The Formation of Reference Price

ABSTRACT - In the absence of an explicit measure, previous research has assumed the applicability of certain models (theories of expectations) in describing the manner in which reference price is formed. The validity of the models used in past research is subject to question. First, it is unclear that the assumed models, e.g., rational expectations,- depict accurately the reference price formation process. Second, the actual models used in these previous studies ignore central elements of the postulated theories of expectations. In particular, they ignore the fact that consumers have access to he current price information in forming their current reference price for a product.

Citation:

Robert Jacobson and Carl Obermiller (1989) ,"The Formation of Reference Price", in NA - Advances in Consumer Research Volume 16, eds. Thomas K. Srull, Provo, UT : Association for Consumer Research, Pages: 234-240.

Advances in Consumer Research Volume 16, 1989      Pages 234-240

THE FORMATION OF REFERENCE PRICE

Robert Jacobson, University of Washington

Carl Obermiller, University of Washington

ABSTRACT -

In the absence of an explicit measure, previous research has assumed the applicability of certain models (theories of expectations) in describing the manner in which reference price is formed. The validity of the models used in past research is subject to question. First, it is unclear that the assumed models, e.g., rational expectations,- depict accurately the reference price formation process. Second, the actual models used in these previous studies ignore central elements of the postulated theories of expectations. In particular, they ignore the fact that consumers have access to he current price information in forming their current reference price for a product.

This study obtains explicit measures of reference price and uses these measures to test the validity of the various models/theories of expectations in describing the formation of reference price. Modeling this process is used to provide insights into the effect of reference price on, for example, consumers' response to price-promotions and brand choice decisions.

INTRODUCTION

When making a purchase decision, consumers must evaluate various alternatives. This evaluation occurs within a given context or decision frame. One element of this context is a standard for comparison of the price of any brand under consideration, i.e., a reference price. The probability of consumers making a purchase is increased if a brand's price is within some range of an acceptable price. Brands that fall above the reference price are likely to be considered economically unacceptable. Moreover, brands that are priced too far below the reference price may be inferred to be lower in quality. In general, reference price can be conceptualized as a standard against which brand prices are compared. Both economic and psychological implications result from a brand's being either above or below a reference price. Marketers, therefore, have a keen interest in the concept of reference price because of its role in the purchase decision and in consumer perceptions of brand quality.

Because many markets are characterized by fluctuating prices, reference price is likely to be dynamic. One would expect consumers to incorporate changing price information into their decision making; failure to do so may work to the disadvantage of both buyers and sellers. A lack of awareness of recent price increases will result in "sticker shock"; and ignorance of decreasing prices will reduce the effectiveness of price competition, as some consumers may pay higher than normal prices.

The dynamism of reference prices presents an intriguing problem for marketers of many frequently purchased consumer goods. Sales promotions have become an increasingly important marketing tool, representing almost twice the expenditure of advertising and with a rate of increase that is 33% greater (Yovovich 1983). Most of the sales promotion expenditure is either directed or passed on to the consumer in the form of temporary price reductions. Price promotion has become so concern in many product categories that the sale price may represent the norm.

Each change in price combines with an existing reference price to affect current- purchase probability; but it does affect future reference prices as well. Thus. temporary price reductions or promotions. which are intended to increase demand, may have negative consequences by lowering consumers' future reference prices for the brand. Consumers' response to the current discounted price, as well as sales when the brand is not price promoted, will be adversely affected by this lowered reference price. This effect could result in several ways: (a) Frequent discounts may provide a history of lower price data points, which consumers access for comparison. (o) They may provide a basis for inferring lower quality, particularly for non-users of the discounted brand. (c) They may create an expectation of future promotions. Whatever the cause, the consequence of lowering reference price is that consumers will perceive the "regular' price as too high. Because of its influence on both current and long-term demand, marketers seek both to know the static level of reference price and to understand the dynamic process of reference price change. Our purpose in the present paper is to investigate the formation of reference prices over a time as a function of price information. We begin with a discussion of the conceptual and operational definitions of reference price.

REFERENCE PRICE, EXPECTATIONS, AND THE "FORWARD LOOKING" CONSUMER

Expectations

Rosch (1975) defined cognitive reference points as any stimuli to which other stimuli are related. Thus, a reference price is any price to which other prices are related. There are many dimensions on which to evaluate a given price, so it is not surprising that researchers have conceptualized the term in a variety of ways. The concept of reference price is both multi-dimensional and ambiguous. Perhaps the prevailing conceptual definition of reference price is the fair or appropriate price (c.f. Nagel 1937). A number of researchers have noted that consumers' determinations of a fair price are subject to contextual mediation (e.g. Puto 1987). For example, one considers a higher price appropriate for the same item in a restaurant rather than a grocery store. Other definitions are at lower levels of abstraction, approaching the empirical. Consumers may, for example, evaluate a given price relative to aspiration (price I would like to pay, or reasonable price (Klein and Ogelthorpe 1985)), budget constraints ("I only have xx dollars."), or ta; get price objectives ("I hope to make the purchase for xx dollars."). The most common approach, however, has been to consider fair and appropriate to result from expectations. Puto (1987) models expectations of price along with objectives as the determinants of initial reference price. Helgeson and Beatty (1987) define reference price as the price consumers expect to pay; they demonstrate its effect on the recall of last purchase price. Liefeld and Heslop (1985) define it as "the price that one would ordinarily expect to find" in their study of the effects of advertised prices on reference price. [We agree that consumers may also consider the price desired, the price that the retailer should (in whatever sense) charge, the price that fits one's budget, as well as other referents. But these other dimensions seem to apply largely to the choice of making a purchase versus not making a purchase. In many cases consumers are choosing between one alternative and another now, or between one alternative now and the same alternative later. In these cases, levels of aspiration, fairness, objectives, etc. seem less relevant than expectations about alternative price levels.] Our conceptual focus, therefore, is on reference price as a price expectation.

The "Forward Looking" Consumer

Gabor (1977) contends that "the price of the last purchase as remembered represents the price image of the good concerned, and it can be of great importance to the price setter to know how it compares with the actual price, since this will indicate how the market will respond to a price change." While previous price may have a role in influencing consumer's perceptions of price, this definition, as noted by Winer (1986), is backward rather than forward looking. This conceptualization has a consumer's reference price dependent on the price at which he could have purchased in the past. Past prices, in and of themselves, are irrelevant to utility maximization. While consumers may take them into account, they are analogous to sun}; costs.

Winer (1986) defines reference price as "the consumer's perceived current price of the brand; it could also be termed anticipated price, since it is the price a consumer expects to observe at the point-of-purchase." He labels the difference between this anticipated price and actual price as "sticker shock." We should expect, however, a difference between reference price and anticipated price. A consumer may be well aware of the price charged at the current period, but may not believe this will be the price of the product at any time in the future. Consider a situation where a consumer knows, e.g., through advertising, that the current price promotion is a substantial and strictly one-time-only discount. While anticipated price will not differ from actual price, we suggest that the probability of purchase will be greater than normal.

The forward looking consumer is assessing the cost/benefit of buying the good now versus buying the good at a future time. We conceptualize reference price, therefore, as the consumer's expectation of the future price of the brand. The "true" value of a good depends on what it will cost in a subsequent time period and the cost of delaying the purchase. Past prices come into play only to the extent they provide information as to future prices. If consumers feel that future prices will be higher, they will accelerate, subject to the cost of holding inventory, their purchase, i.e., stockpile. Conversely, consumers will delay their purchase and either deplete their inventory or forego current consumption if they feel the price will be lower in the future.

Modeling Price Expectations

Several researchers have recently applied reference price models to models of purchase decisions (e.g. Gurumurthy and Little, 1987; Puto. 1987; Raman and Bass. 1937; and Winer, 1986). Of these, only Puto, who conducted a laboratory experiment, measured reference price directly. Other researchers have operationalized he construct by postulating that a model based on observable variables adequately approximates the reference price formation process. The standard practice is to assume that the behavior of price can be used to approximate the behavior of reference price. Gabor (1977), for example, equates reference price With past price. Raman and Bass (1987) assume that the forecast generated from a time series model of past prices adequately predicts current reference price. Winer's (1986) extrapolative model depicts reference price as a weighted average of the previous two periods' prices. Gurumurthy and Little's (1987) adaptive expectation model generates a reference price equal to a weighted average, with the weights decaying exponentially, of all past prices.

There are a number of considerations that suggest that these models used to generate estimates of reference price may be inappropriate. Winer (1985! substitutes actual price for reference price into his models by arguing that actual prices are unbiased estimates of reference price. But, we have argued for a conceptualization of reference price as a forecast of future price. If so, only under very special conditions would it be appropriate to use current price as a proxy for reference price. In addition, it remains to be tested whether reference price is an unbiased predictor of price, whether current or future. Under certain theories of reference price formation. e.g., rational expectations, this will be so. However, it need not be the case.

Second, models that use current price as a proxy for reference price have limited the nature of the postulated reference price models. In particular, they seem to have given rise to models where current price information is not used by consumers in their formation of current reference price. A model that i) assumes price to be an unbiased indicator of reference price and ii) specifies current reference price to depend on current price, will result in a regression of current price on itself. This creates obvious problems. To avoid this, reference price models have limited consumers to the use of past price information only. However, this practice runs counter to most theories of expectations. For instance, rational expectations assumes that consumers efficiently incorporate all available information into their expectations/ forecasts. Information on current price is available to consumers at the time of purchase and they are likely to make use of it. Current price supplies additional, if not immediate (better) information then previous periods' prices. Indeed. it seems thai regardless of the theory of expectations formulation, current price will be used by consumers, since it is perhaps the most readily accessible piece of information. Unlike previous periods' prices, it need not be remembered but merely observed.

Because of these potential limitations in using the behavior of observed price to model the behavior of reference price, explicit measures of reference price would be valuable information. Once these measures of reference price t-e obtained, then tests can be performed to determine the association of the price expectation with the actual price. Tests can also be performed to assess the accuracy of various models in depicting the formation of reference price.

Rational Expectations

A variety of theories have been used to explain how consumers form price expectations. The differences among these theories can largely be attributed to the degree of information processing being undertaken by consumers. At one extreme, is the assumption of rational expectations, Muth (1961). Under this theory, consumers formulate subjective probability distributions of expected future outcomes that are identical to the probability distribution of outcomes generated by the underlying economic theory. In other words, consumers' price expectations are formed as if they made use of the same decision rules used by managers to set price.

Despite its popularity in some disciplines, there is one major concern with the assumption of rational expectations. This concern is over how rational expectations are formed. Bray and Kreps (1981) suggest that rational learning can lead to the development of rational expectations. However, they note that the assumptions needed are so incredible as to make implausible this model for the attainment of rational expectations equilibria. Consumers would have to have extraordinary insights and abilities to calculate the probabilities of events. Still, consumers may not actually carry out the appropriate calculations and probability assessments, but act as if they do so. The classic example is that of a billiards player who must make literally thousands of computations. While few would suggest this is being done, the outcomes are often consistent with the computations' being made.

The assumption of rational expectations can be challenged for assuming a degree of analysis, whether explicit or implicit, typically nol thought to bc undertaken in consumers' purchases. Perhaps a more realistic assumption is that of bounded rationality (Simon 1972). This approach allows consumers typically to have limited information and computational abilities. Rational behavior, therefore, is unlikely. Under bounded rationality consumers use limited information and rules of thumb in their decision making.

For instance, consumers may take the current price to be best predictor of all future prices, i.e., assume prices follow a random walk. However, a consumer has a number of readily available signals that the current price may not be the best predictor of future prices. Advertising and point-of purchase information may suggest that the current price is an exception. In this case, consumers will not base their reference prices solely on the current retail price; they will take into account the previous period's price. Shoppers may, for instance, lift the display sticker covering the previous period's price and take that to be the reference price. Their assumption is that the price of the product will revert back to this previous level at the end of the price promotion.

Testing for Rational Tuna Fish Price Expectations

In order to gain insights into whether reference price formation is consistent with rational expectations, we obtained information on price expectations from students in an introductory marketing class. Each week, for eight weeks, the students were given the current and the list price from a nearby supermarket for five brands of canned tuna fish. Each week they were asked to predict the price for each of the five brands in the upcoming week. [Tuna was selected as a familiar, frequently price promoted product. The results of the experimental study, of course, cannot be expected to be identical to those of the actual consumer. The experimental situation differs from the shopping environment. The subjects studied may also not representative of consumers as a whole. However, ninety-two percent of the students reported buying canned tuna at least occasionally.] We announced that awards of $15, $10, and $5 were to be given to the students having the three most accurate sets of forecasts over the seven week period.

Figure 1 displays the behavior of the prices of five brands of tuna over the period. Starkist started and continued to be "on sale" during the first six weeks of the experiment. This involved a $.08 discount below its list price for the first five weeks and $.60 below its list price for the sixth week. The other brands were not price promoted during the survey period. The prices of the brands, however, did change during this period. First S&W in week 5 and then all the brands in subsequent weeks had both their current and list prices change. [Neither we, nor presumably any of the subjects, had control, influence, or "advance" knowledge of any of the prices. We believe that the behavior of the prices was not unique to this particular period and, in general, was consistent with the behavior of tuna fish price fluctuations.]

We compared the students' forecasts with the actual prices to test if the price expectations are consistent with rational expectations. Tests for rational expectations assess whether the forecast is consistent; with being a conditional expectation of the underlying series. Two such properties of this type of estimator are that it is i) unbiased and ii) efficient

FIGURE 1

CANNED TUNA FISH PRICES

TABLE 1

TEST OF BIAS

An unbiased price forecast will neither systematically under- nor overstate the actual price. That is, a regression of the form

P_t = a₀ + a₁* F_t|t-1 + e_t

where

F_t|t-1 is the price forecast for period t made at period t-l, and

P_t is the actual price in period t

should yield coefficient estimates for a₀=0.00 and a₁=1.00.

Table 1 reports the results of this regression for each of the five brands of tuna fish. For each brand both the intercept and slope coefficient differ significantly from values postulated under the null hypothesis, with F-statistics under the null hypothesis ranging from 190 to 1294 versuS a critical value of approximately 3.00. For Parade, which is the store brand, and Starkist, which is the brand that was on sale during the period, the forecasts are particularly inaccurate. The coefficient indicating the association between the actual and the forecasted price for Parade is significantly negative, i.e., a coefficient of -.51. As evidenced by an estimated value for a₁ of -.02 and an R² Of .00015, the forecast for Starkist apparently has no statistically significant information content. Across all brands, the association of price expectations with price is inconsistent with that postulated b,v the rational expectations hypothesis.

Tests for forecast efficiency involve determining whether the forecasts reflect all available information at the time of the forecast. As a minimum, an efficient price forecast will incorporate all information contained in the previous values of the price series. A common test of efficiency is to estimate a model of the form:

P_t = a₀ + a₁ * F_t|t-1 + a₂ * P_t-1 + e_t

and test the hypothesis that a₂=0.00. [Another test is run the regression P_t = a₀ + a₁ * F_t|t-1 + e_t and then test if e_t is uncorrelated with P. Under the null hypothesis of rational expectations, i.e., a₂=0.00, the tests will yield identical results.] This would imply that information contained in the past value of price is better reflected in the forecasted price. Table 2 reports the results of this regression for each of the five brands of tuna.

The hypothesis of forecast efficiency, and therefore the hypothesis of rational expectations. is rejected for each brand. For each brand, the coefficient for lagged price is statistically significant. The time series information about the behavior of price is not being incorporated fully in the subjects' forecasts. The significance of a₂ indicates that information contained in current price, useful in explaining future price, is not being used by the subjects in forming their price forecasts. Indeed. only for Starkist, the brand extensively price-promoted during the period, do the subjects' forecasts make an autonomous contribution to the explanatory power of the regression.

How is Reference Price Formed?

Given that the manner in which price expectations are formed is inconsistent with rational expectations, the issue becomes finding an alternative model that betters describes the formation of reference price. Perhaps the most frequently used model of the expectations formation process is the adaptive expectations model. Under this theory of expectations formation, individuals form their future

price expectations by adding a fraction of the difference between the actual price and previous periods' forecast to their previous period's forecast. That is,

[1] F_t+1|1 = F_t|t-1 + B^a*(P_t-F_t|t-1)

By repeated substitution for F_t-k, Equation 1 gives rise to the reduced form solution:

F_t+1|1 = S [(1-b^a)^k-1*b^a*P_t-k+1

That is, for 0 < b^a < 1 the price expectation can be expressed as a weighted average of all past prices. As the weights decay exponentially, the importance of prices observed in previous periods become less important over time. For b^a=1.00, Equation I reduces to F_t+1|t=P_t Under this condition consumers assume the current period's price is the best indicator of future prices. For b^a=0.00, the model depicts price expectations to be fixed. This specification thus encompasses a number of plausible characterizations of the formation of price expectations.

Another common model of the formation of expectation is extrapolative expectations. The price expectation formulated at time period t is equal to the current price plus a fraction reflecting the difference between this period's price and last period's price. That is,

[2] F_t+1|t = P_t + b^e*(P_t-P_t-1)

Unlike adaptive expectations, instead of adjusting forecasts to reflect the current forecast error, consumers expect price to continue along some trend. Another way of viewing the relationship between the models is by noting that Equation 1 can also be expressed as F_t+1|t = (1-b^a)^*F_t|t-1 + b^a*P_t. A consumer's reference price is formed by taking a weighted average, depending on b^a, Of last periods forecasted price and this period's price. Equation 2 can be expressed as F_t+1|t = (1-(-b^e))^*P_t + -b^e*(P_t-1).

TABLE 2

TEST OF EFFICIENCY

A consumer's forecasted price is formed by taking a weighted average, depending on -b^e, Of this period's and last period's price.

In order to discriminate between these two models, as well as possibly to determine if another class of model adequately describes the reference price formation process, the following regression was estimated

[3] F_t+1|t = l₀+l₁^*F_t|t-1 + l₂^*P_t + l₃^*P_t-1 + e_t

This representation "nests" both the adaptive and explorative expectation models. Under the hypothesis of adaptive expectations, l₁=1-b^a, l₂=b^a, and l₃=0.00. Under the hypothesis of extrapolative expectations, l₁=0.00, l₂=1+b^e, l₃=-b^e. Tests of the hypothesis are reported elsewhere (Jacobson and Obermiller 1988). The results indicate that neither the adaptive expectations nor the extrapolative expectations model account for the data.

The best fit for the data is offered by a serial correlation model. Reference price depends on price but with serially correlated errors. The pattern of the coefficients is consistent with the model:

[4] F_t+1|t = c + b^sc*P_t + e_t

with e_t = P^*e_t-1 + h_t

The reduced form specification for this model, obtained by substituting (P^*e_t-1 + h_t) for e_t, and then substituting (F_t|t-1 - c - b^sc*P_t) for e_t-1.

[5] F_t+1|t = c^*(1-P) + P^*F_t|t-1 + b^sc*(P_t-P^*P_t-1) + h_t

Implications

Our findings challenge the validity of rational expectations as a mechanism for describing the formation of price expectations. Inconsistent with rational expectations, the subjects' forecasts were both biased and inefficient. There is reason to believe that rational expectations equilibria are unlikely in the context of most price promotions. Even adherents to the theory of rational expectations do not assume that every agent knows the underlying model governing the system. Rather, they suggest that arbitrage takes place where individuals who have the "correct" model dominate the outcome. Well-informed individuals can make profits at the expense of the ill-informed: for example, Muth (1961) argued that those with better expectations could sell the information profitably. This, in turn, leads to a rational expectations equilibrium. This series of events is unlikely to occur for many frequently promoted products. The cost of obtaining "efficient" information typically outweighs its benefits. For example, as the consumers' cost of "inefficiently" buying tuna is nominal, they are unlikely to purchase information from a better-informed individual. Further, imperfect information as to product quality makes arbitrage of products prohibitive. Inefficient consumers can co-exist with efficient consumers.

Our analysis also questions the applicability of some of the commonly used models depicting reference price formation. Conceptually, we argue that models that preclude consumers from using current price information in formulating reference price would appear too restrictive. Why would consumer's make use of previous periods' price information, and not current information? Current price information supplies both additional and more readily available information. Empirically, we find that the adaptive and extrapolative expectation models do not provide an adequate description of how reference price is formed. If the assumed model depicting the formation of reference price is incorrect, then the estimate of reference price and conclusions drawn from analyses using this estimate may also be incorrect.

Perhaps the most important implication of a serial correlation model depicting the reference price formation process concerns the dynamic response to changes in price. Price expectations are affected only by current price and not lagged price. For this model, if price is changed in period t and then returned to its former level in period t+1, the distribution of reference price in period t+1 is not affected. This dynamic property is why the serial correlation model is also known as the current effects model. If, in fact, price has only a contemporaneous effect on reference price, then price-promotions will not have the long-run negative implications that many have postulated.

The applicability of this model to other products and the extent to which marketing activities can influence the manner in which price expectations are formed is a direction for future research. Marketing activities can be expected to influence not only the parameters in models but also the nature of the formation process. Different types of advertising and point-of-purchase information might effect how consumers incorporate the price-promotion into their reference prices. Further work is also needed in assessing inter- and intra-b; and effects of price promotions on price expectations. Our on-going research suggests that reference price for a brand is influenced by competitive price fluctuations. The strategic implications of this competitive effects model needs further investigation.

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