Earnings bracket obstacles in household surveys – How sharp are the tools in the shed?

Earnings functions form the basis of numerous labour market analyses. Non-response (particularly among higher earners) may, however, lead to the exclusion of a significant proportion of South Africa’s earnings base. Earnings brackets have been built into surveys to maintain sufficient response rates, but also to capture information from those who are unsure about the earnings of fellow household members. This data type gives a rough indication of where the respondent lies in the income distribution, however exact figures are not available for estimation purposes. To overcome the mixed categorical and point nature of the dependent variable, researchers have traditionally applied midpoints to bracket earnings. Is this method too rudimentary? It is important to establish whether the brackets are too broad in South African Household surveys to be able to make reliable inferences. Here, midpoints are imputed to interval-coded responses alongside theoretical conditional means from the Pareto and lognormal distributions. The interval regression is implemented as a basis case, as it soundly incorporates point and bracket data in its likelihood function. Monte-Carlo simulation evidence suggests that interval regressions are least sensitive to bracket size, however midpoint imputation suffers distortions once brackets are too broad. Coefficient differences are investigated to distinguish similar from different results given the chosen remedy, and to establish whether midpoint imputations are credibly similar to applying interval regressions. To this end, testing procedures require adjustment, with due consideration of the heteroskedasticity introduced by Heckman 2-step estimates. Bootstrapping enhances conclusions, which shows that coefficients are virtually invariant to the proposed methods. Given that the bracket structure of South African Household Surveys has remained largely unchanged, midpoints can be applied without introducing coefficient bias.