Bayesian estimation of the infrequency of purchase model with an application to food demand in the UK

A Bayesian method of estimating multivariate sample selection models is introduced and applied to the estimation of a demand system for food in the UK to account for censoring arising from infrequency of purchase. We show how it is possible to impose identifying restrictions on the sample selection equations and that, unlike a maximum likelihood framework, the imposition of adding up at both latent and observed levels is straightforward. We find that higher income households consume proportionately more meat and more fresh fruit and vegetables. Regional differences in fruit and vegetable consumption are marked with the highest levels of consumption in London and the South East. The presence of children in a household reduces levels of vegetable consumption. Households employed in the professional or managerial sectors have higher levels of fruit and vegetable consumption. Age has an influence on the consumption of fats and sugars, with consumption declining amongst older households and on the types of fruit and vegetables consumed with younger households preferring more ready meals and prepared fruit and vegetables.