The hazard function of sales: An analysis of UK supermarket food prices

In this paper we examine the empirical pattern of sales behaviour among the UK’s seven largest retail chains using a scanner dataset of weekly food prices on over 500 products over a 2.5 year period. Motivating the analysis is the question ’are products more likely to go on sale that longer they remain unpromoted?’. Theory is not unanimous and empirical and recent empirical studies also offer conflicting evidence. To address the question we estimate the hazard rate of a sale - probability that a product goes on sale in the tth week since the last sale - over the market as a whole and then separately across different national retailers. We pay particular attention to the effects of sales in like-for-like products in rival retailers on the hazard of a sale. We also find that accounting for multiple sales has a pivotal role in determining the slope of the hazard function, which actually reverses sign when proper account is taken of this seemingly innocuous technicality. Correcting for this we find that food products are more likely to be discounted the longer they remain without a sale. This result helps square the circle between price setting and modern theories of sales behaviour. Furthermore, we find that the positive time-dependent pattern varies across product format and brand status. With sales in rivals, branded products in a representative retailer are more likely to be discounted if it has been on sale previously in the rival retailers, however the hazard of a sale in private labels is unrelated to its rival sales. In the individual retailer level, the hazard results show that while most supermarkets exhibit some form of a ’hi-lo’ pricing there is one retail chain does not (showing no time-dependence) preferring an every day low pricing strategy (EDLP).