# On Measuring the Informational Efficiency of Consumer Markets

ABSTRACT - Whether the costs to consumers of imperfect information are-high enough to warrant intervention in markets has long been an important policy issue. But, there toes not appear to be a comprehensive theoretical framework for studying the problem. In this paper, we develop measures of opportunity losses due to not choosing the "best" brand, and of the costs of search, based on a model of optimal search behavior.

##### Citation:

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Brian T. Ratchford and Pola B. Gupta (1987) ,"On Measuring the Informational Efficiency of Consumer Markets", in NA - Advances in Consumer Research Volume 14, eds. Melanie Wallendorf and Paul Anderson, Provo, UT : Association for Consumer Research, Pages: 309-313.
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Whether the costs to consumers of imperfect information are-high enough to warrant intervention in markets has long been an important policy issue. But, there toes not appear to be a comprehensive theoretical framework for studying the problem. In this paper, we develop measures of opportunity losses due to not choosing the "best" brand, and of the costs of search, based on a model of optimal search behavior.

INTRODUCTION

Whether government intervention to improve the informational efficiency of consumer markets is needed has long been an important policy issue (see Beales, et.al. 1981 for a comprehensive discussion). For example, a few studies that have supported the existence of inefficiency have implied that efficiency can be improved either by improving consumer information (Farrell 1980, Dardis and Gieser 1980, Maynes and Assum 1982), or by judiciously imposing strict quality standards (Sepstrup 1978). But, largely because of lack of a comprehensive theoretical framework for studying the problem, whether the costs of informational inefficiency are great enough to warrant intervention is still an open question.

By providing a framework for empirically measuring the costs of information in markets for durable goods, this study provides a first step toward answering this question. While many others have estimated losses due to inefficiency, we shall argue that none of these studies provides a totally satisfactory basis for their estimates. While we currently do not have the share or individual choice data needed to make definitive estimates based on our model, we do go on to present some preliminary estimates of the magnitude of information costs for several durables.

THE LITERATURE ON INFORMATIONAL EFFICIENCY

While there is a vast body of theoretical literature on the impact of imperfect information on market behavior (representative examples are Smallwood and Conlisk 1979, Carlson and McAfee 1983), we are primarily interested in empirical studies of informational efficiency. Broadly speaking, the empirical studies have looked at: correlations between price and quality; retail price dispersion; price of best vs. worst choice; whether a brand is on the efficiency frontier.

There is a large literature which presents correlations between prices and quality ratings provided by Consumer Reports: these are either motivated by attempts to assess how well price acts as a signal of quality (Oxenfeldt 1950, Friedman 1967, Riesz 1978, Dardis and Gieser 1980, Geistfield 1982, Gerstner 1985), or by attempts to measure market efficiency (Morris and Bronson 1969, Sproles 1977). On average, these studies have found a low positive correlation between price and quality, which has been stable over time, and that there is large variation in these correlations across product categories. This has led some authors to conclude that markets generally don't function very efficiently (Morris and Bronson 1969, Sproles 1977). As will be explained in the next section, however, we do not believe that this conclusion necessarily follows from the observed price-quality correlations. Recent work by Tellis and Wernerfelt (1985) develops a theory aimed at explaining observed price-quality relationships, and how these nay vary across markets. While this is a welcome addition to this largely atheoretical body of literature, this work does not attempt to develop measures of the magnitude of information costs, which is the subject of the present study.

Studies of price dispersion in retail markets (Pratt, Wise and Zeckhauser 1979; Maynes and Assum 1982; Shugan 1985) have generally found substantial price dispersion, with maximum prices often several times the minimum for items of essentially the same quality. Maynes and Assum argue that this indicates that retail markets are informationally imperfect. While some of the observed dispersion may be due to unmeasured brand and retailer attributes, it seems hard to argue with this basic conclusion. Moreover, given that information is costly, the finding that retail markets are informationally imperfect does not seem surprising. The studies of retail price dispersion do not address the more critical question of the degree of informational imperfection: exactly how much the imperfections cost consumers is not answered.

By examining price differences between "best" and "worst" choices based on quality rankings in Consumer Reports, Morris and Bronson (1970) estimated that on average consumers can incur a maximum loss of 27.4% by erratic purchasing. Again, however, it is hard to draw any conclusions about the extent of market inefficiency from this estimate: losses depend on whether the market share of the "worst" choice is trivial or large.

While other authors have measured quality using the composite ranking of quality provided by Consumer Reports, Hjorth-Andersen (1984) employed the ratings on each individual attribute in developing his estimates of inefficiency. Using a concept similar to Lancaster's (1966) efficiency frontier, Hjorth-Andersen judged brands which were inferior on all attributes, and still higher in price, compared to at least one other brand, to be inefficient. Employing a number of strong assumptions, he concluded that consumers could save 12.8 percent of their expenditure if all the inefficient brands were removed from the market. There are a number of problems with Hjorth-Andersen's approach: brands may be very close in price and attributes to the dominating brand, or not inefficient at all if all attributes are considered, so that loses resulting from buying these brands are small or nonexistent; on the other hand, Hjorth-Andersen's calculations do not consider possible losses that may result from non-optimal choices among efficient brands.

PROBLEMS WITH EMPIRICAL PRICE-QUALITY RELATIONS

We have stated above that correlations of prices with Consumer Reports quality rankings say little about informational efficiency. To provide a framework for understanding this, let the information cost of making any choice equal the sum of search costs, and the dollar opportunity loss resulting from not choosing the best brand for the money. Consider the case in which neither price nor quality varies much. In this case, information costs will be low even though price and quality may not be highly correlated: choosing some brand other than the best for the money will not produce much of a loss. Conversely, when price and quality vary a lot, information costs may be high even though price and quality show a high correlation: Choosing some brand other than the best for the money may result in a substantial loss. Even when price and quality vary a lot and are not correlated, aggregate losses may not be large if only a small number of consumers fail to avoid brands which are poor buys for the money. In short, observed price-quality correlations provide a poor basis for judging market efficiency.

Though they are widely used, the validity of the Consumer Reports rankings as a measure of quality is also open to question. The major problem is that the weights used for individual attributes in developing the rankings need not reflect the preferences of actual consumers; indeed if consumers are sufficiently heterogeneous in their preferences, it may be impossible to develop a unique quality index that would reflect the preferences of all. On the other hand, if the various attributes are positively correlated, any arbitrary weighting scheme will tend to yield a similar ranking of brands (Curry and Faulds 1986); the Consumer Reports scheme can be used in this case. However, whether attributes have the required positive correlation is an empirical question; the answer to this question will undoubtedly vary across products.

A FRAMEWORK FOR STUDYING INFORMATIONAL EFFICIENCY

Despite the considerable amount of empirical work on the problem, there is no really comprehensive theoretical framework for developing empirical estimates of informational efficiency. We will try to develop such a framework in this section.

We wish to estimate information costs, which are of two types: costs of search, and opportunity losses due to not choosing the optimal brand. An optimizing consumer search to the point where the marginal costs of search were equated with the expected marginal opportunity loss of not choosing the best alternative. At this point, both search costs and opportunity losses will ordinarily be positive; ideally one would add up both costs to construct a composite measure of information costs. In addition, there might be another type of cost: brands currently on the market might be less attractive than the alternatives which would result if information were somehow made less costly (Smallwood and Conlisk 1979). Absent a valid general equilibrium model, this last type of cost might be impossible to estimate.

In our model, we shall assume that the consumer will choose one brand from a set, and spend his remaining budget on other goods and search costs. The utility of alternative brands is defined by values of their attributes X_{1}...M_{m}. For simplicity, we will make the assumption that the consumer's utility function is additive-separable in the good being studied and a composite of all other goods, Y, which is measured in dollars; this assumption allows income to trop out of the comparison between brands. Because the utility function is unique only up to a monotonic transformation, we can, without loss of generality, assume that utility is measured in dollars. Given these assumptions the utility of any brand i becomes:

V

_{i}= f(X_{li},x_{2i},...,x_{mi}) + Y, (1)

and the budget constraint is:

P

_{i}+ Y + C = I, (2)

where P_{i} is price of brand i, C is search cost, I is income, and the price of Y is one dollar because we have chosen to measure Y in dollars. We can substitute Y = I - P_{i} - C in (1). Bust since I - C is a constant across alternatives, it becomes redundant in comparisons between brands, and may therefore be ignored. If, for simplicity only, we assume that f(X_{li}, X_{2i} ,..., X_{mi} ) is linear, we can express the utility associated with the choice of i as:

V

_{i}= S_{k}W_{k}x_{ki}P_{i}(3)

The consumer would like to find the brand with the highest V_{i}, but he must pay the cost of locating it.

The Relation Between Search Costs and Demand

For simplicity, assume that the consumer knows the general distribution of utilities across brands, but not the utility of any given brand (this is a common assumption in economic models of search). There are N brands, and each utility occurs with a frequency 1/N. Then the expected gain from searching for a utility higher than V_{j} is:

The consumer is assumed to use a stopping rule, so that if C > Gi he stops; otherwise he continues searching (for simplicity we assume that C, the cost of search, is constant across brands).

Within this general framework, we can derive a general expression for demand as a function of search costs (Rosen 1978; Carlson and McAfee 1983): the demand function can be either that for a market segment whose members have the same utility function; or for the whole market if preferences are homogeneous. Let the distribution of search costs across this segment be H(C), and let H(T) denote the highest search cost in the market. Let 1,...,N index the brands from lowest to highest utility. Some consumers would have search costs so high that they would buy the lowest utility brand if they encountered it: for these consumers C > G1. But the odds that they encountered this, or any other brand, are only 1/N. If C1 is the cost which would make a consumer indifferent between buying the lowest utility brand and searching further, demand for this brand can be written as:

Q

_{1}= (1/N) (H(T) - H(C_{1})) (5)

where H(T)-H(C_{1}) is the frequency of consumers who have search costs high enough to make them stop searching even if they encountered the lowest utility brand.

Similarly, there are another H(C_{1})-H(C_{2}) consumers who would reject the lowest utility brand, but stop if they encountered the second lowest brand. But the odds of this encounter are l/(N-l). Demand for the second-lowest brand therefore becomes:

Q

_{2}= (1/N) (H(T)-H(C_{1})) + (1/(N-1)) (H(C_{1})-H(C_{2})) (6)

since it also gets its share of the high search cost customers. Similarly,

In sum, demand depends on the distribution of search costs: if these are high, brand shares will tend to equality; if most of these are low, high utility brands will tend to get disproportionate shares.

Extending the framework of Carlson and McAfee (1983) to differentiated products, we can derive a linear demand function if H(C) is uniform:

where l/s is the density of search costs, total demand is I/s. Then, as explained above:

But, since C_{1} is the point of indifference between choosing brand 1 and searching further, Equation 9 can be written as (see Equation 4): N

By similar reasoning, expressions for Q_{2},...,Q_{N} can be derived. After some algebra, the general demand function reduces to:

Substituting the components of V from (3), and adding a random term (u_{i}) for brand-specific utility, we get:

which could, in principle, be estimated by regression.

The coefficient of price identifies s, the density of search costs. In principle, other demand functions could be derived from other distributions of search costs; presumably the best-fitting function would best reflect the actual distribution.

Expressions for Information Costs

The above framework will aid in developing and interpreting expressions for information costs which can be estimated empirically. In general, the opportunity loss due to imperfect information for any segment with homogeneous preferences can be expressed as:

where Q is quality of brand i, V is maximum available utility For the linear demand function in (12), equation (13) can be expressed as (see Appendix for derivatation):

where T-sNQ, is maximum search cost. Average search cost is then T12. Opportunity loss thus depends on the difference between maximum and average utility, which reflects expected losses if choices were made at random, and is reduced by the ratio of the variance in utilities (av) reflective to maximum search cost, which reflects the impact of search. After some further algebrai manipulation (see Appendix), Equation 14 can also be expressed as (for large N):

where C and p are mean value elasticity and price respectively: the more elastic the demand relative to price, the higher the search, and the smaller the loss. Moreover, T = p/e, and average cost per search equals p/2C. So estimates of mean value demand elasticity, average price, and the distribution of utilities are needed to identify the various components of information costs.

It should be emphasized that the above expression for opportunity loss is valid even if our assumptions about search behavior are violated seriously, as long as the hypothesized linear demand function holds. However, another distribution of search costs could readily produce another form for the demand function: for example, another distribution of search costs might produce the logit, a function widely used in empirical work. The logit function can be written as:

The various weights would be estimated either from data on individual choices, or from data on market shares. Unlike the standard logit model in which choice probabilities result from random variation in utility across people or time, the maintained hypothesis would be that these probabilities result from stopping search before the maximum utilitY brand is found.

Raced on the logit. an expression for opportunity loss is:

since b = Elp if N is large. Thus the loss is proportional to maximum utility less a_share weighted average of utilities. A larger b (or c/p) implies less weight to small V , and hence a lower loss. Again, it is significant that tie ratio of elasticity to price determines the magnitude of the loss.

The above logit model assumes homogeneous preferences across those it is estimated on. If preferences are heterogenous, and the estimated logit parameters represent averages, it is easily shown that the loss expression in (17) represents an upper bound.

Up to this point we have only considered opportunity losses. Especially because consumers may lower opportunity losses by spending more on search, it is also necessary to consider expenditures on search. For the case of uniformly distributed search costs, expected aggregate search costs can be expressed as (see Appendix for a derivation):

The first term in parentheses is simply average cost per search; the second term captures the impact of going beyond the initial search. (An expression for the expected number of searches is also presented in Equation A10 of the appendix.) If we combine (14) and (18), we can get an expression for total loss, which is the sum of opportunity losses and search costs:

The term in parentheses represents loss per unit sold. The loss increases with the difference between maximum and average utility, and with average search costs, decreases with the variance of utility relative to search costs. Intuitively, the latter effect represents the impact of search on limiting losses.

EMPIRICAL IMPLEMENTATION OF THE MODEL

In principle, it should be quite feasible to estimate the above relationships empirically: all one needs are estimates of the distribution of utilities across brands, average prices, and the price elasticity of demand. One could, for example, estimate individual utilities by conjoint analysis, and use these estimates to form segments. These estimates would provide the essential data needed to estimate utility distributions. Given data on the distribution of brand choices by segment, one could proceed to estimate price elasticities for each segment. Then losses could be calculated for each segment, and added across segments in to an aggregate figure. It should be possible to obtain the required data on a sample of recent purchasers. Given that estimates are not dependent on any of our admittedly strong assumptions about search behavior, this analysis should provide reasonable estimates of opportunity losses. Because they are dependent on our assumptions about sampling and the distribution of search costs, any estimates of aggregate search costs would be much more problematic.

While we do not at the moment have the desired data on utilities and price elasticities, it is still possible to make some reasonable estimates of losses. While there do not seem to be any published elasticity estimates for brands of most household durables, it is known that price elasticities for most nondurables are on the order of -1.5 to -3 (see the review in Neslin and Shoemaker ]983); it has also been estimated that price elasticities for automobile brands are on the order of -5 to -7 (Cowling and Cubbin 1971). Since our earlier analysis suggests that elasticities should increase with price, unless search costs also increase as fast as price (E - P/T), it seems plausible to assume that price elasticity for appliances is somewhere between the two extremes defined by the inexpensive nondurables and the expensive cars. Accordingly we will base empirical estimates on the alternative assumptions that E = -3 and , E = -5.

While the number of utility functions that consumers might have is unlimited, we will confine our analysis to two functions which might plausibly represent the preferences of at least some consumers. One uses attribute weights obtained from a regression of prices on attributes (hedonic price function; see Rosen 1978): utility is thus defined as the negative of the residual of this regression. This formulation of utility, which has been used before in empirical work (Cowling and Cubbin 1971), should provide a good approximation to preferences if consumers have homogeneous preferences (Rosen 1978).

We also studied losses that would result from a preference function where the attribute weights were those assigned by Consumer Reports. To recover the weights, we regressed the quality ranking on the various attributes: while the dependent variable is, strictly speaking, ordinal, there is considerable evidence that OLS is robust with ranking data relative to procedures designed for ordinal data,such as LINMAP or MONANOVA (Green and Srinivasan 1978). Hence we felt justified in using regression. Spearman correlations between estimated and actual quality rankings were all above .8 for the 5 appliance categories studied. To scale this function with respect to price, we regressed price on estimated quality from the above regression; the negative of the residuals then provided a utility function which maximized the correlation between price and a weighted sum of attributes, where the weights approximate those used by Consumer Reports.

Data on prices and attributes were taken from recent tests in Consumer Reports for the following five products: vacuum cleaners (1982), ranges (1979), refrigerators (1982 washing machines (1985), air conditioners (1982). For the utility functions and elasticities described above, estimates of losses due to imperfect information are presented in Table 1 for these five categories. As Table 1 indicates, there is considerable agreement between the estimates obtained from the alternative utility functions. As expected, more negative elasticities signal lower costs. Average costs per search seem high, particularly for the more expensive appliances when r s -3: one might realistically expect demand for these more expensive appliances to be more price elastic. While search costs and total losses may seem high, it should be kept in mind that each consumer must search at least once: on average an amount equal to c is not discretionary. With the exception of vacuum cleaners, which incur the highest percentage losses and require the most search, mean opportunity losses are on the order of .10; these are generally well below search costs. Finally, our estimates predict little search, on average, a finding which is borne out by empirical evidence (Newman 1977).

ESTIMATES OF AVERAGE LOSSES PER UNIT SOLD DUE TO IMPERFECT INFORMATION, FIVE APPLIANCE CATEGORIES

A tentative conclusion that might be drawn from this analysis is that the costs of imperfect information might be substantial. Whether there is any effective way to lover these costs is, however, an open question. Consumers also appear to behave as if search costs are high. Whether these are really as high as our analysis suggests, or whether consumers simply engage in less-than-optimal search, is also an open question.

CONCLUSIONS

Responding to what we believe to be a deficiency in the existing literature, we have developed a formal framework for studying the costs of imperfect information. We believe that this framework can be employed in empirical studies of information costs, and that it highlights the determinants of these costs.

Nevertheless, the model presented in this paper should be viewed as a beginning; there are a number of ways in which it might be improved. Some of these are:

1. Extension of the demand model to distributions of search costs other than the uniform. This would allow alternative demand models to be estimated, and would allow tests of the sensitivity of results to this assumption.

2. If policy implications are to be analyzed, a general equilibrium framework will have to be developed.

3. The model might incorporate more realistic assumptions about the search process, such as unequal priors for brands.

DERIVATION OF EXPRESSION FOR OPPORTUNITY LOSS FROM LINEAR DEMAND

REFERENCES

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##### Authors

Brian T. Ratchford, State University of New York at Buffalo

Pola B. Gupta, State Universityof New York at Buffalo

##### Volume

NA - Advances in Consumer Research Volume 14 | 1987

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