SummaryThe paper considers the problem of parameter estimation in a model for a continuous response variable Y when an ordinal explanatory variable X is missing for a substantial proportion of the sample and the selection mechanism (non-deletion from the sample) S depends on unobservables after conditioning on all explanatory variables—i.e. there is selection on unobservables, or data are not missing at random. We suggest addressing this endogenous selection problem by joint modelling of the selection mechanism, the ordinal explanatory variable X and the response variable Y. The method is illustrated by re-examining the problem of ethnic gaps in educational achievement at age 16 years in England.