Perverse Substitution Relationships in Demand Studies: The Example of Butter and Margarine

Abstract

Econometric analyses of demand for butter in a number of countries have produced results which appeared to conflict with expectations. Specifically the sign of the co-efficient for margarine price was negative rather than the positive sign expected with a presumed substitute product. Gollnick (1954), who was the first econometrician to meet this problem, advanced the hypothesis of a constant fat budget to explain the paradox. Among other works which reported similar paradoxical results were Hesse (1967), Wierenga (1968 and1974), Oskam and Wierenga (1974), Upton and Wittenberg (1974) and Vertessen (1979). The markets studied were Germany?, Netherlands and Belgium.In this paper we discuss the Gollnick hypothesis (it appears to have been ignored in English language economic journals), explore its mathematical implications, present some recent results which appear to support it and discuss whether the hypothesis might be valid for other products. Existing TheoryThis hypothesis of consumer behaviour implies that there are circumstances other than those defined in conventional theory where 'wrong' signs on price elasticities can be justified. Gollnick (1954) showed that the presumption, in both the Hotelling and Slutsky-Hicks definition of substitute products, that the weighted cross-price elasticities would be equal would not be valid where consumers spent a constant budget on the two substitute products. He warns against defining substitutes or complements by the sign accompanying a regression co-efficient.In present theory the only circumstances where 'wrong' signs in a demand equation or elasticity could be justified arise in a Slutsky equation where the 'income' effect is different in sign from and outweighs the 'substitution' effect. For example the substitution effect in relation to an own price increase in the Slutsky equation is always negative. To obtain a wrong sign the income elasticity would have to be negative and the effect relatively large, implying that the product constituted a substantial proportion of family expenditure. Goods with these characteristics, known as Giffen goods, are unknown in the developed world.

Testing for Sources of Irreversible Consumer Demand

“…The Rotterdam model suggests that demand for cheese and table spreads is substantially more own-price elastic than previous studies indicated (e.g., Boehm, 1975;Haidacher, Blaylock, & Myers, 1988;Heien & Wessells, 1988;Huang, 1993;Pitts & Herlihy, 1982). Weekly data often appear to produce more elastic estimates than do monthly, quarterly, or annual disappearance data.…”

International trade in a differentiated good: Trade elasticities in the world rice market

“…Negative cross-import price elasticities, on the other hand, indicate a complemen-tary relation between the products. A complementary relationship can occur for staple foods (such as rice) with a relatively fixed expenditure outlay, and own-price elasticities less than one (Pitts and Herlihy, 1982). As can be seen in Table 3, this relationship occurs in a number of cases.…”

International trade in a differentiated good: trade elasticities in the world rice market

“…Negative cross-irnport priee elasticities, on the other hand, indicate a cornplernen-tary relation between the products. A complementary relationship can occur for staple foods (such as riec) with a relatively fixed expenditure outlay, and own-price elasticities less than one (Pitts and Herlihy, 1982). As can be seen in Table 3, this relationship occurs in a number of cases.…”