Focusing the search for Giffen behavior.

Johnston, Richard S. ; Larson, Douglas M.

I. INTRODUCTION

In the neoclassical theory of consumer choice, Giffen behavior can exist only if a positive income effect outweighs an always-negative substitution effect. It is a phenomenon, then, associated with highly restrictive--and, therefore, unlikely--characteristics of the consumer's utility function. Over the years there have been numerous attempts to uncover goods that are likely to give rise to such functions, with mixed results. A recent experiment by Battalio et al. |1991~ shows that some animals demonstrate Giffen behavior and suggests that economic theory must accommodate, not abandon, the phenomenon, despite "the very small likelihood of its existence". One difficulty with finding empirical examples of Giffen behavior in humans is that the neoclassical model provides few clues for locating either goods or individuals where the behavior is likely to be seen. Under what circumstances can one expect to observe not only positive income effects but also positive income effects that swamp substitution effects? Hicks |1956, 65~ argued that, for a good to be Giffen, a high proportion of the consumer's income has to be spent on it. Ng |1972~ suggested looking for this where consumers engage in stepwise optimization, with income being distributed initially among categories of goods, along lines first proposed by Strotz |1957~. While the proportion of the consumer's income spent on a good may be low, the proportion of the expenditure assigned to each category could be high, increasing the likelihood of observing the Giffen phenomenon. This suggestion may help to narrow the search but, at least so far, it has provided no guidance for how to select either categories or goods to look at for Giffen behavior. Thus Giffen goods continue to be viewed as theoretically possible but empirically unlikely.

In a recent article, Gilley and Karels |1991~ develop a convincing argument to explain Giffen behavior as a consequence not of preference characteristics but, rather, of a constraint on behavior: in particular, a nutrition constraint. Their results lead them to conclude that "the most likely place...to look for Giffen behavior...would be among the very poor, consuming a few staple items with limited substitution possibilities". Here, then, is a concrete guide for empirical discovery of the phenomenon, although they endorse the view that the behavior is probably rare.

The purpose of this note is to demonstrate that Giffen behavior may be a much more pervasive phenomenon than commonly believed, and we suggest where it may be found.(1) We endorse Gilley and Karels's view that consumer choice may be constrained by more than income. We suggest, however, that such additional constraints are as likely to impose upper, as opposed to lower, bounds on consumption. To make this point, we show that Giffen behavior can occur in the Gilley-Karels framework when the consumer has an excess, rather than a shortage, of food. Thus, while Gilley-Karels argue that Giffen behavior is most likely associated with subsistence incomes, we show that it may well be found where income levels are much higher. The Giffen behavior we find appears in the presence of local satiation, a circumstance likely to characterize the demand for some foods or goods. Whether viewed as a plausible characteristic of preferences, independent of specific functional form, or as a second constraint on choice, recognizing its presence in many choice circumstances helps us to focus the search for Giffen behavior.(2) Other examples of additional upper constraints on consumer choice include time-constrained decision-making as developed by Becker |1965~ and points rationing, considered by Scitovsky |1942~, Tobin |1952~, Goldfarb |1977~, and Wichers |1979~; and these too are promising areas to search for Giffen behavior. II. ADDITIONAL CONSTRAINTS ON CONSUMER CHOICE: UPPER VS. LOWER BOUNDS

In the Gilley-Karels model, the consumer seeks to maximize satisfaction from bundles of food, subject to two constraints: budget and subsistence. The former places an upper limit on the quantity of food consumed while the latter imposes a lower bound. In a two-good world, where both constraints are binding, a reduction in the choice set, either by lowering income or increasing one or both prices, leads the consumer to increase consumption of the lower-priced good. Such a good, then, will appear to have Giffen characteristics: increased price leads to a rise in quantity demanded.

For the Gilley-Karels consumer, the constrained utility maximization problem is Maximize U = U(X,Y)

subject to |Mathematical Expression Omitted~

and |Mathematical Expression Omitted~

where X and Y are two foods whose prices are |P.sub.x~ and |P.sub.y~ and whose unit contributions to nutrition are |C.sub.x~ and |C.sub.y~, respectively. Income and subsistence nutrition (in calories) levels are represented by |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~. At prevailing prices, |Mathematical Expression Omitted~ is too small to allow subsistence on Y alone, but does permit subsistence on X alone. This means that |P.sub.y~/|C.sub.y~ |is greater than~ |P.sub.x~/|C.sub.x~ so that X is the "cheaper" of the two goods in satisfying the nutrition constraint. This is illustrated in Figure 1 by a constraint, NN|prime~, that is steeper than the budget constraint, MM|prime~. The area AN|prime~M|prime~ in Figure 1 is the consumer's feasible choice set.

To make our point about Giffen behavior with local satiation, we reverse the weak inequality (b), so that it becomes

(b|prime~) |C.sub.x~X + |C.sub.y~Y |is less than or equal to~ N,

where N now represents an upper limit on the combinations of X and Y that do not exceed satiation. Thus the feasible choice set for our consumer is area OMAN|prime~.

The way in which this configuration of two constraints gives rise to Giffen behavior can be seen in Figure 1, which shows an example where a price increase in the Gilley-Karels framework would not result in a Giffen response. Here if the N constraint is a lower bound, as in Gilley-Karels, consumption would initially occur at point B where only the money constraint M is effective. A rise in the price of x, with the nutrition constraint remaining ineffective, would be an example of a price change in the standard, single-constraint model: consumption of x would decrease as the consumption bundle becomes B|prime~. If, however, the N constraint is an upper bound, consumption initially occurs at point A where both constraints bind; the increase in price of x results in an increase in its consumption, as the consumption bundle becomes A|prime~. This is a Giffen response exactly as it occurs in the Gilley-Karels model, but it is due here to the presence of a second, upper binding constraint on consumption. If, on the other hand, the preference map were such that the tangency of |U.sub.4~ with the budget constraint occurred to the left of point A (i.e., on line segment MA) and the N constraint were a lower bound, then we would have the Gilley-Karels analysis. Both constraints would be binding, consumption would initially be at A, and after the increase in |P.sub.x~, it would be at A|prime~. Some similarities and contrasts in the two setups are apparent. First, it is interesting to note that in both the Gilley-Karels analysis of Giffen behavior and the present framework, a rise in the price of either good will cause a Giffen response in the consumption of X, the least expensive good. The reason is the same in each model: when both constraints bind, the relevant consumption bundles are A and A|prime~, and an increase in price of either good shrinks the feasible consumption set, causing a substitution in consumption toward the cheaper good (which remains X, so long as N is steeper than M).(3) Similarly, a change in the nutritional content of either good (which causes a rotation of N) will induce a Giffen response in consumption of Y, which is the less nutrition-intensive good.

Second, one can ask what similarities or differences there are in preference maps that will give rise to Giffen behavior. This is easily evaluated by considering the optimal consumption bundles that would result from choice subject to each constraint operating individually. Considering only the initial constraints MM|prime~ and NN|prime~ in Figure 1, if the optimal consumption bundles with each individual constraint occur on line segments NA and MA in the Gilley-Karels model, Giffen behavior will result from the presence of both constraints acting simultaneously on choice. In the present framework with two upper constraints, if optimal consumption bundles occur on line segments NA or AM|prime~, Giffen behavior will result when both constraints are present. Thus, the similarity between the two models is that were there only a nutrition constraint, the addition of a money budget constraint (with a flatter slope) would force the individual to consume more X and less Y than would be optimal in both models. The difference is that were there only a budget constraint, Giffen behavior would follow in the present model when the (maximum) nutrition constraint forces the individual to consume more Y and less X than optimal, whereas it follows in the Gilley-Karels model when the (minimum) nutrition constraint forces the individual to consume more X and less Y than would be optimal. These are essentially the conditions under which both constraints will bind on choice, rather than only a single constraint. III. LOCAL SATIATION, OR GIFFEN BEHAVIOR WITH AN ABUNDANCE OF GOODS

Although it has not received extensive attention in the literature, the notion of local satiation developed by Lipsey and Rosenbluth |1971~ presents a useful counterpoint to the argument that Giffen behavior is most likely found among poor consumers with few substitution possibilities among limited staple foods. Here we briefly motivate the treatment of satiation as an upper bound on consumption of goods such as food, which suggests the possibility that Giffen behavior can be found among consumers choosing among an abundance of food items. A number of goods and services would seem to be described well by the local satiation phenomenon. During a given time period, the average consumer is unlikely to purchase more typewriter ribbon, shoe polish, lawn fertilizer, attorney's services, or copies of today's newspaper in response to higher income levels or lower prices, even if the latter fell to zero.(4)

Satiation is particularly likely to be seen in the consumption of goods and services that are close substitutes for each other but which, as a group, have few close substitutes or are associated with a durable asset. This is especially true of goods for which storage is costly or impossible, including perishable goods.

A similar argument can be made for food. For physiological reasons there is an upper limit to the amount of food and beverage that a consumer can ingest during a short period of time. Among food items that act as close substitutes, such as protein sources in a dinner menu, the consumption level that yields satiation can be interpreted as the total quantity from all sources that would be consumed at zero (current and expected future) price. For simplicity consider two protein sources, chicken and beef, which in varying combinations yield satiation. The line NN|prime~ in Figure 1 can be interpreted as such a "satiation frontier." Amounts up to and including this total quantity of protein yield positive marginal utility, but amounts consumed beyond this decrease satisfaction and, in the absence of storage incentives, would never be observed. In this manner, an upper bound on consumption of food per unit of time is generated by the fact that an individual can be satiated locally in consumption.(5) Let the axes in Figure 1 represent pounds of X (seafood) and Y (beef) per unit time; if, for example, the total quantity of meat yielding satiation is independent of its composition (whether beef or seafood), the constraint NN|prime~ has a slope of -1. For X to be Giffen requires that seafood be cheaper: |P.sub.x~ |is less than~ |P.sub.y~. The consumer who maximizes satisfaction by consuming to satiation chooses more seafood when its price rises because, given the budget for seafood and beef, the loss of effective income accompanying a price rise of either good requires that the less expensive good play a larger role in achieving satiation. The intuition is especially clear if the two goods are nearly perfect substitutes in achieving satiation: the less expensive good provides the least-cost way of reaching satiation, even for own-price increases, so long as it remains the least-cost source of satiation of the two goods.

IV. EMPIRICAL EVIDENCE

We showed above that Giffen behavior will occur with two upper constraints on consumption if the quantity consumed of the less expensive good in the presence of both money and satiation constraints is (a) greater than would be optimal if there were no budget constraint; and (b) less than would be optimal if there were no satiation (nutrition) constraint. The reason is that these conditions imply that both constraints will bind on consumption, and a price change will cause a movement along the other constraint, which implies a Giffen response for the cheaper good.

These conditions suggest specific areas to explore for Giffen behavior in the context of food demand specifically and multiple-constraint choice settings generally. For a given individual, the first of these conditions is more likely to be satisfied at low than at high expenditure levels for food, or where the relative prices of X and Y are high. The second condition suggested is more likely to hold for the consumer whose bundle of X and Y would contain a higher share of X, if satiation were not a factor.

An example which appears to meet these conditions is seafood consumption in Japan. Japan has relatively high food prices, with seafood less expensive than beef, and the highest per capita consumption of seafood of any developed country in the world. A recent study of food demand in Japan by Kim et al. |1988~ estimated positive own-price elasticities for several seafoods at the household level.

Other studies have reported positive price elasticities of demand for some foods while reporting negative price elasticities for their higher-priced substitutes, as the model predicts.(6) Stone |1953~ found that margarine had a positive own-price elasticity, and the own-price elasticity of its closest--and more expensive--substitute, butter, was negative. Lambert |1991~ found that chicken and turkey have positive own-price elasticities, and their higher-priced substitutes, pork and beef, have negative own-price elasticities; Deaton and Muellbauer |1980~ reported a positive own-price elasticity for food in total. Many other examples are scattered throughout the literature, and are often interpreted as problems of data, of model specification, or other econometric difficulties. While there are legitimate identification issues when such a finding arises, the results in this paper suggest that it should not so quickly be dismissed as evidence of Giffen behavior. Hopefully the extensions to the Gilley-Karels paper suggested here will stimulate a more thorough investigation of the issue.

V. IN CONCLUSION

Giffen behavior appears likely to be rather more widespread than currently believed. Rather than being merely a theoretical curiosity of little practical importance, it is an entirely plausible consequence of consumer choice in the presence of multiple constraints. We illustrate the point by arguing that Giffen behavior should not be expected to be confined to low-income consumers facing few choices among staple food items, showing that it can equally well arise for consumers who have abundant food consumption choices and who can achieve local satiation. This, plus the fact that multiple constraints seem likely to characterize many consumer choices, suggests other possible contexts for further empirical searches for Giffen behavior. A related question is whether the argument extends to the case of factors of production, giving additional content to the notion of inferior factors.

1. Gilley-Karels recognize that their model extends to other arenas, pointing to a study that found Giffen behavior among drug addicts who seek to achieve a minimum intoxication level with a limited budget. This example implies a belief, however, that the phenomenon is relatively rare.

2. The argument that local satiation may give rise to Giffen behavior was first advanced some twenty years ago by Lipsey and Rosenbluth |1971~. While this work has been cited by almost all who have written in the area since, the principal idea of the piece--that Giffen behavior may be observed in goods whose characteristics, following Lancaster |1966~, are subject to satiation--has not been explored empirically. We suspect the reason is similar to that associated with the earlier argument about relationships between income and substitution effects: without guidance on where to find satiation in characteristics, the phenomenon remains only a theoretical possibility with little empirical relevance. The contribution of the present paper is to provide concrete suggestions for where and why one might find local satiation and, in so doing, illustrate how the Gilley-Karels framework generalizes to other areas that offer a high likelihood of finding Giffen phenomena. 3. If NN|prime~ is a lower bound on consumption, the feasible choice set shrinks from AN|prime~M|prime~ to A|prime~N|prime~M|double prime~. If NN|prime~ is an upper bound on consumption, the feasible choice set shrinks from OMAN|prime~ to OMA|prime~N|prime~. In both cases, when both constraints bind, the consumption bundle selected moves from A to A|prime~, reflecting less of the expensive good Y and more of the cheaper good X.

4. The consumer could purchase today for future consumption. Aside from the problem of storage, there is the additional question of why the consumer would do this if the zero price were not expected to change.

5. A simple example illustrates the point explicitly. Consider the utility function U = |b.sup.0.5~|s.sup.0.5~ + |z.sup.0.5~, where z |is greater than or equal to~ 0 is a third consumption good introduced for generality, and b |is greater than or equal to~ 0 and s |is greater than or equal to~ 0 are subject to the local satiation condition b + s |is less than or equal to~ 1. The consumer is constrained to choose combinations of b, s, and z such that b + s |is less than or equal to~ 1, and faces the budget constraint

|P.sub.s~ |center dot~ s + 1 |center dot~ b + 9 |center dot~ z |is less than or equal to~ 0.5

where |P.sub.s~ is the price of s, and the prices of b and z are taken to be 1 and 9, respectively.

When |P.sub.s~ increases from .20 to .25, the consumer increases consumption of s from .72 to .74; at an even higher price, |P.sub.s~ = .30, consumption of s is still greater, at .76. In this price range, s is Giffen as the individual adjusts consumption along the satiation constraint. When the price of s rises to .35, however, consumption of s declines to .66, because the consumer maximizes satisfaction without being satiated, consuming b and s such that b + s |is less than~ 1.

6. Dougan |1982~ has argued that while Giffen behavior is a logical possibility for individuals, it is unlikely at the market level. Nonetheless, there are numerous examples in the empirical literature of positive price elasticities, especially in the demand for food.

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