## Miguel Cura Juri and Sebastian Galiani1

Introduction

In this chapter, we report preliminary results of an economic experiment in the field of search theory that we designed at the University of Trento and conducted at Universidad de La Plata, Argentina. The experiment is designed to test the predictions of an intertemporal sequential search problem.

The consumer search problem we evaluate differs from the standard consumer search problem, as described in Sargent (1987), in that consumption takes place at several periods of time and relative prices may vary over time among stores. We assume that real prices follow a first-order Markov stochastic process. Thus, the probability of finding any given store charging the same real price in periods t and t+1 is equal to a constant, p, which is the focus variable of our experiment.

There is previous laboratory work testing the theory of sequential search under diverse search environments but our experiment is the first that studies search behavior in a context of repeated purchases where relative prices vary over time.

Schotter and Braunstein (1981, 1982) test the reservation wage hypothesis and find evidence in support of the basic implications of the standard search theory. Cox and Oaxaca (1989) also find evidence in favor of the reservation wage hypothesis. However, Kogut (1990) tests several predictions of the standard search model and finds evidence contrary to the implications of the model. Notably, he reports a high prevalence of recall (see also, Hey, 1982, 1987).

In this chapter, we provide new evidence on the implications of the standard search model. The intertemporal search model we analyze predicts that the first period reservation price is increasing in p. We test this prediction. Additionally, we also test if our laboratory consumers pay lower prices when p equals one compared to the prices they pay when p equals zero, irrespective of whether subjects exhibit a reservation price strategy.

### Motivation

There is extensive evidence showing that inflation is positively correlated with the variability of prices across markets and across sellers of the same good (see Domberger, 1987; Lach and Tsiddon, 1992). Tommasi (1993) shows that inflation reduces the level of information that current prices contain about future prices. In a highly inflationary environment, it is hard to establish who are the low-price sellers, since the price observed today is not a good predictor of future prices.

Tommasi (1994) analyzes a market for a homogeneous good under price instability conditions. He assumes that buyers purchase a unit of the good every period. Consumers search in a sequential manner and follow a reservation price strategy. In each period, buyers go from store to store and observe the price tags until they buy the good. Each visit entails a search cost. In such a world, inflation exacerbates the informational problem by depreciating the information that current relative prices convey about future relative prices. Tommasi (1994) shows that buyers react by holding smaller information stocks. This translates into higher reservation prices. However, interestingly enough, the total amount of resources spent on search may either increase or decrease. In this chapter, we study the behavior of consumers in Tommasi's model.

We assume that the cumulative distribution of real prices, F(p), is time-invariant. However, the location of each individual seller on that distribution follows the following first-order Markov stochastic process:

Buyers own free recall from last period's accepted price, that is, buyers can recall without cost the store where they bought the good last period. However, recall is uncertain over time. It is assumed that p=f(n), where n is the inflation rate and fn<0, even though the results of our experiments hold independently of the reasons why p varies. If p=0, prices are not related intertemporaly, and each period's search behavior is as described in the standard static search model (see Sargent, 1987). When p=1, all searches should be undertaken in the initial period (see Tommasi, 1994). We evaluate this empirical prediction in the experiment we conduct.

### The consumers program

In what follows, we match the notation of the model with that of the experiment we conduct. The buyer purchases one unit of the good per period. There are three periods. During a period, a consumer can visit as many stores (i.e. draw prices from the distribution of prices) as he wishes. However, consumers face a real cost per search (i.e. price per drawn) c. Finally, each subject is willing to pay for the good the same amount of money, v. Thus, the objective of a consumer is to minimize his expected expenditure, or

P, with probability p

a drawing from F(p) with probability 1 — p

Min E

where pt and nt are the price paid for the unit of the good purchased and the number of stores visited at period t.

If both F(p) and p are known, and satisfy all the conditions for an interior solution (see Tommasi, 1994), the first period reservation price p solves

The reservation price is such that the search cost just equals the expected gain from additional search. Notice that p affects reservation prices in the same way as the consumers discount factor does. Then, it is straightforward to show that the reservation price is decreasing in the correlation coefficient p.

### Experimental procedures

The experiment was conducted at Universidad de La Plata in Argentina using undergraduates as subjects. Sixteen subjects were recruited for an "economic experiment"; they were told that they would be paid in cash at the end of the session but were not told the nature of the experiment. A small pilot of this experiment was conducted at the University of Trento.

Each subject was exposed to three levels of the focus variable p: 1, 0.5, and 0. Subjects may understand the experiment better (or just change their behavior) over time (trials). To control this nuisance we blocked the treatment variable p using a balanced design (see Friedman and Sunder, 1994).

General instructions were read aloud to subjects at the beginning of each session. After the instructions were read, both the experiment and the experimental tasks were exemplified by conducting one experimental sequence for each level of the treatment variable. Before starting the experiment, we verified that subjects understood the meaning of p by asking them what price they expect to observe if they recall the store where they bought the good in the previous period for each value of the focus variable.

Each subject was randomly assigned to a different sequence of treatment levels. The four alternative sequences in which subjects were treated are the following: 1, 0.5, and 0; 0, 0.5, and 1; 0.5, 0, and 1; and 0.5, 1, and 0.

During a session, each subject was presented with six search problems, two for each level of the focus variable p, in one of the four sequences listed above. Each search problem or search sequence consists of three periods. Prior to these search sequences, each subject had participated in a series of twelve (unpaid) training search problems; four for each of the three levels of the treatment variable p presented in the same following order: p=0, p=1, and p=0.5.

Finally, subjects knew in advance the way they were rewarded in the experiment. In each search sequence, they also knew p and F(p). Each experiment lasted approximately 30min. Subjects received $2 for their participation in the experiment plus where j indexes the six rewarded search sequences, I{pt> o¡ is an indicator

function that equals 1 if the subject buys one unit of the good in period t of sequence j and equals 0 otherwise; v was established at $1.2, p ~ Uniform(0, 2], and c was set equal to $0.1.

### Experimental results

Our results are still explorative. The sample size of our experiment is smaller than the one needed to draw significant conclusions about the behavior of economic agents in the context of our experiment. Nevertheless, the analysis of the results of the experiment allows us to draw important preliminary conclusions.

First, we evaluate whether when p equals one subject's only search during the first period as it is predicted by theory. We find that subjects depart from optimal behavior. We find that in 18.7 percent of the search sequences in which p is one, subjects search prices during the second period of the sequence departing from predicted optimal behavior. The proportion of search periods in which subjects depart from theoretical optimal behavior is statistically different from zero at the 1 percent level of significance (t31=3). It is worth noting that in this chapter, all the statistics are adjusted for the presence of random groups or cluster effects in the data. They are likely to arise because we have more than one observation by individual.

Interestingly enough, these departures from optimal behavior are positively correlated with both the prices and the number of prices drawn in the first period. This finding is similar to the one reported by Kogut (1990). Thus, it seems that subjects may depart from optimal behavior after they have searched enough without finding a price below the reservation price.

Turning to the analysis of accepted prices, we first evaluate if they are in agreement with theoretical reservation prices and, second, we test if individuals pay lower prices when prices are invariant over time (i.e. p=1) in comparison to the case in which prices are extremely unstable over time (i.e. p=0).2

Table 18.1 summarizes the relevant results. The optimal reservation price is calculated from equation (18.3). It is worth noting that mean accepted prices are close to expected accepted (theoretical) prices. For example, when r equals zero the reservation price is 0.632. The first price encountered in a trial that is equal or lower than 0.632 should be accepted. For a uniform distribution, accepted prices would be equally likely anywhere between 0 and 0.632, and, hence, the average expected accepted price is 0.316, which is remarkably close to the mean accepted price during the first period for the search sequences in which p=0. We test the hypothesis that the mean accepted prices are equal to the expected accepted prices against a two-tails alternative hypothesis. We do not reject the null hypothesis when p=0 at any conventional level of significance, however, we do reject the null

### Table 18.1 Prices and search by treatment

Notes t-Statistics are computed using standard errors robust to the precesence of cluster groups in the data. ** Statistically different from zero at the 0.05 level of significance.

Price

Figure 18.1 Theoretical and observed distribution of accepted prices.

Price

Figure 18.1 Theoretical and observed distribution of accepted prices.

hypothesis when p=1 at the 5 percent level of significance although we do not reject it at the 1 percent level of significance.

Figures 18.1 and 18.2 present the cumulative distribution of accepted prices together with the expected theoretical distribution of accepted prices for p=1 and p=0. Overall, we do not find significant deviations with respect to the optimal price strategy. In both cases, the observed distributions of accepted prices do not depart significantly from the theoretical distributions. Approximately 80 percent of the accepted prices are below the reservation price.

We also test if the mean accepted price when p=1 equals the mean accepted price when p=0 against the alternative hypothesis that the former price is lower than the latter price, and we reject the null hypothesis at the 10 percent level (but not at the 5 percent level) of significance (i15=-1.85). Thus, accepted prices are, on average, lower when p=1 than when p=0.

Finally, we consider the total search costs associated to price instability. N( 1) is equal to 7.2 andMO) is equal to 9.2, where N(p) = 'n,(p).3Thus, price instability has two costs well identified in our experiment: it increases the average price accepted by consumers and it increases the cost of making transactions.

### Preliminary conclusions

In this chapter, we have reported the preliminary results of an economic experiment in the field of search theory conducted at University of La Plata, Argentina. The experiment is designed to test the predictions of a model of sequential search by an individual agent in an intertemporal consumption context.

Our results are still explorative. The sample size of our experiment is smaller than the one needed to draw significant conclusions about the behavior of the economic agents in the context of our experiment. Nevertheless, the analysis of the experiment allows us to draw some preliminary conclusions.

We find that in 18.7 percent of the search sequences in which p=1, subjects did not recall the accepted price in the first period during the second period of the search sequence, departing from predicted optimal behavior.

Nevertheless, we do not find significant deviations with respect to the optimal price strategy. In both cases, that is, when p=1 and when p=0, the observed distributions of accepted prices do not depart significantly from the respective theoretical distributions.

Finally, we also find that the mean accepted price when p=1 is lower than the mean accepted price when p=0 at conventional levels of significance. In addition, we find that the total cost of search is greater when p=0 than when p=1. Thus, price instability has two costs well identified in our experiment: on the average, both accepted prices and transaction costs are higher.

Notes

1 We thank Dan Friedman and seminar participants at the summer camp on Experimental Economics, Program in Adaptative Economic Dynamics, University of Trento, Italy; UC at Santa Cruz, UTDT, and Universidad de La Plata for useful comments.

2 Due to sample size considerations, we do not exploit the information for the case in which p=0.5 here. We lack statistical power to test differences between the behaviors in the laboratory in this case and any of the other two cases.

3 Note that most of our results only exploits the information of the first period in each search sequence. Thus, we could have had only two periods per sequence instead of three. However, the value of information on prices increase with the number of periods it is worth. Thus, we consider that three periods is a reasonable compromise solution to the trade-off we face.

### References

Cox, J. and Oaxaca, R. (1989) "Laboratory experiments with a finite horizon job search model," Journal of Risk and Uncertainty, 2:301-329. Domberger, S. (1987) "Relative price variability and inflation," Journal of Political Economy, 95:547-566.

Friedman, D. and Sunder, S. (1994) Experimental Methods: a Primer for Economists,

Cambridge, MA: Cambridge University Press. Hey, J. (1982) "Search for rules of search," Journal of Economic Behavior and Organization, 3:65-81.

Hey, J. (1987) "Still searching," Journal of Economic Behavior and Organization, 8:137144.

Kogut, C. (1990) "Consumer search behavior and sunk costs," Journal of Economic Behavior and Organization, 14:381-392. Lach, S. and Tsiddon, D. (1992) "The behavior of prices and inflation: an empirical analysis of disaggregated price data," Journal of Political Economy, 100:349-389. Sargent, T. (1987) Dynamic Macroeconomic Theory, Cambridge: Harvard University Press. Schotter, A. and Braunstein, Y. (1981) "Economic search: an experimental study," Economic Inquiry, 19:1-25.

Schotter, A. and Braunstein, Y. (1982) "Labor market search: an experimental study," Economic Inquiry, 20:133-144.

Tommasi, M. (1993) "Inflation and relative prices: evidence from Argentina," in E.Sheshinski and Y.Weiss, eds, Optimal Pricing, Inflation, and Cost of Price Adjustment, Cambridge: MIT Press.

Tommasi, M. (1994) "The consequences of price instability on search markets: towards understanding the effects of inflation," American Economic Review, 84:1385-1396.

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