Ask prices, offers, and time to sale in an online exchange.

Farmer, Amy ; Stango, Victor

I. INTRODUCTION

In this article, we consider the role served by the ask price posted by sellers in an online exchange for used computers. The functional role served by the ask price in this exchange is similar to that in other bilateral exchange settings: the ask price is not binding and essentially serves as a starting point for negotiations. Furthermore, every offer that we observe by buyers lies well below the ask price. This type of bargaining institution is common in online marketplaces and also in markets for used cars, housing, and goods sold through want ads placed in newspapers.

The general finding of empirical literature examining these other markets is that ask prices convey information. A high ask price may indicate a desire by the seller to hold out for a higher offer. In such a setting, ask price dispersion may arise if sellers trade off higher prices against the likelihood of making a sale. High ask prices will then lead to higher sale prices on average but longer time on the market. The standard justification for the inverse relationship between ask prices and time on the market is that a seller asking a high price will receive fewer offers if search by buyers is costly. Most of the existing findings in support of this view have focused on real estate markets.

As an empirical matter, it is not clear that ask prices should play a similar role in the online setting that we examine. Although the notion that sellers have differing reservation prices seems plausible, if the market is characterized by perfect information and costless search, then ask prices will serve no functional role. This is important because there is a general anecdotal view that online markets serve as sufficiently effective mechanisms for information transmission that search is costless. In such a setting, an initial ask price posted by the seller would be irrelevant.

One caveat to this view is that although information is readily available online, it may be costly to process. The used computers sold on this exchange are complex products that differ on a number of dimensions. Viewing the large amount of information available and forming an estimate of willingness to pay in such a situation is a nontrivial task. Though the cost in terms of time and effort required to process this information does not fall as neatly within the imperfect information paradigm as does the housing market, it is clearly analogous. The search costs involved in visiting and walking through a house for sale are substantial, but relative to the value of the house they may be no larger than the costs of viewing and assessing the characteristics of a used computer. It is possible then that the immediate access to information online may not eliminate search costs. One contribution of our research, therefore, is an assessment of the extent to which online markets can be thought of as search markets. Our approach is to see whether the relationship between ask prices, offers, and time to sale on the exchange is similar to that in other markets characterized by costly search.

Our data differ in some key ways from that available in more traditional settings. For example, data regarding the number of offers a given property receives are rarely available in housing markets. Nor, in many cases, is the sequence of offers for a given property observable. In our case, we observe the number of offers made and the level of each offer. A disadvantage of our data is that we do not observe final transaction prices, because once computers are sold they are removed from the publicly available listings on the exchange. Thus we cannot directly estimate the relationship between ask prices and sale prices. We can, however, estimate the relationship between the ask price and the level of the highest outstanding (i.e., rejected) offer that the computer received. This allows us to test the implication that sellers with high ask prices are more likely to reject offers of a given level. This prediction has not been tested in previous work because rejected offers are rarely recorded.

An advantage of our data relative to that used in other studies is that in many bilateral exchange markets there are characteristics of the good that are observed by both parties to the transaction but would be unobservable to an econometrician investigating the transaction. Again, this is a common problem in housing markets, in which the characteristics of the house are typically unknown or may be too qualitative to permit an econometric analysis. In contrast to these other settings, we view listings on the online computer exchange exactly as buyers view them. Thus the standard omitted variable concern that arises in this type of analysis is greatly reduced.

We conduct the empirical analysis by outlining a standard set of hypothesis tests regarding the relationship between ask prices, offers, and time to sale in search models. In general, the search models predict that higher ask prices should indicate a willingness on the part of the seller to hold out for a higher offer. In such a setting, sellers with high ask prices will reject higher offers than sellers with low ask prices; thus, the ask price will be positively correlated with the highest outstanding offer at any given point in time. The search models also predict that a higher ask price should lead to fewer offers and a longer time to sale. If search is costly, buyers will be deterred from making offers on goods with high ask prices because they expect a low probability of sale. A corollary of these models is that the gains from pursuing a high ask price strategy are likely to be greater in markets in which the variance of buyers' willingness to pay is greater. We proxy for this variance by using an independent assessment of market strength for each computer under the supposition that buyers' tastes are more idiosyncratic in thinner (weaker) market segments. Our view that thinner segments have a greater variance in buyers' willingness to pay is borne out by the data; the variance of offers is higher in lower-strength segments, holding computers' values constant.

The empirical section of the article first examines the incidence of offers for our sample of computers and assesses whether the level of the ask price affects the number of offers that a computer receives. Because computers have heterogeneous values, we normalize the ask price by an independent measure of the resale value of the computer. This allows us to compare computers with different values based on the relative magnitude of their ask prices. We find that computers with high ask prices (relative to their value) receive fewer offers. This result is consistent with the search model. We also find that this result is stronger in thinner market segments, suggesting that segments with idiosyncratic buyer tastes are more likely to display the patterns predicted by the search model.

The next part of the article examines the relationship between the ask price for a given computer, and the level of the highest offer outstanding when we observe it. Essentially this involves estimating a hedonic pricing equation for computers and testing for an independent effect of the ask price on offers. We find that in thinner (i.e., more idiosyncratic) markets, there is a positive relationship between ask prices and outstanding offers. The relationship is weak or nonexistent in thicker market segments. This suggests that sellers with high ask prices are more likely to reject offers of a given level.

We then examine the relationship between the ask/value ratio and time to sale. Our data limit the scope of this inquiry, because computers disappear from the exchange once they are sold. Thus we can only infer time to sale by asking whether a computer is more or less likely to remain on the exchange during our sample period as a function of the ask/value ratio. Using these data, we find that high ask prices extend time to sale and that the relationship is stronger in thinner market segments.

Our conclusion is that despite the prevalence of information in the market, ask prices play a role consistent with the predictions of search models. The results of this article highlight the importance of information processing costs, even in online markets that appear quite transparent. We discuss this point further in the conclusion.

II. THE ONLINE COMPUTER EXCHANGE

We take our data from the United Computer Exchange (UCE), an online exchange between buyers and sellers of used computers. The UCE serves two functions: It facilitates bilateral exchange, and it provides a form of quality certification. (1)

Listing a computer and making offers are free. Sellers register to list their computer and complete a form listing the characteristics of the computer. There are 17 fields in which sellers may list characteristics. Some of these may take on roughly continuous values (such as memory and hard drive space), whereas others are more discrete or qualitative (such as the existence of an Ethernet card). When the listing is created, the seller also submits an "ask price." The ask price is not binding and is typically high relative to any objective assessment of the value of the computer. In our data, the average ask price is more than twice as high as the average highest offer for a computer. This ratio is larger than that we would see in housing or used car markets.

The set of information available to the buyer therefore consists of the listed characteristics of the computer, the date on which the computer was listed, the ask price, and the date and level of any previous offers submitted. Potential buyers may view listings on the UCE Web page and submit offers for any computers they find desirable. Buyers may submit an unlimited number of offers for any number of computers they desire. Once an offer has been submitted, it appears on the Web page of the computer for which the offer stands. A seller may view offers at any time by visiting the UCE web page. The fact that the seller has viewed the offer is noted on the Web page. The fact that an offer has been viewed but not accepted constitutes a signal that that offer has been rejected. (2)

The process of negotiation is often quite drawn out, and commitment occurs late in the process. A computer in our data set may have been on the exchange for a few months when observed and may have received only one offer several weeks after it was listed. Sellers need not accept any bids, and they face no time limit after which they must sell the computer. Even after a seller notifies a buyer of acceptance of an offer, the buyer has an opportunity to retract it.

Despite the late and bilateral nature of commitment, once it has been made it is extremely costly for either party to cancel the transaction. Once both parties have agreed to the transaction, the seller pays to ship the computer to UCE, which performs a simple set of diagnostic tests. If the computer is in working order, it is then mailed to the buyer at the buyer's expense. After receiving the computer, the buyer can still cancel the transaction if goods are not as promised. In this event, the buyer pays the costs of returning the computer to UCE. At that point, the seller may relist the computer or pay shipping costs to have the computer returned to the seller's residence. (3)

If, after receiving the computer, the buyer agrees to the transaction, a check goes to UCE. UCE takes 5% from the buyer's total. Sellers pay a sliding scale fee for the service based on the transaction price of the computer that they sell. (4) UCE then mails the remainder of the transaction price to the seller. Once the transaction is complete, the listing is removed.

It is worth emphasizing at this point that this exchange is not an auction. There is no commitment to buy or sell until late in the process. The ask price is not a binding reservation price. There is no time limit before which a transaction must occur. Thus, although many other online auctions exist (e.g., eBay), we should view the UCE as closest to a centralized forum for bilateral exchange. This motivates our theoretical discussion of search models.

III. THE RELATIONSHIP BETWEEN ASK PRICES, OFFERS, AND TIME TO SALE

In this section we discuss some models that explain a functional role for ask prices. We outline the empirical predictions of these models, discuss their applicability to an online exchange, and contrast them with some alternative explanations regarding the role of ask prices.

We should note first that in a perfect information setting with costless search, ask prices will play no functional role. Even if ask prices were correlated with sellers' reservation prices, sellers would have no economic incentive to list different ask prices because buyers would disregard them. (5) For the ask price to play a functional role, buyer behavior must be affected by the ask price. This will only occur if "search" is costly for buyers (we will outline an interpretation of search in this online setting later).

Models of Search and Ask Prices

The standard search framework assumes that there is imperfect information regarding some component of buyers' valuations for the good being offered by sellers. (6) Many models also incorporate some imperfect information regarding sellers' reservation prices. In such a setting, the typical approach is to model the market as one in which the imperfect information problem is resolved only after one party, typically the buyer, pays some search cost. (7) In the simplest formulation of these models, all buyers must pay the same search cost; marginal search costs may also increase in the number of searches, although this is not essential. Search is sequential; buyers "visit" each seller and must then choose to purchase from the current seller or visit another. The derivation of equilibrium in these models often involves the construction of a stopping rule for buyers, in which buyers trade the expected surplus from continued search against the costs of continued search.

Models that incorporate ask prices into the search framework typically take two approaches, both of which involve justifying a negative relationship between the ask price and the arrival rate of buyers. One approach is to simply assert that the ask price affects the arrival rate of buyers, based on an intuitive appeal regarding buyers' interpretation of the ask price. (8) This will occur, for example, if buyers believe that the ask price is correlated with the seller's (unobserved) reservation price. A second, more formal approach assumes that although the final transaction price will be the outcome of bargaining and will therefore vary, the ask price is a commitment by the seller to an upper bound on the transaction price. (9) Thus the ask price bounds the surplus received by the buyer at some minimum value. Buyers facing different ask prices will therefore choose to visit the sellers with lower ask prices first, holding the cost of search constant. Sellers with lower ask prices will obtain a higher arrival rate of buyers and receive more offers). (10) Whether or not the relationship between arrival rates and ask prices is formally modeled, all of these models imply a negative relationship between ask prices and the arrival rate. (11) Because any buyer who "arrives" makes an offer, this also implies that higher ask prices will lead to fewer offers.

These models can motivate variation in ask prices for identical goods in two ways. First, if sellers differ on some dimension--the most tractable dimension is typically the discount rate--then they will find different selling strategies optimal. Sellers who are patient will ask higher prices and hold out for a high-valuation buyer. As a consequence of this strategy, sellers with high ask prices will receive fewer offers because they will deter low-valuation buyers from inspecting their good. They will also have longer time on the market. (12)

Search models also predict a relationship between ask prices, offers, and transaction prices. High-reservation price sellers will reject higher offers than will low-reservation price sellers. This has two implications. First, higher ask prices will be associated with higher transaction prices. Second, given equal offers for identical computers, those on computers with high ask prices should be more likely to be rejected by sellers. Thus, if we observe a snapshot of the market, higher ask prices should be associated with higher outstanding offers.

Another source of equilibrium ask price dispersion arises in models with many sellers. (13) Sellers with identical goods may choose different ask prices, trading off a higher expected selling price against a longer expected time to sale. Even if sellers are themselves identical and face the same outside option, price dispersion can be sustained through the imposition of a zero-profit constraint. The zero-profit constraint requires that the gains from raising the ask price (higher offers and a higher final transaction price) must be exactly offset by the losses (a lower probability of sale today). Although these models are set up slightly differently from those in the previous paragraph, they yield the same empirical implications. High ask prices will be associated with higher outstanding offers but will receive fewer offers and have a longer time to sale.

A final result of certain search models is that the variance of buyers' valuations will affect seller strategies. These models find that a higher variance of buyers' valuations leads to higher ask prices, because the profitability of the high ask price strategy grows. (14) In addition, the models predict that a higher variance of valuations will lead to longer time on the market, as sellers have more to gain by holding out for a high offer. (15) As a general empirical matter, we would expect that in settings with high variance in buyers' willingness to pay, the predictions of the search model would be more strongly supported. (16)

Existing Empirical Work

Most of the existing literature testing the predictions regarding search behavior and ask prices uses data from housing markets. Yavas and Yang (1995) find that higher ask prices deter potential buyers and will result in a longer time to sale. (17) Genesove and Mayer (1997) also find that houses with higher ask prices receive higher final prices and remain on the market longer. Glower et al. (1998) find that a more motivated seller (for example, someone who has already purchased another home) will ask less, sell faster, and for a lower price. The general conclusions of this literature are fairly consistent, and provide strong support for the predictions of search theory in these markets. One limitation of the work already mentioned is that it does not examine offers made by buyers that are rejected; in most housing markets, such data typically are not recorded. One exception to this is recent work by Ortalo-Magne and Merlo (2000), which contains observations for both offers and transaction prices.

Some of the work also tests the hypothesis that the variance of buyers' willingness to pay will affect ask prices, offers, and time to sale. Glower et al. (1998) hypothesize that houses with "atypical" features should be ones for which buyer's valuations have a higher variance. Their empirical work shows that atypicality is associate with higher list prices, higher sale prices, and longer time on the market. Haurin (1988) also finds that atypical houses are longer on the market and have higher list prices relative to their selling price. Thus there is also some support for the prediction of search theory regarding the variance of buyers' willingness to pay.

Our work has both advantages and disadvantages relative to these other articles. As we noted in the introduction, a disadvantage is that we do not observe final transaction prices. We do observe the sequence of offers, which is rare in the context of previous work. This allows us to test whether higher ask prices actually deter buyers from making offers. It also allows us to test whether sellers with higher ask prices are more likely to reject offers of a given level, by examining the highest offer outstanding when the computer is observed. Data concerning the number of bids also allows the role of market strength to be examined in this context.

Applying Search Theory to an Online Exchange

At this point it is worthwhile to discuss the applicability of these models to the online computer exchange. For the models to apply, we need to view the online exchange as a market in which buyers have uncertain valuations of the computers for sale. Buyers would also need to engage in costly search to determine their willingness to pay and place an offer.

It may seem counterintuitive to view this market as one in which buyers have different valuations that are uncertain before they engage in search. However, we should note that the goods for sale--used computers--are multidimensional goods that can vary in complex ways. As we noted, there are 17 listed characteristics for each computer, and each characteristic can take on a host of values. (18) When variations in these characteristics are taken into account, very few computers on the exchange are identical to any other. (19) Moreover, there is no clear quality increment on which we can index computers of a given model type; one computer may have more memory and less hard drive space (or a slower modem) than another. It is almost surely the case that buyers value different bundles of characteristics differently. (20)

Given that buyers have different valuations and that computers are so heterogeneous, we can think of the search cost associated with making an offer as the time and effort for the buyer to sort through the complex bundle of attributes and arrive at a valuation for the computer. One can see that it would take a nontrivial amount of time, for example, to evaluate three or four computers of identical model type but differing characteristics. Buyers would "visit" each computer and then choose from the set of computers listed on the exchange the one computer (or group of computers) that seems closest to their desired bundle of characteristics; from this point, a buyer would engage in detailed comparison. After engaging in this search, the buyer would be in a position to submit an informed offer on each machine.

The role of the ask price in such a setting might be similar to that in housing markets. Given limited time and a pool of eight or ten computers of a given model type, the buyer might screen the computers and examine only those four with the lowest ask prices. In fact, the institutions of the exchange encourage this sort of screening. At the outset of viewing the listings, the buyer is presented with a search dialog that shows various major features of the computers, such as processor speed, memory, and storage capacity. The buyer can select on these feature to bring up a subset of the listings for detailed examination. Importantly, one of these features on which the buyer can screen is the ask price--thus a low-valuation buyer who used this feature would automatically screen out more computers than a high-valuation buyer.

As a theoretical matter it is difficult to say whether search costs as we have outlined them here would be significant enough to lead to the same patterns of ask prices, offers, and time to sale observed in other search markets. Our approach is therefore to test the predictions of the search model in this setting to assess empirically the role of ask prices and the overall relevance of search models in this online setting.

Competing Explanations for an Empirically Significant Ask Price

Before we move to the empirical tests, it is worth discussing some alternative explanations regarding the role of ask prices. As we shall see, the predictions of the search model are observationally distinct from these competing explanations.

One might think that a natural alternative hypothesis would be that ask prices serve as a signal of unobserved quality. It is possible to construct models in which sellers with high ask prices convey positive information regarding some unobservable component of quality. We should note, however, that the features of the exchange are set up to mitigate such problems. Essentially, the UCE serves as a quality certification device that ensures that all delivered machines are in working order. Nonetheless, there are undoubtedly variations in working quality even among all machines of minimum acceptable quality.

However, even if ask prices served as signals of unobserved quality, the empirical predictions of the signaling model run counter to the predictions of the search model. It is true that both models would predict a positive relationship between ask prices and offers, controlling for the observable characteristics of the computer. However, the signaling model would also predict a positive correlation between ask prices and the number of offers received. This would occur because computers with higher ask prices would be more valuable than those with lower ask prices, and the data indicate that high-value computers have greater market strength. Of course, the data can only be instructive about the relationship between high-value observable characteristics and market strength; although there is no guarantee that the market for high-quality unobservable traits is also thicker, it seems as if this would be a likely corollary. Note that this is in contrast to the negative correlation predicted by the search model. Finally, for similar reasons of market strength, the signaling model predicts a negative relationship between the ask price and time to sale, whereas the search model predicts a positive relationship. (21)

Another factor that could lead to an observed empirical relationship between ask prices and offers are omitted variables. If there were characteristics of computers that were unobservable to the researchers observing a series of offers, but observable to both parties to the exchange, then ask prices might reflect unobservable information regarding the computer. (22) Again though, there are institutional features of the market that argue against the existence of such unobservables. Because the exchange occurs online, the exact set of information observed by buyers is available. As with the signaling explanation, the biases introduced by the presence of unobservables run counter to the predictions of the search model. Though it is true that higher ask prices would be associated with higher offers if ask prices captured unobservables, it is also true that higher ask prices would be positively correlated with number of offers and negatively correlated with time to sale. The latter two relationships are opposite to those predicted by the search model.

IV. THE DATA

Our data consist of listings, ask prices, and offers for a sample of 301 Macintosh units. Each listing contains the date on which the listing was created: these extend from 10 January 1998 to 10 May 1998. Each observation also contains the date and amount of each offer. We recorded listings and offers on 11 June 1998, and updated them on 28 June 1998.

We also obtained estimates of the market value and "market strength" of each computer. This information is contained in a quarterly report published by UCE. The report contains average national values (prices) for used Macintosh units. The listed values are for typical configurations for the most common Macintosh models. We will discuss how we handle deviations from the typical configuration. The market strength variable is a measure of national transaction volume for the particular model, on a scale of 1 to 100. It is therefore a rough measure of how thick the market is for each model. The summary is readily available to buyers and sellers on the UCE Web site. In our sample, the values and market strength figures are taken from the report released on 10 March 1998. Thus our sample contains listings and ask prices for the two months prior to and following the release of the report.

Table 1 presents summary statistics for our sample and for subsamples stratified by market strength. Stratifying the sample in this way is a preliminary attempt to see how patterns in the data might vary as the thickness of the market segment for a particular model varies. Our supposition is that thinner (weaker) market segments are more likely to possess a high variance of buyer willingness to pay; we support this claim later with data. As a first pass at the effects of market strength, we classify market strengths below the median as "low" and those above the median as "high." The first row of the table shows the average number of days each computer was on the exchange when it was first observed. Recall that this date is four months after our earliest listing. For the sample of listings, the average time on the exchange is roughly two months. This value is essentially the same for high- and low-strength machines.

The second row shows the average value of all computers in the sample and the average values for the low and high market strength subsamples. Not surprisingly, the average value for a computer with high market strength is much larger (by nearly three times) than that for a computer with low market strength.

The next rows show data on the incidence of offers. The most striking thing about these data is that relatively few offers are made. For the sample as a whole, 43% of computers had not received any offers by the observation date. Thirty-five percent had received only one offer, and only 9% had received more than one offer. In general, computers with higher market strength receive more offers. Only 29% of computers with high market strength had received no offers, and 56% of those with low market strength had received no offers. It seems most correct based on these data to think of the markets in which these computers are sold as being fairly thin. (23)

The next row shows the average log-difference between the ask price and the computer's value. For the entire sample, this difference is over 80%. Thus, the ask price is typically quite high relative to the value of the computer. This difference is more pronounced for computers with low market strength. For these machines, the log-difference between the ask price and the value of the computer is over 100%. It is 60% for the computers with high market strength. Thus the raw data seem to suggest that sellers in thinner markets are more likely to purse a high ask price strategy. (24)

The next row shows the average log-difference between the highest offer received and the computer's value for the subset of computers that received at least one offer. On average, the highest offer is quite close to the computer's value; the log-difference is less than 8% for the sample as a whole. There is a difference between computers with high and low market strengths. The average log-difference between the highest offer and the value is over 10% for the low-strength subsample, whereas it is only 6% for the high-strength subsample.

Finally, we note that the offers for the low-strength subsample vary considerable more than those for the high-strength, controlling for the value of the computer. The coefficient of variation for the ratio of the high offer to the computer's value is 0.37 for the high-strength subsample and 0.78 for the low-strength subsample. (25) This is important because our reason for focusing on market strength is that we believe that in thinner (low-strength) markets, the variance of buyers' willingness to pay is higher. The evidence here is consistent with that assumption--the variance of offers made on computers with low market strength is much higher than the variance of offers on computers with high market strength.

The final row shows the percentage of the computers we observed initially that were no longer on the exchange when we next recorded data. Just over 40% of the computers observed initially were gone when we recorded data 17 days later. This percentage is slightly higher for computers with high market strength than for computers with low market strength, and the direction of the difference seems intuitive. In the empirical work, we will assume that all computers that are gone from the exchange on our second observation date were sold rather than just removed from the market. Although this may not be completely accurate, it would only bias the results against our main empirical finding regarding time to sale. (26)

V. ESTIMATING THE RELATIONSHIP BETWEEN ASK PRICES, OFFERS, AND TIME TO SALE

In this section we conduct three sets of empirical tests. We first examine the incidence of offers using the entire sample of computers. Under the search hypothesis, higher ask prices should deter offers, and this effect should be stronger in thinner markets. We then examine the determinants of the highest outstanding offer for the subsample of computers that received at least one offer. The search model predicts that higher ask prices should be associated with higher offers, and that this effect should be stronger in thinner markets. Finally, we examine the determinants of time to sale. The search model predicts that higher ask prices should be associated with longer time to sale, and that this result should be stronger in thinner markets.

The Incidence of Offers

We model the number of offers received for a computer as the outcome of a Poisson process, in which the data take on only whole number values and the probability that an outcome is observed is:

(1) Pr[ y = [y.sub.i] = ([e.sup.-[[lambda].sub.i][[lambda.sup.[y.sub.i].sub.i]/[y.sub.i]!)], y = 0, 1, ...

The model is specified by assuming that

(2) In [[lambda].sub.i] ([[epsilon].sub.i) = [beta]*[Chars.sub.i] + [PHI]*[Strength.sub.i] + [[epsilon].sub.i].

This simple specification allows the number of offers to be a function of observable characteristics of the computer and its market strength. The set of characteristics includes the value of the computer. This value variable captures most important features of the computer--its processor type and speed, the number of expansion slots, typical memory and hard drive sizes, and a standard bundle of video and network/Internet capabilities. Including this variable rather than each of the above-mentioned characteristics is advantageous because the value of the computer is in all likelihood a complex nonlinear function of the observable features. Estimation of this function would be problematic, given these nonlinearities and the likely interaction effects between various attributes of the computer. In any case, all else equal, we would expect computers in thicker submarkets to receive more offers. It is likely that the value of the computer reflects market thickness because computers with higher values are typically newer and have a wider range of practical uses. Also, value and market strength are positively correlated in the data. Because computers differ from the base specification with which their value is associated, in some specifications we also include extra memory or hard drive space relative to the mean for that model. To the extent that these characteristics affect value, they might change the likelihood of an offer. In preliminary estimates we also included a variety of other observable characteristics of the computer; none of these other characteristics was significant, so they are excluded from the results that we present. (27)

The set of characteristics also includes the length of time for which the computer has been on the exchange. We would expect time on the exchange to be positively correlated with the number of offers, particularly given the assumption of most search models that buyers arrive sequentially. Time on the exchange might be endogenous, however, if there are unobserved variables that affect the number of buyers that make offers. Dealing with this endogeneity is difficult because there are no clear suitable instruments. In the empirical work we therefore simply present results both including and excluding time on the exchange to assess its impact on the coefficients of interest.

We also attempt to control for deviations from base configuration by including other characteristics of the computer. In preliminary estimates using the complete set of observable characteristics, only two variables proved to affect offers significantly. We therefore include only these two variables, which measure the deviation of the computer's memory and hard drive space from the mean levels for that model type.

To measure the effect of the ask price, we also include the log-difference between the ask price and the independent assessment of the computer's value as a right-hand-side variable: (28)

(3) In [[lambda.sub.i]([[epsilon].sub.i) = [beta]*[Chars.sub.i] + [PHI]*[Strength.sub.i] + [gamma]*1n([Ask.sub.i]/[Value.sub.i]) + [epsilon].sub.i].

Under the prediction of the search model, higher ask prices (relative to value) should reduce the incidence of offers. A corollary of this is that in thinner submarkets, the prediction of the model should be stronger. We test this in two ways. We first estimate equation (3) for both "high-strength" and "low-strength" subsamples, where high and low are defined relative to the median market strength (as in Table 1). (29)

The results of this model are presented in Table 2. For the sample as a whole, we find that higher ask/value ratios reduce the number of offers received for the computer. The magnitude of the coefficient implies that a one-standard-deviation increase in ask/value from its mean reduces the expected number of offers by 0.25. Though not excessively large, this is an economically significant result. As a point of comparison, this effect is similar to either a $200 decrease in value or an additional 28 days of time on the exchange. The coefficient does not change significantly when time on the exchange is omitted.

The next sets of columns show results based on the stratification into high and low market strength. (30) The results are quite striking. The coefficient on the ask price is close to zero and is not statistically significant for the high-strength subsample. On the other hand, in the low-strength subsample the coefficient is large and statistically significant.

The magnitude of the coefficient implies that a one-standard-deviation increase in the ask/ value ratio is associated with roughly 0.50 fewer offers.

To conclude this section, we can note two features of the empirical results regarding the incidence of offers. First, all else equal, computers with high ask prices relative to their values receive fewer offers for at least some of the observations. This constitutes a rejection of a perfect information model in which ask price should be irrelevant and is also inconsistent with the hypothesis that higher ask prices reflect the presence of unobservable product characteristics. Second, the pattern of results when we stratify the sample by market strength is consistent with search models in which the variance of offers affects the gains to pursuing a high ask price strategy. In the next section we test the next set of predictions of the search model by examining the relationship between the ask price and the level of the highest outstanding offer.

Ask Prices and Offer Levels

Recall that the search models predict that higher ask prices should be associated with higher offers for the computers that ultimately receive offers. (31) In this section we test this prediction.

The most straightforward approach to estimating this relationship is to include the ask price in a standard hedonic regression. We specify this model as

(4) [Offer.sub.i] = [[alpha].sub.0] + [delta]*[Spread.sub.i] + [beta]*[Chars.sub.i] + [lambda]*[Strength.sub.i] + [[epsilon].sub.i],

where the dependent variable is the highest offer outstanding for a given computer when it is observed. (32) The right-hand-side variables include the set of computer characteristics, including the computer's value. We also include market strength; this may pick up any components of value not captured by the value variable.

In the base specification, we measure the independent effect of the ask price on offers by including the difference between the ask price and the computer's value (the "spread") as an explanatory variable. (33) Under the search model, we would see a positive relationship between this spread and the highest offer received for a computer. We allow this relationship to vary based on market strength in two ways. We estimate the model separately for the high- and low-market-strength subsamples. We also include in some specifications interaction terms between the spread and market strength:

(5) [Offer.sub.i] = [[alpha].sub.0] + [delta]*[Spread.sub.i] + [gamma]*[Spread.sub.i]*[Strength.sub.i] + [beta]*[Chars.sub.i]+[lambda]*[Strength.sub.i] + [epsilon.sub.i].

Using this hedonic specification with offers as the dependent variable raises two specification issues. The first is a standard sample selection problem; the sample includes only those computers that have received offers. This can be handled in a straightforward manner with standard sample selection techniques. In the work that follows, we use a standard two-step estimation technique that selects based on a binary variable indicating whether the computer has received at least one offer. (34)

The second issue derives from the fact that computers depreciate fairly rapidly. This introduces temporal concerns, because ask prices, computer values, and offers may have been submitted at different times for the same computer. Consider two computers that are identical but were listed on different dates. The newer machine is likely to have had a lower value at the time of listing, due to depreciation. Thus it would probably have both a lower ask price and lower offers--but these would reflect differences in the true value of the computer. To deal with this issue, we construct a variable measuring the time (in days) between the listing of the computer and the date on which the offer was submitted. We include this variable in the specification. We also include an interaction between this time variable and the ask price, an interaction between the time variable and the computer's value, and an interaction between market strength and the computer's value.

Table 3 shows results of these models. The first column shows results for the sample as a whole, and the second and third columns segment the sample into computers with high and low market strength. (35) The coefficient on the ask-value spread is positive and statistically significant for the sample as a whole. This result masks some differences across levels of market strength, however. For high-strength computers, the coefficient is smaller and is not statistically significant, whereas it is much larger and significant for low-strength computers. The magnitude of the coefficient for the low-strength subsample suggests that for each dollar that the ask price exceeds the estimate of the computer's value, the highest offer for that computer is higher by 36 cents. This is certainly significant in economic terms.

The coefficient on the interaction term also suggests that the impact of the ask price varies depending on market strength. For the sample as a whole and the high-strength subsample the coefficient on the interaction term is not statistically significant. However, for the low-strength subsample it is negative and significant, suggesting that the impact of the ask price is even greater in thinner markets.

The coefficient on market strength is also informative. It is positive in the high-strength subsample and statistically significant when the interaction term is included. This result seems intuitive--all else equal, computers in stronger markets receive higher offers. On the other hand, the coefficient on market strength for the low-strength subsample is negative and significant in the specification that omits the interaction term. This suggests that the highest outstanding offer is negatively related to market strength. This is consistent with the search model, in which the gain to holding out for a high price is greater in a thinner market.

The coefficient on the computer's value is what one would expect. In the high-strength subsample, the coefficient on the computer's value is close to (and not significantly different from) one. This suggests that for these computers, offers generally move one-for-one with value. Additionally, the coefficients on extra memory and hard drive space seem intuitive; all are positive, and in the low-strength subsample both memory and hard drive space are statistically significant.

The temporal variables also generally match expectations. The variable measuring the time between the observation date and the offer is positive and significant in most specification, suggesting that offers made earlier in the sample period were higher. The interaction term between the ask-value spread and the time since the offer is negative and significant in most specifications. This suggests that for computers that have been on the exchange longer when the offer is submitted, the influence of the spread is smaller.

As a final point, we can note that the adjusted [R.sup.2] for the high-strength subsample is much higher (0.80) than that for the low-strength subsample (0.60). This accords with the notion that in the low-strength subsample, buyers' valuations are more idiosyncratic. It is therefore more difficult to "fit" their offers regarding the observable characteristics of the computer.

Ask/Value Ratios and Time to Sale

In this section we assess the effect of the ask price on time to sale. Unfortunately, as we mentioned earlier, we do not observe final transactions and cannot observe time to sale directly. We do observe whether the computer remains on the exchange in our second observation date, and we use that to proxy for time to sale. Our assumption is that all else equal, computers that are gone on our second observation date have a quicker time to sale than those that remain. This is a slightly noisy measure, because we cannot be sure that removal from the exchange occurred because of a sale.

Our specification is a probit model, in which the dependent variable indicates whether the machine was gone when we conducted our second observation. The right-hand-side variable of interest is the log-difference between the ask price and the computer's value. The other right-hand-side variables are time on the exchange, the computer's value, its market strength, and extra memory and hard drive space. Again, we stratify the sample by market strength and also include an interaction term between the ask price term and market strength.

Table 4 shows results of these models. For the sample as a whole, the coefficient on ln(Ask/Value) is negative and statistically significant, indicating that computers with higher ask prices are more likely to remain on the exchange between our observation dates. At the means, the magnitude of the coefficient suggests that a one-standard-deviation increase in the log-difference between the ask price and the computer's value is associated with a nine-percentage-point fall in the probability that it remains on the exchange. Although there is no way to directly impute the increase in time on the exchange associated with this figure, it seems economically significant given that for the sample as a whole over 60% of computers remain on the exchange between our observation dates.

Once again, the results are nonexistent in the high-strength subsample and stronger for the low-strength subsample. The coefficient on the log-difference between the ask price and the computer's value is significant in the specification without the interaction term. In the specification with the interaction term, the interaction term is negative and significant, indicating that the effect of the ask price on the probability of sale increases in thinner markets.

VI. DISCUSSION AND CONCLUSION

Our results show that the relationship between ask prices, offers, and time to sale in the online computer exchange is consistent with search models. We find that higher ask prices are associated with higher outstanding offers at the time of observation. This implies that sellers with higher ask prices are more likely to reject equivalent offers, and by extension implies that higher ask prices are associated with higher final transaction prices. We also find that higher ask prices reduce the probability of sale between our observation dates, suggesting that high ask prices extend time to sale. Finally, we find that higher ask prices are associated with fewer offers. This implies that high ask prices deter buyers from making offers, suggesting that search or information processing for buyers is costly. These results are more pronounced for thinner markets in which buyers' preferences are idiosyncratic. Thicker markets tend to demonstrate characteristics closer to that of a competitive market in which ask prices have little effect.

It may seem surprising that despite the large amount of information available at low cost in this market, buyer and seller behavior fits the pattern predicted by search models. In prima facie terms this market possesses price information of very high quality; in fact, the exchange itself serves as an information transmission device by providing estimates of each computer's value. It would also seem that the costs of placing an offer are quite low.

It seems that the complexity of the good--a personal computer, which is a bundle of characteristics that may interact with each other in highly nonlinear ways--creates information processing costs that are significant. These costs may seem fairly small, especially compared to the time costs of visiting a house and inspecting it thoroughly. However, it is important to remember that the typical price of a used computer is also very small relative to the price of a house. In relative terms, the time costs of evaluating two computers that differ slightly on many dimensions may be high enough to deter consumers from undertaking many such comparisons.

The general intuition suggested by this work is that the wealth of information on the Internet may not guarantee frictionless outcomes. This notion is consistent with some recent empirical work examining e-commerce. Brynjolfsson (2000) finds, for example, that online book retailers (such as Amazon.com) may enjoy a price advantage of as much as 10% for repeat customers. Brynjolfsson and Smith (2000) find that despite extremely low search costs, there still exists substantial price dispersion in Internet book and CD markets; Internet prices for these goods differ by 25%, on average. They conclude that "branding, awareness and trust remain important sources of heterogeneity among Internet retailers." We would add to this the notion that if information is costly for consumers to process, a market may perform in a manner akin to one with costly search in the more classical sense.

TABLE 1 Descriptive Statistics for the Computer Sample

 Market Strength

 All High Low

Days on exchange 61 57 65
when observed (32) (29) (34)
Value 407 593 226
 (285) (266) (160)

Percent with
No offers 0.43 0.29 0.56
One offer 0.35 0.42 0.29
More than one offer 0.09 0.10 0.08
Log(ask/value) 0.83 0.60 1.05
 (0.59) (0.29) (0.72)
Log(high offer/value) 0.077 0.06 0.103
 (0.464) (0.384) (0.570)
Percent gone on second 0.43 0.45 0.4
observation date
N 301 150 151

Notes: Figures are mean. Standard deviations are shown in parentheses
below means. "High" and "Low" market strengths are relative to median.

TABLE 2
Offer Incidence
 Market Strength

Variable All

Log(ask price/value) -0.699 ** -0.473 **
 (0.172) (0.159)
Value 0.0016 ** 0.0018 **
 (0.0003) (0.0003)
Time on exchange 0.009 **
 (0.002)
Extra RAM 0.002 -0.001
 (0.002) (0.002)
Extra HD space 0.047 0.031
 (0.081) (0.079)
Market strength -0.009 -0.011 *
 (0.006) (0.006)
N 301

 Market Strength

Variable High

Log(ask price/value) -0.146 -0.024
 (0.324) (0.303)
Value 0.0013 ** 0.0014 **
 (0.0004) (0.004)
Time on exchange 0.003 0.015 **
 (0.003) (0.003)
Extra RAM -0.003 -0.004
 (0.003) (0.003)
Extra HD space 0.047 0.040
 (0.089) (0.088)
Market strength 0.008 0.007
 (0.011) (0.011)
N 150

 Market Strength

Variable Low

Log(ask price/value) -1.102 ** -0.872 **
 (0.270) (0.258)
Value 0.0033 ** 0.0027 **
 (0.0011) (0.0011)
Time on exchange

Extra RAM 0.009 * 0.012 **
 (0.005) (0.005)
Extra HD space 0.026 0.075
 (0.245) (0.209)
Market strength -0.038 ** -0.040 **
 (0.013) (0.013)
N 151

Notes: Poisson regression. Dependent variable is number of offers
received. "High" and "Low" market strengths are relative to median
(66). Extra RAM and HD space are measured as (positive or negative)
deviation from mean for given model.

* Significant at 10%.

** Significant at 5%.

TABLE 3
Effect of Ask Price on Offers

 Market Strength

Variable All

Value 0.852 ** 0.853 **
 (0.105) (0.105)
Ask-value 0.340 ** 0.292
spread (0.087) (0.247)
Ask-value spread * 0.001
market strength (0.003)
Value * time since 0.006 ** 0.006 **
offer (0.001) (0.001)
Ask-value spread * -0.004 ** -0.004 **
Time since offer (0.001) (0.001)
Time since offer 1.603 ** 1.645 **
 (0.688) (0.718)
Extra RAM 0.001 0.05
 (0.587) (0.636
Extra HD space 38.99 ** 39.90 **
 (18.31) (19.04)
Market strength 1.418 1.317
 (1.382) (1.481)
Inverse Mill's 64.16 107.47
ratio (66.69) (84.60)
N 165
Adj. [R.sup.2] 0.83 0.83

 Market Strength

Variable High

Value 0.863 ** 0.850 **
 (0.247) (0.231)
Ask-value 0.126 0.463
spread (0.220) (0.863)
Ask-value spread * -0.004
market strength (0.009)
Value * time since 0.006 * 0.006 **
offer (0.003) (0.003)
Ask-value spread * -0.003 -0.003
Time since offer (0.002) (0.002)
Time since offer 1.334 0.958
 (2.458) (2.377)
Extra RAM 0.037 -0.159
 (1.523) (1.458)
Extra HD space 59.44 58.61
 (55.33) (50.73)
Market strength 11.99 13.21 *
 (7.79) (7.84)
Inverse Mill's 518.67 469.39
ratio (407.68) (392.78)
N 92
Adj. [R.sup.2] 0.81 0.81

 Market Strength

Variable Low

Value 0.648 ** 0.488 **
 (0.170) (0.165)
Ask-value 0.362 ** 1.010 **
spread (0.151) (0.298)
Ask-value spread * -0.012 **
market strength (0.005)
Value * time since 0.008 ** 0.007 **
offer (0.002) (0.002)
Ask-value spread * -0.007 ** -0.007 **
Time since offer (0.002) (0.002)
Time since offer 1.749 ** 1.337 *
 (0.801) (0.752)
Extra RAM 2.588 ** 2.294 **
 (1.254) (1.134)
Extra HD space 60.97 * 38.69
 36.20) (34.53)
Market strength -4.016 ** 0.950
 (2.007) (2.436)
Inverse Mill's 139.44 * 124.35
ratio (74.79) (92.69)
N 73
Adj. [R.sup.2] 0.6 0.6

Notes: Sample selection model. Dependent variable is level of highest
outstanding offer. First-stage model is probit with dependent variable
equal to one if computer received at least one offer. "High" and "Low"
market strengths are relative to median (66). Extra RAM and HD space
are measured as (positive or negative) deviation from mean for given
model.

* Significant at 10%.

** Significant at 5%.

TABLE 4
Time to Sale

 Market Strength

Variable All

Log(ask price/value) -0.371 ** -0.077
 (0.164) (0.385)
Log(ask price/value) * -0.007
market strength (0.008)
Value 0.0006 0.0004
 (0.0005) (0.0005)
Extra RAM 0.005 0.005
 (0.003) (0.003)
Extra HD space 0.218 * 0.229 *
 (0.122) (0.124)
Market strength -0.008 -0.001
 (0.007) (0.012)
N 301

 Market Strength

Variable High

Log(ask price/value) -0.288 4.833
 (0.416) (3.34)
Log(ask price/value) * -0.066
market strength (0.043)
Value 0.0006 0.0004
 (0.0006) (0.0006)
Extra RAM 0.005 0.005
 (0.004) (0.004)
Extra HD space 0.169 0.172
 (0.145) (0.147)
Market strength 0.001 0.043
 (0.013) (0.031)
N 150

 Market Strength

Variable Low

Log(ask price/value) -0.444 * 0.544
 (0.233) (0.557)
Log(ask price/value) * -0.027 *
market strength (0.014)
Value 0.0005 -0.0009
 (0.0012) (0.0014)
Extra RAM 0.004 0.006
 (0.007) (0.008)
Extra HD space 0.366 * 0.417 *
 (0.212) (0.218)
Market strength -0.005 0.031
 (0.013) (0.023)
N 151

Notes: Dependent variable is dummy variable equal to one if computer is
gone on second observation date. "High" and "Low" market strengths are
relative to median (66). Extra RAM and HD space are measured as
(positive or negative) deviation from mean for given model.

* Significant at 10%.

** Significant at 5%.

(1.) Since we collected our data, the exchange discontinued person-to-person operations and is now a business-to-business clearinghouse. The details that follow pertain to the person-to-person business as it existed in 1998.

(2.) Though the rejection is not binding, we would imagine that after some period of time elapses (a few weeks, at the most), a buyer will interpret a "seen" offer as a rejected offer.

(3.) UCE's construction o f the transaction process seems designed to mitigate the problems inherent in online sales of used goods: adverse selection and hold-up. Forcing sellers to pay costs of shipping to UCE before the initial quality check deters (at least some) sellers with lemons. Though the UCE quality certification process is minimal, the exchange grants buyers a right of refusal even after a machine has passed the initial test. At this point, however, buyers rejecting machines must also incur a sunk cost of rejection. This seems designed to deter hold-up. We are grateful to a referee for making this point. These issues seem particularly important given the importance of trust and reputation in many online settings; see, for example, Jin and Kato (2002), Houser and Wooders (2000), Melnick and Alto (2002), and Resnick and Zeckhauser (2002) for more on these issues.

(4.) During the time period of our sample, sellers paid 15% of the transaction price for computers sold for less than $1500 ($60 minimum), 12% for computers sold for $1500-$3000, and 10% for computers sold for more than $3000. This is in addition to the buyer's fee.

(5.) If sellers (irrationally) persisted in setting ask prices that were correlated with their reservation prices, then we would see a positive correlation between ask prices and the highest outstanding offer for a given computer. We might also see a positive correlation between ask prices and time to sale. We would not see an inverse relationship between ask prices and the number of offers that a computer received, because buyers would not be deterred from (costlessly) making offers on computers with high ask prices, no matter how small the probability of making a transaction.

(6.) It may be the case that sellers do not know buyers' reservation prices or that neither buyers nor sellers know the willingness to pay of a particular buyer for a particular good.

(7.) In Yavas and Yang (1995) buyers and sellers each know their reservation price but not that of the other party. This does not change the intuition of the model.

(8.) Green and Vandell (1994) take this approach in considering a seller's choice of the optimal list price.

(9.) This is the approach in Arnold (1999), Chen and Resenthal (1996), and Yavas and Yang (1995).

(10.) Quan and Quigley (1991) develop a search model in which ask prices are completely binding. The same result--that higher offers deter buyers--occurs in their model.

(11.) The Chen and Rosenthal (1996), Yavas (1992), Yavas and Yang (1995), and Arnold (1999) models all examine the case of a single seller of a unique good. These models all yield a unique ask price for a given set of model parameters. They also yield an inverse relationship between ask prices and arrival rates in equilibrium.

(12.) Glower et al. (1998) use comparative statics to show that an increase in the seller's discount rate leads to a higher list price, a higher expected sale price, and longer time on the market.

(13.) This arises in the Quan and Quigley (1991) model. In their model, ask prices are binding, but the intuition would still apply as long as setting a higher ask price deterred low-valuation buyers from making offers.

(14.) See Read (1988) for a model that allows the variance of buyers' valuations to change.

(15.) See Haurin (1988) for a search model with this feature.

(16.) Consider the limiting case in which buyers' valuations are known with certainty. The search model would no longer apply, and ask prices would be irrelevant.

(17.) They find that this is true for mid-priced houses but is not true for high- and low-priced houses.

(18.) Though the amount of memory and hard drive space is easily quantifiable, other attributes are less so. For example, the model category itself represents a bundle of characteristics (number of expansion slots, standard video adapter, etc.) that is fairly complex and would certainly have heterogeneous value for buyers.

(19.) Of the 300 computers for which we have data, only 16 are functionally identical to another on the exchange.

(20.) A simple way in which these valuations would differ, for example, is in buyers' relative valuations of the presence of a modem versus a network card, depending on their Internet use and access to a direct (e.g., T1) Internet connection.

(21.) Note that if we do not assume that market strength for unobserved quality mimics that of observed quality traits, the signaling model would offer no predictions concerning the number of offers or the time to sale. This still differs from the search models, which provide clear predictions. The quality signaling model also has no implication regarding the variance of buyers' willingness to pay.

(22.) This problem plagues studies of real estate transactions. For example, Glower et al. (1998) must construct a "predicted sale price" for houses that they observe, because actual sale prices might reflect omitted variables.

(23.) Of course, the exchange is not the only option for sellers; nonetheless it is clear that this market is not one in which buyers are continuously outbidding each other (as in, for example, many Internet auctions).

(24.) It is also possible that older computers with low market strength are more likely to have additional memory, hard drive space, or other features that will inflate their values above that for the base configuration. We control for this possibility in the estimates that follow.

(25.) The coefficient of variation is the standard deviation divided by the mean. For the high-strength subsample, the mean of (high offer/ask) is 1.14, and the standard deviation is 0.42. For the low-strength subsample, the mean of (high offer/ask) is 1.32, and the standard deviation is 1.04.

(26.) To see this, suppose a seller with a high ask price has a high reservation price, because he or she has a good outside option or is inclined to keep the computer. All else equal, such a seller would be more likely to remove his or her computer from the exchange than one with a lower ask price. We find that the opposite is true.

(27.) The other characteristics were a set of dummy variables representing the presence of features superior to that in the base configuration. There were six such dummies, one each indicating the presence of extra features for graphics or audio, one indicating the presence of a modem, one indicating the presence of a network card, and two indicating the presence of extra storage devices. None of the coefficients on these variables were significant either jointly or individually.

(28.) Using the ratio of the ask price to value (without logs) yielded qualitatively identical results.

(29.) In unreported results, we also estimate a pooled specification that allows for the impact of market strength using a linear interaction term. The interaction term is not significant and leaves the other coefficients unchanged.

(30.) An alternative way of specifying the relationship between market strength and the effect of the ask/value ratio would be to construct an interaction term. In unreported estimates, we find that a simple linear interaction term is not significant. It is possible that the relationship between market strength and the ask/value coefficient is highly nonlinear.

(31.) Our test explicitly examines the effect of the ask price on the highest outstanding offer and therefore tests whether offers are more likely to be rejected by high-ask price sellers. But it also implicitly tests whether computers with high ask prices ultimately receive higher transaction prices, under the assumption that final transaction prices are correlated with higher outstanding offers.

(32.) In fact, if high ask prices deter low-valuation buyers, we would expect that the distribution of received offers (not just the highest) would be higher for computers with high ask prices. Though we do not report the results of this model, this is in fact the case. A specification that includes the average offer yields a positive and statistically coefficient on the ask-value spread. Nor is this coefficient statistically different from that on the ask-value spread when only the highest offer on each computer is included in the model.

(33.) Our specification assumes that if the ask price affects offers, its marginal effects are identical in dollar terms across all computers. One could instead allow the ask price to enter the model using the percentage markup of the ask price over the computer's value, but this would create problems of interpretation given that the dependent variable is in dollars.

(34.) We do not report these results, but the model includes a set of right-hand-side variables identical to those in the Poisson model reported in Table 2. Their results are qualitatively the same as the Poisson results.

(35.) Note that segmenting the sample into high and low market strengths no longer divides the sample evenly, as the median market strength of the entire sample differs from the median market strength for the subsample of computers that received at least one offer.

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AMY FARMER and VICTOR STANGO *

* We thank Richard Cox for helpful data entry and the anonymous referees for their comments. All errors are our own.

Farmer: Professor, Department of Economics, Walton College of Business, University of Arkansas, Fayetteville, AR 72701. Phone 1-479-575-6093, Fax 1-479-575-3241, E-mail afarmer@walton.uark.edu

Stango: Senior Economist, Federal Reserve Bank of Chicago, 230 S. LaSalle St., Chicago, IL 60604. E-mail victor.stango@chi.frb.org