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Testing Models of Consumer Search using Data on Web Browsing and Purchasing Behavior

By: Babur De los Santosy,Ali Hortacsuz,Matthijs R. Wildenbeestx

1 Introduction
Since Stigler's (1961) seminal paper, models of costly search have been at the heart of many economic models trying to explain imperfectly competitive behavior in product and labor markets.

The theoretical literature typically models consumer search in two ways: following Stigler's original model, a strand of literature assumes non-sequential search behavior, where consumers sample a fixed number of stores, and choose to buy the lowest price alternative.1 A much larger strand of the literature, starting with McCall (1970) and Mortensen (1970), points out that consumers cannot commit to a non-sequential search strategy in instances where the expected marginal benefit of an extra search exceeds the marginal cost. Thus, this literature argues that a sequential search model provides a better description of actual consumer search.

Unfortunately, beyond the a priori reasons put forth by the literature, there have been few empirical studies of whether actual consumers follow sequential or non-sequential strategies. This is, no doubt, due to the diculty of collecting data on individual search behavior. Therefore, most of what we know about individual level search behavior is from laboratory experiments. The majority of the experimental literature on search has focused on sequential search.3 Schotter and Braunstein (1981) have reported that on average subjects tend to search in a fashion that is consistent with sequential search strategies, although subjects tend to search too little to be searching optimally. Kogut (1990) and Sonnemans (1998) find evidence that individuals are making decisions based on the total return from searching instead of on the marginal return from another draw as they would do if searching sequentially, resulting in too little search. Moreover, Kogut (1990) finds that in about a third of the time individuals accepted old o ers, which violates optimal policy.

Zwick et al. (2003) also find large rates of recall among participants of an experiment in which a randomly selected object with a known rank order has to be selected. Harrison and Morgan (1990) directly compare non-sequential and sequential strategies to so-called variable-sample-size strategies. The latter strategy is described in Morgan and Manning (1985) and is a generalization of both non-sequential and sequential search since it allows individuals to choose both sample size and how many times to search. Harrison and Morgan (1990) report that experimental subjects indeed employ the least restrictive strategy if they are allowed to do so.

Aside from experimental studies, Hong and Shum (2006) and Chen, Hong, and Shum (2007) are the only papers that we are aware of that have attempted to discriminate between sequential and non-sequential search models using data from a real-world market. Hong and Shum (2006) collect data on textbook prices, and estimate structural parameters of search cost distributions (i.e. the demand parameters) that rationalize the prices set by competing firms.

They find larger search-cost magnitudes for the parametrically estimated sequential search model than for the non- parametrically estimated non-sequential search model. Similar data is used in Chen, Hong, and Shum (2007) to conduct a nonparametric likelihood ratio test for choosing among the nonpara- metrically, moment-based non-sequential and parametrically estimated sequential search models. Although certain parameterizations of the sequential search model are found to be inferior, they conclude that it is dicult to distinguish between the non-sequential search model and the log- normal parameterization of the sequential search model in terms of fit.

This paper utilizes novel data on the web browsing and purchasing behavior of a large panel of consumers to test classical models of consumer search. Our data, described in some detail in Section 2, allows us to observe the online stores visited while shopping for a particular item, and which store the consumer decided to buy from. As pointed out by Kogut (1990) and as we will argue in more detail in Section 3 below, under the reservation price (utility) rule prescribed by the \benchmark" model of sequential search, a consumer always buys from the last store she visited, unless she has visited all stores in her choice set. In Section 4, using data on consumers shopping for books online, we find that this prediction is rejected by a large number of consumers in our data set.

In Section 3, we discuss the Rosen field and Shapiro (1981) model, which relaxes the assumption that consumers \know" the distribution of prices while deciding on their search strategy, and allow for learning of the price distribution. Importantly, in this setting, the sequential search model can not be rejected based on recall patterns alone. Instead, we derive bounds on search costs that rationalize observed search behavior, and conduct tests based on the consistency of these search cost bounds across shopping trips. In Section 5, we explore whether misspecification of the search model is quantitatively important in our particular setting. In particular, we estimate consumer search cost distributions (the demand parameters) under various search rules. We find that the estimated search costs under the non-sequential search assumption display much less dispersion within person than the search costs estimated under the sequential search with Bayesian learning model. This means the non-sequential search model leads to more stable parameter estimates, and we thus conclude that non-sequential search may provide a more accurate description of observed behavior.

Finally, in Section 7 we use the favored non-sequential search model to estimate the price elasticities faced by online retailers, and, under static profit maximization, the markups charged by these retailers. To do this, Section 6 derives expressions for demand elasticities implied by the non-sequential search model. One important feature of this model is that we allow for asymmetric sampling: due to for instance advertising or prior shopping experience, consumers' first draw may be skewed towards some online retailers (e.g. Amazon) over others. Our results, reported in Section 7, indicate higher price elasticities than reported by Chevalier and Goolsbee (2003), especially for Amazon. A further discussion of our results vis a vis prior findings is in Section 7.1.nd Goolsbee (2003), especially for Amazon. A further discussion of our results vis a vis prior findings is in Section 7.1.

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Testing Models of Consumer Search using Data on Web Browsing and Purchasing Behavior