A Comment on Curhan's “The Relationship between Shelf Space and Unit Sales in Supermarkets”

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In a recent article [1] Curhan reports that 11 variables commonly believed to affect shelf space elasticities explained only about 1% of the variation observed in his carefully chosen sample. He suggests that more discriminating independent variables might be proposed to explain space elasticity . . . , but doubts that their inclusion will materially improve explanation. He concludes, on the basis of his findings, that simulation of the merchandising effects of shelf space reallocations on sales and profits is likely to remain impractical. Curhan's rather disappointing empirical results could, of course, be caused by failure to include some important independent variables (which he doubts) or to a misspecification of the functional form of the estimating equation (e.g., the true equation could be nonlinear). I will suggest here, however, that the problem is a more basic one, familar to economists, known as simultaneous equation bias [2,3]. The problem, briefly stated, is that the store managers and/or COSMOS make shelf space allocation decisions to increase gross store profits. The attempt to maximize gross store profits will obscure whatever relationship originally existed between unit sales, shelf space, and other variables in Curhan's regression equation. I will show that gross profit maximization implies that the product of the gross profit per square foot of shelf space and the shelf space elasticity must be equal for all items in the same store. Put in other terms, gross profit maximization implies a perfect negative correlation between item gross profit per square foot and item shelf space elasticity in the same store. It is obvious that if the manager or the COSMOS program attempts to equalize or nearly equalize gross profit per square foot, then all shelf space elasticities will also be nearly the same. Thus, in the extreme case, unit sales could be affected by each of his independent variables in precisely the manner expected by Curhan and yet the regression equation fail completely because of lack of variability in the dependent variable. The theory given below is rich enough to enable us to put crude bounds on the shelf space elasticities, given information on gross profit per square foot and on the cost of space expansion. The results bracket the observed range of shelf space elasticities reported by Curhan and, at the same time, provide an explanation of the absolute size of these (roughly .2) and for the rather small variability observed (the range is from .201 to .244). This finding must be qualified by pointing out that the theory refers to elasticities at the store level, whereas Curhan reports averages for his four test stores. It would be interesting to know how much worse the theory does in explaining results at the store level.