selling Fruits or Vegetables - Department of ...

The equation to calculate the conditional PE of j x using the maximum
2
likelihood estimated beta coefficients ( ) from the truncated second stage regression
is:
E
2
vv0, x
it
2 2 2 2 2 2
|
it it 2
x
it
x
it
xit
j 1
x
j
71
(3.4)
where λ represents the inverse mills ratio (IMR): the probability density function divided
by the cumulative density function.
2
j is the estimated coefficient of x j from the
truncated regression and is the estimated variance from the truncated regression. The
result of this equation is the PE of a given variable on fresh produce sales among those
who chose to sell. The household-specific PEs from equations (3.3) and (3.4) are then
used to calculate APEs over the entire sample and the sub-sample that sold,
respectively. 18
Finally, the equation to calculate the unconditional partial effect of x j can be
understood in two additively separable parts, each of which uses estimated beta
1
coefficients from stages 1 and 2 together ( and
2
) to determine the effect of x j
on expected sales (in this case) among all households in the sample, not just those who
sold:
18 Note that, because PEs are calculated for each household, APEs can in principle be
calculated for any subset of the sample that the analyst wishes. For example, APEs could
be calculated by total sales quintiles, or by land holding category, or by any other
disaggregation that may be of interest.