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

mean of each time-varying explanatory variable in
K x 1 and L x 1 vectors of parameter coefficients, and
74
2 1 2
x ; and are their associated
1
a i and
2
a i are each equation’s
respective error terms. Adding the c i specification to the right hand side of equations
3.1 and 3.2 above yields the following, with transformed error terms
where
1
u it =
1
e it +
Stage 1 it p * =
Stage 2 it v * =
1
1
a i and
2
u it =
2
e it +
2
a i :
1 1 1 1
xit xi
where it p = 1 if p it * > 0; otherwise p it = 0,
2
2 2 2 2
xit xi
u
u
1
it
2
it
1
u it and
2
u it ,
1 1
it | it x u ~ N(0, σ 2 ) (3.8)
2 2
u it | xit
~ N(0, σ 2 ) (3.9)
where v it = v it * if v it * > 0 and p it = 1; otherwise v it = 0.
Since
1
x i and
2
x i have the same value for each household across both years
(the average of the values in each year by household), but differ across households, when
all the variables are included and estimated in the same regression, any time-constant
unobserved heterogenaity that follows equations 3.7 and 3.8 is controlled for. This also
achieves the same outcome as a random effects estimation using a panel data linear
model (Ricker-Gilbert, Jayne and Chirwa 2011, Goeb 2011, Mather, Boughton and Jayne
2011).