The burgeoning literature on collective models has focused on attempts to estimate such models of household behaviour. However, estimation when accounting for participation decisions and nonconvex budget sets has proved difficult, delaying the use of collective models for policy analysis. The paper first suggests a piecemeal approach to empirically identify a collective model with discrete labour supply choices and nonconvex taxation. Then, we compare the predictions (for the purpose of tax policy analysis) of such model with the ones obtained by the unitary model of household behaviour. The exercise consists in assessing the distortions that affect positive and normative analysis of a current French tax reform when using a unitary model estimated on data generated by the collective one. The size of errors suggests that more effort should be devoted to the estimation and operationalization of collective models with taxation.