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Quantitative Marketing and Economics

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01.09.2010

A simple test for distinguishing between internal reference price theories

verfasst von: Tülin Erdem, Michael L. Katz, Baohong Sun

Erschienen in: Quantitative Marketing and Economics | Ausgabe 3/2010

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Abstract

A large literature demonstrates the empirical importance of internal reference price effects. There are several theories regarding how and why these effects arise. We offer a simple test that distinguishes between the two leading theories based on economically rational behavior: price as a signal of quality and price as a predictor of future prices. Our test builds on differences in how past consumer purchases interact with internal reference prices. We first validate the reliability of our test by applying it to synthetic data. We then apply our test to purchases of ketchup and diapers and find: (1) quality signaling is the dominant mechanism behind reference price effects in both categories; (2) consistent with the quality-signaling theory, reference price effects diminish as various measures of consumer experience increase; but (3) in both categories there are many individuals for whom price-prediction effects dominate quality-signaling effects.

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There are models of new product introduction and consumer learning in which either a low introductory price (Tirole 1992, page 111) or an inefficiently high introductory price (Bagwell and Riordan 1991) can signal high quality. In the former model, a product’s mean price increases over time, whereas in the latter, a product’s mean price decreases.

Perhaps less plausibly, quality signaling can also arise in a one-period model in which all consumers are uninformed about quality. Signaling can be sustained when firms charging higher prices signal higher quality, but have lower unit sales due to the nature of consumer tastes. This mechanism requires that firms have exogenously given quality levels and marginal costs that increase in quality.

Guadagni and Little labeled this past-purchase term as “brand loyalty.” The broader literature, however, uses brand loyalty to refer both to positive state dependence (positive past purchase feedback) and unobserved heterogeneity. As discussed by Keane (1997), our Eq. 2 is the standard operationalization of positive state dependence. We account for unobserved heterogeneity separately in our model. Hence, we do not adopt the brand loyalty label for our past-purchase (use experience) variable.

Additional discussion of the inventory variable is presented in the Appendix.

An alternative approach to updating would be to update reference prices conditional on category purchase. In addition to failing to mesh with empirical findings (see Briesch et al. 1997 for a survey of the literature), this alternative approach suffers from a lack of internal consistency. To see why, observe that, if at least some consumers buy at low prices rather than at high, this behavior suggests that households check prices when they are high as well as low. Updating reference prices only when households make purchases would underestimate the reference price.

The role of memory also merits attention in passing. Although such effects can, in theory, be important, past work has shown that they do not matter much empirically (see Briesch et al. 1997). Hence, we do not include them in our model.

Katz and Shapiro (1986) provided an early test of the information-based kinked demand theory using scanner panel data for coffee.

Erdem et al. (2003) have shown that the best model of ketchup prices is that they fluctuate around a mean while exhibiting serial correlation. Those authors assume there is no learning about the price process over time; households are assumed either to know the process exactly or not to know it all, and the former assumption fits the data better than does the latter.

In addition, this may indicate that the consumer has a high overall willingness to pay for the product (otherwise the household would have foregone purchasing entirely). This would be true under either mechanism.

Although we leave the issue for another paper, it is also worth observing that there may be other implications of the two mechanisms that could be used to determine their joint presence. For example, as shown by Hendel and Nevo (2006b), the price-expectations mechanism gives rise to certain predictions about the relationship between prices and interpurchase durations that the presence of a quality-signaling mechanism would not offset. In the present paper, we implicitly account for purchase timing by modeling purchase incidence, which is allowed to be a function of inventories, but we do not offer a full model of inventory behavior.

We also checked for situations whether zero brand sales were observed for an extended and consecutive periods of time. Although zero brand sales for few consecutive periods occur (which are usually the cases when zero sales are correlated with consumer preferences) at some stores, prolonged/extended and consecutive zero sales were very rare.

The mean prices of the excluded brands were generally less than those of Huggies and Pampers, but greater than those of Luvs and store brands. Thus, it does not appear that the excluded brands were targeted at especially price-conscious consumers.

A large number of households in our dataset purchased diapers on only one occasion, suggesting that they were making purchases for children temporarily visiting. Alternatively, although our data set covers a high percentage of stores in each city, it is possible that what appear in our sample as single-purchase households are actually households that made repeated purchases at stores outside of our sample. In any event, we exclude these households from our analysis because we have no means of measuring their experience.

After other exclusions, we lost only 16 households in Chicago and 21 households in Atlanta due to this restriction.

The median interpurchase time for ketchup was 10.45 weeks. The mean and standard deviation of interpurchase times were 12.46 weeks and 7.36 weeks, respectively.

For each estimation, we used an initialization period to set the initial values of the reference price and experience measures. Based on the distribution of interpurchase times, we used an initialization period of 21 weeks for diapers and 24 weeks for ketchup. We also tried several other period lengths, and our results were insensitive to the specific choices.

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Titel: A simple test for distinguishing between internal reference price theories
verfasst von: Tülin Erdem
Michael L. Katz
Baohong Sun
Publikationsdatum: 01.09.2010
Verlag: Springer US
Erschienen in: Quantitative Marketing and Economics / Ausgabe 3/2010
Print ISSN: 1570-7156
Elektronische ISSN: 1573-711X
DOI: https://doi.org/10.1007/s11129-010-9087-7

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