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

that in most cases, the heads are responsible for making decisions for the entire
household regarding use of the available physical and human assets.

Accounting for income persistence, delineating the education variable and
including the respective interaction term, model (6) above becomes:

INCit = α0 + INCit-1α1 + Edit β1 + INCit-1*Edit α2+ Xitδ + Zitλ + αi+ μit (7)

where: Ed is the education variable, and X and Z are as earlier defined. To control for any
omitted unobserved factors that may potentially correlate with the above variables or
other included explanatory variables, we have explicitly accounted for them in the above
model: αi represents the time invariant unobservable effects and μit is a purely random
component.

Estimation

The dynamic panel data model (7) has implications on the estimation methods often
used. First, the unobserved effects are most likely correlated with the lagged dependent
variable (LDV), thus rendering OLS inconsistent. Secondly, even though we could get rid
of the unobserved effects through differencing or fixed effects, it is logical that future
values of the LDV are potentially correlated with the idiosyncratic error term (Cov
(INCis, μit) ≠ 0, for s>t) implying that the within estimation is also inconsistent. This
problem also bedevils Generalized Least Squares (GLS) since it requires strict exogeneity
of the regressors. The most viable solution to this problem has been to take first
differences to eliminate the unobserved effects and then instrument for the lagged
difference variable (Ahn and Schmidt, 1995; Wooldridge, 2002).

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