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Abstract We conduct an empirical analysis of consumer preferences and search costs on an Internet platform. Using data from a major French platform (PriceMinister), we show descriptive evidence of substantial price dispersion among adverts for the same product, of consumers often not choosing the cheapest advert and sometimes choosing an advert dominated in price and non-price characteristics by another available advert. We consider a sequential search model where consumers sample adverts in an endogenous order based on their preferences and search costs. We show that the optimal search-and-purchase strategy can be characterized by a set of inequalities which can feasibly be tested on transaction and advert data. This allows us to estimate, for each transaction, a set of preference and search cost parameter values, thus allowing for flexible consumer heterogeneity in preferences and search costs. The estimated model can then describe a wide range of consumer search and purchase behaviours. We find that the model can explain almost all transactions in the data and requires non-zero preferences and search costs for at least 50% and 22% (respectively) of observations. We also find evidence of heterogeneous and sometimes substantial search costs. 1. Introduction The advent of e-commerce, in particular Internet platforms, was initially presumed to increase competition and thus decrease price dispersion, since it allowed the gathering of information at little physical and time cost. However, casual observation of trading websites as well as the emergence of rich data sets documenting the variance of prices among adverts and transactions convey a compelling message: price dispersion remains and can be substantial (see e.g.Baye et al., 2004). Potential sources of dispersion have been investigated by the recent economic literature. First, differences in non-price characteristics across sellers or adverts can generate price dispersion even for a specific product. Secondly, acquiring or processing information about all relevant characteristics may still be costly for consumers and these search costs may reduce the scope for the “law of one price” to prevail. Accordingly, the consumer search literature has been at the forefront of the analysis of Internet markets. A recent paper by Anderson and Renault (2016) provides a detailed survey of this literature, stressing that “appropriate theoretical frameworks should involve sufficient heterogeneity among agents on both sides of the market” and also explaining that “the analysis of ordered search constitutes an essential ingredient for modelling recent search environments”. The latter point follows from the fact that consumers may search across alternatives in a specific, possibly endogenous, order. In this article, we provide empirical evidence on the importance of consumer preferences and search costs based on a new structural estimation approach. We consider the (partial-equilibrium) model of Weitzman (1979), where consumers search sequentially for alternatives in an endogenous order and we show that the optimal search-and-purchase strategy can be characterized by a simple set of inequalities. These inequalities lend themselves to a feasible set-estimation approach inspired by the revealed preferences literature. One strength of our approach is that we allow for almost unconstrained heterogeneity in preferences and search costs. This, combined with the endogenous sampling strategies predicted by the model, leads our structural model to account for a wide range of consumer search behaviours and rationalize nearly all transactions observed on the platform under study. Our estimation approach and the model we use thus makes our analysis contribute to the two main features of the consumer search literature put forward by Anderson and Renault (2016). We estimate the model on an administrative record of all transactions and all adverts on the website priceminister.com, which is one of the main e-commerce platforms in France. For each transaction, we have information on all the adverts that were available at that particular date for the very same product, identified by a barcode. These are the adverts that were on the computer screen when the consumer searched for this specific product on this website. In this article, we will focus on CD transactions. Adverts vary in price and also in other characteristics such as the condition of the item, the seller’s reputation, etc. We show substantial price dispersion among adverts and among transactions for the same product. We also find that consumers often do not buy the cheapest available advert and sometimes even choose an advert that is clearly dominated (in price and in non-price characteristics) by another available advert. These stylized facts motivate our structural analysis which focuses on two objects: consumers’ taste for non-price characteristics and search costs. Our structural analysis builds on a sequential model of directed search (on prices) à laWeitzman (1979). We now briefly describe this framework to fix ideas. Assume that a consumer wants to buy a specific product and is presented with a finite number of adverts. Consistently with the design of the PriceMinister website, we assume that prices are observable at no cost and may thus be used by the consumer to determine his optimal search order, but that consumers must pay a search cost to examine an advert’s characteristics and compute the corresponding utility.1 The consumer samples adverts one at a time and incurs the same search cost for each draw. The consumer chooses in which order he samples adverts, recall is allowed and the search can stop before all adverts have been sampled. The optimal search and purchase strategy has been derived by Weitzman (1979) and depends on the consumer’s beliefs about advert characteristics given price and on the consumer’s search cost and marginal willingness to pay (MWP hereafter) for these characteristics. Combining this search-and-purchase rule with heterogeneity in consumer MWPs and search costs leads to an important feature of our analysis, which is that it can describe a wide range of sampling patterns. In particular consumers do not necessarily search in ascending price order and/or do not necessarily buy the last item sampled. Some consumers will sample very few adverts, others will almost exhaust all the offers. These different patterns will arise from heterogeneity in search costs and in consumer preferences. Hence, a consumer’s choice set is formed endogenously, depending on his (individual-specific) MWP and search cost. Whilst the optimal stopping rule is often incorporated in consumer search models, the analysis of the optimal search order as a direct consequence of the consumer’s preferences and search costs within a structural estimation is one of the main innovations of our article. To estimate the model we derive two analytical results. First, we show that the optimal search and purchase rule derived by Weitzman (1979) is equivalent to a set of tractable inequalities. Secondly, we derive a simple characterization of the set of parameters consistent with each transaction. Estimation proceeds in three steps. The first step consists in projecting advert non-price characteristics onto one “hedonic” scalar. The second step estimates consumers’ beliefs about the distribution of this hedonic characteristic conditionally on advert price, using the observed joint distribution of advert prices and characteristics. The last step is close in spirit to the revealed preference literature (see Blow et al., 2008, Cherchye et al., 2009 and Cosaert and Demuynck, 2014) and uses the conditions derived from our theoretical analysis to find, for each transaction, which values of the MWP and search cost parameters are consistent with the fact that the bought advert was chosen over the alternative adverts. We do not impose any restriction on the shape of consumer heterogeneity with respect to search costs or to the MWP for the advert “hedonic” scalar.2 Note also that we are not excluding the case where the consumer only cares about prices (i.e. his MWP is zero) and/or faces no search costs (and can sample all adverts for free). Our approach will then produce bounds on the distributions of MWPs and search costs which will be informative to assess the importance of search costs and consumer preferences in our data. We are, to the best of our knowledge, the first to use this empirical approach in the consumer search literature. Our benchmark specification can explain 95% of the CD transactions observed on the website in a specific quarter in 2007, which is our benchmark estimation sample. As mentioned above, many transactions are such that the advert sold is dominated by an alternative advert in price and hedonic characteristics. A hedonic perfect-information model cannot explain these transactions (unless consumers only care about prices and the two adverts are at the same price), whereas our model is able to rationalize 76% of these transactions with reasonable values of the MWP and search costs. Since the cheapest advert is bought in slightly less than 50% of transactions, a strictly positive MWP is needed to explain half of the transactions in our data. Importantly, we find that strictly positive search costs play a substantial role on the Internet platform we study. Indeed, 22% of the transactions we explain require a search cost strictly larger than zero and are thus inconsistent with a perfect-information model. To investigate the degree of heterogeneity in preferences and search costs in our set-estimation approach, we borrow from a recent article by Stoye (2010) and compute, for each of these parameters, the minimal variance compatible with our estimated bounds. Whilst the minimum variance distribution of MWP’s displays little dispersion, we find evidence of heterogeneity in search costs. Our estimated model illustrates a varied set of search patterns. For example, when setting individual search costs to the minimum value for each explained transaction, we find that consumers who face strictly positive search costs buy the first advert that they sample 63% of the time. Besides we find that for 13% of transactions with positive search costs, the consumer has carried on sampling after finding the advert that he eventually buys. The model estimates also allow us to quantify the utility cost incurred by consumers who face strictly positive search costs, and whether this cost comes mainly from searching (sampling cost) or from the fact that consumers do not always buy the best available advert. Our benchmark model estimation relies on observed advert characteristics and rules out that unobserved attributes may affect the consumer’s decision. We show in an extension that our approach can account for unobserved characteristics, at the cost of making a parametric assumption on their distribution. Our estimation strategy can still be adopted and produces results which are in line with those we find in our benchmark estimation. We end this introduction with a review of the consumer search literature that this article contributes to. Early empirical works include Hortaçsu and Syverson (2004) who consider that investors search sequentially for funds and have homogeneous preferences for fund attributes and heterogeneous search costs. In their framework, the link between a fund’s sampling probability and the investor’s preferences is not modelled. Hong and Shum (2006) estimate a search cost distribution for consumers searching for the best price (no other product attributes) for academic textbooks, considering both a sequential and a non-sequential search model. An alternative parametric approach exploiting the equilibrium conditions of the non-sequential search model has been suggested by Moraga-González and Wildenbeest (2008) and a semi-parametric approach has been developed by Moraga-González et al. (2013). De Los Santos et al. (2012) use data on the search and purchase books across different Internet websites and reject sequential search on the grounds that consumers do not necessarily buy from the last store visited. As we argue in our article, allowing for directed sequential search instead of random search makes our sequential search model consistent with this feature. Two recent articles have estimated search costs in models where consumers learn about the distribution of utilities through searching: Koulayev (2014) and De Los Santos et al. (2017). In these papers the order in which adverts are sampled is either random or imposed, but not linked to consumer preferences. In contrast, our approach allows for endogenous sampling order but rules out learning. Sequential directed search models building on Weitzman (1979) have recently been estimated, mostly using Internet data. The first paper we are aware of is Kim et al. (2010) and more recent contributions include Kim et al. (2016), Ursu (2017), Honka and Chintagunta (2016), and Chen and Yao (2016).3 Our article departs from these existing studies on at least three dimensions. First, we do not not require data on search behaviour to (set) identify search costs and preferences, we only use choice and offer data. Our approach can thus be taken to a large set of applications whereas search data (i.e. data on which options consumers “click” on) are still relatively rare. Secondly, in most of these papers, the advert attribute that is unobserved prior to sampling is modelled as an unobserved (to the econometrician) taste shock, the distribution of which is parameterized and independent of the observed characteristics driving consumer search. The two exceptions we are aware of are Kim et al. (2016), where the unobserved attribute’s variance may depend on ex ante observable characteristics and Chen and Yao (2016), where consumers can sort adverts along one dimension and then infer on the advert characteristics from its position on the computer screen. In our article, we assume that prices are observed ex ante but that consumers must pay a search cost to find out the advert “hedonic” index, which is allowed to be related to the price through a flexibly estimated function. We think that this is closer to Weitzman (1979)’s model as prices can be seen as a signal that carries information on the distribution of characteristics. The third difference between our article and previous studies is that we allow for a very flexible modelling of consumer heterogeneity in both preferences and search costs and are thus able to capture a wide range of search behaviours. Indeed, some transactions will be explained by a perfect-information model (no search cost), others by a model where consumers search in increasing price order and others where search order is non-monotonic in price. Within our approach, the search costs and MWPs we find for a given transaction do not influence those found for other observations through some parametric distribution of either of these two parameters. We believe this allows us to give robust empirical evidence on search costs and preferences on the Internet platform we study. Since our main estimation targets are demand-side structural objects, namely consumer preferences and search costs, we retain a partial equilibrium analysis and focus on developing a flexible estimation approach whilst allowing for heterogeneity and elaborate search strategies. Naturally, our results trigger questions related to the price-setting behaviour of sellers in view of these heterogeneous search costs and preferences on the consumers’ side. We will however leave these questions for future research and refer here to the relevant literature for an equilibrium analysis. The theoretical literature on consumer search models is vast, starting with Stigler (1961) and continuing with important contributions in the 1980s (a non-exhaustive list includes Burdett and Judd, 1983, Wolinsky, 1986 and Stahl II, 1989) aiming at overcoming the Diamond (1971) paradox. More recent contributions include Anderson and Renault (1999) who study consumer search product differentiation, Janssen and Moraga-González (2004) who analyse firm behaviour with oligopolistic competition and non-sequential search, or Moraga-González and Petrikaite (2013) who derive an equilibrium sequential search model where consumers can direct their search towards merging firms depending on their expectations over price. On a more empirical branch of the literature, Zhou (2011) presents an (exogenously) ordered search model in which firms visited late in the search process enjoy some monopoly power since consumers visiting them do so when they have a low valuation of the products offered by firms already visited.4 Another recent paper by Dinerstein et al. (2017) uses rich data on eBay to estimate an equilibrium non-sequential search model with homogeneous consumers and to simulate the effects of changes in the platform’s design. Our article is organized as follows. Section 2 details the model and derives the conditions used to identify the sets of preference and search cost parameters. Section 3 presents our data and gives empirical evidence on price dispersion and consumer search and purchase behaviours on an Internet platform. Section 4 details the three steps of our empirical strategy and Section 5 shows the estimation results on fit, search costs, preferences, and heterogeneity. Section 6 uses the model estimates to describe consumer search behaviour. An extended version of model is derived and estimated in Section 7 and Section 8 concludes. 2. The model 2.1. Consumers’ search and purchase decision Consider a buyer who wishes to purchase one unit of a specific product (for instance a given CD) on an Internet platform. Let |$J\geq 1$| be the number of adverts for this product that are currently posted on the platform. Each advert |$j\in\{1,...,J\}$| consists of a price |$p_j$| and a vector of characteristics |$x_j$|. In our application, |$x$| will contain the seller’s reputation index, its size (i.e. the number of transactions carried out on the website to date), its status (professional or not), and the condition of the good being sold. We assume that the consumer’s outside option, that is, the utility of not buying anything, is very low so that one advert is always bought.5 Preferences. The utility of buying an advert |$(p,x)$| is given by: \begin{equation} \label{eq: udef} u\left(p,x,\gamma\right)=\gamma x-p. \end{equation} (2.1) The parameter |$\gamma$|, which has the same dimension as |$x$|, is the consumer’s MWP for the advert’s characteristics and summarizes the consumer’s preferences for these characteristics. We allow consumers to have heterogeneous preferences so |$\gamma$| may vary across individuals. For notational convenience, we will sometimes write the utility offered by advert |$j$| as |$u_j$|.6 Search. In order to acquire information on adverts’ relevant characteristics, consumers may need to engage in a costly search process. We assume that consumers search sequentially, with possibility of recall. This means that they sample adverts one at a time and can always buy any advert previously sampled.7 Drawing an advert incurs a search cost |$s\geq 0$| which, like the preference parameter |$\gamma$|, is allowed to vary between consumers. Drawing an advert means being able to observe all the advert characteristics and thus finding out the level of utility it offers. The search cost |$s$| can be thought of in a number of ways, such as a cost of looking at the advert characteristics or a cost of processing the information given by the new advert. This search cost is assumed to be constant across draws. Note that we do not rule out the case |$s=0$|i.e. the perfect-information model whereby a consumer simply buys the advert offering the highest utility. We assume that consumers can see all the available advert prices instantly and at no cost but have to pay the search cost |$s$| to observe a given advert’s characteristics |$x$|. This follows from the design of the website used in our empirical application. When consumers are looking at adverts for a given product, they first see all adverts ranked by increasing order of price. The price is shown in a larger font than other characteristics (such as seller reputation, etc.). We thus think that it is realistic to assume that collecting information on prices is costless for consumers but that they must pay a utility cost to gather additional information on adverts as these details are less visible and not ranked by default. Consumers can use advert prices to direct their search. Note that in this directed search model, the perfect-information case obtains not only when |$s=0$| but also when |$\gamma=0$|. Indeed, if a consumer only cares about prices and if information about advert prices is available at no (search) cost, this consumer will look at all the advert prices and buy the cheapest advert, as if there were no search frictions. Beliefs and advert distribution. The consumer believes that the |$J$| adverts presented to him are independent draws from a joint distribution of prices and characteristics |$\left(P,X\right)$|, denoted |$F_{P,X}$|.8 We assume that consumers’ beliefs are homogeneous and remain the same during the search process, that is, we rule out learning.9 This will allow us to derive a simple optimal search strategy for consumers. We also need to consider the conditional distribution |$F_{X|P}$|, which is what consumers believe to be the cdf of |$X$| for a given price |$P$|. Let |$F^0_{P,X}$| denote the cumulative distribution function (cdf) of prices and characteristics in the population of all adverts actually posted on the platform (for a given product category) in a given time window. This distribution follows from sellers’ pricing strategies. For instance, sellers may differ with respect to their characteristics |$x$| and, given their value of |$x$| and the distribution of consumers’ preferences and search costs, set prices that maximize their expected profit. The resulting distribution, |$F^0_{P|X}$|, combined with the distribution of seller characteristics |$F^0_X$| leads to the observed distribution of prices and characteristics |$F^0_{P,X}$|. In this article, since we restrict our analysis to a partial equilibrium, we will take |$F^0_{P,X}$|, which we can directly observe in the data, as given. A natural way to anchor consumers’ beliefs would be to assume that |$F_{P,X}=F^0_{P,X}$|. In a full-equilibrium setting, this means that consumers’ beliefs are consistent with sellers’ pricing strategies. From an empirical perspective, this assumption allows us to estimate consumers’ beliefs as the observed distribution of prices and characteristics in the population of adverts. However, as we will discuss in detail in Section 4.2, one may impose further restrictions on the beliefs in order to limit the level of sophistication in consumers’ predictions. 2.2. Consumers’ search and purchase decision We already know that a consumer with |$s=0$| will buy the advert offering the highest utility and that a consumer with |$\gamma=0$| will buy the cheapest advert. We now present the optimal search and purchase strategy used by consumers for whom |$s>0$| and |$\gamma>0$|. This strategy has been characterized in an influential article by Weitzman (1979). We will first present this result in the context of our model and then show how it can be used to identify consumers’ preference and search cost parameters. We give a more formal presentation of the consumers’ sequential search problem in Appendix A. A first step is to define the following quantity, which will drive the individual consumer’s search strategy: the “reservation utility” of an individual with preference parameters |$(s, \gamma)$|, denoted |$r(p,s,\gamma)$|, which represents the utility level at which this individual is indifferent between sampling a new item priced |$p$|, thus incurring a search cost |$s$|, and not sampling it, thus staying with a utility of |$r(p,s,\gamma)$|. This threshold utility satisfies the following condition: \begin{equation} \label{eq: rdef} s = E_{X|P=p}\Big[\big(u(p,X,\gamma) - r(p,s,\gamma)\big) \cdot\boldsymbol{1}\left\{u(p,X,\gamma)>r(p,s,\gamma)\right\}\Big], \end{equation} (2.2) where the expectation is taken over the distribution of advert characteristics |$X$| given that the price is equal to |$p$|, and |$\boldsymbol{1}\{\cdot\}$| is the indicator function. In other words, the expected gain over |$r(p,s,\gamma)$| of sampling this item is equal to the search cost |$s$|.10 It is apparent from equation (2.2) that this “reservation utility” depends on the price |$p$|, on the individual parameters |$\gamma$| and |$s$| but also on consumers’ beliefs regarding the joint distribution of |$X$| and |$P$|. We will sometimes denote the reservation utility offered by advert |$j$| simply as |$r_j$|, instead of |$r\left(p_j,s,\gamma\right)$|. Note that all consumers share the same beliefs but are heterogeneous with respect to |$(s,\gamma)$|. This model rationalizes the search order and this order will vary across consumers as the sequence of reservation utilities is individual specific. The optimal sequential search and purchase strategy, as derived by Weitzman (1979), is the following: The consumer draws adverts in decreasing order of reservation utilities |$r$|. The consumer stops searching when the highest utility he has drawn is larger than the largest reservation utility among adverts not yet drawn. When stopping the consumer buys the advert with the highest utility among the ones he has sampled. Ties are assumed to be resolved in the following way. If several adverts have the same reservation utility |$r$|, consumers sample them in a random order. If several adverts that have been drawn offer the same maximum level of utility, the consumer chooses one randomly. When indifferent between stopping his search and sampling another advert, the consumer stops searching. 2.3. Identification of preferences and search costs In the spirit of the revealed preference literature (see Blow et al., 2008), we now identify sets of parameters that are consistent with the choices observed in the data. Consider a transaction where advert |$i$| is sold. We may also refer to this transaction as transaction |$i$|.11 From now on, for each transaction, all quantities (|$p$|, |$x$|, |$u$|, |$r$|) will be indexed by |$i$| if they refer to the advert bought, and by |$j$| if they refer to an advert which was available (i.e. on the screen) but was not bought. We derive necessary and sufficient conditions for a pair |$(s,\gamma)$| to be consistent with the fact that |$i$| was bought while advert |$j$| was also available but not chosen. These conditions will characterize a set |$S_{ij}$|. We can then define the set |$S_i$| of parameters consistent with transaction |$i$| as the intersection of all the sets |$S_{ij}$| for all available adverts for this transaction.12 First, we assess whether a transaction can be explained by a perfect-information model: \begin{eqnarray} (s=0,\gamma)\in S_i & \Leftrightarrow & \gamma x_i-p_i\geq \underset{j}{\max}\left\{\gamma x_j-p_j\right\}, \label{eq: CRs0} \\ \end{eqnarray} (2.3) \begin{eqnarray} (s,\gamma=0)\in S_i & \Leftrightarrow & p_i\leq \underset{j}{\min}\left\{p_j\right\}. \label{eq: CRg0} \end{eqnarray} (2.4) In words, consumers with no search costs should buy the best advert and consumers who only care about prices should buy the cheapest advert (since information on prices is available for free). We now turn to the case where both the search cost |$s$| and the preference parameter |$\gamma$| are strictly positive. The identified set |$S_{ij}$| is characterized as follows: Proposition 2.1. Let |$s>0$| and |$\gamma>0$|. Then |$(s,\gamma)\notin S_{ij}$| if and only if \begin{equation} \label{eq: CR0a} \Big( u_i\geq r_i \quad\text{ and }\quad r_j>r_i \quad\text{ and }\quad u_j\geq r_i \Big) \\ \end{equation} (2.5)or \begin{equation} \label{eq: CR0b} \Big( u_i<r_i \quad\text{ and }\quad r_j>u_i \quad\text{ and }\quad u_j>u_i \Big). \end{equation} (2.6) The proof is in Appendix B. This gives us a simple accept/reject rule for each value of |$(s,\gamma)$| to rationalize the transaction |$i$| being observed while advert |$j$| was present on the screen. Our characterization of |$S_{ij}$| thus follows from simple inequalities. For each transaction |$i$| and each value of |$(s,\gamma)$|, we just need to compute the instantaneous and reservation utilities and check whether equations (2.5) or (2.6) holds for any advert |$j$|. If this is not the case, this parameter value rationalizes the transaction. The problem with this approach is that reservation utilities |$r$| are only implicitly defined by an equation that involves both preference and search cost parameters, see equation (2.2). In the next section, we show how we make our characterization of the identified sets far more tractable. 2.4. The case of a scalar hedonic index So far, we have considered a general case where the non-price characteristics of adverts consisted of a vector |$x$|. In this section, we assume that |$x$| is a scalar and that it is valued positively by all consumers so that |$\gamma\geq 0$|. |$\gamma$| now represents the individual’s MWP for the hedonic index |$x$|. This assumption and the results from the previous section lead a more tractable characterization of the sets of identified parameters. In practice, the scalar index |$x$| will be obtained as a function of advert characteristics (in our case, |$x$| will be a linear index of seller’s reputation, product condition, etc.), which is assumed to be the same for all consumers. This approach still allows for heterogeneity in preferences but slightly restricts it in that, under this assumption, consumers have homogeneous marginal rates of substitution between two non-price advert characteristics. However, the MWP |$\gamma$| for the hedonic index |$x$| varies across consumers, indeed there is no restriction on the distribution of the scalar |$\gamma$| other than it being positive or zero. This is not restrictive as, in our data, we can find an advert characteristic for which the MWP is unlikely to be strictly negative (for instance, seller reputation or product condition). We will show in detail in Section 4.1 how we construct a structural projection of advert characteristics onto the scalar hedonic index |$x$|. We now introduce the following function: \begin{equation} \label{eq: psidef} \psi_p(x) = E_{X|P=p}\left[(X-x)\cdot\boldsymbol{1}\left\{X>x\right\}\right]. \end{equation} (2.7)|$\psi_p(x)$| reflects the expected gain over |$x$| (the scalar hedonic index) when an item of price |$p$| is sampled. An important feature of this function, which will be very useful for estimation, is that it does not depend on |$(s,\gamma)$|. The function |$\psi_p$| is differentiable and strictly decreasing in |$x$| on the support of |$X$| given price |$p$|. We can thus define its inverse |$\psi^{-1}_p$|. Note also that |$\psi$| characterizes the consumer’s beliefs and that the condition |$\psi_{p'}\geq\psi_p$| is equivalent to second-order stochastic dominance of |$F_{X|P=p'}(\cdot)$| over |$F_{X|P=p}(\cdot)$| (see Hadar and Russell, 1969). Hence, if consumers believe that the distribution of |$X$| improves with price, this is reflected by the fact that |$\psi_p$| increases with |$p$|. Importantly, we can use the definitions in equations (2.2) and (2.7), to derive another expression for |$r(p,s,\gamma)$| which conveniently mirrors that of utility: \begin{equation} \label{eq: rpsi} r(p,s,\gamma)=\gamma\cdot\psi_p^{-1}\left(\frac{s}{\gamma}\right)-p. \end{equation} (2.8) We can now give a tractable characterization of the identified set |$S_{ij}$|. First, we use conditions (2.3) or (2.4) for the cases where |$s=0$| or |$\gamma=0$|, respectively. With a scalar hedonic index, these conditions are easier to interpret. Indeed, let us say that advert |$j$| (alternative) is “better” than advert |$i$| (bought) if |$j$| is both cheaper (|$p_j\leq p_j$|) and of better quality (|$x_j\geq x_i$|) than |$i$| with at least one of these inequalities being strict. When there exists an advert |$j$| that is “better” than the bought advert |$i$| then the transaction |$i$| cannot be explained by a perfect-information model (|$s=0$|) unless |$p_i=p_j$| in which case the transaction can be explained by |$s=\gamma=0$|. On the other hand, the absence of a “better” alternative advert does not necessarily mean that a transaction can be explained without search costs. For example, consider the case where advert |$i$| is sold whilst adverts |$j$| and |$k$| were available, advert |$i$| is cheaper and offers less quality than |$j$|, and is more expensive and offers better quality than |$k$|. Hence, neither |$j$| nor |$k$| is “better” than |$i$|. Assume further that |$\frac{p_j-p_i}{x_j-x_i}<\frac{p_i-p_k}{x_i-x_k}$|. In this case a pair |$(s=0,\gamma)$| cannot be in |$S_i$| since the value of |$\gamma$| would have to be lower than |$\frac{p_j-p_i}{x_j-x_i}$| (the MWP has to be low enough to rationalize |$i$| being preferred to |$j$|) and larger than |$\frac{p_i-p_k}{x_i-x_k}$| (the MWP has to be high enough to rationalize |$i$| being preferred to |$k$|). Hence, a perfect-information model cannot explain this transaction. If |$s$| and |$\gamma$| are strictly positive, we plug the expressions of the utility and reservation utility, (2.1) and (2.8), into the inequalities (2.5) and (2.6) to obtain the following characterization: Proposition 2.2. Let |$x$| be a scalar, |$s>0$| and |$\gamma>0$|. Then |$(s,\gamma)\notin S_{ij}$| if and only if \begin{align} \label{eq: CRa} \Bigg( \frac{s}{\gamma}\geq\psi_{p_i}\left(x_i\right) \quad \text{ and } \quad \gamma\left[\psi^{-1}_{p_j}\left(\frac{s}{\gamma}\right)-\psi^{-1}_{p_i}\left(\frac{s}{\gamma}\right)\right]>p_j-p_i \notag\\ \text{ and } \quad \gamma\left[x_j-\psi^{-1}_{p_i}\left(\frac{s}{\gamma}\right)\right]\geq p_j-p_i \Bigg) \qquad\quad \end{align} (2.9)or \begin{equation} \label{eq: CRb} \Bigg( \frac{s}{\gamma}<\gamma\left[\psi^{-1}_{p_j}\left(\frac{s}{\gamma}\right)-x_i\right]>p_j-p_i \quad\text{ and } \quad \gamma\left(x_j-x_i\right)>p_j-p_i \Bigg) \end{equation} (2.10) The main advantage of equations (2.9) and (2.10) compared to (2.5) and (2.6) is that the conditions are now simple plug-in functions of the parameter values |$(s,\gamma)$|. Once we have an estimate of the |$\psi^{-1}_p$| functions for each price (and this can be done without looking at consumers’ choices), finding the set of parameters consistent with a given transaction can be done by a simple grid-search method, using (2.9) and (2.10) as a pass/reject criterion. 3. Data and descriptive statistics 3.1. The PriceMinister website We use data from PriceMinister, a French company organizing online trading of new and second-hand products between buyers and professional or non-professional sellers. We will focus on the company’s French website www.priceminister.com. PriceMinister is one of the largest e-commerce websites in France with 11 million registered users and over 120 million products for sale in 2010 (the site opened in 2001).13 Whilst many different goods can be bought from the website (books, television sets, shoes, computers, etc.), we will focus on CDs and, in a robustness check, on DVDs. “Cultural” goods (books, CDs, video games, and DVDs) represented the vast majority of transactions during our observation period. The website is a platform where sellers, professional (registered businesses), or non professional (private individuals), can post adverts for goods, which can be used or new.14 When a potential buyer searches for a specific item, the website returns a page of available adverts. These include the price (adverts are sorted by increasing prices by default), the condition of the item: new or used (“as new”, “very good”, “good”), the seller’s status (professional or not), reputation (to be defined shortly), and size (the number of transactions completed by the seller).15 In this article, we focus on the consumer’s search behaviour when faced with a page of adverts for a specific product. We do not model how the consumer has decided to reach this page and this website. Since our data relate to transactions, we know that the consumer must have reached the page of adverts for this product before he made his purchasing decision, and we carry out our analysis conditionally on this. A seller’s reputation is the average of feedbacks received since the creation of the seller’s account. To explain the feedback mechanism, we now describe how transactions take place on the website. When a buyer purchases a given product from a given seller, the buyer’s payment is made to PriceMinister in the first instance. At this point the seller is informed that a buyer has chosen her product and ships the item to the buyer. Once the buyer has received the product, he is prompted to give his feedback on the transaction through the website. PriceMinister then closes the transaction and pays the seller.16 The buyer’s feedback consists of a grade, or rating, which is any integer between 1 (very disappointed) and 5 (very satisfied). The default provided on the feedback form is equal to 5.17 The seller’s reputation as posted on the website is the average of the feedbacks received for all completed transactions, rounded to the nearest first decimal. A seller’s size at a given date is then the number of transactions that she has completed so far. We should mention that PriceMinister differs from other e-commerce websites that are studied in the economic literature with respect to several features that are important for our analysis. First, PriceMinister itself does not sell any products: it is a platform (unlike, e.g., Amazon). Hence consumers may not direct their search towards the seller that also operates the platform. Secondly, prices are posted by sellers, there are no auctions (unlike eBay).18 3.2. The data We were given two administrative data sets by PriceMinister: one with all the transactions between 2001 and 2008, and one with all the adverts posted between 2001 and 2008. In this article, we will focus on transactions of CDs which took place in the third quarter of 20