Income Growth and Mobility of Rural Households in Kenya: Role of Education and Historical Patterns in Poverty Reduction

∆INCit = ∆INCit-1 α1 + ∆Edit β1 + ∆(INCit-1*Edit ) α2+ ∆Xitδ + ∆Zitλ +∆ μit     (8)

Taking first differences of the data does clearly help to eliminate the time-
invariant unobservable factors, but this comes at a cost of reducing variation in the
regressors. This problem is however minimized in this case since our panel has more than
a year’s gap, resulting in somewhat longer differences (3-4 years between periods). The
first difference approach also helps us to explain changes in the economic wellbeing of
households.

In this study, and to ensure consistency of the estimated parameters, equation (8)
above is thus estimated using First Difference Two-stage Least Squares (FD-2SLS) so as
to account for the endogeneity of the lagged income difference (LID) in the model.
Following Anderson and Hsiao (1982) and Wooldridge (2002), we use previous lags of
income level (INCit-2) as instruments for the (LID) variable. Since we effectively can only
use one such instrument from our data, we also use lagged mean rainfall deviation (Rit-2)
as another potential instrument. The rainfall variable provides over-identifying
restrictions to allow testing the validity of the instrument set. To account for the potential
lack of strict exogeneity of the interaction term with education, we use the respective
lagged interaction term (INCit-2*Edit-2) as an instrument. It is however important to note
that the use of previous income levels as potential instruments is only legitimate when
there is no serial correlation in the errors (Arellano and Bond, 1991; Wooldridge, 2002 ).
This is nevertheless not applicable in this case as we effectively only have a cross-section
of differenced data after accounting for historical patterns and unobserved heterogeneity.

10

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