Numeric competence, confidence and school quality in the South African wage function: towards understanding pre-labour market discrimination

Highly convex estimates of average returns to education commonly found in South Africa are usually rationalised as being the result of a surplus of unskilled workers and a shortage of skilled workers in the economy (Keswell & Poswell, 2004). However, due to the absence of appropriate micro level data in the past, unbiased estimation of these returns has been difficult. This paper investigates potential sources of estimation bias using the NIDS 2008 survey, one of the first to contain concurrent information on individual labour market outcomes, numeric proficiency and quality of education received (which is highly diverse and unequal across the population). We compare naïve estimates in all relevant sub-samples with estimates that attempt to correct for the sample selection on numeracy (as the test was voluntary), as well as selection into employment. We also correct for (and exploit information on) the choice of test difficulty given to respondents, an option which was not intended in the design stage of the survey. This feature allows rough estimates of the influence of respondents’ confidence in their abilities on wages. More importantly, the sample selection adjustments allow us to control for numeracy and school quality, which influence the classic problem of ability bias in returns to education. We estimate the bias in returns to education as well as the extent of racial labour market discrimination that can be accounted for by schooling outputs rather than other features of the labour market. We assess whether convex returns to education can be explained by an unequal distribution of school quality, or whether conventional explanations (such as labour demand) remain the main explanation. Suggested remedies for selection on the endogenous numeracy measure include instrumental variables and a “Double Heckman” approach. Typical instrumental variables used in labour market analysis are poorly captured and restrict sample sizes to the extent that estimates often become nonsensical. The latter (non-standard) adjustments for sample selection issues show some promise but further evaluation and tests are required to fully rely on these results. Convex returns to education remain strongly present in the African population (after accounting for inequalities in schooling outputs), while they are concave for the white population. Bias in these returns is unreliably estimated for whites and Asians, but is highest for the more educated at a peak of 4.55 and 5.84 percentage points for the African and coloured populations respectively. Returns to numeracy, when more reliably identified, are convex. School outputs (measured in numeracy test scores and historical school performance) constitute a sizable part of discrimination estimates, accounting for between 18% and 36% of unexplained racial wage premia.