Table 2a shows OLS estimates of the parameters of the earnings function, by year and age group, for Kenya. Table 2b shows results for Tanzania.
We focus on the role of education.
We now investigate whether the data pool over time and/or across age groups.
We start from a model where the explanatory variables are interacted with time and age group in such a way as to make the specification equivalent to separate earnings functions as in Tables 2a-b, and then test for the joint significance of the relevant interaction terms.
Results are reported in Table 3.
For both countries we can reject at the one per cent level the hypothesis that all the time and age group effects are jointly zero (row 1), hence the earnings equations in Tables 2a-b do not pool.
We accept the null hypothesis that the coefficients on the control variables (i.e. age and its square, tenure, male and capital city) do not vary across age groups and over time (row 2), and firmly reject the hypothesis that the earnings education profile is constant across age groups and over time (row 3).
Thus, the control variable effects appear stable over time and across age groups; the education effects do not.
We drop the interaction terms associated with the control variables, and the cross terms between time and age group, yielding specification 2.
The remaining time and age group effects are highly significant (row 1), and there is strong evidence that the shape of the earnings education profile varies across age groups for both countries (row 8).
The interaction terms {time x age group x education} are redundant (row 9), and so we drop these next.
Table 4 shows the resulting specifications, our preferred models, and Figures 3a-b show the predicted earnings education profiles.
Figure 3a: Predicted Earnings Based on Preferred Specification: Kenya
Figure 3b: Predicted Earnings Based on Preferred Specification: Kenya
Figure 4a: Predicted Earnings Based on Preferred Specification: Tanzania
Figure 4b: Predicted Earnings Based on Preferred Specification: Tanzania
OLS Results of the Preferred Model
For both countries and for both age groups there is strong evidence that earnings are convex in education.
For both countries the results suggest the earnings profiles differ across age groups
the earnings profile for the young age group is virtually flat for less than twelve years of education, indicating small or no marginal returns to education before the tertiary level.
In Kenya there is a clear upward intercept shift referring to 1995, which was sustained in 2000 for the old age group but not for the young. There is little evidence for intercept shifts over time in Tanzania.
Looking specifically at the first and last wave of the data, we accept the hypothesis that the earnings profiles exhibit the same shape for Kenya, and reject it for Tanzania.
For Tanzania there is evidence of a gradual and systematic change in the shape of the earnings profile for more than twelve years of education, with increased convexity as a result.