Asymmetric Consumer Search and Reference Prices Peter McGee Department of Economics, National University of Singapore AS2 Level 6, 1 Arts Link, Singapore 117570 Email: [email protected] Ph: (65)6516-6108, Fax: (65)6775-2646∗†

May 2014

Abstract In a laboratory search environment with a known price distribution and a common search cost among subjects, subjects who experience an upward shift in the price distribution are significantly more likely to search than subjects who experience a downward shift in the price distribution. Although the features of the search environment do not provide any theoretical predictions of asymmetric search in a standard framework, a simple model of reference-dependent preferences in which consumers view potential purchases as ”losses” or ”gains” relative to a reference price can generate predictions of asymmetric search. Empirical results incorporating the previous purchase price as the reference price provide support for the reference price explanation, but do not fully account for asymmetric search behavior early in search episodes following a price shift.

∗ †

JEL Classifications: C91, D03, D12 Keywords: search experiment, asymmetric search, reference price

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Introduction

In the gasoline market, consumers search more when prices are rising than when prices are falling (Lewis and Marvel 2011). This observation, along with other anecdotal evidence, has generated theoretical interest in asymmetric consumer search to explain the well-documented asymmetric “rockets and feathers” price adjustment phenomenon in which output prices increase faster in response to input price increases than they fall in response to input price decreases.1 Existing search models that give rise to asymmetric search in equilibrium assume that consumers have different beliefs about the price distribution and/or heterogeneous costs of search (Yang and Ye 2008; Tappata 2009; Lewis 2011; Cabral and Fishman 2012).2 In this study, I demonstrate that consumers search asymmetrically in the laboratory even when they are fully informed about the price distribution and its movements and have a common cost of search. In this environment, none of the common theoretical levers—costs, information, budget constraints—can explain the observed asymmetric response to a price change. I then turn to a simple model of reference-dependent preferences as a potential behavioral explanation for asymmetric search in which consumers evaluate the benefits of search against a reference price. In the experiment, search is sequential and each price draw costs subjects a known, constant amount. Subjects are given a budget and must make a purchase in each of 50 search episodes. One price is made available to subjects and remains available at no cost for the duration of the search episode, but other price draws cannot be recalled once passed over. The price distribution shifts at various points during the experiment, and subjects are fully informed about the price distribution throughout the experiment. Subjects who experience an upward shift in prices are significantly more likely to search than those who 1

Peltzman (2000) examines 242 markets for both intermediate and final goods and finds that in two-thirds of those markets, prices exhibited “rockets and feathers” pricing. Industry specific studies have documented rockets and feathers pricing in the markets for gasoline (Lewis 2011), banking (O’Brien 2000), beef and pork (Goodwin and Holt 1999), and fresh fruits and vegetables (Pick et al. 1991). 2 The asymmetry in these models and in this paper is always such that consumers search more after a price increase than after a price decrease.

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experience no shift in prices or a downward shift in prices. Asymmetric search following upward and downward shifts in prices may reflect referencedependent search decisions. If consumers measure their well-being partly in terms of deviations from a reference price, then a consumer facing a price greater than his reference price faces the prospect of a loss, while the consumer facing a price less than his reference price faces the prospect of a gain. Using a simple model of reference-dependent preferences (Koszegi and Rabin 2006), I show that the likelihood of search can be a function of the consumer’s reference price, with consumers facing a loss more likely to search than those facing a gain. Following an upward shift in the price distribution, consumers are more likely to encounter a price above their reference price, hence the increased likelihood of search. The search behavior observed in the experiment is consistent with reference-dependent preferences if subjects use the purchase price in the previous search episode as their reference price: facing a price above the previous purchase price is associated with significant increase in the likelihood of search, but facing a price below the previous purchase price does not significantly influence search decisions. The effect of losses relative to the past purchase price is larger in magnitude for early search decisions, suggesting that subjects may update their reference price over the course of a search episode. Shifts in the price distributions still have significant effects on early search decisions after controlling for feelings of gains and losses relative to the previous purchase price, leaving open the possibility that there is more at play in asymmetric search due to price changes than just gain-loss considerations. Asymmetric search in the field is likely to have many causes. Nonetheless, the intuition behind reference-dependent preferences that have made them important in other economic decisions are no less prevalent in consumer search. Firms need to understand and account for this potential behavioral cause of asymmetric search when considering how to adjust their prices. The remainder of the paper is organized as follows. Section 2 discusses the relevant theoretical and experimental work dealing with asymmetric search. Section 3 lays out the experimental design. Section 4 discusses the findings without considering reference-

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dependent preference. Section 5 introduces reference-dependence and additional empirical results, and Section 6 briefly concludes.

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Literature

2.1

Asymmetric Search: Theory and Evidence

Several papers have modeled asymmetric search an explanation of the “rockets and feathers” pricing pattern. While asymmetric price adjustment is well documented, asymmetric search is not due to the inherent difficulties in measuring search behavior in the field. Lewis and Marvel (2011) cleverly use traffic for a website that allows consumers to upload and view local gas station prices as a proxy for individual search in gasoline markets. Search behavior closely tracks the asymmetric path of gasoline prices, which is characterized by “rockets and feathers” pricing. Lewis and Marvel find that increased search forces more competitive pricing among firms, reducing retail margins and price dispersion. Because search reduces retail margins and results in less price dispersion, they argue that this asymmetric search may cause the “rockets and feathers” pricing observed at retail gasoline outlets. The models of Yang and Ye (2008), Tappata (2009), Lewis (2011), and Cabral and Fishman (2012) all generate predictions of asymmetric search as explanations for “rockets and feathers.” To generate these predictions, the models exploit various features of the search environment: consumer search costs, consumer beliefs about the price distribution, consumer knowledge of the costs faced by firms, and the nature of search (sequential versus non-sequential). These theoretical levers all play important parts in search behavior in the field, but one aim of this study is to show that asymmetric search can also be generated in the absence of these features.

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2.2

Reference Dependence and Consumer Decisions

Key elements of prospect theory—that losses loom larger than gains for consumers (loss aversion), that individuals are risk-seeking over losses and risk-averse over gains, and that individuals exhibit biases in the way they consider probabilities and process information —have been integrated into economic theory and used to explain target incomes (Camerer et al. 1997), disposition effects (Weber and Camerer 1998), endowment effects (Kahneman et al. 1990), and the purchase of insurance (Ciccheti and Dubin 1994), among other things.3 Recently, economists have begun to take advantage of theoretical work (Koszegi and Rabin 2006; 2009) which incorporates the utility of gains and losses and a standard consumption utility into one model (e.g., Crawford and Meng 2011). The role of reference points and reference prices in consumer decisions has also been studied extensively in the empirical marketing literature, e.g., reference prices affect have been found to affect brand choice (Kalyanaram and Little 1989; 1994; Winer 1989).4 Reference points more generally can also have asymmetric effects on consumer behavior. Hardie et al. (1993) find that the likelihood that a consumer chooses a certain brand of orange juice is significantly affected by whether or not the measurable attributes of that brand represent a “loss” or a “gain” relative to a reference brand of orange juice. The effect of relative “losses” is larger than that of relative “gains” when the measurable attribute was either price or quality. Similar effects have been found for other goods such as yogurt (Mayhew and Winer 1992) and eggs (Putler 1992). Most importantly, “internal” reference prices—reference prices that come from a consumer’s experience as opposed to “external” reference prices suggested by an advertisement or promotion—have been found to be functions of past prices observed by the consumer (Kalwani et al. 1990; Briesch et al. 1995).5 In particular, Krishnamurthi et al. (1992) use the last price paid as the reference price and find significant effects of reference 3 Camerer (2004) provides a survey of the most common areas in which prospect theory has been applied to economic theory. 4 Kalyanaram and Winer (1995) is a useful survey. 5 External reference prices have also been found to have effects on consumer decisions. See, for example, the effect of an external reference price in an advertisement on search behavior in Urbany et al. (1988).

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prices on brand choice and purchase quantity in the market for coffee.6

2.3

Search in Experiments

From its beginnings, the experimental search literature has been investigating how close experimental subjects come to theoretical predictions in different environments, e.g., finite versus infinite horizon, known versus unknown distributions, recall versus no recall of foregone prices. The picture that has emerged over time is one in which subjects often come close to optimal behavior but are also observed to frequently search too little relative to a risk-neutral benchmark (Schotter and Braunstein 1981; Braunstein and Schotter 1982; Cox and Oaxaca 1982; Hey 1987). In the spirit of Simon (1955), early work by Hey observes that working out the optimal solution requires calculations that are beyond the capabilities of most searchers, so searchers may use other search strategies. This has led to interest not in just how close to optimality subjects come, but in how they actually search, resulting in work focusing on things such as heuristic search rules (Hey 1981; 1982), and the observation that many searchers are concerned with total costs of search, rather than marginal costs of search (Kogut 1990; 1992; Sonnemans 1998; 2000). Schunk and Winter (2009) and Schunk (2009) examine the roles of risk aversion and loss aversion in search. The undersearch observed in many experiments could potentially be explained by a certain degree of risk aversion. Neither paper finds that measured risk aversion significantly predicts search behavior but that measures of loss aversion do. Schunk (2009) goes further by developing a model that incorporates reference prices into search decisions. The primary difference between the setting studied here and that in the Schunk experiment is that subjects have the ability to recall past prices in the Schunk experiment but not here. Although the intuition that undersearch might be caused by comparison to a reference price is common to both studies, there would be no prediction of asymmetric search in the Schunk environment: reference prices are updated with each price draw because of recall, meaning 6

The authors find similar effects in a second product market but do not reveal what market because the data are proprietary.

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the reference price can only go down with each draw, and, as the reference price goes down, the likelihood that the next draw will be a “bad” price relative to the reference price goes up. This would lead to undersearch, but not to oversearch. Many search experiments find undersearch, but there is also some limited evidence of oversearch. Both Zwick et al. (2003) and Zwick and Lee (1999) observe oversearch relative to a benchmark model. The former paper observes oversearch in a much different environment than the one found in this paper (e.g. multiattribute search, probabilistic recall), but the latter has a great deal in common with the design of this experiment. In Zwick and Lee, a buyer and seller negotiate and the buyer has the ability to walk away from the offer on the table and search from a distribution of potential sellers. In some cases the buyer has the ability to come back to the price offered by the initial seller, in other cases not, but the authors find that when the price offered by the initial seller in the current bargaining round is higher than the initial price set in the previous bargaining round, buyers are significantly more likely to search from outside sellers. Finally, Castilla and Haab (2010) also investigate reference-dependent preferences as a source of asymmetric search in a quasi-experimental setting. Using an online survey, they elicit how much a consumer paid the last time he purchased gasoline. Respondents are then asked to consider a hypothetical scenario in which they need gas and encounter a price that is either higher or lower than the price they paid the last time. Respondents can choose to either purchase at this given price or continue to search, where the search is costly. They find that subjects who face a price above their previous purchase price choose to search 45% of the time versus 12% for those who face a price below their previous purchase price, and attribute the asymmetry to reference-dependent preferences. There are a number of methodological differences between the Castilla and Haab study and the present experiment—e.g., they do not employ shifts in the price distribution, decisions in their study are hypothetical—which limit direct comparisons, but their evidence is suggestive that reference dependence plays a role in search decisions as hypothesized in this study.

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3

Experimental Design

The data come from four sessions conducted at Ohio State University with a total 49 undergraduate subjects. The sessions are summarized in Table 1. Each experimental session consisted of two practice search episodes followed by 50 search episodes for which the subject could potentially be paid. In every search episode, subjects had a budget of 350 Experimental Currency Units (henceforth ECUs, where $1=50 ECU) to make a single purchase. Subjects were provided an initial price at no cost and could either purchase at that price or choose to search for another price. Subjects who searched paid 5 ECU from their budget and received a single price drawn randomly from the support of the price distribution.7 Subjects knew that prices were initially drawn from a uniform distribution over the interval [150, 250], and they were informed in the instructions that the price distribution would shift during the session. Subjects did not know when prices would shift but they knew that they would be informed when prices changed. The price distribution shifted at the beginning of search episodes 7, 18, 24, 33, and 41; the price distribution did not change during a search episode. Subjects did not know the process by which the prices were shifted and price shifts were independent across subjects.8 The distribution from which prices were drawn was displayed at the top of the subject’s screen; Figures 1 and 2 show the user interface in cases with and without shifts in the price distribution, respectively. At the beginning of the session, six prices were drawn randomly from the support of the price distribution for each individual subject and denoted as the prices of retailers A, B, C, D, E, and F. The prices do not change unless there is a shift in the price distribution. If the distribution shifts, each price is shifted by the same amount so that its relative position in the distribution (and among the other retailers) does not change during the session. Retailer F’s price is the price provided at no cost to a subject and 7

Prices were drawn with replacement, which subjects were made aware of in the instructions. The shift of the price distribution, x, was drawn with probability 0.5 from a discrete uniform distribution over the interval [−70, −30] and with probability 0.5 from a discrete uniform distribution over the interval [30, 70] such that after the shift prices were drawn from a discrete uniform distribution over the interval [150 + x, 250 + x]. 8

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remains available to the subject throughout the search episode. Although retailer F’s price is always available to a subject, there is no recall of other foregone prices, so if a subject obtains through search a price P ′ that is lower than retailer F’s price, P ′ will no longer be available to him if he chooses to take another price draw. The prices for retailers A-E are not available to a subject and are provided to ensure that shifts in the distribution are salient to subjects. The motivation for this is that, although price changes were announced at the top of the screen, subjects focusing on just retailer F may mistakenly view a change in retailer F’s price as a change in its relative position in the same distribution rather than a change in the distribution itself, thus changing the expected benefits to search.9 Subjects were paid for 5 randomly selected search episodes and the average earnings were $25.51 per subject for a session lasting about two hours. At the end of every session, subjects completed the low-stakes risk preference measure from Holt and Laury (2002, henceforth HL). X chance of receiving $2.00 In the HL measure, subjects make ten choices between lottery A ( 10

and 1 −

X 10

X chance of receiving $1.60) and lottery B ( 10 chance of receiving $3.85 and 1 −

X 10

chance of receiving $0.10) where X increases from one for the first choice to ten for the tenth choice. The HL score is increasing in risk aversion, such that more risk-averse subjects select lottery A for more decisions. One of the ten choices was chosen at random, and subjects were paid according to the outcome for the lottery they selected for that choice. Average earnings on the risk preference measure were $2.51. There are 2,450 subject-search episode observations. Within each search episode, a subject may choose to search several times. Every time a subject makes a choice to either purchase or search for a lower price is a “decision” made by the subject. For example, if a subject chooses to purchase at retailer F’s price without ever searching, that subject has made one decision during the search episode. If the subject takes four price draws and then purchases, the subject has made five decisions. In the 2,450 subject-search episode 9

It was important to make sure that subjects were aware of the price distribution because one of the largest advantages of the laboratory in this context is that subjects are not taking price draws to learn about the distribution of prices.

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observations there are 8,274 such decisions.

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Search

4.1

Basic Search Model

Experimental economists have expended a great deal of effort trying to illuminate the exact strategies employed by searchers. Although much of this research has focused on the deviations from optimal search, search is found to often be broadly consistent with the basic model and it remains a useful benchmark even in though it does not match the experiment exactly. In the canonical model (Stigler 1961; Lippman and McCall 1976), a risk-neutral searcher who faces a sequential price search process with a marginal cost of search c, no recall of foregone price draws, in an infinite horizon, and with prices drawn from a uniform 1

distribution over [0, b], sets a reservation price equal to (2cb) 2 .10 In the experiment with b = 100 and c = 5, the reservation price is approximately P + 31.6, where P the lower bound of the distribution. The subject should search whenever the minimum of the current price draw and retailer F’s price is above the reservation price. This benchmark model applies only to searchers who are risk-neutral; the reservation price will be higher for risk-averse searchers than risk-neutral searchers, while it will be lower for risk-loving searchers, with the exact difference depending on the shape of the utility function. Subjects in the experiment also face a budget constraint. In practice the budget constraint does not bind, but when utility is linear and search is budget-constrained, consumer search rules are governed by a sequence of non-decreasing reservation prices (Manning and Manning 1997) such that the likelihood that one searches should be increasing in the remaining budget, i.e., a subject is willing to accept a higher price as he depletes his budget. 10

This reservation price is derived in the appendix.

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4.2

Search Behavior

Relative to the risk-neutral benchmark, subjects should start searching in 1,750 of the 2,450 subject-search episode observations and should immediately purchase at retailer F’s price in 700. Subjects who should search according to this benchmark do so in 90.3% of cases, while subject’s who should not search do so 24% of the time.11 In the basic model with recall, an individual should never go back to purchase at an earlier price because his reservation price is constant. Nonetheless, past studies have shown that subjects frequently do go back; for example, Kogut (1992) finds that approximately 34% of subjects go back. The evidence suggests that subjects who do exercise recall do so because they are concerned with total costs of search rather than just the marginal cost of search. In the experiment, the only price that a subject could recall was retailer F’s price, so one would expect less recall. Subjects who initially pass on retailer F’s price go back and purchase at retailer F’s price in 11.3% of search episodes. Due to the budget constraint, it is possible that an increasing reservation price would eventually result in retailer F’s price being acceptable, but 49.2% of those who go back do so after only a single price draw. Of the 8,274 subject decisions, the risk-neutral benchmark implies that subjects should search in 4,735, and subjects do so in 90.0% of those cases. Subjects should not search in the remaining 3,539 decisions but choose to do so 44.2% of them. Breaking out decisions by whether or not a shift occurred, in search episodes with no shifts the fraction of those predicted to search who do search is 90.2% and those who ought not search but do is 43.2%. In search episodes with a shift, 88% of those who ought to search do so, and 52% of those who ought not search choose to search. Fewer subjects who should search actually do so in search episodes in which prices shift than in search episodes with no shift, while more subjects who should not search choose to do so in search episodes in which prices shift than in search episodes with no shift. 11

Ironically, subjects choose to begin searching in 1,749 subject-search episodes, which is almost exactly the number who should when compared to the risk-neutral benchmark, though it obviously masks the deviations—both undersearch and oversearch—from the benchmark model.

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Subject behavior is broadly consistent with the benchmark, but to more rigorously examine the predictions of the basic model, I estimate the following latent relationship using a logit model ∗ Yijt = Xβ + αi + ϵijt

(1)

where i is the individual (i = 1, ..., 49), j is the decision (j = 1, ..., 34), and t is the search episode (t = 1, ..., 50). The observed outcome is the decision to search, which takes on the value Yijt

   1 :Y∗ ≥0 ijt =  ∗  0 : Yijt <0

The vector X includes, among other things, Benef itijt , which is the difference between the lowest price available and the risk-neutral benchmark reservation price. Although the reservation price is a function of an individual’s risk preferences, the likelihood of search is increasing in this difference irrespective of risk preferences. It also includes Budgetijt , which is the remaining budget and should have a positive effect on likelihood of search, as reservation prices ought to be higher with each successive price draw for any value of the expected benefit to search. Also included in X are dummy variables for blocks of ten periods (i.e., D11−20 is a dummy variable equal to one if 10 < t ≤ 20, D21−30 is equal to one if 20 < t ≤ 30, and so on) and the interactions of these dummies with Benef itijt and Budgetijt . The dummies and interactions are to account for any learning or experience effects as subjects become more familiar with the experimental environment or come closer to approximating the benchmark reservation price. There is also a great deal of heterogeneity in search behavior: there are four subjects who never search while one subject searches 34 times in one search episode. This may be due to factors such as particular tastes for search, different heuristic search rules, or having a particularly attractive price for Retailer F. To account for this I include subject fixed effects in the parameter αi . Finally, ϵijt is the econometric error term with mean zero. For all models, I report robust standard errors clustered at the subject level. 11

The marginal effects can be found in column 1 of Table 2. As predicted by the basic model, the difference between the lowest available price and the risk-neutral reservation price is positive and significant: a 10 ECU increase in the expected benefit is associated with a 7.9 to 9.5 percentage point increase in the likelihood of search. There seems to be some early learning, as three of the four interactions with the block dummies are significant at the 10% level or better, but this learning appears to take place during the first 10 search episodes; I cannot reject the null hypothesis that the estimated effects of the interactions are all equal (p = 0.720). The effects of the remaining budget are also consistent with the basic model, though only modestly: a 10 ECU decrease in the remaining budget in the last 20 search episodes—equivalent to 2 searches—is associated with a significant decrease in the likelihood of search of approximately 3 percentage points.12 Do subjects respond asymmetrically when the price distribution changes by searching more when prices go up than when prices go down? To answer this question, I introduce U p and Down to the model in column 2 of Table 2. U p is the amount by which the price distribution is shifted upward in a search episode relative to the previous search episode, while Down is the amount by which the price distribution is shifted downward in a search episode relative to the previous search episode.13 After the inclusion of U p and Down, the marginal effects and significances of the expected benefit to search, the remaining budget, and the time trends are essentially unchanged. U p and Down indicate that search is asymmetric, but the effects are small: a 10 ECU upward shift in the prices is associated with a 0.9 percentage point increase in the likelihood of search (p = 0.013), while a downward shift of the same magnitude is associated with a 1 percentage point decrease in the likelihood of search (p = 0.012). 12

Conditional on searching, the average number of searches is 4.3. U p and Down are defined relative to the previous search episode. As an example, suppose a subject has experienced a shift and the support of the price distribution is [127, 227]. After the next shift, the support of the price distribution is [162, 262]. The magnitude of U p in this case would be 35. Overall there were 134 search episodes in which a subject experienced an upward shift defined in this way, with a mean of 51.1 and a median of 41.5; there were 111 search episodes in which a subject experienced a downward shift, with a mean of 57 and a median of 56. 13

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The specification in column 2 of Table 2 assumes that the effects of shifts on search behavior do not vary with the size of the shift, but this may not be the case if subjects are concerned with total profits from search and not just marginal benefits. The price distribution shifts but the budget does not, so when a subject experiences a large upward shift, he will pay a higher price and have a smaller total profit, whereas a small upward shift will have less impact on total profits. In column 3 of Table 2, I allow for non-linear effects in the shifts by adding U p2 and Down2 . Consistent with a concern for total profit, U p2 is negative and significant (p = 0.016), such that upward shifts increase the likelihood of search, but large upward shifts increase the likelihood of search by less. Down2 is positive, but not significant at any conventional level (p = 0.341). Allowing for non-linearities in the way a price shift affects search behavior, the net effect of a 10 ECU upward shift in prices— approximately 4 percentage points—is more than four times larger than when constraining price shifts to have a linear effect on search behavior. The models of asymmetric search in the asymmetric price adjustment literature generate the asymmetry by assuming that different individuals have different beliefs about the price distribution and/or they have heterogeneous costs of search, but search is still asymmetric when these potential causes are of no avail. The question remains: why do subjects respond in the observed asymmetric fashion to shifts in the price distribution?

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A Reference Price Explanation for Asymmetric Search

Potential gains and losses relative to a reference point may also contribute to asymmetric search. If a consumer’s search decisions are influenced by what he expects to pay for a good— a reference price—then the prospect of purchasing at a price above his reference price may feel to him like a loss, while the prospect of purchasing at a price below his reference price feels like a gain. Mitigating feelings of loss will increase the benefit to search for consumers who face a price above their reference price.

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To formally see how the incorporation of reference prices into a search model might potentially lead to asymmetric search, consider an indirect utility formulation of the referencedependent preferences model proposed by Koszegi and Rabin that allows a consumer’s utility to be a function of the absolute level of consumption and gains and losses relative to a reference price.14 The consumer’s indirect utility, V , is given by

V (B, P |PR ) ≡ m(B, P ) + f (B, P |PR )

where B is the budget, P the price a consumer faces for the good, and PR the consumer’s reference price for the good. Indirect consumption utility is given by m(B, P ), while f (·) is a “gain-loss” utility function given the consumer’s reference price PR . The gain-loss utility function takes the form

f (B, P |PR ) = µ(m(B, P ) − m(B, PR ))

where µ(x) = ηx for x > 0, µ(x) = ηλx for x < 0, and η > 0 and λ > 1. The parameter η can be interpreted as how much importance a consumer places on gain-loss considerations, while the parameter λ can be thought of as the impact of loss aversion. The loss aversion parameter is assumed to be larger than 1 to reflect that losses loom larger than gains. Assume there is no diminishing marginal sensitivity to gains and losses (i.e., for all x ̸= 0, µ′′ (x) = 0), there is no budget constraint, no recall of foregone prices, a fixed cost of search c, and prices uniformly distributed over [0, b].15 Proposition 5.1. The probability that any individual searches is weakly decreasing in his reference price. The proof of Proposition 5.1 can be found in the appendix, but the intuition is very simple. As an individual’s reference price increases, more prices are going to be acceptable 14 15

The implications of using indirect utility are addressed in footnote 21 of Koszegi and Rabin (2009). This model reduces to the risk-neutral benchmark if P = PR .

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purchase prices, and the likelihood that a new price draw is worse than a price in hand also goes up. Allowing for potential losses to have a larger effect magnifies the trade-off between purchasing at the price in hand and continuing to search. Reference point formation in any context is largely a black box, but the previous purchase price is often used as a reasonable candidate in consumer decisions. In column 1 of Table 3, I re-estimate the model in Table 2 but add Gain and Loss, where Gain is the absolute difference between the previous purchase price and the lowest available price when the previous purchase price is higher, and Loss is the absolute difference between the previous purchase price and the lowest available price when the previous purchase price is lower. The marginal effects of the expected benefit and remaining budget on the likelihood of search are smaller in magnitude after the inclusion of Gain and Loss, but otherwise consistent with the effects in Table 2: a 10 ECU increase in the expected benefit is associated with approximately a 6.6 percentage point increase in the likelihood of search and a 10 ECU reduction in the budget is associated with approximately a 0.7 percentage point decrease in the likelihood of search. The magnitude of the asymmetry between U p and Down is essentially the same as in column 3 of Table 2, though neither marginal effect is significantly different from 0 (p = 0.144 and p = 0.195, respectively). There is no significant effect on a subject’s search behavior when he faces a price that is a gain relative to the previous purchase price, but facing a price that is a loss relative to the previous purchase price is associated with a significant increase in the likelihood of search: a price that is 10 ECUs higher than the previous purchase price is associated with 1.3 percentage point increase in the likelihood of search (p = 0.08). Subjects may update their reference price over the course of a search episode, so using the previous purchase price as the reference price may be most reasonable when the subject is making his initial search decisions in an episode. In columns 2 and 3 of Table 3, I break out decisions made earlier and later in a search episode. In column 2, I use only data from the first two decisions in a search episode, while column 3 uses data from from the third decision onward. Three differences between columns 2 and 3 stand out. First, the differences

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suggest that gains and losses relative to the previous purchase price are more important to early decisions: facing a price that is 10 ECUs higher than the previous purchase price is associated with a 2.5 percentage point increase (p < 0.001) in the likelihood of search for the first two decisions in a search episode, but only a 0.9 percentage point increase (p = 0.019) in the likelihood of search for later decisions. This is consistent with updating reference prices during search such that the previous purchase price is less central to the reference price. Second, shifts in the price distribution have large and significant impacts on early search decisions even after controlling for gains and losses relative to the previous purchase price: an 10 ECU upward shift in the price distribution increases the likelihood of search by approximately 10.5 percentage points while a similar downward shift in the price distribution reduces the likelihood of search by approximately 6.5 percentage points. Although gains and losses play a role in the search decision and there are no obvious theoretical reasons for shifts in the price distribution to influence search, there remains something unexplained about asymmetric responses to price shifts.16 Finally, the effect of the expected benefit to search is 43.2% larger for later decisions in an episode and price shifts have smaller, insignificant effects on later search decisions, making subjects’ later search decisions more consistent with the risk-neutral benchmark.

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Conclusion

Consider a driver in need of gas who drives past a gas station. For many drivers, a price $0.40 per gallon more than his last purchase will spur them to keep going in the hopes of finding a price more like what they last paid; conversely, a price $0.40 cheaper might cause drivers to jump at the opportunity to purchase at such a “low” price. This example illustrates the effects of reference points and the accompanying psychic “gains” and “losses” may have on 16

It could be that the effects of price shifts reflect gains and losses relative to a different reference price. In unreported results, I constructed a variety of reference prices using weighted averages of Retailer F’s price, the most recent price draw, the prices of Retailers A-E, and lagged purchase prices. The effects of price shifts on the first two search decisions in a search episode were significant for every variant of the reference price.

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search behavior. While intuitively appealing, there is sparse empirical documentation of asymmetric search due to the difficulty of measuring search behavior. The search environment here is a very simple one—no recall, a known price distribution, a fixed cost of search—and no feature of the search problem suggests an asymmetric response to upward and downward shifts in the price distribution. In particular, existing models of asymmetric search in the asymmetric price adjustment literature rely on heterogeneous costs of search or heterogeneous beliefs about the price distribution, which are not present in the experiment. Despite this, subjects are significantly more likely to search following an upward shift in the price distribution. An alternative is that consumers form reference prices and deviations from the reference price affect utility. In the experiment, subjects who experience an upward shift in the price distribution are more likely to face a price above their reference price than those who experience a downward shift in the price distribution. Losses loom larger than gains in the reference-dependent preferences model, so those who experience a “loss” are more likely to search than those who experience a “gain.” The results are consistent with referencedependent preferences, with subjects facing a “loss” more likely to search than those facing a gain. Interestingly, however, shifts in the price distribution have asymmetric effects on search behavior early in a search episode even after controlling for gains and losses relative to the reference price, suggesting that more is at play in asymmetric search. Marketers have long recognized the importance of reference prices on consumer decisions, and asymmetric search of the sort in this experiment has been mooted as an explanation for the “rockets and feathers” asymmetric price adjustment pattern. Asymmetric search generated by reference-dependent preferences may have important consequences in other markets, too. For instance, individuals who receive smaller raises than they expected may be more likely to look for another job than those who receive larger than expected raises, or, similar to the findings in Simonsohn and Loewenstein (2006), individuals moving from a high cost city might do less house hunting in a low cost city than a consumer moving from

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a low cost city to a high cost city. Advertisers who find a way to insinuate their price as a reference price may be able to insulate themselves from some of the competitive effects of price search. Both firms’ strategies and consumer welfare are significantly affected by understanding the mechanisms underlying asymmetric consumer search. There is still a great deal of work to be done to understand the nature of asymmetric search. Why do price shifts have an asymmetric effect on some search decisions in a simple framework after controlling for both the expected benefit to search and the “reference price?” There is also the always difficult problem of determining not only what the reference point is, but how it is updated. It seems reasonable that something as simple as allowing recall, as in Schunk (2009), could change how reference points are determined and search decisions are evaluated. It is also possible that subjects are using rules of thumb to search, as has been shown in numerous previous studies; how do reference price considerations influence search heuristics? Do reference points change within the same heuristic? Do searchers use different heuristics based on whether they feel as though they are facing a loss or a gain? These questions are left to future research.

18

References Yale Braunstein and Andrew Schotter. Labor Market Search: An Experimental Study. Economic Inquiry, 20(1):133–144, 1982. Richard Briesch, Lakshman Krishnamurthi, Tridib Mazumdar, and S. P. Raj. A Comparative Analysis of Reference Price Models. Journal of Consumer Research, 24(2):251–262, 1995. Luis Cabral and Arthur Fishman. Business as Usual: A Consumer Search Theory of Sticky Prices and Asymmetric Price Adjustment. International Journal of Industrial Organization, 30:371–376, 2012. Colin Camerer. Prospect Theory in the Wild: Evidence from the Field. Princeton University Press, In: Advances in Behavioral Economics, Eds. Colin Camerer, George Loewenstein, and Matthew Rabin:148–161, 2004. Colin Camerer, Linda Babcock, George Loewenstein, and Richard Thaler. Labor Supply of New York City Cab Drivers: One Day at a Time. Quarterly Journal of Economics, 112 (2):407–441, 1997. Carolina Castilla and Timothy Haab. Asymmetric Search and Loss Aversion: Choice Experiment on Consumer Willingness to Search in the Gasoline Retail Market. Working Paper, 2010. Charles Ciccheti and Jeff Dubin. A Microeconometric Analysis of Risk-Aversion and the Decision to Self-Insure. Journal of Political Economy, 102(1):169–186, 1994. James Cox and Ronald Oaxaca. Laboratory Experiments with a Finite-Horizon Job-Search Model. Journal of Risk and Uncertainty, 2(3):301–329, 1982. Barry Goodwin and Matthew T. Holt. Price Transmission and Asymmetric Adjustment in the U.S. Beef Sector. American Journal of Agricultural Economics, 81:630–637, 1999.

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Bruce Hardie, Eric Johnson, and Peter Fader. Modeling Loss Aversion and Reference Dependence Effects on Brand Choice. Marketing Science, 12(4):378–394, 1993. John Hey. Are Optimal Search Rules Reasonable? And Vice Versa? (And Does it Matter Anyway?). Journal of Economic Behavior and Organization, 2:47–70, 1981. John Hey. Search for Rules for Search. Journal of Economic Behavior and Organization, 3: 65–81, 1982. John Hey. Still Searching. Journal of Economic Behavior and Organization, 8:137–144, 1987. Daniel Kahneman, Jack Knetsch, and Richard Thaler. Experimental Tests of the Endowment Effect and the Coase Theorem. Journal of Political Economy, 98(6):1325–1348, 1990. Manohar Kalwani, Chi Kin Yim, Heikki Rinne, and Yoshi Sugita. A Price Expectations Model of Customer Brand Choice. Journal of Marketing Research, 27:251–262, 1990. Gurumurthy Kalyanaram and John Little. A price response model developed from perceptual theories. Sloan School Working Paper, 3038-89, 1989. Gurumurthy Kalyanaram and John Little. An empirical analysis of latitude of price acceptance in consumer package goods. Journal of Consumer Research, 21(2):408–418, 1994. Gurumurthy Kalyanaram and Russel S. Winer. Empirical Generalizations from Reference Price Research. Marketing Science, 14(3):161–169, 1995. Carl Kogut. Consumer Search Behavior and Sunk Costs. Journal of Economic Behavior and Organization, 14:381–392, 1990. Carl Kogut. Recall in Consumer Search. Journal of Economic Behavior and Organization, 17:141–151, 1992. Botond Koszegi and Matthew Rabin. A Model of Reference-Dependent Preferences. Quarterly Journal of Economics, 121(4):1133–1165, 2006. 20

Botond Koszegi and Matthew Rabin. Reference-dependent consumption plans. American Economic Review, 99(3):909–936, 2009. Lakshman Krishnamurthi, Tridib Mazumdar, and S.P. Raj. Asymmetric Response to Price in Consumer Choice and Purchase Quantity Decisions. Journal of Consumer Research, 19 (3):387–400, 1992. Matthew Lewis. Asymmetric Price Adjustment and Consumer Search: An Examination of the Retail Gasoline Market. Journal of Economics and Management Strategy, 20(2): 409–449, 2011. Matthew Lewis and Howard Marvel. When do consumers search?

Journal of Industrial

Economics, 59(3):457–483, 2011. Steven Lippman and John McCall. The Economics of Job Search: A Survey. Economic Inquiry, 14:155–189, 1976. Richard Manning and Julian R.A. Manning. Budget-Constrained Search. European Economic Review, 41:1817–1834, 1997. Glenn Mayhew and Russell Winer. An empirical analysis of internal and external reference prices using scanner data. Journal of Consumer Research, 19(1):62–70, 1992. James O’Brien. Estimating the Value and Interest Rate Risk of Interest-Bearing Transactions Deposits. Board of Governors of the Federal Reserve System, Finance and Economics Discussion Paper No. 46, 2000. Sam Peltzman. Prices Rise Faster than They Fall. Journal of Political Economy, 108: 466–502, 2000. Daniel H. Pick, Jeffrey Karrenbrock, and Hoy F. Carmen. Price Asymmetry and Marketing Margin Behavior: An Example for California-Arizona Citrus. Agribusiness, 6:75–84, 1991.

21

Daniel Putler. Incorporating Reference Price Effects into a Theory of Consumer Choice. Marketing Science, 11(3):287–309, 1992. Andrew Schotter and Yale Braunstein. Economic Search: An Experimental Study. Economic Inquiry, 19(1):1–25, 1981. Daniel Schunk. Behavioral Heterogeneity in Dynamic Search Situations: Theory and Experimental Evidence. Journal of Economic Dynamics and Control, 33:1719–1738, 2009. Daniel Schunk and Joachim Winter. The Relationship Between Risk Attitudes and Heuristics in Search Tasks: A Laboratory Experiment. Journal of Economic Behavior and Organization, 71:347–360, 2009. Herbert Simon. A Behavioural Model of Rational Choice. Quarterly Journal of Economics, 64:99–118, 1955. Uri Simonsohn and Geoerge Loewenstein. Mistake 37: The Effect of Previously Encountered Prices on Current Housing Demand. Economic Journal, 116:175–199, 2006. Joep Sonnemans. Strategies of Search. Journal of Economic Behavior and Organization, 35: 309–332, 1998. Joep Sonnemans. Decisions and Strategies in a Sequential Search Experiment. Journal of Economic Psychology, 21:91–102, 2000. George Stigler. The economics of information. Journal of Political Economy, 69(3):213–225, 1961. Mariano Tappata. Rockets and Feathers: Understanding Asymmetric Pricing. RAND Journal of Economics, 40(4):673–688, 2009. Joel E. Urbany, William O. Bearden, and Dan C. Weilbaker. The Effect of Plausible and Exaggerated Reference Prices on Consumer Perceptions and Price Search. Journal of Consumer Research, 15(1):95–110, 1988. 22

Martin Weber and Colin Camerer. The Disposition Effect in Securities Trading: An Experimental Analysis. Journal of Economic Behavior and Organization, 33(2):167–184, 1998. Russell Winer. A multi-stage model of choice incorporating reference prices. Marketing Letters, 1:27–36, 1989. Huanxing Yang and Lixin Ye. Search with Learning: Understanding Asymmetric Price Adjustments. RAND Journal of Economics, 39(2):547–564, 2008. Rami Zwick and Ching Chyi Lee. Bargaining and Search: An Experimental Study. Group Decision Negotiating, 8:463–487, 1999. Rami Zwick, Amnon Rapoport, Alison King Chung Lo, and A.V. Muthukrishnan. Consumer Sequential Search: Not Enough or Too Much? Marketing Science, 22(4):503–519, 2003.

23

Figure 1: User Interface

24

Figure 2: User Interface After a Shift in the Distribution

25

Table 1. Session Details

Session Subjects 1 12 2 15 3 11 4 11

Exchange Rate 50 ECU = $1 50 ECU = $1 50 ECU = $1 50 ECU = $1

Per search episode Budget 350 ECU 350 ECU 350 ECU 350 ECU

26

Average Earnings $26.33 $26.00 $24.19 $25.27

Table 2. Marginal Effects from Logit Models of the Likelihood of Search Variable Benef it

(1) 0.0079*** (0.0009)

(2) 0.0077*** (0.0013)

(3) 0.0072*** (0.0020)

Budget

0.003 (0.0007)

0.0004 (0.0006)

0.0006 (0.0004)

Episode11−20

-0.2775 (0.4210)

-0.2191 (0.4021)

-0.1503 (0.3734)

Episode21−30

0.0240 (0.4366)

0.0381 (0.4379)

0.1182 (0.3826)

Episode31−40

-1.0681** (0.4546)

-0.9938** (0.4843)

-0.8534* (0.4982)

Episode41−50

-1.1327** (0.4851)

-1.0430** (0.5224)

-0.8692 (0.5315)

Benef it

×

Episode11−20

0.0021* (0.0012)

0.0021* (0.0013)

0.0018 (0.0013)

Benef it

×

Episode21−30

0.0025* (0.0014)

0.0024* (0.0014)

0.0021 (0.0014)

Benef it

×

Episode31−40

0.0031** (0.0014)

0.0030** (0.0015)

0.0027* (0.0016)

Benef it

×

Episode41−50

0.0020 (0.0019)

0.0019 (0.0019)

0.0017 (0.0018)

Budget

×

Episode11−20

0.0007 (0.0013)

0.0005 (0.0012)

0.0003 (0.0011)

Budget

×

Episode21−30

-0.0002 (0.0013)

-0.0003 (0.0013)

-0.0005 (0.0011)

Budget

×

Episode31−40

0.0030** (0.0013)

0.0028** (0.0014)

0.0024* (0.0014)

Budget

×

Episode41−50

0.0032** (0.0014)

0.0029* (0.0015)

0.0024 (0.0015)

U pward P rice Shif t

0.0009** (0.0004)

0.0043* (0.0023)

Downward P rice Shif t

-0.0010** (0.0005)

-0.0024 (0.0020)

U pward P rice Shif t2

-3.64 x 10−5 ∗ (2.04 x 10−5 )

Downward P rice Shif t2

1.45 x 10−5 (1.66 x 10−5 )

Observations

8,074

8,074

8,074

BIC

7546.84

7549.17

7556.13

* p<0.10, ** p<0.05, *** p<0.01

Note: Standard errors clustered at the subject level are reported in parentheses. All models include individual fixed effects. Marginal effects are evaluated assuming the fixed effect is 0.

27

Table 3. Marginal Effects from Logit Models of the Likelihood of Search Including Gains and Losses Variable Benef it

(1) 0.0066** (0.0033)

(2) 0.0074*** (0.0014)

(3) 0.106*** (0.0009)

Budget

0.0007*** (0.0002)

Episode11−20

-0.0327 (0.3177)

-0.0477 (0.0358)

0.3034 (0.3485)

Episode21−30

0.2307 (0.3213)

-0.0848* (0.0477)

0.3674 (0.4718)

Episode31−40

-0.6121 (0.5233)

-0.0304 (0.0518)

-0.3316 (0.3712)

Episode41−50

-0.6148 (0.5884)

-0.0821 (0.0524)

-0.7907 (0.5112)

0.0001 (0.0008)

Benef it

×

Episode11−20

0.0011 (0.0012)

0.0011 (0.0020)

0.0006 (0.0012)

Benef it

×

Episode21−30

0.0015 (0.0014)

0.0012 (0.0019)

0.0023 (0.0015)

Benef it

×

Episode31−40

0.0019 (0.0023)

0.0042* (0.0011)

0.0006 (0.0017)

Benef it

×

Episode41−50

0.0011 (0.0009)

0.0013 (0.0032)

0.0007 (0.0013)

Budget

×

Episode11−20

-1.68 x 105 (0.0009)

-0.0010 (0.0011)

Budget

×

Episode21−30

-0.0008 (0.0009)

-0.0011 (0.0014)

Budget

×

Episode31−40

0.0017 (0.0015)

0.0009 (0.0011)

Budget

×

Episode41−50

0.0017 (0.0017)

0.0023 (0.0016)

U pward P rice Shif t

0.0044 (0.0030)

0.0113*** (0.0027)

0.0011 (0.0014)

Downward P rice Shif t

-0.0029 (0.0022)

-0.0068*** (0.0025)

-0.0014 (0.0026)

U pward P rice Shif t2

-3.27 x 10−5 (2.27 x 10−5 )

-8.60 x 10−5 ∗ ∗∗ (2.49 x 10−5 )

9.14 x 10−7 (1.01 x 10−5 )

Downward P rice Shif t2

-9.23 x 10−6 (-1.40 x 10−5 )

3.02 x 10−5 (2.24 x 10−5 )

1.79 x 10−6 (2.05 x 10−5 )

Gain

-0.0005 (0.0007)

-0.0009 (0.0014)

-0.0010 (0.0008)

Loss Observations

0.0013* (0.0007) 7,912

0.0025*** (0.0007) 3,922

0.0009** (0.0004) 3,982

BIC

7357.38

3401.67

3618.42

* p<0.10, ** p<0.05, *** p<0.01

Note: Standard errors clustered at the subject level are reported in parentheses. All models include individual fixed effects. Marginal effects are evaluated assuming the fixed effect is 0. Column 2 uses only the first two search decisions in a search episode. Column 3 uses only search decisions after the first two in any given search episode.

28

A

Appendix

A.1

Basic Search Model

To derive the risk-neutral individual’s reservation price, let V (p) be the expected price paid plus the expected total search costs when the individual has a price of p in hand. Prices are distributed over [0, b] according to F (p). The Bellman equation is {

∫

} V (h)dF (h)

b

V (p) = min p, c +

(1)

0

where c is the marginal cost of search. Define ∫

b

p¯ = c +

V (h)dF (h)

(2)

0

such that V (p) = p if p ≤ p¯ and V (p) = p¯ if p ≥ p¯. Rearranging (2), ∫ p¯

∫

p¯

dF (h) + p¯ 0

∫

b

dF (h) = c + p¯

∫

p¯

hdF (h) + p¯ 0

b

dF (h)

(3)

p¯

Simplifying and using integration-by-parts on the left-hand side, this becomes ∫

p¯

F (h) = c

(4)

0 1

With a uniform distribution, this yields a reservation price (¯ p) equal to (2cb) 2 .

29

A.2

Proof of Proposition 1

Let V (p, pR ) be the expected benefit to purchase when an individual with reference price pR has the opportunity to purchase at p. The individual’s Bellman equation is { } ∫ b V (p, pR ) = min p − Ip>pR (ηλ(pR − p)) − Ip
(1)

0

The second term in the bracket is a constant for a given reference price and price distribution, so (1) can be rewritten as    p − Ip>pR (ηλ(pR − p)) − IppR (ηλ(pR − p)) − Ip
      ∫b    c + 0 V (h, pR )dF (h)     ∫   if p − Ip>p (ηλ(pR − p)) − Ip

c + b V (h, pR )dF (h) R R 0

(2)

Individuals search over prices, so it is useful to rewrite (2) in terms of acceptable purchase prices. To do this, I solve for a reservation price, p¯, at which ∫ p¯ − Ip¯>pR (ηλ(pR − p¯)) − Ip¯
b

V (h, pR )dF (h) 0

Having defined p¯, I can say that the individual searches when p > p¯ and purchases when p ≤ p¯. I consider three cases: p¯ > pR , p¯ < pR , and p¯ = pR .

30

Case (1): p¯ > pR

The price at which the individual is indifferent between purchasing at the price in hand or continuing to search when the price in hand is above the reservation price is determined by the expression

∫

b

(1 + ηλ)¯ p − ηλpR = c +

V (h, pR )dF (h) 0

Solving for p¯ yields

( p¯ =

ηλ − η 2 2bc + p 1 + ηλ 1 + ηλ R

) 12 (3)

Case 2: p¯ < pR

The price at which the individual is indifferent between purchasing at the price in hand or continuing to search when the price in hand is above the reservation price is determined by the expression

∫ (1 + η)¯ p − ηpR = c +

b

V (h, pR )dF (h) 0

Solving for p¯ yields p¯ = (

2cb 1 )2 1+η

(4)

Case 3: p¯ = pR

The price at which the individual is indifferent between purchasing at the price in hand or continuing to search when the price in hand is above the reservation price is determined by the expression

∫ p¯ = c +

b

V (h, pR )dF (h) 0

Solving for p¯ yields p¯ = (

2cb 1 )2 1+η

31

(5)

Combining (3), (4), and (5), I can characterize the reservation price as a function of just pR    ( 2cb ) 12 1+η p¯(pR ) =   ( 2bc + 1+ηλ

1

2cb 2 ) : pR ≥ ( 1+η ηλ−η 2 21 p ) 1+ηλ R

1

2cb 2 : pR < ( 1+η )

The reservation price is weakly increasing in the reference price, so the highest price at which the individual is willing to purchase is weakly increasing in the reference price. If more prices are acceptable, search is less likely.

32