Model (3) also accounts for historical patterns by including a lagged income
variable but this time in the initial formulation of the model such that it is differenced
with the other variables. This is only possible with at least a three year panel. The
coefficient of the lagged income variable however remains negative and significant
whether the level or differenced form is used. The rest of the coefficients also remain
stable across the two models except for the education variable. Models (4) and (5) both
interact the LID with education; in the latter, we instrument for the LID and its
interaction with education as discussed in the methods section. As shown from the
results, the parameters from the two models show fairly similar patterns but with a few
exceptions.
A major difference though and one that is of main interest in this paper is the
coefficient of the LID. Without accounting for the endogeneity of the LID, the coefficient
is negative and significant and does not vary significantly with education of the head.
This implies that households are recovering from income shocks and worse off
households become better in future periods and vice versa. This result is consistent with
findings from earlier studies which find overwhelming support for the convergence of
household incomes towards the mean. This scenario may exist when a larger proportion
of the full income of a household consist of transitory gains/losses which are less
persistent allowing quick recovery of shocks or de-cumulation of gains. This result may
not be surprising given that without using instrumental variables methods, the lagged
income variable consists of both the permanent and the transitory components.
The above results however change when we account for the weak exogeneity of
the LID. The coefficient of the LID turns positive and significant and seems to vary
15