The value of education in low skill economies: some evidence from Kenyan and Tanzanian Manufacturing
In depth
Econometric framework
Endogenous Education
- Standard concern: Education may be positively correlated with unobserved labour market ability. OLS estimates of returns to education upward biased as a result.
- Related concern: Returns to education may be correlated with unobserved market ability. If so, this may bias OLS estimates towards convexity.
- Different concern: Self-selection based on unobserved factors into the manufacturing sector may give rise to selection bias.
- We now report results that should be more robust to these potential problems than the OLS estimates.
Econometric Framework
Write the earnings function as
, (1')
where
= zero-mean variable denoting unobserved ability
= a continuous function,
= a residual orthogonal to all random terms on the right hand side of (1'),
and the rest of the notation is as in Section 2.
- Unobserved ability thus is potentially correlated with both schooling and the parameter vector
, and so the latter is thus now explicitly a random coefficient.
- Reduced form eq. for schooling:
, (2)
where
is a vector of variables (instruments) that are independent of 
and uncorrelated with 
. - Spline function f(.):
,
i.e. unobserved ability affects the slopes of the different segments of the earnings-education profile but not the differences in the slopes between segments (could easily be generalised). - For simplicity, let
, (3)
where
and 
are constants.
- Conventional form of ability bias:
-
is linear and increasing in 
,
-
does not affect 
(i.e. 
in 
), and
- earnings equation is linear in education (i.e.
):
. (4) - With
and 
unobserved, OLS estimates of the return to education will be upward biased.
- If, in addition, the return to education is random and correlated with unobserved ability (i.e.
in 
), so that
, (5)
then this will result in a non-linear association between education and earnings in the data which is not causal. - If
and 
, so that individuals who tend to get a lot of education tend to have high earnings conditional on education, and high returns to education, then failure to control for this unobserved factor in the estimation will generally lend support to a convex earnings-education profile even though the true functional form is linear.
Example: Simulate data set in which a is binary (high or low), and in which individuals with a high taste for education have high returns. True earnings function is linear with average slope coefficient equal to 0.15. Pattern: 
| lnw | Coef. | Std. Err. | t | P>|t| | [95% Conf. Interval] | |
| educ | .2391963 | .0038265 | 62.51 | 0.000 | .2316946 | .246698 |
| educsq | .0183558 | .0020592 | 8.91 | 0.000 | .0143188 | .0223929 |
| _cons | .2019013 | .0046966 | 42.99 | 0.000 | .1926939 | .2111086 |
| N = 5000. | ||||||