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Abstract In many markets consumers have imperfect information about the utility they derive from the products that are on offer and need to visit stores to find the product that is the most preferred. This paper develops a discrete choice model of demand with optimal sequential consumer search. Consumers first choose a product to search; then, once they learn the utility they get from the searched product, they choose whether to buy it or to keep searching. The set of products searched is endogenous and consumer specific. Therefore imperfect substitutability across products does not only arise from variation in characteristics but also from variation in search costs. We apply the model to the automobile industry. Our search cost estimate is highly significant and indicates that consumers conduct a limited amount of search. Estimates of own-price elasticities are lower and markups are higher than if we assume consumers have full information. Keywords: consumer search, differentiated products, demand and supply, automobiles JEL Classification: C14, D83, L13 ∗

We thank Jean-Pierre Dub´e, Amit Gandhi, Elisabeth Honka, Jean-Fran¸cois Houde, Sergei Koulayev, Ariel Pakes, Steven Puller, Stephan Seiler, Marc Santugini, Philipp Schmidt-Dengler, Michelle Sovinsky, and Frank Verboven for their useful comments and suggestions. This paper has also benefited from presentations at the D¨ usseldorf Institute for Competition Economics, Illinois State University, Katholieke Universiteit Leuven, The Ohio State University, Penn State University, Texas A&M University, Tilburg University, Tinbergen Institute, University of Chicago, University of Illinois at Urbana-Champaign, University of Michigan, University of North Carolina, University of Zurich, 2009 Workshop on Search and Switching Costs at the University of Groningen, 2010 IIOC meeting in Vancouver, 2010 Marketing Science Conference in Cologne, 2011 European Meeting of the Econometric Society in Oslo, 2012 IOS ASSA Meeting in Chicago, 9th Invitational Choice Symposium in Noordwijk, 2014 Barcelona GSE Summer Forum, 2014 Workshop on Search and Switching Costs at Indiana University, and 2014 MaCCI Workshop on Consumer Search in Bad Homburg. Financial support from Marie Curie Excellence Grant MEXT-CT-2006-042471 and grant PN-II-IDPCE-2012-4-0066 of the Romanian Ministry of National Education, CNCS-UEFISCDI is gratefully acknowledged. † Vrije Universiteit Amsterdam, E-mail: [email protected] Moraga-Gonz´ alez is also affiliated with the University of Groningen, the Tinbergen Institute, the CEPR, and the Public-Private Sector Research Center at IESE (Barcelona). ‡ Sapientia University Miercurea Ciuc, E-mail: [email protected] § Indiana University, Kelley School of Business, E-mail: [email protected]

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Introduction

In many markets, such as those for automobiles, electronics, computers, and clothing, consumers typically have to visit stores to find out which product they like most. Though basic information about products sold in these markets is usually easy to obtain either from television, the Internet, newspapers, specialized magazines, or just from neighbors, family, and friends, consumers search because some relevant product characteristics are difficult to quantify, print, or advertise. In practice, since visiting stores involves significant search costs, most consumers engage in a limited amount of search.1 Earlier work on the estimation of demand models (Berry, Levinsohn, and Pakes, 1995, 2004; Nevo, 2001; Petrin, 2002) has proceeded by assuming that consumers have perfect information about all the products available in the market. In the market settings referred to above, the full information assumption is, arguably, unrealistic. In a recent study of the US computer industry, Sovinsky Goeree (2008) shows that departing from the perfect information assumption is important for obtaining realistic estimates of demand and supply parameters. In her model, firms distribute advertisements about the existence and characteristics of the computers they sell. Advertisements are perfectly informative and consumers differ in the likelihood with which they are exposed to them. As a result consumers end up having heterogeneous and limited information about the existing alternatives in the market. Yet, in the setting of Sovinsky Goeree (2008) consumers do not need to incur any search costs to evaluate the utility they derive from the alternatives they happen to be informed of via the advertisements. This paper adds to the literature on the structural estimation of demand and supply by presenting a discrete choice model of demand with optimal sequential consumer search. To the best of our knowledge our paper is the first to do this in a Berry, Levinsohn, and Pakes (1995) (BLP hereafter) framework. The distinctive feature of the BLP framework is that a product’s utility depends on a structural error term, which is known as an unobserved product characteristic in this literature. This structural error is crucial for modeling price endogeneity, and naturally leads to estimation based on aggregate data. The key difference between our demand model and that in BLP is that in our model consumers do not know all the relevant information about the products 1 Several recent empirical papers have found that consumers search relatively little. For instance, Honka (2014) reports that consumers obtain an average of 2.96 quotes when shopping for car insurance. De los Santos, Horta¸csu, and Wildenbeest (2012) find that over 75 percent of consumers visited only one online bookstore before buying a book online, whereas De los Santos, Horta¸csu, and Wildenbeest (2017) find that the mean number of online retailers searched is less than 3 for MP3 players. Some other examples of markets in which consumers are found to search little are S&P 500 index funds (Horta¸csu and Syverson, 2004) and automobiles (Moorthy, Ratchford, and Talukdar, 1997; Scott Morton, Silva-Risso, and Zettelmeyer, 2011).

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available and have to search in order to evaluate them. Search is costly and consumers search sequentially through the available options. The costs of searching vary across individuals and firms so consumers choose to visit distinct sellers even if they have similar preferences. In our model consumer product information is thus endogenous and consumer specific. As a result, imperfect substitutability across products does not only arise from product differentiation but also from the variation in consumer information sets generated by costly search. Similar to the effects of advertising in Sovinsky Goeree (2008), search frictions thus generate heterogeneous and limited consumer information. We apply the model to the automobile market. The automobile market is precisely a market in which advertisements, reports in specialized magazines, television programs, and the Internet convey much but not all the relevant information about the models available. As a result, a great deal of new car buyers visit dealerships to view, inspect, and test-drive cars. Given prior information about the products available at the various sellers (such as size, horsepower, fuel efficiency, price, and design of a car), as well as the costs of search (which we relate to dealership locations and certain consumer demographics), each consumer chooses the order in which she will visit the sellers and, after each visit, whether to stop searching and buy one of the alternatives inspected so far or else to continue searching at the next seller. Following Weitzman (1979), the solution of this search problem consists of ranking the sellers in terms of reservation utilities, visiting them in descending reservation utility order, and stopping search when the highest observed utility is above the reservation utility of the next best option. The complexity of the real-world setting to which we apply our model—specifically, many alternatives available in the market that differ in ex-ante observable characteristics and search costs—makes the computation of the consumers’ buying probabilities a challenge. When there is a large number of alternatives available in the market, there are many ways through which a consumer may end up buying a particular car. For example, with just three alternatives, there are eleven distinct search paths a consumer may follow before deciding to buy a given car. As the number of alternatives increases, the number of search paths grows exponentially, which renders the problem initially intractable in settings like ours. To address this challenge, we adapt recent findings from the theoretical search literature by Armstrong (2017) and Choi, Dai, and Kim (2016) that make it possible to compute the buying probability of a given alternative without having to go explicitly through the myriad of possible ways in which a consumer may end up considering the alternative in question. We use data from the Dutch market for new cars to estimate the model. We provide background

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information on this market in Section 2. Survey data reveal two important facts. First, consumers visit a limited number of car dealers before buying a car—on average two for new car purchases— and the number of visits varies substantially across consumers. Second, a great deal of the dealer visits involve test-driving cars.2 We interpret these two facts as suggesting that models of perfect information and models of imperfect information in which consumers just shop for lower prices are likely to be inapt. This leads to a model formulation in which consumers have imperfect information about product features and they have to search to evaluate the alternatives before buying. In Section 2 we also provide some reduced-form evidence that search behavior is related to demographics such as income, family size, age, and distances to dealerships. We develop our search model in Section 3. Following Armstrong (2017) and Choi, Dai, and Kim (2016), we express a consumer’s search and purchase decision as a discrete choice problem in which a consumer chooses the alternative that offers the highest minimum of the reservation value and realized utility among all available alternatives. We show how to use these probabilities to estimate the model, but, because these expressions are generally not closed form, the estimation of the model is relatively slow. To speed up the process, we develop a method that significantly reduces the computational complexity of the model. We solve the model backwards: starting from a distribution for the minimum of the reservation value and realized utility that leads to closed-form expressions for the buying probabilities, we derive the search cost distribution that rationalizes this distributional assumption. This alternative procedure is extremely practical and turns out to deliver estimates of demand, elasticities of demand, and markups that are very similar compared to those obtained for alternative search costs distributions in the more general procedure. We estimate the model using data on car characteristics and market shares, as well as individuallevel choice and search data derived from the survey mentioned above. In Section 4 we provide a discussion on how variation in the data allows us to identify the parameters of the utility function as well as the search cost distribution. We discuss the specifics of the estimation procedure in Section 5. The data and estimation results are presented in Section 6. One advantage of our model is that it nests the demand model of BLP by taking search costs to zero. Our search cost estimates are highly significant. Moreover, taking into account search costs leads to less elastic demand estimates and higher estimates of price-cost margins compared to the standard BLP setting. We conclude that accounting for costly search and its effects on generating heterogeneity in consumer choice sets 2 According to survey data discussed in Section 2, respondents that were looking to buy a new car made a test drive in 45 percent of dealer visits, and 75 percent made at least one test drive at one of the visited dealerships.

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is important for explaining variability in purchase patterns. In Section 6 we also use the estimates to perform several counterfactual analyses. Specifically, taking our estimates as a starting point, we perform simulations that allow us to study the effects of lowering the costs of visiting dealerships on prices and profits. By offering home-delivered test drives, these traveling costs can be brought down to near zero.3 Our simulation results indicate that (sales-weighted) average prices decrease by over seven percent when distance-related search costs go down to zero, with price decreases exceeding ten percent for some cars. We find that the closer a dealer (on average) is to consumers, the less its price will be affected by changes in distance-related search costs. This could be explained by the fact that brands that operate a network of many dealers tend to be active in a relatively competitive segment of the market, which means that more competition due to lower search frictions does not affect their pricing strategy much. We also simulate the competitive effects of changes in the way manufacturers use their dealer networks. When a manufacturer incorporates a new brand to the group of brands it sells, it has the choice whether to reorganize business and start retailing the new brand together with the existing ones. This is typically a long run decision because such reorganizations involve the re-design and refurbishing of showrooms, which may involve large sunk costs. Our estimates of the gains from such business reorganizations provide lower bounds for these sunk costs. We find that mergers of existing dealership networks could have nontrivial effects on sales, prices, and profits.

Related literature Our paper builds on the theoretical and empirical literature on consumer search. At least since the seminal article of Stigler (1961) on the economics of information a great deal of theoretical and empirical work has revolved around the idea that the existence of search costs has nontrivial effects on market equilibria. Part of the effort has gone into the study of the effects of costly search in homogeneous product markets (see for instance Burdett and Judd, 1983; Reinganum, 1979; Stahl, 1989). In this literature a fundamental issue has been the existence of price dispersion in market equilibrium. Another tradition has been the study of costly search in markets with product differentiation. In a seminal contribution, Wolinsky (1986) notes that search costs generate market power even in settings with free entry of firms. More recent contributions investigate how product diversity (Anderson and Renault, 1999), product quality (Wolinsky, 2005), and product design (Bar-Isaac, Caruana, and Cu˜ nat, 2012) are affected by costly search. As in our model, in this literature consumers search for a good product fit, and not for lower prices. Our search model 3

In the US, Seattle startup Tred allows consumers to test-drive and buy cars without having to visit the dealership.

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is most closely related to the framework of Wolinsky (1986) but we allow for asymmetric multiproduct firms, consumer heterogeneity in both preferences and search costs, and, like in Choi, Dai, and Kim (2016) and Haan, Moraga-Gonz´alez, and Petrikait˙e (2017), for price deviations to be observable before searching. Some recent empirical research on consumer search behavior has focused on developing techniques to estimate search costs using aggregate market data. Hong and Shum (2006) develop a structural method to retrieve information on search costs for homogeneous products using only price data. Moraga-Gonz´ alez and Wildenbeest (2008) extend the approach of Hong and Shum (2006) to the case of oligopoly and present a maximum likelihood estimator. Horta¸csu and Syverson (2004) study a search model where search frictions coexist with vertical product differentiation. Our paper contributes to this line of work by incorporating consumer search into the BLP framework. A number of recent papers present related models of search and employ micro- or aggregate-level data on search behavior to estimate preferences as well as the costs of searching. Although several of these papers also focus on search for a good product fit (Kim, Albuquerque, and Bronnenberg, 2010; Kim, Albuquerque, and Bronnenberg, 2017), most of these papers assume that consumers are searching for prices (De los Santos, Horta¸csu, and Wildenbeest, 2012; Seiler, 2013; Honka, 2014; Koulayev, 2014; Pires, 2016; Dinerstein, Einav, Levin, and Sundaresan, 2017; Honka, Horta¸csu, and Vitorino, 2017). An important difference between these papers and ours is that they do not model unobserved product characteristics and hence they do not allow for price endogeneity.4 A further distinction can be made according to whether consumers are assumed to search sequentially or non-sequentially. A computational advantage of non-sequential search (De los Santos, Horta¸csu, and Wildenbeest, 2012; Honka, 2014; Moraga-Gonz´alez, S´andor, and Wildenbeest, 2015; Murry and Zhou, 2017) is that consumers’ search decisions are determined before any search activity takes place, and therefore do not depend on realized search outcomes.5 This allows one to formulate the search and purchase decision as a two-stage problem in which the consumer selects products in the first stage, and then makes a purchase decision from products that appear in this choice set. A complicating factor is that without restrictions on the number of choice sets, there is a dimensionality problem, and the literature has focused on various ways to deal with this when estimating such models.6 4 Honka, Horta¸csu, and Vitorino (2017) use a control function approach to address advertising endogeneity in a three-stage structural model (consisting of awareness, consideration, and choice). 5 This work is also related to “consideration set formation” models in the marketing literature, which relate consideration set heterogeneity to advertising or search frictions (see, for example, Roberts and Lattin, 1991; Mehta, Rajiv, and Srinivasan, 2003). 6 For instance, Honka (2014) invokes assumptions that allow her to use the Marginal Improvement Algorithm of Chade and Smith (2006) to limit the number of choice sets, whereas an earlier version of this paper (Moraga-Gonz´ alez,

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In sequential search models search decisions do depend on search outcomes, which complicates the estimation of such models and typically leads to high-dimensional integrals for choice and search probabilities. While this may be manageable in applications with a small number of products or search decisions (as in Koulayev, 2014), the approach we use in this paper reduces this dimensionality problem by integrating out different search paths that lead to a purchase decision and is therefore useful for larger choice sets. Kim, Albuquerque, and Bronnenberg (2017) propose an alternative method that avoids the use of high-dimensional integrals and estimate their probit choice model by maximum likelihood using view rank and sales rank data for camcorders sold at Amazon.com. Another alternative approach is put forward in Jolivet and Turon (2017), who derive a set of tractable inequalities from Weitzman’s optimal sequential search algorithm that can be used to set identify demand-side parameter distributions; they estimate their model using individual purchase data for CDs sold at a French e-commerce platform. Note that both Kim, Albuquerque, and Bronnenberg (2017) and Jolivet and Turon (2017) do not explicitly deal with price endogeneity. Our paper also fits into a broader literature that estimates demand for automobiles, which includes BLP, Goldberg (1995), and Petrin (2002).7 Recent papers in this literature have studied car dealership locations and how this affects consumer demand and competition. For instance, Albuquerque and Bronnenberg (2012) use transaction level data as well as detailed data on the location of consumers and car dealers to estimate a model of supply and demand and find that consumers have a strong disutility of demand for travel. In a related paper, Nurski and Verboven (2016) focus on dealer networks to study whether the exclusive contracts often used in the European car market act as barrier to entry. The most important difference between these papers and our paper is that they assume consumers have perfect information about all the alternatives in the market. This means distance from a consumer to a car dealer is interpreted as a transportation cost, i.e., distance is treated as a product characteristic that enters directly in the utility function. In contrast, in our paper distance enters as a search cost shifter and as such generates variation in the subsets of cars sampled by consumers. In Section 4 we discuss how sequential search theory allows for the separate identification of the effects of distance on utility and search costs. We compare the two approaches when estimating the model in Section 6 and show that the elasticity estimates and markups from the search cost model are quite different from those obtained from the transportation cost model. S´ andor, and Wildenbeest, 2015) achieved tractability by adding a choice-set specific error term that is Type I Extreme Value (minimum) distributed to the costs of searching a group of alternatives. 7 See Murry and Schneider (2016) for an overview of studies on the economics of retail markets for new and used cars.

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Dutch Car Market

In 2008 approximately 500,000 new passenger cars were sold in the Netherlands, which makes it the sixth biggest car market in Europe in terms of sales. The top selling make is Volkswagen, which in 2008 had a market share of 9.2 percent, followed by Ford (8.7 percent), Opel (8.3 percent), Peugeot (8.2 percent), and Toyota (8.0 percent). The most popular car models tend to be small in size—in 2008, the two top selling models were the Peugeot 207 and Opel Corsa (both are in the so-called supermini class) followed by the Volkswagen Golf (small family car class). In this section we use survey data to provide some background information on search behavior in the Dutch car market and to motivate the search model we will develop in Section 3. The data was obtained from TNS NIPO (tns-nipo.com), a Dutch survey agency. As part of their ongoing investigation (named “De Nederlandse Automobilist”) on the characteristics and behavior of Dutch motorists, over 1,200 car drivers are surveyed every year. These drivers are part of TNS NIPObase, which is a panel of around 200,000 respondents. The dataset contains 2,530 observations—1,297 for the survey carried out in 2010 and 1,233 for the 2011 survey. Our data consists of a subset of the questions in the survey and focuses on two aspects of consumer decision making: product orientation and the purchase decision. Each observation corresponds to a single respondent. All questions in the survey relate to the car that is owned by the respondent at the time of questioning. We have information about the make and model of that car, as well as the year in which the car was bought. We also know whether the car they bought was used or new. In addition, the respondents answered questions that provide useful information on how consumers search in this market. In particular, respondents reported the brands of the dealerships they visited before buying the car, and for which brands they made a test drive at the dealer.8 Respondents also reported how many different dealerships were visited of the same brand as the brand that was purchased by the respondent, and the maximum number of different dealerships that were visited on the same day.9 Finally, the respondents answered questions about their household income, household size, age, whether there are children living in the household, and zip code. Figure 1 gives a histogram of the number of dealers of different brands visited (conditional on searching) by respondents who bought a new car. We focus on purchases between 2003 and 2008 only, since that period overlaps with the aggregate data we will be using for the main analysis, giving us a total of 1,250 respondents who bought a car between those years, of which 540 were new 8

The specific questions that were asked are: “For which of the following brands did you visit a dealer?” and “For which of the following brands did you make a test drive at the dealer?” 9 Approximately two-thirds of respondents who bought a new car and visited dealerships of multiple brands did not make those visits on the same day, which is consistent with a sequential search strategy.

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Figure 1: Histogram number of dealers visited for new car purchases cars. The average number of dealers of different brands visited for new car purchases is 2, which is slightly below the average of 3 dealers found by Moorthy, Ratchford, and Talukdar (1997) for the United States in the early nineties. Although 47 percent of respondents who searched visit at least one dealer of a single brand only, the distribution is positively skewed with some consumers visiting dealers of as many as 12 different brands.10 The survey data can be used to argue that a model in which consumers have perfect information is unlikely to be an accurate representation of demand. A first natural interpretation of the full information model is that consumers know all they need to know in order to conduct a purchase decision. Under this interpretation, there is no need to visit more than one dealer and every visit would result in a purchase. Our survey data rejects this proposition. In fact, as shown in Figure 1, a substantial number of consumers visits more than one car dealership. Moreover, in 2008 around 44 percent of consumers did not buy a new car conditional on having visited at least one dealer that year. An alternative interpretation of the full information model is that even though consumers do not observe all relevant car characteristics before visiting the dealerships, consumers can visit them and learn the utility they derive from the various cars at zero cost. Under this interpretation, consumers would then visit dealers of all brands in the market before conducting a purchase. The survey data also rejects this argument because, although some respondents visited as many as 12 10 Approximately 16 percent of respondents who bought a new car claim they have not visited any dealers. A relatively large proportion of the non-visits are (company) car leases—although only 18 percent of new car purchases in the survey data are company car leases, they represent over 25 percent of the non-visits. Other possible explanations for purchases occurring without any dealer visit are online car purchases, and parallel imports. Buying a new car online is only possible in the Netherlands since 2006, when the online car dealer nieuweautokopen.nl started operating.

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dealers before having bought their car, not a single consumer visited a dealer of each of the 39 brands in the market. The survey data also suggests that an imperfect information model in which the sole purpose of the visits is to compare, or to negotiate, prices is unlikely to be a good representation of demand. The survey gives some information on what consumers do while visiting car dealers. In 45 percent of the dealer visits a test drive was involved. Moreover, among those who visited one or more dealers to shop for a new car, over 75 percent made at least one test drive at one of the visited dealerships. If price were the only relevant characteristic that consumers search for in this market, we would not observe this many test drives being made. Because, arguably, test drives are done to learn car characteristics (including whether the car is a good fit) that can hardly be learnt otherwise, the survey data is consistent with a search model in which the main reason for visiting car dealers is to learn more about the product and not just about its price.11 Besides information on dealer visits, the survey data contains demographic information such as zip code, household income, family size, age, and household composition. To obtain a better insight into what explains the differences in search behavior across the respondents, we run several regressions. We first use the information on dealer visits from the survey to investigate what determines the number of dealer visits. Column (A) of Table 1 gives the results of an ordered probit regression in which we explain the number of dealer visits by the log of household income, a dummy for whether there are kids living in the household, a dummy for whether the partner of the head of household is 65 years or older, and a dummy for whether the respondent purchased a new car. In addition we include year fixed effects as well as fixed effects for the make that was ultimately bought. As shown in the table, the log income coefficient is positive and highly significant. Even though this suggests that higher income leads to more search, this does not necessarily mean that higher income respondents have lower search costs because more wealthy consumers also tend to buy more expensive cars and the benefits from search may be higher for this type of cars. Although only significant at the ten percent level, having children in the household reduces the number of searches, while being older increases the number of searches. The new car dummy indicates that people visit more dealers when buying a new car than when buying a used car, which may reflect 11

Close to 47 percent of the consumers who search for and bought a new car visited only one dealer of a given brand, making it unlikely that these consumers were visiting dealers for price shopping. Around 36 percent visited 2 or 3 dealers of the same brand. While we cannot rule out price shopping for these consumers, there are other potential explanations for this observation. For example, consumers visit several dealers of the same brand because not all dealers have cars available for test driving for the models they are interested in. Though most consumers in the Netherlands order new cars which means they have to wait for delivery, some consumers value immediacy and visit various dealers to learn what cars are on inventory. A limitation of our study is that we do not observe data that helps discern among these potential reasons for visiting various dealers of the same brand.

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the fact that it is less common to buy a used car at a car dealer than it is when buying a new car. In specification (B) we focus on new car purchases only. Although this does not change the income coefficient much, the effect of children in the household is now twice as large, whereas the senior dummy is no longer significantly different from zero. Table 1: Dealer visits

Variable

Number of dealer visits (A) (B) Coeff. Std. Err. Coeff. Std. Err.

log(income) kids senior new car distance

0.215 -0.154 0.185 0.602

Pseudo R2 # obs

0.052 1,013

(0.067)∗∗∗ (0.083)∗ (0.093)∗∗ (0.074)∗∗∗

0.203 -0.303 0.079

(0.099)∗∗ (0.140)∗∗ (0.125)

0.041 442

Probability of dealer visit (C) (D) Coeff. Std. Err. Coeff. Std. Err. 0.085 -0.081 0.082 0.246 -0.070 0.102 35,385

(0.024)∗∗∗ (0.031)∗∗∗ (0.033)∗∗ (0.027)∗∗∗ (0.020)∗∗∗

0.067 -0.115 0.043

(0.032)∗∗ (0.048)∗∗ (0.042)

-0.079

(0.028)∗∗∗

0.098 15,028

Notes: ∗ significant at 10%; ∗∗ significant at 5%; ∗∗∗ significant at 1%. Data is for 2003-2008. All specifications include year and make dummies. Specifications (B) and (D) use data for new car purchases only. For some respondents income is missing, so the number of observations used to estimate specifications (A) and (B) is less than the number of respondents buying a car (1,250) and those buying a new car (540).

To see how the physical distance from a respondent to a dealer location affects decisions on whether or not to visit a dealer, in specifications (C) and (D) we regress an indicator for whether a dealer is visited by a respondent on the same set of covariates as before, as well as the Euclidian distance between the centroid of the zip code where the respondent resides and the nearest dealer of each of the car brands in our data. Specification (C) takes all car purchases into account, whereas in specification (D) we only focus on new car purchases. The effects of income, kids, and senior are similar to the results for the ordered probit regressions: income is positively related to a dealer visit, children negatively, and senior positively, although the effect for the latter disappears when we condition on new car purchases. In both specifications distance has a negative impact on the probability of visiting a dealer and is highly significant. We interpret these results as suggesting that distance from the consumer to a car dealer is related to search frictions. This interpretation is consistent with the fact that, according to the survey, 41 percent of new car buyers responded that distance was a factor they took into account when determining which dealers to visit. That distance matters is also reported in related work. Albuquerque and Bronnenberg (2012), using individual car transaction data in the San Diego metropolitan area between 2004 and 2006, find that consumers have a strong disutility for travel when buying a car. Similarly, Nurski and Verboven (2016) find that dealer proximity is an important determinant of demand for automobiles in Belgium. While these

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papers interpret distance as a transportation cost parameter that directly lowers utility, we treat it also as a variable that increases the cost of searching cars and creates limited and heterogeneous information. The above findings suggest search frictions play a role in the car market. Not only is there substantial heterogeneity across respondents in how many dealers they visit, but also consumers tend to visit car dealers to learn more about the characteristics of the cars they sell instead of just for making a purchase or obtaining price information. Moreover, demographics such as income and location seem to play a role in the decision which dealers to visit. These observations lead us to formulate our search model in the next section. Specifically, we develop a discrete choice model with optimal consumer search, in which consumers search for a good fit and in which we relate search costs to consumer demographics including the distance to the nearest car dealer of each brand. Although some versions of the model can be estimated using aggregate data only, we estimate it supplemented with choice and search related micro moments from the survey data in order to aid identification.

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Economic Model Utility and demand

We consider a market where there are J different cars (indexed j = 1, 2, . . . , J) sold by F different firms (indexed f = 1, 2, . . . , F ). We shall denote the set of cars by J and the set of firms by F. The utility consumer i derives from car j is given by: uij = αi pj + x0j (β + Vi σ) + ξj + εij ,

(1)

where αi is a consumer-specific price coefficient, the variable pj denotes the price of car j and the vector (xj , ξj , εij ) describes different product attributes from which the consumer derives utility. As usual, xj includes a 1 in order to allow for a constant term in the utility function. We assume that the consumer observes the product attributes contained in xj and ξj without searching, such as horsepower, weight, transmission type, ABS, air-conditioning, and number of gears, characteristics (including dealership locations) that are readily available from, for instance, the Internet, specialized magazines and consumer reports. The variable εij , which is assumed to be independently and identically Type I Extreme Value (TIEV) distributed across consumers and products, is a match parameter and measures the “fit” between consumer i and product j. We assume that εij cap-

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tures “search-like” product attributes, that is, characteristics that can only be ascertained upon close inspection and interaction with the car, like comfortability, spaciousness, engine noisiness, and gearbox smoothness.12 We assume that the econometrician observes the product attributes contained in xj but cannot observe those in ξj and εij . The variable ξj is often interpreted as (unobserved) quality, and, since quality is likely to be correlated with the price of a car, this will lead to the usual price endogeneity problem. Consumers differ in the way they value price and product characteristics. The parameter αi and the expression (β + Vi σ) capture consumer heterogeneity in tastes for price and product attributes. Here σ is a parameter and Vi is a diagonal matrix that contains either demographic characteristics or standard normal draws on its main diagonal such that the first component corresponds to the first component of xj , the second to the second component of xj , and so on. Following Petrin (2002), we allow the price coefficient αi to vary across income groups, i.e., α (1) y i αi = α(2) yi

for yi < y; (2) for yi ≥ y,

where α(1) and α(2) are deterministic parameters, yi is the yearly income of consumer i, and y is a chosen income bound. The utility from not buying any of the cars is ui0 = εi0 . Therefore, we regard product j = 0 as the “outside” option; this includes the utility derived from not purchasing a new car. We allow for multi-product firms: firm f ∈ F supplies a subset Gf ⊂ J of all products. In the car industry dealers typically sell disjoint sets of cars, so we shall assume that Gf ∩ Gg = ∅ for any f 6= g, f, g ∈ F. We assume consumers must search to find out the exact utility they derive from each of the cars available. To be more specific, we assume that before searching a consumer i knows (i ) the location of each car dealership and the subset of makes and models available at each dealership, (ii ) car characteristics pj , xj and ξj for each car j, (iii ) the distribution F of match values εij , and 12

According to our data consumers visit dealers for the purpose of inspecting and test driving cars. Some consumers might know a car’s “fit” ex-ante, for example because a family member, friend, or neighbor owns that specific car, or because they may have rented it while on vacations somewhere. We model these consumers as having zero search costs for the specific car in question. Having zero search costs may also explain not visiting any dealership (see footnote 10).

13

(iv ) the utility of her outside option εi0 . We thus regard the search of a consumer i as a process by which she discovers the exact values of the matching parameter εij upon visiting a dealership that sells product j.13 Consumers search sequentially with costless recall, i.e., they determine after each dealer visit whether to buy any of the inspected cars so far, to opt for the outside option, or to continue searching. Let cif denote the search cost of consumer i for visiting dealer f . We assume that search costs vary across consumers and dealers.14 Let Fifc be the cumulative distribution of consumer i’s c . We allow the search cost distribution to cost of searching dealer f , with corresponding density fif

have full support, although, as we explain in Section 3.3, only the non-negative part affects search behavior (see also footnote 19).

3.2

Optimal sequential search

The utility function in equation (1) can be rewritten as uij = δij + εij , where δij is the mean utility consumer i derives from product j. As explained above, in this expression the consumer knows δij , but has to search to discover εij . Let F denote the distribution of match values εij , i.e., F (z) = exp(− exp(−z)). We assume F (z) is the same for all consumers and cars. Since we allow for consumer-specific taste parameters, the distribution of consumer i’s utility uij from a given car j differs across consumers. This leads to the usual aggregation problem we need to deal with. Since we assume the utility shock εij is an IID draw from a TIEV distribution, the utility distribution for car j faced by consumer i is Fij (z) = F (z − δij ) = exp (− exp (δij − z)) , that is, the distribution of uij is Gumbel with location parameter δij and scale parameter 1.15 13

In general, one can distinguish between store search and brand search. In our model consumers search among different brands. The difference with store search is that the same brand may be sold by several stores, which is not the case in the Dutch car market. 14 We allow for the possibility that a consumer has zero search costs for one or more cars; if a consumer has zero search cost for a specific car this means that she knows the match utility she derives from the car in question ex-ante (see also footnote 12). Since we allow search costs to be consumer-firm specific, having zero search costs for one car does not imply zero search costs for all cars. Also note that by letting search costs be consumer-firm specific, the model is more flexible in rationalizing choice sets than a setting in which search costs are only consumer specific. 15 Throughout the paper, when we refer to the Gumbel distribution, we mean the distribution with CDF

14

Since search happens at the dealer level, indexed by f , it is useful to define the random variable Uif as the highest utility consumer i gets from the cars sold by dealer f , i.e., Uif = max {uij } . j∈Gf

Denoting the distribution of Uif by Fif , we get Fif (z) = Pr[Uif ≤ z] =

Y

Fij (z) =

j∈Gf

where δif = log

P

h∈Gf

Y

F (z − δij ) = F (z − δif ),

j∈Gf

exp(δih ) .

Having determined the distribution of the maximum utility a consumer i can get at a dealer f , we are now ready to describe consumer i’s optimal search strategy. Following Weitzman (1979) we first define the expected gains to consumer i from searching for a car at dealer f when the best utility the consumer has found so far is r: Z Hif (r) ≡

∞

(z − r)dFif (z).

(3)

r

If consumer i’s expected gains are higher than the cost cif she has to incur to search the products of firm f , then she should pay a visit to firm f . Correspondingly, we define the so-called reservation value rif as the solution to equation Hif (r) − cif = 0

(4)

in r. Notice that Hif is decreasing and strictly convex so equation (4) has in general a unique solution. Therefore −1 rif = Hif (cif ).

Note that rif is a scalar, and that for each consumer i there is one such scalar for every dealer f . Weitzman (1979) demonstrates that the optimal search strategy for a consumer i consists of visiting sellers in descending order of reservation values rif and stopping search as soon as the best option encountered so far (which includes the outside option) gives a higher utility than the reservation value of the next option to be searched. The following result, which decomposes the reservation value into a utility component and a exp(− exp(−(z − µ)/β)), where µ is a location parameter and β is a scale parameter. When we refer to the TIEV distribution we mean the distribution with CDF exp(− exp(−z)) (sometimes referred to as the standard Gumbel distribution). The difference between the two distributions is that the TIEV distribution has location parameter normalized to zero and scale parameter normalized to 1, whereas these parameters can vary for the Gumbel distribution.

15

search cost component, will be useful later: Lemma 1 Consumer i’s reservation value for firm f can be written as rif = δif + H0−1 (cif ), where Z

∞

(z − r)dF (z).

H0 (r) ≡ r

The proof is in Appendix A. This lemma shows that there are two sources of variation in the consumer reservation values: they vary because utility distributions differ across sellers and because the costs of searching distinct sellers also differ. This lemma is also useful for explaining the separate identification of search cost and utility parameters, which we will discuss in more detail in Section 4. Note that because εij is TIEV distributed, the result in Lemma 1 implies Z

∞

H0 (r) = γ − r + exp(−r)

exp(−t) dt, t

where γ is the Euler constant and the integral is the exponential integral.

3.3

Buying probabilities and market shares

Because we allow for both consumer and firm heterogeneity, Weitzman’s (1979) solution is, a priori, extremely hard to implement in our setting. With just three options for example, there are eleven different search paths a consumer can follow before purchasing from a specific seller. As the number of sellers grows, the number of search paths increases exponentially. To solve this problem, we next utilize a recent finding by Armstrong (2017) and Choi, Dai, and Kim (2016) which consists of a methodology for the computation of the purchase decisions without having to take into account the myriad of search paths consumers may possibly follow.16 For every dealer f , let us then define the random variable

wif = min {rif , Uif } ≡ min rif , max {uij } . j∈Gf

(5)

Armstrong (2017) and Choi, Dai, and Kim (2016) show that the solution to the sequential search problem (searching across dealers in descending order of reservation values and stopping and buying 16

See also Armstrong and Vickers (2015) for an earlier account of the fact that sequential search models produce demands consistent with discrete choice.

16

the best of the observed products when its realized utility is higher than the next highest reservation value) is equivalent to picking the dealer with the highest wif from all the dealers and choosing the car with the highest utility from that dealer. Accordingly, the probability that buyer i buys product j is sij = Pij|f Pif ,

(6)

where Pij|f

= Pr uij ≥ max uih h∈Gf

(7)

and

Pif = Pr wif ≥ max wig .

(8)

g∈{0}∪F

Here Pij|f denotes the probability of picking product j out of the Gf products of firm f while Pif is the probability of buying from firm f . Note that in Pif the symbol maxg includes consideration of the outside alternative as well. Also note that the outside option does not appear in Pij|f since a consumer will never buy the outside option conditional on buying from firm f . Because computing Pij|f is standard (see below in Section 3.4), we focus now on the computation of the probability Pif . The distribution of wif = min {rif , Uif } can be obtained by computing the CDF of the minimum of two independent random variables.17 This means Fifw (z) = 1 − 1 − Fifr (z) (1 − Fif (z)) ; = Fifr (z)(1 − Fif (z)) + Fif (z),

(9)

where Fifw and Fifr are the CDF’s of wif and rif , respectively; recall that Fif (z) is the CDF of Uif , the maximum utility of all products sold at firm f , which has been specified above. To obtain the distribution of the reservation values, we can use equation (3): Fifr (z) = Pr (rif < z) = Pr [Hif (rif ) > Hif (z)] = Pr [cif > Hif (z)] = 1 − Fifc (Hif (z)) . Substituting this into equation (9) gives Fifw (z) = 1 − Fifc (Hif (z)) (1 − Fif (z)) .

(10)

Equation (10) shows that even if we allow Fifc to have negative support, only the distribution for positive values matter. This means the part of the search cost distribution that has negative 17

Specifically, if Z = min {X, Y } with X, Y independent, then FZ (z) = 1 − (1 − FX (z)) (1 − FY (z)).

17

support behaves like an atom at zero. To obtain the probability that consumer i buys from firm f , we can use that the wig ’s in equation (8) are independent. We can therefore take the product of each Figw evaluated at wif to get the CDF over all g 6= f , which, after integrating out wif , gives this expression for Pif : Z

Y

Pif =

w Figw (z) fif (z) dz.

(11)

g6=f

Finally, the unconditional choice probability can be obtained from sij in equation (6) by integrating out the consumer-specific variables. Denoting by τi the vector of all consumer-specific random variables in sij , the probability that product j is purchased is the integral Z sj =

sij dFτ (τi ),

(12)

where Fτ is the CDF of τi .

3.4

Computation and distributional assumptions

There are two difficulties in the computation of the market shares. The first difficulty is the computation of the buying probabilities sij in equation (6). For this, we need to calculate the probabilities Pij|f and Pif , which are given in equations (7) and (11), respectively. Since εij is an IID draw from a TIEV distribution, Pij|f has the familiar closed form: exp (δij ) exp(δij ) . = exp(δif ) h∈Gf exp (δih )

Pij|f = P

There is no closed-form solution for the probability Pif in equation (11) for arbitrary search cost distributions, even when assuming εij follows a TIEV distribution. Nevertheless, we can compute Pif by first plugging equation (3) into the distribution of w given in equation (10), deriving the w , and then performing the integration in equation (11) using numerical methods. density fif

The second difficulty is the computation of the integral in equation (12). Such an integral cannot be computed analytically but, following BLP and most of the literature, can be estimated by Monte Carlo methods by drawing the demographic characteristics and random coefficients of, say, N consumers, and then computing sˆij for each consumer i = 1, . . . , N . The Monte Carlo P estimator of sj is then taken as the sample mean sˆj = N1 N ˆij . i=1 s These two difficulties together make the estimation of the demand model somewhat slow because

18

in every iteration the two integrals in equations (11) and (12) need to be computed. Moreover, when using the supply side of the market to obtain estimates of marginal costs and price elasticities these difficulties become more notable because the first order conditions involve derivatives of the market shares. Although we can cope with these issues (see our estimates for normally distributed search costs in Section 6), it is nevertheless desirable to reduce the computational complexity of our model for further work and future applications. In what follows we propose an alternative to numerical integration of equation (11) that significantly speeds up the estimation of the model. The idea is to obtain a closed-form expression for equation (11). If we succeed, the computation of the buying probabilities and the first order conditions for profits maximization become much easier and estimation of the model becomes more amenable. We first observe that equation (10) suggests a one-to-one relationship between the search cost distribution and the distribution of the random variable w that determines the visiting probabilities: Fifc (Hif (z)) =

1 − Fifw (z) 1 − Fif (z)

.

(13)

This relationship is extremely useful because it suggests that, for a given distribution of the maximum utility at a seller Fif , we can choose an appropriate distribution for the w’s, Fifw , for which a search cost distribution exists that rationalizes it according to equation (13). To see this more clearly, we can use the change of variables c = Hif (z) in equation (13) to obtain Fifc (c) =

−1 (c)) 1 − Fifw (Hif −1 (c)) 1 − Fif (Hif

=

1 − Fifw (δif + H0−1 (c)) 1 − Fif (δif + H0−1 (c))

=

1 − Fifw (δif + H0−1 (c)) 1 − F (H0−1 (c))

,

(14)

where we have used Lemma 1 to derive the second equality. Denote by µif the location parameter of the search cost distribution, which contains the search cost covariates. To obtain a closed-form expression for the buying probabilities it is convenient to assume that the wif ’s follow a Gumbel distribution. Moreover, we want to make sure that the search cost distribution in equation (14) is a function of µif but at the same time does not depend on δif , which can be achieved by assuming that the location parameter of Fifw is δif − µif , i.e., Fifw (z) = exp (− exp (−(z − (δif − µif )))) .

(15)

Evaluating this expression at δif + H0−1 (c) gives Fifw = exp(− exp(−(H0−1 + µif ))), which equals

19

F (H0−1 + µif ). Substituting this into equation (14) gives Fifc (c) =

1 − F (H0−1 (c) + µif ) . 1 − F (H0−1 (c))

Using that ∂H0−1 (c)/∂c = −1/(1 − F (H0−1 (c))), the corresponding search cost density is given by −1 c (c) · f H −1 (c) f H (c) + µ − F if 0 0 if c fif (c) = , 2 1 − F (H0−1 (c)) where f (·) is the density of match values εij . Because we have taken the utility shock distribution F to be the TIEV distribution we get: Fifc (c)

=

1 − exp − exp −H0−1 (c) − µif 1 − exp(− exp(−H0−1 (c)))

.

(16)

Notice that a positive µif is necessary for Fifc (c) to be a proper distribution, which can be achieved by letting µif be function of search cost shifters according to a log-exp function form, i.e., µif = log 1 + exp t0if (λ + Wi ν ,

(17)

where the vector tif includes search cost shifters that are consumer and/or firm specific, such as the distance from the household to the dealership and the household’s income, λ and ν are search cost parameters, and Wi is a diagonal matrix that contains random draws from the standard normal distribution in its first entry as well as other demographics characteristics. Given this, it is straightforward to verify that the search cost distribution in equation (16) is increasing in c and takes value 1 when c approaches infinity. Moreover, it has an atom at zero, that is Fifc (0) = exp(−µif ), which conveniently allows for a fraction of consumers to know their match values with the cars sold by dealer f ex-ante; as µif increases, this share becomes smaller and becomes negligible as µif grows large.18 Finally, we observe that, on the positive support, the distribution given by equation (16) has a shape relatively similar to the normal distribution. To see this, we plot in Figure 2 the search cost distribution in equation (16) and the corresponding density for µif = 2. Also shown (in red) is a normal distribution and density with mean µif = 2 and variance set to 1. Note that the two distributions are relatively similar on the positive real line.19 The dashed green curves in Figure 18 The estimated probability of the atom according to our estimates presented in Section 6 is rather small: it has mean 0.026 (with standard deviation 0.115) and median 0.000 across consumers and dealers. 19 Note that in our model there is no loss of generality by allowing consumers to have negative search costs for some cars. This is because if there were consumers with a negative cost of searching a particular dealer, they would behave

20

2 are for a Gumbel distribution (for the minimum) with location parameter µif = 2 + γ = 2.577 and scale parameter set to one.20 . This particular distribution is useful as a comparison because it is closed form and has a shape similar to the search cost distribution given by equation (16).21 � � (�)

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(a) Search cost CDF

�

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(b) Search cost PDF

Figure 2: Search cost distribution for µif = 2 The distribution of reservation values Fifr can be derived by solving equation (9) for Fifr , i.e., Fifr (z) =

Fifw (z) − Fif (z) 1 − Fif (z)

.

Using Fifw (z) as specified in equation (15), we get Fifr (z) =

exp (− exp (δif − µif − z)) − exp(− exp(δif − z)) . 1 − exp(− exp(δif − z))

(20)

Under the search cost distribution given by equation (16), wif follows a Gumbel distribution with location δif − µif and the calculation of the probability of buying from firm f in equation (8) exactly in the same way as consumers with zero search cost. As a result, without loss of generality, we can allow for search cost distributions with full support, such as the normal distribution. 20 The Gumbel distribution for the minimum is the mirror image of the Gumbel distribution. It is used to model the minimum of a number of draws from various distributions and has CDF 1 − exp(− exp((z − µ)/β)). R∞ 21 For large values of x, the exponential integral x exp(−t) dt that appears in H0 (r) is approximately zero, which t −1 means x = H0 (c) = c − γ, where γ is the Euler constant. We therefore get the following closed-form expression for c Fif (c): 1 − exp(− exp(c − γ − µif )) c Fif (c) = . (18) 1 − exp(− exp(c − γ)) For large c the denominator goes to 1, which means that for large µif we can approximate this by a Gumbel (minimum) distribution, i.e., c Fif (c) = 1 − exp(− exp(c − (µif + γ))). (19)

21

is straightforward, i.e., Pif =

exp (δif − µif ) . PF 1 + g=1 exp (δig − µig )

The probability of buying product j is sij = Pif Pij|f and simplifies to sij

=

exp (δif − µif ) exp [δij ] ×P PF 1 + g=1 exp (δig − µig ) h∈Gf exp [δih ]

=

exp (δij − µif ) exp (δij − µif ) = PF PF P 1 + g=1 exp (δig − µig ) 1 + g=1 h∈Gg exp (δih − µih )

=

exp (δij − µif ) , PJ 1 + k=1 exp (δik − µig )

(21)

where in the last line g denotes the firm that produces product k. Note that the numerator in the second expression contains δij and not δif . An advantage of the closed-form expression for the buying probabilities in equation (21) is that it makes the estimation of the model of similar difficulty as most standard discrete choice demand models.

3.5

Search probabilities

As we will explain in Section 4 when discussing identification, we will use individual search data in addition to aggregate data on market shares. In particular, we shall employ data on the share of consumers not searching beyond the outside option as well as the share of consumers searching only one time. We now compute those probabilities. The probability that a consumer does not search beyond the outside option can be calculated as follows. Take a consumer i whose outside option is ui0 . This consumer chooses to refrain from searching with probability Z

∞

Z

ui0

vi0 = Pr[ui0 ≥ max {rik }] = k6=0

−∞

−∞

dFifrmax (z)dF (ui0 ) =

Z

∞

−∞

Fifrmax (z)f (z)dz,

where Fifrmax (z) stands for the distribution of the maxk6=0 {rik } and is given by Fifrmax (z) =

Y

r Fik (z) =

k6=0

Y

c (1 − Fik (Hif (z))) .

k6=0

The share of consumers not searching at all is obtained by integrating over all consumers, i.e., Z q0 =

vi0 dFτ (τi ),

22

(22)

where the integral is taken over the non-observable characteristics (random coefficients) of all consumers. This integral can be estimated by Monte Carlo by drawing from the distributions of demographics and random coefficients as well as the utility distribution of the outside option.22 We now compute the probability a consumer i searches only one time. For this we need that the outside option is not good enough and that the best of the outside option and the first searched option is good enough to stop, i.e., vi1 =

X

Pr ui0 < max {rik } and max {ui0 , uif } > max {rik } and rif k6=0

f

k6=0,f

> max {rik } . k6=0,f

The sum across f appears because the first searched option can be any of the dealerships. We can simplify this to (see Appendix B for details): X

vi1 =

Pr ui0 < rif and max rik < ui0 k6=0,f

f

+

X

Pr ui0 < max rik and max rik < uif and max rik < rif . k6=0,f

f

k6=0,f

k6=0,f

This probability can be written as vi1 =

XZ f

∞

−∞

Fifw

(y) −

Fifr (y)

r (y)f (y)dy Fi,−f

+

XZ f

∞

−∞

w r (x)dx. (x)F (x)fif Fi,−f

(23)

r r are the CDF and PDF of maxk6=0,f {rik }. and fi,−f where Fi,−f

The share of consumers searching only one time is then given by Z q1 =

vi1 dFτ (τi ).

(24)

Again, this probability can be computed by Monte Carlo by jointly sampling from the taste distributions as well as the utility distribution of the outside option (for the first integral of equation (23)) and the distribution of wif (for the second integral).23 22 Specifically, let V be a TIEV draw (obtained as − log (− log U ) with U uniform on (0, 1)). A draw from the density of the outside option is then V . 23 More specifically, let V be a TIEV draw (obtained as − log (− log U ) with U uniform on (0, 1)), which we can use directly for the first integral of equation (23). For the second integral of equation (23), from the draws of the random w coefficients we compute δif − µif . A draw with density fif is then δif − µif + V .

23

3.6

Supply side

We include the supply side in order to obtain estimates of price-cost markups. We assume each firm f ∈ {1, . . . , F } supplies a subset Gf of the J products. Let M denote the number of consumers and let mcj denote the marginal cost of producing product j. Then the profit of firm f is given by Πf (p) =

X

(pj − mcj )Msj (p).

j∈Gf

Following BLP we assume mcj depends log-linearly on a vector of observed product characteristics affecting cost, wj , and an unobserved cost characteristic ωj : log(mcj ) = wj0 η + ωj .

(25)

We expect the unobserved cost characteristic ωj to be correlated with the unobserved demand characteristic ξj . For instance, if the researcher does not observe whether a car has a navigation system as standard equipment, then cars having this characteristic will have a higher unobserved demand characteristic and, because it is more costly for the firm to include a navigation system, a higher unobserved cost characteristic as well. We will account for this correlation in the estimation procedure. We assume firms maximize their profits by setting prices, taking into account prices and attributes of competing products as well as the locations of all dealers. Let p denote the vector of Nash equilibrium prices. Assuming a pure strategy equilibrium exists, any product j should have a price that satisfies the first order condition sj (p) +

X

(pr − mcr )

r∈Gf

∂sr (p) = 0. ∂pj

To obtain the price-cost markups for each product we can rewrite the first order conditions as p − mc = ∆(p)−1 s(p), where the element of ∆(p) in row j column r is denoted by ∆jr and

∆jr

− ∂sr , if r and j are produced by the same firm; ∂pj = 0, otherwise.

24

(26)

The derivation of the partial derivatives of the market shares with respect to price is straightforward in case of Gumbel distributed w’s.24 Details on the derivation of the market share derivatives with respect to price for general search cost distributions are provided in Appendix C. Note that for market share derivatives it matters whether consumers observe deviation prices before or after search. In our context, because consumers can easily observe list prices while being at home, we adopt the assumption that consumers observe (deviation) prices before they start searching. Notice that this assumption differs from most of the literature on consumer search for differentiated products (Wolinsky, 1986; Anderson and Renault, 1999) and, as demonstrated in recent work (see, e.g., Armstrong and Zhou, 2011; Haan, Moraga-Gonz´alez, and Petrikait˙e, 2017), this assumption has implications for the behavior of prices and search costs.25

4

Identification

Before discussing identification in detail we briefly sketch the main issues. Our starting point for identification is the conditional moment restrictions assumption commonly used in the literature for demand estimation using aggregate data. This approach needs instruments for endogenous variables and random coefficients. In this regard it is known that the BLP-type instruments for price may be weak in markets with many alternatives, like the one for cars, especially if the number of observed markets is low. In order to improve identification from aggregate data, we also use individual-level search and purchase data. In addition to the price instruments we also construct instruments for distances from consumers to car dealers to deal with dealer location endogeneity. A practically relevant issue regarding identification is that there may potentially be common covariates in utility and search cost, whose effects should be separately identified. In what follows we address these issues in turn. We first use intuitive identification arguments, similar to those made in the literature, for situations in which one uses aggregate data with appropriate instruments and there is no overlap of covariates in utility and search cost. Then we turn to the more difficult case in which there are covariates that appear similarly in utility and search cost. We provide both intuitive and formal arguments on how combining aggregate data and 24

R For the case of Gumbel distributed w’s,R the own-price derivative ∂sj /∂pj = (∂sij /∂pj )dFτ (τi ), where ∂sij /∂pj = αi sij (1 − sij ). The derivative ∂sj /∂pk = (∂sij /∂pk )dFτ (τi ), where ∂sij /∂pk = −αi sij sik . 25 In a standard search model a firm chooses its price to maximize the payoff from the consumers who visit. By changing the price a firm thus affects the selling probability, but not the visiting probability. In contrast, when prices are observed from home like in our model, changing the price affects both the visiting and the buying probability. While in most standard models prices increase in search costs, in models where prices are observable before search, prices can be decreasing in search costs. We will return to this point later in the paper when we study the equilibrium effects of moving towards a full information equilibrium.

25

individual-level search data can separately identify the utility and search cost parameters. Since the focus in this case is on the separate identification of the utility and search cost parameters, we consider a simpler version of the model in which the demand side unobserved characteristics are omitted. We show through formal arguments that when both aggregate and individual-level data are available and there are common covariates in utility and search cost, the version of the model in which the w’s are Gumbel distributed is identified. We argue that in the general model, even though it is difficult to find similar formal arguments, identification is facilitated by the fact that the search cost variables are transformed nonlinearly relative to the utility variables. Following the literature, our main identification assumption is that the demand and cost unobservables ξj and ωj are mean independent of a set of exogenous instruments Z, i.e., the conditional moment restrictions are E[(ξj , ωj )|Z] = 0. Since ξj captures unobserved quality differences between products, it is likely to be positively correlated with price, which leads to the usual endogeneity problem that arises when estimating aggregate demand models. In our setting we have to deal with an additional endogeneity problem that affects the distance variable in equation (17), which is used as our main search cost shifter: since dealers may prefer to locate in areas where there is most demand for their cars, distances from consumers to car dealers are likely to be correlated with price, and in turn with unobserved quality differences, which leads to distance being endogenous in our model as well. For instance, if sellers of cars with high unobserved quality are located near wealthy neighborhoods, while sellers of cars with low unobserved quality are not, then it may seem that the main reason why the cars of low unobserved quality are not bought much by consumers from the wealthy neighborhoods has to do with their location while the true principal reason is their low unobserved quality; this will lead to an overestimation of the effect of distance on the purchase probabilities. To deal with both endogeneity problems, we follow the literature and use instrumental variables. Identification when price and dealer locations are endogenous requires the use of appropriate instruments. The set of instruments we use to control for possible correlation between unobserved characteristics and price as well as unobserved characteristics and distances are similar to those used by BLP. That is, in addition to product characteristics, which are exogenous by assumption, we add the number of cars and the sum of characteristics of the cars produced by the same firm, as well as the number of competing cars and the sum of characteristics of all competing cars. In addition, we use instruments that are specifically meant to deal with the distance endogeneity problem

26

by using variables that relate to the cost of operating a dealership. These instruments are based on variation in property values as well as local taxes—the likelihood of opening a dealership at a certain location is inversely related to the local cost associated with that location, independent of whether the location is suitable for other reasons. More specifically, we use the interaction of average local taxes and average local population density, and the range of property values interacted with a variable that indicates how urban the dealership locations are on average. Armstrong (2016) argues that the usual BLP-type instruments are weak and may not identify the price coefficients in a small number of large markets like the car market. BLP dealt with this problem by using sales data from 20 years (see page 877 of BLP), which creates variation in the instruments used due to the fact that the number and types of cars present in the market change from year to year. Unfortunately, we only have data for 6 years which means that the variation in the instruments we obtain from our data is more limited than theirs. We propose two solutions for this problem. Firstly, following Goldberg (1995) and Berry, Levinsohn, and Pakes (2004), we complement aggregate data with consumer-level choice and search data based on a survey among consumers (for similar approaches see Petrin, 2002; Sovinsky Goeree, 2008). Secondly, the additional instruments we use to deal with the distance endogeneity problem can also be regarded as cost shifters, which means they instrument for price as well. Next we provide a discussion on how variation in the data allows us to identify the parameters of the model, assuming we have appropriate instruments for prices and dealer locations. Throughout this discussion we assume there are no common covariates in utility and search cost; later on we provide a more formal discussion of the common-covariates case. In our model, variation in car sales can be attributed to (i ) variation in the observable and unobservable characteristics of the cars; (ii ) variation in the observed and unobserved costs of visiting the dealers, which we relate to demographic characteristics such as distances from the households to the closest dealers of the brands, household income, and age of the head of the household; and (iii ) variation in additional observed and unobserved consumer characteristics that affect a buyer’s valuations for the different car characteristics, such as income, and the number of children in the household. We are interested in the identification of the parameters in the utility function, which are α, β and σ, as well as the parameters of the search cost distribution λ and ν. Price and sales variation that correspond to variation in observed cost shifters identifies the marginal cost parameter vector η. The identification of the utility parameters largely follows the identification strategy of BLP and Sovinsky Goeree (2008). Intuitively, an increase in market share of a model j that is associated with a change in one of the observable characteristics of model j identifies the mean utility parameters.

27

Furthermore, the σ parameter that captures consumer heterogeneity in the taste distribution can be identified by consumers’ substitution patterns. For instance, if the change in market share following a change in one of the observed characteristics of model j is mostly originating from models with similar characteristics, then the estimate of σ is likely to be large, while if consumers substitute towards other products in proportion to market shares, as happens in the conditional logit model, the estimate of σ is likely to be small. The parameters of the search cost distribution can be identified using variation in the cost of visiting firms. Intuitively, suppose we have two cars with similar (observed and unobserved) attributes. Under full information, these two cars should have similar market shares. If this is not the case, then it is because there must be variation in the cost of searching these two cars. Conditional on car attributes, a small change in mean search costs λ will therefore induce variation in consumer choice sets that will ultimately be reflected in market shares, which enables us to identify the mean search cost parameters. The ν parameter captures heterogeneity in how observed search cost shifters affect search costs and, similar to σ in the utility specification, can be identified by substitution patterns following a change in a search cost shifter. For instance, if the increased market share as a result of more dealership locations originates mostly from brands that have a similar dealership structure, then the estimate of ν is likely to be larger. Moreover, we use individual-level search and purchase behavior data in addition to market level data, which allows us to relate variation in observed demographics in the micro data to variation in the tastes for product characteristics. We now turn the discussion to the case in which there are covariates that appear similarly in utility and search cost. Even though the empirical specifications we estimate in Section 6 do not have this feature, this may be relevant in practice.26 We consider a simpler version of our model, namely one in which the demand side unobserved characteristics are omitted. In this case the same set of parameters are to be identified as in the original model but we can ignore price and distance endogeneity. Here we assume the researcher uses individual-level search and purchase data in addition to the aggregate data. Specifically, we use the probability of buying from a given dealer as well as the probability that a consumer searches one dealer and decides not to buy any of the products offered by this dealer. These two types of probabilities are sufficient to show identification when the w’s are Gumbel distributed. It is more difficult to determine the probabilities that lead to clear identification arguments in the general model, but as we will argue later on, we believe the same arguments also apply to the more general setting in which the w’s are not necessarily Gumbel 26 Although in our main specification in Section 6 we allow for distance covariates in both utility and search cost, we interact the distance variable that appears in the utility function with the cost of maintenance.

28

distributed. First we consider the case of Gumbel distributed w’s, that is, when the distribution of the w’s is given by equation (15). In this case the conditional probability Pif that consumer i buys from dealer f given in Section 3 can be aggregated over consumers into aggregate dealer-level market shares Z sf =

exp (δif − µif ) dFτ (τi ). PF 1 + g=1 exp (δig − µig )

These quantities can be inferred from aggregate product-level market shares, so no individual-level data are needed.27 Based on parametric identification arguments for the random coefficient logit model, the total effects of the variables involved in δif − µif can be identified. For example, if the distance from consumer i to dealer f appears linearly both in δif and µif with coefficients βδ and βµ then we can identify the difference (βδ − βµ ) but not βδ and βµ separately. Intuitively, we know that the decision from which dealer to buy depends on both the maximum utility from the products of the dealer and the search cost. Therefore, using data on firm choice we can only identify the total effects from a combination of these quantities. Consider now the other probability type. The probability that consumer i searches only dealer f and opts for the outside alternative is

vif 0 = Pr ui0 < max {rik } and ui0 > max uif , max {rik } and rif > max {rik } k6=0 k6=0,f k6=0,f = Pr ui0 < rif and ui0 > max uif , max {rik } and rif > max {rik } k6=0,f k6=0,f = Pr ui0 < rif and ui0 > uif and ui0 > max {rik } k6=0,f Z ∞ Y r Fik (x) Fif (x) f (x) dx. = 1 − Fifr (x) −∞

k6=0,f

Since the distribution of reservation utilities can be written as Fifr (z) =

exp(− exp(δif − µif − z)) − exp(− exp(δif − z)) , 1 − exp(− exp(δif − z))

Q r the expression 1 − Fifr (x) k6=0,f Fik (x) in the integral contains δik −µik and δik for k = 1, . . . , F while Fif (x) = F (x − δif ) contains δif . As explained above, the expressions δik − µik are identified from the dealer market shares, so in the probabilities vif 0 the only unknowns left are the utility 27 By using individual-level choice data in addition to the market shares we can improve identification due to the additional variation across consumers.

29

parameters involved in the δik ’s. These can be identified based on parametric random coefficient discrete choice model identification arguments, because in the survey data we can observe the event that consumer i searches only dealer f and does not buy anything for all consumers and dealers. Intuitively, this event carries information on the consumer’s preferences for the products offered by dealer f beyond the information provided by the dealer choice, and this yields separate identification of the two sets of parameters. Finally we briefly consider the general model. In this case the above two types of probabilities as well as other simple probabilities such as the probability of searching one dealer (see Appendix B) are rather complicated, which makes it difficult to separate the total effects in a way similar to the case of Gumbel distributed w’s. However, we believe that in this case it is also valid that different types of probabilities can identify different combinations of the maximum utility and search cost parameters, which eventually yields separate identification of the parameters in a way similar to solving a system of nonlinear equations. We also note that, compared to the case of Gumbel distributed w’s, where δif and µif are in a linear relationship in the expression of Fifw (see equation (15)), in the general model these two expressions are related nonlinearly. This follows from Lemma 1, which implies that wif = δif + min H0−1 (cif ), εif ,

(27)

where εif is TIEV distributed. Because the theory of sequential search implies that H0−1 is strictly convex, this expression tells us that purchase probabilities and ultimately market shares respond differently to changes in search cost variables in comparison to changes in utility variables. This variation facilitates separate identification of utility and search cost parameters even when using only aggregate market shares data.

5

Estimation

Our estimation procedure closely resembles BLP, except that our market share expressions explicitly take consumers’ sequential search behavior into account. As shown by BLP, the parameters of the demand and supply model without search frictions can be estimated by generalized method of moments (GMM). Their GMM procedure accounts for price endogeneity by solving for the unobservables ξj and ωj in terms of the observed variables and taking these as the econometric error term of the model. In this section we provide a method to estimate the search model by GMM as well. As in BLP, we can compute the vector ξ = (ξ1 , . . . , ξJ ) of unobserved characteristics as 30

the unique fixed point of a contraction mapping. The fact that this mapping is indeed a contraction follows from the fact that the first order derivatives of the market shares with respect to the unobserved characteristics have the same form as in BLP (see Appendix D for more details). We use the SQUAREM algorithm (Varadhan and Roland, 2008) instead of standard contraction iterations, which is found to be faster and more robust than the standard BLP contraction (Reynaerts, Varadhan, and Nash, 2012).

5.1

Moments

We consider macro- and micro moments. For the macro moments, following BLP, the predicted market share sj (θ) of product j should match observed market shares sˆj , or sj (δ(θ), θ) − sˆj = 0. We use the contraction mapping mentioned in the previous paragraph to solve for δ(θ). The first moment unobservable follows from δ(θ) and is ξj = δj (θ) − xj β.

(28)

The second moment unobservable follows from the parametric marginal cost specification and the first order conditions—combining equations (25) and (26) and solving for ωj gives ωj = log p − ∆−1 s(θ) − wj0 η.

(29)

Since we have individual-level data, we are able to construct micro moments as well. The survey data provides for each respondent information on their latest car purchase as well as their search behavior related to that car purchase. We supplement the BLP moments with micro moments that are based on these survey responses as well as corresponding model predictions—following Petrin (2002) we let the GMM estimation routine select the parameters of the model such that the predicted probabilities match the observed probabilities in the survey data. We use three sets of choice and search related micro moments. The first relates demographic information to buying decisions. For this, we consider micro moments based on the following type of conditional expectations: E [1{ai ∈ T }|qi ∈ Rk ] , k = 1, 2 where R = {R1 , R2 } .

31

(30)

In this expression,

1{ai ∈ T } is an indicator for the event that consumer i makes choice ai ∈

{0, 1, . . . , J} from a certain group of products T , and qi is a generic demographic characteristic, which is partitioned in two subsets according to R. For instance, we use two micro moments that match the model’s predicted average probability of buying a new car conditional on income level to the survey data, i.e., E[1{i purchases new vehicle} | {yi < y}], E[1{i purchases new vehicle} | {yi ≥ y}], where

1{i purchases new vehicle} is an indicator for the event that consumer i purchases a new

vehicle and {yi < y} and {yi ≥ y} correspond to the events that consumer i is in the low or high income group, respectively. Other used micro moments of this type are listed in Table 6 of Section 6 and include the probability of purchasing an MPV or SUV conditional on family size and the probability of buying a family car conditional on the presence of children in the household.28 The second set of micro moments relates demographic information to search decisions. The type of micro moments we use for this is similar to the type given in equation (30), but with the number of searches as the choice variable instead of the type of car bought. Specifically, these micro moments match to the survey data the model’s predicted average probability of searching once as well as searching more than once conditional on income level, the number of dealers nearby, whether there is a cluster of dealers nearby (i.e., a 5 digit zip code that has more than 7 dealers within 5 kilometers), and whether the head of household is senior. We note that the type of events used in Section 4 to show identification, namely, that consumers search a given dealer and do not buy any of the products offered, are not exactly the same as the events on which these micro moments are based. The reason for using these micro moments in the estimation is that they correspond to more observations. Due to this, they can be used with different conditioning events in the estimation, and therefore, potentially more information can be extracted. The third set of micro moments matches the predicted purchase of a car from a group of products T , but instead of being conditional on demographics, as in equation (30), they are conditional on buying a specific car brand. As explained in Section 4, these micro moments are useful for separately identifying distance in utility function and distance in the search cost specification. For further details on the computation of this type of micro moments as well as the other two types, we refer 28

Note that even though we observe search behavior at the car model level, our micro moments are constructed for groups of products. This is intentional: the total number of car models is relatively large in comparison to number of respondents to the survey, which means we do not get good coverage at the car model level.

32

to Appendix E.

5.2

GMM estimation

We use GMM to estimate the model. As also mentioned in Section 4, the estimation relies on the assumption that the true values of the demand and cost unobservables are mean independent of a set of exogenous instruments, that is, E[(ξj , ωj )|Z] = 0, where Z is a matrix of instruments with 2J rows and ψ(θ) = (ξ1 (θ), . . . , ξJ (θ), ω1 (θ), . . . , ωJ (θ))0 . Let the sample moments be gJ (θ) =

1 0 Z ψ (θ) . 2J

(31)

Denote the column vector of micro moments by gN (θ); let g(θ) =

gJ (θ) gN (θ)

be the column-vector of both macro- and micro moments. The GMM estimator of θ is θˆ = arg min g (θ)0 Ξg (θ) , θ

where Ξ is a weighting matrix. In Appendix F we discuss several alternatives for Ξ; however, in our application we use Ξ=

(Z 0 Z)−1

0

0

IM

where IM is the identity matrix of dimension M , which is the number of micro moments. Some parameters enter linearly in the model, so we can concentrate them out of the above GMM minimization. By using equations (28) and (29) and denoting X1 =

x

0

0 w

and δ (θ2 ) =

δD (θ2 ) δC (θ2 )

we get ψ (θ) = δ (θ2 ) − X1 θ1 . By assuming θ2 known we can obtain θ1 as the linear IV estimator θb1 = X10 ZΞZ 0 X1

−1

33

X10 ZΞZ 0 δ (θ2 ) ,

and substituting this in gJ (θ) we obtain a new sample moment, which is a function of θ2 only, g J (θ2 ) =

−1 0 1 0 Z ψ (θ2 ) , where ψ (θ2 ) = δ (θ2 ) − X1 X10 ZΞZ 0 X1 X1 ZΞZ 0 δ (θ2 ) . J

Note that by using δD (θ2 ) in sij (θ), the micro moment (see equation (A37) in the Appendix) does not depend on θ1 ; denote by g N (θ2 ) the vector of micro moments that are the same as gN (θ) but formally depend on δD (θ2 ) instead of ξ and θ1 . Also, let g (θ) =

g J (θ) g N (θ)

.

The GMM estimator of θ2 based on this is θˆ2 = arg min g (θ2 )0 Ξg (θ2 ) . θ2

6

Data and Results

6.1

Data

Our data set consists of prices, sales, physical characteristics, and locations of dealers of virtually all cars sold in the Netherlands between 2003 and 2008. We include a model in a given year if more than fifty cars have been sold during that year; this means “exotic” car brands like Rolls-Royce, Bentley, Ferrari, and Maserati are excluded. This leaves us with a total of 320 different models that were sold during this period—in any given year about 230 different models. We treat each model-year combination as one observation, which results in a total of 1,382 observations. The data on product characteristics are obtained from Autoweek Carbase, which is an online database of prices and specifications of all cars sold in the Netherlands from the early eighties until now.29 Characteristics include horsepower, number of cylinders, maximum speed, fuel efficiency, weight, size, and dummy variables for whether the car’s standard equipment includes air-conditioning, power steering, cruise control, and a board computer. Transaction prices are not available, so all prices are listed (post-tax) prices, normalized to 2006 euros using the Consumer Price Index.30 29

See autoweek.nl/carbase. The tax when buying a new car in the Netherlands consists of a sales tax as well as an additional automobile tax. The sales tax (BTW) in the period 2003-2008 was 19 percent. The automobile tax (BPM) was 45.2 percent of the pre-tax price during most of the sampling period, but was lowered to 42.3 percent in February 2008. The automobile tax paid also depends on whether the car uses diesel or gasoline (gasoline users deduct e1,540 from the pre-tax price 30

34

In practice, prices for cars are typically determined by bargaining between the car sales person and the consumer. Because we only observe list prices, bargaining is difficult to incorporate in our model; instead we assume that the list price is the price the consumer pays. Not taking bargaining into account affects the analysis in two ways. First of all, if bargaining is important, consumers may visit multiple dealerships in order to get a better deal. Ignoring bargaining therefore means that we are implicitly assuming that the main reason for visiting dealerships is to learn more about the products. As we have argued in Section 2, the survey data seems to be largely consistent with this view. Secondly, bargaining affects the prices consumers pay, which means bargaining also affects the gains from search. However, unless the gains from bargaining are very different across brands, this is not very likely to affect the results. Moreover, most car dealerships in the Netherlands have very few cars in stock due to space limitations, which means there is typically less incentive for car dealerships to offer discounts on the list price in comparison to for instance the United States, where it is more common to have a large number of cars in stock. We have supplemented the data set with several macroeconomic variables, including the number of households and average gasoline prices, as reported by Statistics Netherlands. The total number of households allows us to construct market shares (calculated as sales divided by the number of households), while average gasoline prices are used to construct our kilometers per euro (KPe) variable, which is calculated as kilometers per liter (KPL) divided by the price of gasoline per liter. We define a firm as all brands owned by the same company. We use information on the ownership structures from 2007 to determine which car brands are part of the same parent company—the 39 different brands in our sample are owned by 16 different companies. For instance, in 2007 Ford Motor Company owned Ford, Jaguar, Land Rover, Mazda, and Volvo. Table 2: Summary statistics Year

No. of Models

Sales

Price

European

HP/ Weight

Size

Cruise Control

KPL

KPe

Family Car

MPV or SUV

2003 2004 2005 2006 2007 2008 All

213 228 233 231 236 241 1,382

481,913 476,581 457,897 475,636 495,091 489,584 479,450

19,562 19,950 20,540 20,367 20,509 18,613 19,916

0.762 0.749 0.727 0.715 0.712 0.714 0.730

0.787 0.788 0.794 0.804 0.810 0.813 0.799

7.153 7.184 7.270 7.271 7.330 7.271 7.247

0.229 0.308 0.301 0.308 0.281 0.293 0.286

14.480 14.696 14.861 15.120 15.112 15.813 15.018

12.497 11.737 10.987 10.707 10.356 10.290 11.091

0.426 0.408 0.403 0.361 0.363 0.381 0.390

0.216 0.235 0.242 0.234 0.240 0.188 0.226

Notes: Prices are in 2006 euros. All variables are sales weighted means, except for the number of models and sales.

of a car before applying the automobile tax (e1,442 during most 2008), while diesel users add e328 (e308 in 2008)). Moreover, from July 2006 on there are additional additions or deductions to the pre-tax price that are based on the energy efficiency of the car and whether the car is a hybrid or not.

35

Table 2 gives the sales weighted means for the main variables we use in our analysis. The number of models has increased from 213 in 2003 to 241 in 2008. Sales were lowest in 2005 and peaked in 2007. Prices have been going up mostly in real terms, although 2008 saw a sharp decrease, due to a tax cut in 2008 (see also footnote 30) and possibly as a result of the onset of the most recent recession. The share of European cars sold shows a downward trend, mainly to the benefit of cars that originate from East Asia. The ratio of horsepower to weight has been increasing steadily. The share of cars with cruise control as standard equipment increased in the first half of the sampling period, but then decreased somewhat. Cars have become more fuel efficient during the sampling period. Nevertheless, as shown in the KPe column of Table 2, fuel efficiency has not increased enough to offset rising gasoline prices—the number of kilometers that can be traveled for one euro has decreased over the sample period. The share of family cars has steadily declined over time, while cars that are classified as either multi-purpose vehicle (MPV) or sport utility vehicle (SUV) saw their market shares increase until 2007, followed by a sharp drop in 2008. During this period the share of cars classified as supermini went up from 32 percent to over 40 percent of the market.31 In addition to car characteristics we use information on the location of car dealerships and combine this with geographic data on where people reside to construct a matrix of distances between households and the different car dealerships. These distances are later used to proxy the cost of visiting a dealership to learn all product characteristics of a vehicle. We also use data on the distribution of household characteristics as search cost covariates. Our demographic and socioeconomic data on households are obtained from Statistics Netherlands. These data are available at various levels of regional disaggregation (neighborhoods, districts, city councils, counties, and provinces). Since the purpose of our study is to estimate the importance of search costs, we choose to work at the highest level of regional disaggregation, that is, at the neighborhood level. This permits us to proxy the costs of traveling to the different car dealers rather accurately. Statistics Netherlands provides a considerable amount of useful demographic and socioeconomic data at this level of disaggregation. For every neighborhood, the demographic data include the number of inhabitants and their distribution by age groups, the number of households, the average household size, the proportion of single-person households, and the proportion of households with children. The socioeconomic 31 The classification we use is based on the Euro NCAP Class vehicle classification. The largest class in terms of sales-weighted market share in the period 2003-2008 is the supermini class with a market share of 0.347, followed by the small family car class (0.214), the large family car class (0.176), and the small MPV class (0.148). In our analysis we combine the small and large family car classes into a single family car class (combined sales-weighted market share of 0.390 during 2003-2008), and combine the small and large MPV classes, as well as the small and large off-road 4x4 classes into a single MPV/SUV class (combined market share of 0.226). The combined market share of cars in other classes (executive, luxury, sports cars, and vans) is 0.037.

36

data include the average home value, the average income per inhabitant and income earner, as well as the total number of cars and their ownership status (company leased versus privately owned). We only include neighborhoods with a strictly positive number of inhabitants, which leaves us with a total of 11,122 neighborhoods for 2007.32 Most neighborhoods are relatively small; the mean number of inhabitants is 1,471. In addition to demographic data we have information on the exact location of each neighborhood on the map of the Netherlands. Using a geographical software package we use this information to construct a proxy for the distance that needs to be travelled when visiting a car dealership. To be able to do this, for every brand we have first obtained the addresses of all its dealerships in the Netherlands. For instance, Saab has a total of 37 dealers in the Netherlands. Since we have the exact addresses of the 37 dealerships of Saab, for every neighborhood, we can compute the Euclidean distance from the center of the neighborhood to the closest Saab dealer. We do this for all car manufacturers and obtain a matrix of 11,122 by 39 containing the minimum distances from the center of a neighborhood to a car dealer. There is a lot of variation in the distances to the closest dealer of each brand across neighborhoods. Volvo, arguably a brand similar to Saab but with very different sales, has a total of 114 dealerships in the whole country—clearly on average the minimum distance to a Volvo dealer is much smaller than the minimum distance to a Saab dealer. A similar picture arises for other brands. For instance, Audi has 161 dealers, whereas BMW has only 57, even though both brands are active in the luxury segment of the market and in this case both have similar sales figures. Table 3 gives some descriptive statistics for the distances to the nearest dealer for all the car brands in our data. Opel is the most accessible: almost 79% of all households live within 5 kilometer from an Opel dealer. Porsche has the lowest percentage of households within 5 kilometer: only 6.4% of households is within easy reach. As argued above, the location of car dealers may be endogenous to the model because they may choose to locate in areas where there is most demand for the cars they sell. For instance, dealers of luxury brands may locate near wealthy neighborhoods, while mainstream brands may not. This, if not properly dealt with, may result in the effect of distance appearing more important than it actually is. The possible endogeneity of location can in principle be addressed by including a rich set of interactions between car characteristics and demographics (see also Nurski and Verboven, 2016).33 32

There are 284 neighborhoods for which the number of inhabitants is zero. These are neighborhoods that tend to be located in industrial areas, ports, and remote rural areas. There are a few neighborhoods for which we miss some of the relevant variables. To complete the data set we proceed by using information obtained at lower levels of disaggregation (districts or city councils). 33 Nurski and Verboven (2016) run several alternative specifications to deal with the possible endogeneity of distance,

37

Table 3: Descriptive statistics for distances

Brand Alfa Romeo Audi BMW Cadillac Chevrolet/Daewoo Chrysler/Dodge Citro¨ en Dacia Daihatsu Fiat Ford Honda Hyundai Jaguar Jeep Kia Lancia Land Rover Lexus Mazda Mercedes-Benz Mini Mitsubishi Nissan Opel Peugeot Porsche Renault Saab Seat Skoda Smart Subaru Suzuki Toyota Volkswagen Volvo

Number of dealerships

Number of cars sold in 2008

Weighted average distance

Percentage of households within 5 km

75 161 57 15 137 32 162 98 99 142 233 65 138 16 43 115 50 20 13 121 83 37 108 114 233 187 8 196 37 127 97 21 45 124 141 188 114

3,050 16,738 15,170 198 7,421 2,589 24,139 4,549 9,186 21,010 42,504 8,479 17,433 752 784 12,236 761 1,421 1,044 7,582 10,446 3,417 7,805 10,259 40,405 40,250 531 37,526 1,938 13,061 9,461 952 1,422 14,547 38,997 45,034 16,487

7.96 4.68 8.35 18.96 5.00 12.51 4.40 7.25 6.23 4.86 3.66 7.99 5.08 18.32 10.13 5.74 11.12 14.43 19.55 5.57 6.58 11.41 5.57 6.02 3.55 4.14 25.70 4.18 11.46 6.08 6.18 13.65 10.96 5.00 4.69 4.05 5.33

42.1 68.0 38.5 14.3 64.9 25.4 69.9 55.3 52.9 66.6 78.1 39.6 63.2 14.6 36.2 54.7 34.5 16.9 16.4 57.7 48.0 29.2 53.9 51.9 78.7 72.6 6.4 70.9 24.3 57.3 50.5 20.1 27.7 60.2 66.6 74.1 61.3

Notes: Averages are weighted by number of households in each neighborhood.

Moreover, we instrument distance by using several variables related to the fixed cost of operating a dealership, which is likely to affect location decisions. Endogeneity of dealer location may still cause estimation problems if the instruments for distance are weak—in order to alleviate this problem we use micro data, which facilitates identification in the way explained in Section 4. Our last dataset, discussed in Section 2, is obtained from two separate surveys that were administered by TNS NIPO, a Dutch survey agency, in 2010 and 2011. The focus of the survey is on characteristics and the behavior of Dutch car owners. Each of the in total 2,530 respondents that participated in the survey has answered specific questions on which dealers were visited in relation but find the effect of distance to be very robust across specifications.

38

to the most recent purchased car, which provides us with useful information on how consumers search in this market. In addition, we have information about the respondent’s household income, household size, age, kids, and zip code. We use these data for the estimation of the micro moments. We exclude respondents for which we do not observe income or a zip code, which leaves us with 2,024 observations. For the micro moments we focus on new car purchases in 2008 only—we assume that all respondents that did not buy a new car in 2008 went for the outside option, which includes not buying a car and buying a used car. According to data from the survey, slightly over 7 percent of the respondents bought a new car in 2008, which equals the share of households in the Netherlands that bought a new car in 2008.34

6.2

Estimation results

In this section we report the estimation results for the search model. We also report results for the full information model, so we can see how taking into account search frictions affects the estimates of demand parameters and markups. We first show results for the conditional logit model. The advantage of the logit model is that it allows us to explore the effects of search frictions in a very simple setting, which is particularly useful for studying how the model behaves under different distributional assumptions for the search cost distribution. We next estimate a more complex model in which we allow for random coefficients. In this specification we also use moments that are based on individual-level data from the survey, which will help identification (Armstrong, 2016) and can improve the precision of the estimates (Petrin, 2002). Conditional logit model Table 4 gives the parameter estimates for the simplest version of the model, the conditional logit model. We use a simplified version of equation (1)—we only allow for a single price coefficient and do not allow for any random coefficients so the indirect utility function is given by uij = αpj + xj 0 β + ξj + εij .

(32)

34 The survey data is from 2010 and 2011, and given that the survey is about the last car bought, it is likely that purchases of new cars in earlier years are underrepresented (if a consumer bought her last car in 2008, she may have bought a car in 2004 as well; the problem is that the 2004 purchase will not be in the survey data). For construction of the micro moments it is important that the probability of buying a new car from the survey data reflects the aggregate probability of buying a new car, and we found this to be the case for purchases in 2008 only, which corresponds to the most recent year in our market share data.

39

As a benchmark case, in the first two columns we present the demand estimates for a model without search frictions. The results in column (A) are obtained by regressing log(sj ) − log(s0 ) on product characteristics and price using ordinary least squares. The results in column (B) are obtained by using an instrumental variables (IV) approach to control for possible correlation between unobserved characteristics and price. As in most of the previous literature, we assume the car characteristics to be exogenous. Since markups relate to how far away other car models are in the characteristics space, this means prices will be correlated with the characteristics of other car models and these characteristics can be used as instrumental variables. In addition, we use instruments that are related to the cost of operating a dealership—even though these are primarily meant to deal with location endogeneity, they may also serve as instruments for price.35 Except for horsepower per weight, in both specifications all parameter estimates have the expected sign—horsepower per weight has an unexpected negative impact in the OLS specification. The price coefficient increases in magnitude in the IV specification, which is to be expected given that higher unobserved quality components should lead to higher prices. As a result the number of products with inelastic demands decreases substantially, from 97 percent of all cars for the estimates in column (A) to one percent in column (B). The results indicate that cars produced by non-European firms yield negative marginal utility, which means cars produced by European firms (e.g., Peugeot/Citro¨en, Fiat, Volkswagen, etc.) have a higher mean consumer valuation than cars produced by non-European firms (e.g., Toyota, Honda, etc.). Size, a higher mileage per euro, and cruise control as standard equipment all affect the consumers’ mean utility in a positive way. Finally, consumers consider MPVs and SUVs to have a positive marginal utility. In the last three columns of Table 4 we present the demand estimates using our consumer search model. We only use distance as a search cost shifter—we relate the search cost parameter λ to distances from the centroid of a neighborhood to the nearest dealers. Even in the simple conditional logit framework, once we include search frictions, there is no longer a closed-form solution for the market share equations, so we proceed by simulating them. Specifically, we randomly draw 512 neighborhoods from the demographic data, where each neighborhood is weighted by number of inhabitants.36 Next we use the distances to the nearest dealer for each of the brands in our 35

Specifically, the BLP-type instruments we use are own product characteristics, the number of other cars produced by the firm, the number of cars produced by rival firms, the sum of product characteristics (cruise control, fuel efficiency, and whether the car is a family car or MPV/SUV) of other cars produced by the firm, as well as the sum of the same product characteristics of cars produced by rival firms. The distance instruments we use are the interaction of average local taxes and average local population density, and the range of property values interacted with a variable that indicates how urban the dealership locations are on average. 36 These draws are in fact a certain type of quasi-random draws, which contains 83 = 512 draws (see S´ andor and Andr´ as, 2004).

40

sample to simulate search behavior for the 512 selected “consumers.” We estimate the model by GMM, using the same instruments as when estimating specification (B), and use (Z 0 Z)−1 as the weighting matrix. The results shown in column (C) of Table 4 are obtained using the search cost distribution specified in equation (16), and show that search costs are positively related to distance and significantly different from zero at the one percent level. The advantage of the search cost distribution we use in specification (C) is that it gives closedform expressions for the buying probabilities. However, the model can be estimated using different search cost distributions by using numerical integration to obtain the probability that a consumer buys from firm f , as in equation (11). In specification (D) we use this approach and use a normal distribution for search costs. Although the effect of distance in the search cost specification is smaller when using a normal distribution, the estimates for the utility parameters are very similar and do not seem to depend much on the difference in parametric specification.37 As shown in specification (E), the estimated utility parameters are also very similar when using a Gumbel (minimum) distribution. Note that a Gumbel (minimum) distribution is very similar in shape to the search cost distribution specified in equation (16) (see also Figure 2), which results in an estimated search cost parameter that is of similar magnitude. So regardless of whether we use a normal search cost distribution, a Gumbel (minimum) distribution, or the one based on equation (16), a comparison of the estimation results with search to those without search shows that the price coefficient significantly goes down in absolute value, which suggests that at least in the conditional logit model, ignoring search frictions may result in an overestimation of consumer price sensitivity. We will come back to this when discussing the results for the complete model below. Complete model The demand side estimates for the complete model are based on the utility function in equation (1) and the search cost distribution that is derived from Gumbel distributed w’s, as specified in equation (16). We use the same car attributes as those shown in Table 4 for the estimation of the simplified model. As before, we estimate the mean marginal utility of each of these attributes, but now we allow the marginal utility for some of the attributes to differ across consumers by estimating a variance term for these attributes. Specifically, for fuel efficiency we use a standard normal draw for the corresponding component of the diagonal matrix Vi . For MPV/SUV the corresponding component of the diagonal matrix is (kids) × υ3i , where kids is a dummy for whether 37

The difference arises because the variance of search costs is different across specifications. The standard deviation of the normal distribution of search costs we use in specification (D) is normalized to one—when the standard deviation is normalized to 1.6 instead, the estimate for distance goes up to 0.180.

41

there are children present in the household and υ3i is a χ2 (3)-distributed draw truncated at 95%. An advantage of using this distribution is that it is bounded and skewed toward positive taste (see also Petrin, 2002). We allow for heterogeneity in the price parameter in accordance with equation (2). This means that in addition to normalizing prices by household income, we allow α to differ according to income groups (as in Petrin, 2002). A simulated consumer’s household income is randomly drawn from a log-normal distribution with scale parameter 0.28 (which is estimated outside the model) and neighborhood-specific location parameter such that the mean (after-tax) household income level in the neighborhood where the simulated consumer resides matches the neighborhood data from Statistics Netherlands. The income bound y we use corresponds to a household income (after tax) of e25,000.38 The senior dummy is obtained from the neighborhoodspecific percentage of households with a head of household older than 65 years, i.e., the senior dummy equals 1 if that percentage is larger than a uniform draw on (0, 1) and zero otherwise. Similarly, the kids dummy is obtained from the neighborhood-specific percentage of households with kids, i.e., the kids dummy equals 1 if that percentage is larger than a uniform draw on (0, 1) and zero otherwise. The estimation of the supply side is based on equation (25), where we use the fact that car model j’s marginal cost mcj equals the difference between its price and markup ∆(p)−1 s(p). Our cost-side variables are based on the attributes in the utility function and include a constant, indicators for non-European and cruise control, and the natural logarithm of HP/weight, kilometers per liter, and size. By including micro moments we can estimate a richer search cost specification than the one used in the estimation of the conditional logit model. Specifically, in addition to distance we let search costs depend on the logarithm of household income as well as a dummy for whether the head of household is senior, where both are multiplied by distance. In addition, we estimate the mean and standard deviation of a normal distributed random search cost constant. 38 For the choice of income bound we are constrained by the income bins used in the survey. The chosen bound approximately equals a household income of e30,200 before taxes, which corresponds to one of the cutoffs used to create bins in the survey data.

42

Table 4: Estimation results conditional logit

Variable Preference parameters constant HP/weight non-European cruise control fuel efficiency size family car MPV/SUV price Search cost parameters distance

Full information OLS IV Logit Logit Demand Demand (A) (B) Coeff. Std. Err. Coeff. Std. Err.

-12.050 -1.074 -0.509 0.102 2.650 2.362 0.264 0.269 -0.012

(0.706)∗∗∗ (0.237)∗∗∗ (0.074)∗∗∗ (0.087) (0.272)∗∗∗ (0.634)∗∗∗ (0.097)∗∗∗ (0.100)∗∗∗ (0.004)∗∗∗

—

-17.952 3.947 -1.255 0.421 2.109 9.760 -0.608 0.242 -0.131

(1.240)∗∗∗ (0.762)∗∗∗ (0.143)∗∗∗ (0.123)∗∗∗ (0.367)∗∗∗ (1.323)∗∗∗ (0.176)∗∗∗ (0.132)∗ (0.017)∗∗∗

—

GMM/IV Logit Demand (C) Coeff. Std. Err.

Search GMM/IV Logit Demand (D) Coeff. Std. Err.

GMM/IV Logit Demand (E) Coeff. Std. Err.

-13.271 1.605 -0.855 0.086 2.260 5.158 -0.103 0.218 -0.061

(1.269)∗∗∗ (0.797)∗∗ (0.144)∗∗∗ (0.122) (0.268)∗∗∗ (1.388)∗∗∗ (0.174) (0.104)∗∗ (0.020)∗∗∗

-12.609 1.561 -0.839 0.083 2.253 5.088 -0.097 0.215 -0.060

(1.248)∗∗∗ (0.799)∗ (0.144)∗∗∗ (0.122) (0.266)∗∗∗ (1.390)∗∗∗ (0.174) (0.104)∗∗ (0.020)∗∗∗

-13.069 1.592 -0.850 0.085 2.258 5.138 -0.101 0.217 -0.061

(1.259)∗∗∗ (0.797)∗∗ (0.144)∗∗∗ (0.122) (0.267)∗∗∗ (1.387)∗∗∗ (0.174) (0.104)∗∗ (0.020)∗∗∗

0.180

(0.061)∗∗∗

0.107

(0.032)∗∗∗

0.191

(0.062)∗∗∗

43

R2 Objective function

0.345 n.a.

n.a. n.a.

n.a. 0.025

n.a. 0.024

n.a. 0.024

Average own-price elasticity

-0.340

-3.813

-1.771

-1.744

-1.763

–

–

Eq.(16)

Normal

Gumbel (min)

Search cost distr.

Notes: ∗ significant at 10%; ∗∗ significant at 5%; ∗∗∗ significant at 1%. The number of observations is 1,382. Standard errors are in parenthesis. The number of simulated consumers used for the estimation of specifications (C)-(E) is 512.

The estimation results for the search model are presented in the first two columns of Table 5. In specification (A) we allow for a random coefficient on the interaction of MPV/SUV and the kids dummy as well as a random coefficient on fuel efficiency.39 The price coefficients are statistically significant at high significance levels. All else equal, consumers prefer larger and more powerful cars. The estimated coefficient of the non-European dummy is negative and highly significant, which, consistent with the results for the conditional logit model, indicates consumers on average prefer cars produced by European firms versus cars produced by non-European firms. We use cruise control as a measure of luxuriousness; as expected, consumers put a positive value on cruise control being a standard option. The mean parameter estimate for fuel efficiency is negative, although the relatively large estimate of the corresponding standard deviation parameter indicates that there is substantial heterogeneity in consumers’ marginal valuation for fuel efficiency. The parameter estimate corresponding to the interaction of MPV/SUV and kids indicates that households with kids put positive value on larger cars such as MPVs and SUVs. Except for the cost parameter on log(km per liter), all cost parameters have the expected signs.40 The distance-related search cost parameters are highly significant. The estimates indicate that search costs are positively related to distance, but that the effect is smaller for households with higher income and senior households. The estimates for the distribution of the random search cost constant indicate that there is a lot of variation in constant search costs. Moreover, the estimated mean is relatively high, which is consistent with a high proportion of consumers not searching in any given year. In addition to serving as a search cost shifter, the distance from a consumer to the nearest dealer of a brand could also be part of the utility function. One way in which it could enter utility is because of service: if consumers prefer to have their cars serviced at the dealer, a car’s indirect utility is likely to be directly affected by distance to the closest dealership. To control for this, we add distance from the consumer to the nearest dealer to the utility function in specification (B). 39

Although not reported, we have estimated versions of the model with more random coefficients. Even though most of the estimated base coefficients change somewhat as a result of allowing for more random coefficients, the price and search cost parameter estimates appear robust to changes in the number of random coefficients. We prefer a specification with less random coefficients since this increases the precision of the estimates. Moreover, with a full set of random coefficients it is very difficult to do counterfactual exercises due to numerical issues when solving for the price equilibrium (see also Skrainka, 2012). 40 BLP get a similar result with respect to fuel efficiency for their main specification. Their explanation is that fuel efficiency is positively correlated with sales, so if sales is negatively correlated with marginal costs (which happens if there are increasing returns to scale), the fuel efficiency parameter may be biased downward. By adding a log(sales) variable to one of their specifications, the sign on fuel efficiency is reversed. However, with our data this does not work, which can be explained by the observation that almost none of the cars is produced in the Netherlands, so domestic sales are not a good predictor of total production. Another explanation is related to the way the fuel consumption variable is defined. The variable we use is the average fuel consumption while the fuel consumption within towns or cities is usually different. So for those consumers who mainly use their cars within towns or cities our fuel consumption variable is measured with error.

44

We interact distance with the average monthly maintenance cost of service to control for variation in service needs. Since maintenance cost vary at the model level, this interaction creates variation in the effects of distance even when we condition on the brand the consumer buys from, which is used to construct some of our micro moments and is helpful variation to separate distance in the utility function from distance in the search cost specification. According to the estimates, distance has a negative effect on utility, which may capture the negative effect on utility of service visits to dealers located farther away from the consumer. The estimated price coefficients are less negative when distance is part of utility, although most of the other parameter estimates are similar to those for specification (A). The last two columns of Table 5 give parameter estimates in case we assume consumers have full information, as in BLP. The results in column (C) of this table are obtained using the same preference and cost side parameters as in specification (A) of the table, although we can no longer use the search related micro moments. The estimated price coefficients point to a significantly higher marginal disutility of price in comparison to the estimates for the search model. In column (D) we add distance interacted with the cost of maintenance to the utility function.41 This interaction term has a negative parameter estimate, and although only marginally significant, this is consistent with the idea that distance in the utility captures the negative effect on utility of service visits to dealers located farther away from the consumer.42 Table 6 gives the estimated probabilities used for the micro moments as well as those from the survey data. All specifications are able to match the probabilities from the survey data relatively well—most estimated probabilities used as micro moments are well within 10 percent of the corresponding probabilities from the survey data.

6.3

Demand elasticities and markups

Table 7 gives demand elasticity estimates for a selection of car models sold in 2008 for both the search model (using the estimates in column (B) of Table 5) and the full information model (using the estimates in column (D) of the table). For all models, demand is estimated to be more inelastic in the search model than in the full information model. This means that assuming consumers have 41 Using distance instead of distance × maintenance in specifications (B) and (D) of Table 5 gives very similar results. 42 As explained before, our search model allows us to add more search cost covariates than distance only. For instance, in both search specifications we include household income and a dummy for whether the household has a senior member, which improves the fit of the search model. We note that while the search model offers a natural justification for adding income or other demographic information to the model, it is difficult to justify adding these variables to the utility function in a full information model, which may explain why the existing literature has not followed this approach.

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Table 5: Estimation results with micro moments

Search Variable

(A) Coeff. Std. Err.

(B) Coeff. Std. Err.

Full Information (C) (D) Coeff. Std. Err. Coeff. Std. Err.

Price coefficients (price/income) income less than 25k -4.154 income more than 25k -4.898

(0.028)∗∗∗ (0.024)∗∗∗

-3.827 -4.026

(0.032)∗∗∗ (0.044)∗∗∗

-5.236 -7.626

(0.236)∗∗∗ (0.441)∗∗∗

-5.059 -7.293

(0.275)∗∗∗ (0.520)∗∗∗

Base coefficients constant HP/weight non-European cruise control fuel efficiency size family car MPV/SUV

-9.422 2.155 -0.852 0.525 -0.865 9.953 -0.207 -0.214

(0.291)∗∗∗ (0.092)∗∗∗ (0.035)∗∗∗ (0.045)∗∗∗ (0.121)∗∗∗ (0.278)∗∗∗ (0.028)∗∗∗ (0.032)∗∗∗

-9.018 2.101 -0.868 0.320 -0.769 8.980 -0.142 -0.241

(0.277)∗∗∗ (0.088)∗∗∗ (0.034)∗∗∗ (0.043)∗∗∗ (0.116)∗∗∗ (0.268)∗∗∗ (0.027)∗∗∗ (0.032)∗∗∗

-17.138 4.429 -1.364 0.558 -1.372 12.747 -0.471 -0.143

(0.332)∗∗∗ (0.120)∗∗∗ (0.041)∗∗∗ (0.050)∗∗∗ (0.138)∗∗∗ (0.323)∗∗∗ (0.033)∗∗∗ (0.038)∗∗∗

-16.983 4.481 -1.355 0.499 -1.320 12.411 -0.463 -0.154

(0.338)∗∗∗ (0.125)∗∗∗ (0.041)∗∗∗ (0.050)∗∗∗ (0.139)∗∗∗ (0.322)∗∗∗ (0.033)∗∗∗ (0.038)∗∗∗

3.448 0.365 —

(0.059)∗∗∗ (0.009)∗∗∗

3.438 0.366 -0.057

(0.055)∗∗∗ (0.009)∗∗∗ (0.008)∗∗∗

2.363 0.368 —

(0.065)∗∗∗ (0.009)∗∗∗

2.328 0.367 -0.034

(0.066)∗∗∗ (0.009)∗∗∗ (0.018)∗

Cost parameters constant log(HP/weight) non-European cruise control log(km per liter) log(size)

3.148 0.986 -0.167 0.158 -0.975 1.850

(0.015)∗∗∗ (0.021)∗∗∗ (0.011)∗∗∗ (0.011)∗∗∗ (0.033)∗∗∗ (0.064)∗∗∗

3.226 1.056 -0.220 0.115 -1.048 2.320

(0.020)∗∗∗ (0.022)∗∗∗ (0.011)∗∗∗ (0.012)∗∗∗ (0.038)∗∗∗ (0.083)∗∗∗

3.199 1.014 -0.199 0.109 -0.852 1.308

(0.010)∗∗∗ (0.015)∗∗∗ (0.007)∗∗∗ (0.008)∗∗∗ (0.029)∗∗∗ (0.050)∗∗∗

3.198 1.021 -0.200 0.109 -0.858 1.338

(0.010)∗∗∗ (0.015)∗∗∗ (0.007)∗∗∗ (0.008)∗∗∗ (0.030)∗∗∗ (0.051)∗∗∗

Search cost parameters distance × log(income) × senior constant (mean) constant (st.dev.)

2.273 -0.557 -0.230 10.470 5.979

(0.038)∗∗∗ (0.009)∗∗∗ (0.004)∗∗∗ (0.064)∗∗∗ (0.052)∗∗∗

2.198 -0.542 -0.228 10.524 5.945

(0.034)∗∗∗ (0.008)∗∗∗ (0.003)∗∗∗ (0.060)∗∗∗ (0.047)∗∗∗

— — — — —

Random coefficients fuel efficiency MPV/SUV × kids distance × maintenance

— — — — —

Objective function

0.652

0.632

0.334

0.332

Average own-price elasticity

-3.375

-2.899

-4.781

-4.625

Notes: ∗ significant at 10%; ∗∗ significant at 5%; ∗∗∗ significant at 1%. The number of observations is 1,382. The number of simulated consumers used for the aggregate moments is 512. The number of simulated consumers used for the micro moments is 25 per respondent. Standard errors are in parenthesis.

full information while in reality they do not, will lead to an overestimation of price sensitivity for most car models. The cross-price elasticities show the opposite pattern: the percentage change in market share as a result of a percent increase in price of a rival model is in the majority of the cases larger in the search model than in the full information model. In the search model, consumers with a relatively high buying probability for a specific model are likely to have a relatively low search cost constant, which results in higher purchase probabilities for other car models as well, explaining the higher cross-price elasticities.

46

Table 6: Fit micro moments Survey

Search (A) (B)

Full info (C) (D)

Purchase related probabilities E[1{i purchases an MPV or SUV} | {i has a family size ≤ 3}] E[1{i purchases an MPV or SUV} | {i has a family size > 3}] E[1{i purchases a family car} | {i has children in the household}] E[1{i purchases a family car} | {i has no children in the household}] E[1{i purchases a new vehicle} | {yi < y}] E[1{i purchases a new vehicle} | {yi ≥ y}]

0.012 0.021 0.036 0.026 0.038 0.085

0.008 0.019 0.024 0.026 0.043 0.089

0.008 0.018 0.024 0.025 0.042 0.088

0.008 0.022 0.026 0.025 0.039 0.086

0.008 0.022 0.026 0.025 0.039 0.086

Conditional on purchase E[1{i purchases a super mini} | {i buys}] E[1{i purchases a family car} | {i buys}] E[1{i purchases an MPV or SUV} | {i buys}]

0.331 0.446 0.223

0.324 0.438 0.216

0.324 0.438 0.216

0.324 0.439 0.216

0.324 0.438 0.216

Search related probabilities E[1{i searches once} | {yi < y}] E[1{i searches once} | {yi ≥ y}] E[1{i searches once} | {# of dealers within 10km of i < 15}] E[1{i searches once} | {# of dealers within 10km of i ≥ 15}] E[1{i searches once} | {i is senior}] E[1{i searches once} | {i is not a senior}] E[1{i searches once} | {dealer cluster within 5km of i}] E[1{i searches once} | {no dealer cluster within 5km of i}] E[1{i searches at least twice} | {yi < y}] E[1{i searches at least twice} | {yi ≥ y}] E[1{i searches at least twice} | {# of dealers within 10km of i < 15}] E[1{i searches at least twice} | {# of dealers within 10km of i ≥ 15}] E[1{i searches at least twice} | {i is senior}] E[1{i searches at least twice} | {i is not a senior}] E[1{i searches at least twice} | {dealer cluster within 5km of i}] E[1{i searches at least twice} | {no dealer cluster within 5km of i}]

0.041 0.057 0.034 0.052 0.048 0.050 0.043 0.055 0.055 0.089 0.042 0.079 0.087 0.072 0.085 0.066

0.038 0.057 0.041 0.050 0.046 0.050 0.052 0.047 0.055 0.090 0.042 0.079 0.086 0.072 0.087 0.065

0.038 0.057 0.040 0.050 0.046 0.049 0.052 0.047 0.054 0.090 0.043 0.079 0.086 0.072 0.086 0.066

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Table 7: Demand elasticity estimates Hyundai Accent

Mitsubishi Lancer

Volkswagen Golf

Opel Astra

Nissan Qashqai

Mercedes B Class

Mazda MX-5

Audi A4

Search Hyundai Accent Mitsubishi Lancer Volkswagen Golf Opel Astra Nissan Qashqai Mercedes B Class Mazda MX-5 Audi A4

-1.5047 0.0006 0.0006 0.0006 0.0006 0.0004 0.0005 0.0005

0.0029 -1.8846 0.0026 0.0026 0.0028 0.0022 0.0026 0.0025

0.0390 0.0406 -2.0567 0.0391 0.0403 0.0297 0.0352 0.0394

0.0284 0.0285 0.0281 -2.2216 0.0311 0.0200 0.0246 0.0249

0.0212 0.0222 0.0209 0.0225 -2.4470 0.0183 0.0213 0.0210

0.0070 0.0074 0.0066 0.0062 0.0078 -2.6098 0.0083 0.0081

0.0004 0.0005 0.0004 0.0004 0.0005 0.0004 -2.9110 0.0005

0.0357 0.0378 0.0378 0.0332 0.0387 0.0350 0.0387 -3.2617

Full information Hyundai Accent Mitsubishi Lancer Volkswagen Golf Opel Astra Nissan Qashqai Mercedes B Class Mazda MX-5 Audi A4

-2.5215 0.0005 0.0005 0.0005 0.0004 0.0004 0.0004 0.0004

0.0021 -3.0762 0.0019 0.0021 0.0019 0.0016 0.0017 0.0017

0.0324 0.0288 -3.3257 0.0330 0.0301 0.0260 0.0272 0.0278

0.0266 0.0231 0.0237 -3.5376 0.0245 0.0208 0.0218 0.0225

0.0164 0.0151 0.0156 0.0177 -4.0174 0.0151 0.0157 0.0165

0.0056 0.0055 0.0058 0.0064 0.0064 -4.4468 0.0068 0.0073

0.0003 0.0003 0.0003 0.0004 0.0004 0.0004 -4.7478 0.0004

0.0248 0.0251 0.0267 0.0301 0.0305 0.0316 0.0321 -5.1636

Notes: Demand elasticities are calculated for 2008. Percentage change in market share of model i with a one percent change in the price of model j, where i indexes rows and j columns. Elasticities for the search model are calculated using estimates from specification (B) in Table 5; those for the full information model are based on specification (D) in Table 5.

Table 8 makes a comparison between the average own-price elasticities for those consumers that live in a neighborhood that is on average relatively close to dealerships (average distance to dealers less than 6 kilometers) and those that live further away (average distance 6 kilometers or more). The first two columns are based on the estimates for the search model and show that for most car models included in the table, those that live closer to dealerships are more price sensitive. Part of this reflects a difference in income between the two groups of consumers—consumers that live closer to the dealerships also have lower incomes on average, which makes them more price sensitive irregardless of the effect of distance. Indeed, the last two columns of the table give the own-price elasticities for the full information model, and show that those located further away have more inelastic demand for all cars models included in the table, which is consistent with the income difference explanation. However, whereas more expensive cars such as the Mazda MX-5 and Audi A4 face more elastic demand from consumers that are located further away according to the search model, in the full information model those cars face more inelastic demand from those consumers, just as the less expensive cars in the table. This difference likely reflects that according to the search model estimates, search costs are negatively related to income. Table 9 compares the estimated markups between the search model and the full information

48

Table 8: Own-price elasticity estimates according to distance Search Avg dist Avg dist < 6km dist ≥ 6km Search Hyundai Accent Mitsubishi Lancer Volkswagen Golf Opel Astra Nissan Qashqai Mercedes B Class Mazda MX-5 Audi A4

-1.6286 -1.9900 -2.1564 -2.2533 -2.4378 -2.6591 -2.8996 -3.2148

-1.3351 -1.7402 -1.9639 -2.1944 -2.4558 -2.5422 -2.9251 -3.3086

Full information Avg dist Avg dist < 6km dist ≥ 6km

-2.5726 -3.1422 -3.3778 -3.6046 -4.0830 -4.5218 -4.8374 -5.2452

-2.4748 -3.0173 -3.2807 -3.4804 -3.9620 -4.3801 -4.6724 -5.0966

Notes: Own-price elasticities are calculated separately according to average distance to the dealers (less than or more than 6 km). Elasticities for the search model are calculated using estimates from specification (B) in Table 5; those for the full information model are based on specification (D) in Table 5.

model. Consistent with the elasticity patterns reported in Table 7, estimated markups in the search model are higher for all the cars. The estimated average percentage markup across all models in 2008 is 41 percent for the search model versus 24 percent for the full information model. These numbers are not unrealistic: BLP report an average ratio of markup to retail price of 24 percent for their main specification and they note that it is “not extraordinarily high” (BLP, p. 883), whereas Petrin (2002) finds an average markup of 17 percent for the model with micro moments. Goldberg (1995), on the other hand, obtains higher markup estimates: wholesale price markups of on average 38 percent, which implies even larger retail price markups. In both the search model and the full information model, the Volkswagen Golf is the most profitable model among the ones listed in Table 9, and one of the most profitable models in general.

6.4

Robustness

Table 10 shows the parameter estimates for several alternative specifications. In specification (A) we re-estimate the main specification but use a normal search cost distribution instead of the one given by equation (16), which is based on a Gumbel distribution for w. Most of the estimated utility parameters are relatively similar to those for the main specification reported in column (B) of Table 5, and, as a result, the estimated average own-price elasticity is about the same. However, a difference between the results in column (A) and those for the main specification is that the parameters of the search cost distribution are uniformly lower than those for the main specification, which is consistent with the results for the conditional logit specification (see also footnote 37). Column (B) gives estimates when using a Gumbel (minimum) search cost distribution—both utility 49

Table 9: Markups

Hyundai Accent Mitsubishi Lancer Volkswagen Golf Opel Astra Nissan Qashqai Mercedes B Class Mazda MX-5 Audi A4

price

pre-tax price

markup over MC

Search percentage markup

variable profit

markup over MC

11,708 14,992 16,632 17,799 21,083 25,290 26,701 30,383

8,153 10,189 11,206 11,697 13,559 16,574 17,216 19,324

4,962 4,986 5,627 5,326 5,703 6,152 6,274 6,491

60.86 48.94 50.21 45.54 42.06 37.12 36.44 33.59

1.36 4.87 76.85 48.85 31.93 12.22 0.63 46.57

2,921 3,034 3,252 3,222 3,356 3,570 3,658 3,847

Full information percentage variable markup profit 35.82 29.78 29.02 27.54 24.75 21.54 21.25 19.91

0.80 2.96 44.42 29.55 18.79 7.09 0.37 27.60

Notes: Prices and markup over MC are in Euros. Variable profit is in Euro×1 mln. Markups and profits for the search model are calculated using estimates from specification (B) in Table 5; those for the full information model are based on specification (D) in Table 5. Percentage markup is calculated as (p∗j − mcj )/p∗j , where p∗j is the pre-tax price of car j. Variable profit is calculated as qj · (p∗j − mcj ), where qj is the sales of car j.

and search cost parameters are similar to those for the main specification. Specification (C) of Table 10 only uses the buying micro-moments. We limit the search cost parameters to distance and distance×income—as discussed in Section 4, without using searchrelated micro moments it is difficult to separately identify the constant in the utility function and the constant in the search cost specification. Although there are some small differences between these estimates and those for the main specification, including more elastic demand estimates, our finding that demand is more elastic in the full information case remains valid even when using similar micro moments in both the search model and full information model. Moreover, the search model outperforms the full information model in terms of fit, as indicated by a comparison of objective function values of specification (C) of Table 10 and specification (C) of Table 5.

6.5

Counterfactuals

In this section we study the effects of three changes in the primitives of the model, using the search model estimates reported in column (B) of Table 5. First, we look at what happens to equilibrium prices when the costs of visiting dealers change. Some dealers have recently started to bring cars to buyers for test driving at home or work.43 We model this situation as if the cost of transportation to the dealership went down all the way to zero. Secondly, we make a comparison between prices in the search model and prices in the full information model by using the estimates for the search model to simulate a full information equilibrium. Finally, multi-brand firms sometimes choose to retail their products using different dealership networks. A well-known case of this in the automobile industry 43

See http://www.edmunds.com/car-news/phil-long-dealership-group-sells-and-services-cars-and-will-travel.html as well as footnote 3 in the introduction.

50

Table 10: Estimation results alternative specifications Variable

Coeff.

(A) Std. Err.

Coeff.

(B) Std. Err.

Coeff.

(C) Std. Err.

Price coefficients (price/income) income less than 25k -3.263 income more than 25k -3.965

(0.126)∗∗∗ (0.240)∗∗∗

-3.600 -3.708

(0.033)∗∗∗ (0.057)∗∗∗

-3.596 -6.329

(0.281)∗∗∗ (0.433)∗∗∗

Base coefficients constant HP/weight non-European cruise control fuel efficiency size family car MPV/SUV

-8.768 1.900 -0.641 0.311 -0.655 7.876 -0.116 -0.187

(0.267)∗∗∗ (0.081)∗∗∗ (0.032)∗∗∗ (0.041)∗∗∗ (0.110)∗∗∗ (0.257)∗∗∗ (0.027)∗∗∗ (0.031)∗∗∗

-8.846 1.887 -0.790 0.281 -0.645 8.359 -0.101 -0.218

(0.271)∗∗∗ (0.085)∗∗∗ (0.033)∗∗∗ (0.042)∗∗∗ (0.113)∗∗∗ (0.262)∗∗∗ (0.027)∗∗∗ (0.032)∗∗∗

-14.532 3.564 -1.117 0.385 -0.909 10.436 -0.335 -0.110

(0.318)∗∗∗ (0.107)∗∗∗ (0.037)∗∗∗ (0.046)∗∗∗ (0.131)∗∗∗ (0.297)∗∗∗ (0.031)∗∗∗ (0.037)∗∗∗

Random coefficients fuel efficiency MPV/SUV × kids distance × maintenance

2.640 0.303 -0.000

(0.050)∗∗∗ (0.008)∗∗∗ (0.007)

3.261 0.351 -0.028

(0.061)∗∗∗ (0.009)∗∗∗ (0.002)∗∗∗

2.238 0.311 —

(0.069)∗∗∗ (0.008)∗∗∗

Cost parameters constant log(HP/weight) non-European cruise control log(km per liter) log(size)

3.086 0.971 -0.184 0.171 -0.863 1.377

(0.012)∗∗∗ (0.018)∗∗∗ (0.009)∗∗∗ (0.010)∗∗∗ (0.030)∗∗∗ (0.055)∗∗∗

3.212 1.017 -0.203 0.134 -1.055 2.361

(0.020)∗∗∗ (0.024)∗∗∗ (0.013)∗∗∗ (0.013)∗∗∗ (0.038)∗∗∗ (0.084)∗∗∗

3.189 1.049 -0.210 0.117 -0.892 1.571

(0.011)∗∗∗ (0.016)∗∗∗ (0.008)∗∗∗ (0.009)∗∗∗ (0.032)∗∗∗ (0.056)∗∗∗

Search cost parameters distance × log(income) × senior constant (mean) constant (st.dev.)

1.287 -0.314 -0.152 5.877 3.470

(0.024)∗∗∗ (0.006)∗∗∗ (0.003)∗∗∗ (0.050)∗∗∗ (0.043)∗∗∗

2.237 -0.544 -0.259 10.645 6.072

(0.039)∗∗∗ (0.009)∗∗∗ (0.004)∗∗∗ (0.065)∗∗∗ (0.056)∗∗∗

2.052 -0.490 — — —

(0.124)∗∗∗ (0.033)∗∗∗

Objective function

0.597

0.634

0.307

Average own-price elasticity

-2.927

-2.728

-3.813

Notes: ∗ significant at 10%; ∗∗ significant at 5%; ∗∗∗ significant at 1%. The number of observations is 1,382. The number of simulated consumers used for the aggregate moments is 512. The number of simulated consumers used for the micro moments is 25 per respondent. Standard errors are in parenthesis. The estimation of specification (C) does not use the search-related micro moments.

is the 1998 merger between Daimler-Benz and Chrysler whose retail networks largely remained separate. Business analysts have suggested that this likely hindered Chrysler’s market penetration in Europe (see also Finkelstein, 2002). We explore what happens to prices and profits when Toyota, one of the multi-brand firms that does not yet sell all its cars in the same dealership location, starts doing so.

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Change in search costs To see how prices change if search costs for all consumers and dealers decrease simultaneously, we take the estimates reported in column (B) of Table 5 and simulate equilibrium prices and market shares when setting the distance-related part of each consumer’s search cost equal to a specific percentage of the estimated distance-related search cost. The average decrease in price when moving to zero search costs is 4 percent. Interestingly, we find that the further away (on average) a particular brand is from consumers, the more prices decrease as a result of a reduction in distance-related search costs. For instance, the average price decrease at Opel, which has 233 dealer locations, is 2.4 percent, while 7.3 percent at Subaru, which has only 45 locations. This could be explained by the fact that most of the brands that have many dealers tend to be active in a relatively competitive segment of the market, so a more competitive market due to lower search frictions does not affect their price strategy much. Moreover, we observe that the price effect is largest for relatively small and inexpensive models such as the Hyundai i10, Toyota Aygo, and Nissan Micro. On the other hand, for large and expensive car models such as the Volvo XC90 and Audi Q7 we see relatively low price decreases, which is likely to be caused by their relatively low demand elasticity. Table 11 summarizes the effects on prices for the same car models as in Table 9. For all models in the table, prices decrease when search costs go down. For instance, the simulated prices of the Hyundai Accent and Mitsubishi Lancer drop by more than 4 percent when distance-related search costs are reduced to zero. The same pattern arises for the weighted and unweighted average prices across all cars, which suggests that prices are overall increasing in distance-related search costs. In addition to the benefits arising from lower search costs and better matching with the products, the results in Table 11 show that consumers also benefit because of lower prices. Firms benefit as well—even though prices and average percentage markups are mostly increasing with search costs, the results in Table 11 show that lower margins are accompanied by higher sales. As a result, variable industry profits are higher when search costs are lower. Notice that these results assume a similar reduction in search costs for all firms—later in this section we will simulate the effects of firm-specific changes in search costs as a result of changes in a firm’s dealership network.

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Table 11: Simulated prices for different levels distance-related search costs percentage of distancerelated search costs 100% 50% 0% Price Hyundai Accent Mitsubishi Lancer Volkswagen Golf Opel Astra Nissan Qashqai Mercedes B Class Mazda MX-5 Audi A4

full info (λ = −∞)

11,708 14,992 16,632 17,799 21,083 25,290 26,701 30,383

11,186 14,711 16,286 17,499 20,791 24,736 26,303 30,081

10,813 14,302 16,006 17,316 20,400 24,258 25,817 29,753

10,787 14,268 15,957 17,307 20,403 24,359 25,929 29,826

Average (sales weighted) Average

18,613 29,214

17,859 28,688

17,293 28,288

17,699 28,455

Share not searching Market share outside good

0.8765 0.9324

0.8604 0.9228

0.8245 0.9087

— 0.8962

43.26

42.27

41.36

41.54

489,584 2,737

559,122 2,986

660,916 3,383

751,472 3,868

Average percentage markup Total sales Industry profits (mln e)

Notes: Prices are in Euros. The prices shown are simulated prices when search costs are x percent of the distance-related part of the estimated search costs from specification (B) in Table 5, where x is between 0 and 100 percent. The last column gives simulated prices for the full information model.

Full information In Table 11 we also report prices when using the estimates to simulate the pricing equilibrium under the full information model.44 A comparison of the average sales-weighted price under full information with actual prices suggests that prices are on average $914 higher because of search frictions.45 As shown in the last column of the table, for several models the simulated prices under full information exceed the simulated prices for the search model when the distance-related part of search costs is set to zero percent. The non-monotonic relationship we find between prices and search costs when moving from the search model to the full information model deserves an ex44

The full information model can be obtained by setting search costs to zero in the search model. In the Gumbel distributed w case this means that µif has to be equal to zero, which requires that λ → −∞. This implies that the simulated prices under the full information model are not necessarily similar to those when all search costs parameters are set to zero. Moreover, to make sure that the market share of the outside options does not drop to unrealistic proportions when simulating the full information equilibrium, we adjust δij by deducting the part of search costs that is constant. Note that this will not affect the price equilibrium in the search model, but will make the outside option in the full information model more attractive. 45 In a related study, Murry and Zhou (2017) use individual-level transaction data for new cars to quantify how geographical concentration among car dealers affects competition and search behavior and find that search frictions lead to an average price increase of $422.

53

planation. As noted before, in our model an increase in search costs has three different effects. First, as can be seen in Table 11, as search costs increase the share of consumers not searching goes up. If the consumers who remain in the market are the more elastic ones, as demonstrated in Moraga-Gonz´ alez, S´ andor, and Wildenbeest (2017), firms get an incentive to lower their prices. Second, as it is standard in search models, higher search costs give firms enhanced market power over the consumers who visit, and thereby firms have an incentive to raise their prices. Finally, because we have a model in which prices are observed before search, higher search costs increase competition for visits, and this puts downward pressure on prices (see also footnote 25). The latter effect is because consumers in our model determine whether to continue searching or not by making a tradeoff between the expected utility and the search costs of visiting an additional dealer. Since the former depends on the observed prices of the cars, a lower price for a specific car model makes it more likely a consumer visits the dealer selling that car, which leads to a negative relation between search costs and prices. Which of the three effects will dominate depends on the level of search costs as well as the level of competition. Both of these are determined at the model level, which explains why we find that simulated prices can be increasing for some car models when search costs go down, while decreasing for other cars. Selling different makes at same dealership Most of the 16 firms in our data own several brands. For instance, the Volkswagen Group owns Audi, Seat, Skoda, and Volkswagen, and the Toyota Group owns Daihatsu, Lexus, and Toyota. Whereas firms typically sell their brands in separate dealerships, in a setting where search frictions are important it might be beneficial to sell multiple brands at the same location.46 Although in the Netherlands most manufacturers sell their brand at separate, single-brand dealerships, some manufacturers let some (or all) of their brands be sold under one roof. For instance, Audi and Volkswagen are typically sold at the same dealership, just as BMW and Mini (both part of the BMW Group). To study the effects of retailing different brands within a single dealership on prices, market shares, and profits, we let all Toyota dealerships sell Lexus as well, while at the same time we eliminate the locations of the Lexus dealerships. In terms of the model this means that by visiting this combined Toyota-Lexus dealer, consumers observe relevant characteristics for all Toyota and 46

Moraga-Gonz´ alez and Petrikait˙e (2013) show that a firm that puts on display all its products unfolds the economies of search associated to one-stop shopping, which makes the firm more attractive for consumers and tends to increase profitability. However, a firm that stocks more products together increases competition with the rival firms and this tends to lower profits. Which of these effects dominates depends on the magnitude of search costs.

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Lexus models. Since Toyota has the most dense dealership network of the two brands, the number of dealers selling Lexus’ cars goes up substantially, from 13 to 141, which means that average search costs for Lexus go down considerably. Table 12 reports the simulated sales, market shares, prices, and variable profits of the major brands in our dataset after prices have been re-optimized following the change in Toyota’s dealership network. Although most manufacturers see a modest decline in sales following the change, sales for Lexus cars go up by 1,093 units, which is an increase of approximately 105 percent. Part of this increase in sales is due to Lexus cars becoming cheaper—as shown in the table, the average list price for Lexus cars decreases by e2,001. Since average list prices for cars sold by other manufacturers do not change much, this leads to additional sales for the Lexus brand, regardless of the shift in search costs. In fact, if prices are kept constant following the change in dealership networks, Lexus sales go up by 834 units, which suggests that the additional 259 units that are sold when prices are allowed to change is due to Lexus’ lower prices. Variable profits tell a similar story: they slightly decline for most manufacturers, while the Toyota Group profits go up by roughly 5.8 million. Notice that in this calculation we have ignored changes in the fixed costs associated to this business reorganization, as well as any possible changes in brand preferences for Lexus or Toyota following the changes. For instance, it could happen that consumers’ perception of the value of a Lexus car drops when it is sold in the same dealership as a Toyota car. To analyze this in more detail, we calculate how much mean utility for a Lexus car has to drop such that a dealership merger would no longer be profitable: if Lexus’ mean utility goes down by more than 0.643, variable profits for the Toyota Group will go down following the change. Using the average estimated price coefficient, this corresponds to a decrease in value of roughly e4,316. In the case of Lexus being sold at Toyota dealership, the change in dealership structure is quite dramatic: Lexus increases the number of selling points from 13 to 141. In general, having more dealers will improve sales, and will lead to higher variable profits. However, in some cases the change in dealership structure may make a brand worse off, despite having more dealership locations. For instance, as shown in Table 13, when letting all Nissan dealerships sell Dacia cars as well, while at the same time eliminating all Dacia locations, Nissan’s dealership structure is less favorable to Dacia’s old structure, resulting in higher prices, lower sales, and lower overall variable profits for the Renault-Nissan alliance.

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Table 12: Sales, market shares, and prices for new dealer network Group

sales (units) before after

BMW Daimler-Chrysler Fiat Ford Fuji General Motors Honda Hyundai Kia Mitsubishi Porsche PSA Peugeot Citroen Renault-Nissan Suzuki Toyota Daihatsu Lexus Toyota Volkswagen

18,587 14,771 24,821 68,746 1,422 49,962 8,479 17,433 12,236 7,805 531 64,389 52,334 14,547 49,227 9,186 1,044 38,997 84,294

18,556 14,747 24,794 68,644 1,420 49,899 8,469 17,409 12,219 7,792 533 64,305 52,269 14,527 50,203 9,170 2,137 38,895 84,179

3.80 3.02 5.07 14.04 0.29 10.20 1.73 3.56 2.50 1.59 0.11 13.15 10.69 2.97 10.05 1.88 0.21 7.97 17.22

489,584

489,964

100.00

Total

prices (e) before after

profits (mln e) before after

3.79 3.01 5.06 14.01 0.29 10.18 1.73 3.55 2.49 1.59 0.11 13.12 10.67 2.96 10.25 1.87 0.44 7.94 17.18

50,527 42,581 18,594 38,692 23,560 24,096 23,017 16,521 19,100 27,808 76,783 21,520 21,088 12,477 30,018 11,618 64,262 25,021 27,945

50,530 42,582 18,593 38,692 23,560 24,094 23,017 16,519 19,098 27,808 76,807 21,517 21,085 12,475 29,584 11,627 62,261 25,037 27,940

115.94 91.67 122.58 405.49 8.30 268.50 46.66 91.84 63.36 40.09 6.41 353.28 275.55 72.23 276.05 47.46 7.87 220.73 499.26

115.74 91.52 122.41 404.72 8.29 268.07 46.60 91.69 63.26 40.01 6.44 352.67 275.09 72.11 281.88 47.41 14.07 220.40 498.31

100.00

29,214

29,181

2,737.22

2,738.80

market shares (%) before after

Notes: Profits exclude fixed costs. Results are obtained using the estimates from specification (B) in Table 5.

Table 13: Sales, market shares, and prices for change in Renault-Nissan network Group

sales (units) before after

BMW Daimler-Chrysler Fiat Ford Fuji General Motors Honda Hyundai Kia Mitsubishi Porsche PSA Peugeot Citroen Renault-Nissan Dacia Nissan Renault Suzuki Toyota Volkswagen

18,587 14,771 24,821 68,746 1,422 49,962 8,479 17,433 12,236 7,805 531 64,389 52,334 4,549 10,259 37,526 14,547 49,227 84,294

18,606 14,778 24,848 68,777 1,423 49,990 8,484 17,455 12,253 7,815 531 64,440 51,688 3,875 10,247 37,566 14,565 49,267 84,340

3.80 3.02 5.07 14.04 0.29 10.20 1.73 3.56 2.50 1.59 0.11 13.15 10.69 0.93 2.10 7.66 2.97 10.05 17.22

489,584

489,260

100.00

Total

prices (e) before after

profits (mln e) before after

3.80 3.02 5.08 14.06 0.29 10.22 1.73 3.57 2.50 1.60 0.11 13.17 10.56 0.79 2.09 7.68 2.98 10.07 17.24

50,527 42,581 18,594 38,692 23,560 24,096 23,017 16,521 19,100 27,808 76,783 21,520 21,088 7,960 25,497 21,068 12,477 30,018 27,945

50,526 42,580 18,592 38,691 23,559 24,095 23,015 16,518 19,098 27,806 76,783 21,519 21,153 8,548 25,501 21,064 12,473 30,017 27,943

115.94 91.67 122.58 405.49 8.30 268.50 46.66 91.84 63.36 40.09 6.41 353.28 275.55 21.21 57.45 196.88 72.23 276.05 499.26

116.05 91.70 122.66 405.61 8.31 268.59 46.67 91.91 63.42 40.12 6.41 353.50 273.85 19.47 57.42 196.96 72.28 276.22 499.37

100.00

29,214

29,218

2,737.22

2,736.68

market shares (%) before after

Notes: Profits exclude fixed costs. Results are obtained using the estimates from specification (B) in Table 5.

56

7

Conclusions

In many markets consumers have imperfect information about the utility they get from the various alternatives available and have to engage in costly search to find out which products they prefer most. While the theoretical consumer search literature is well established, much less work exists trying to estimate demand and supply for environments in which consumer search is important. This paper has contributed to the literature by presenting and estimating a discrete choice model of demand with optimal sequential consumer search. While doing so, we have allowed for unobserved product heterogeneity as in BLP, which sets our paper apart from recent contributions on the theme. In our model consumers are initially unaware of whether a given product is a good match or not. Consumers search sequentially for differentiated products, taking into account their preferences for the various alternatives as well as the costs of searching them. The optimal strategy is to rank alternatives according to reservation utilities, visit the alternatives starting from the alternative with the highest reservation utility, and to stop searching when the highest observed utility exceeds the reservation utility of the next best alternative. To solve the model, we use recent findings from consumer search theory that re-characterize the search problem as a standard discrete choice problem (Armstrong, 2017; Choi, Dai, and Kim, 2016). Although the model can be estimated for arbitrary search cost distributions, we have shown that for specific assumptions on the search cost distribution we can obtain a closed-form expression for a consumer’s choice probability, which dramatically speeds up the estimation and has no major impact on the estimates of demand, elasticities and markups. We have provided various approaches to estimate the model and have applied them to the Dutch market for automobiles. We use distances from consumers to the nearest dealer of a specific brand as well as household characteristics reflecting the opportunity cost of time to specify consumer search costs. Even though versions of the model can be estimated using only aggregate data such as market shares, product characteristics, and consumer and dealer locations, we have supplemented the data with a survey on actual dealer visits for a large number of respondents, which allows us to add more search cost covariates, strengthen the identification, and improve the precision of the estimates. The survey reveals that consumers conduct a rather limited amount of search before buying. Moreover, a great deal of the searches involves test-driving a car. Our estimation results have shown that search costs are both significant and economically meaningful. Assuming, instead, that search frictions are negligible and consumers have full information results in higher (absolute) own-price

57

elasticity estimates, as well as lower estimated percentage markups. According to our estimates, the price of the average car is approximately e914 higher than in the absence of search frictions. In line with recent theoretical work, we have argued that the effects of lower search costs in a market are potentially ambiguous. On the one hand, lower search costs result in more search and thereby lead to stronger pressure on firms to cut prices. On the other hand, lower search costs make it easier for a firm to enter the search set of a consumer, which weakens the incentives of firms to cut prices. Finally, higher search costs push some inelastic consumers out of the market which changes the overall elasticity of demand. In our application we have found that prices can go up for some car models when moving from a search model to a full information model. Finally, we have investigated the effects of changes in the way car manufacturers use their dealership networks to retail their cars. Intuition suggests that the effect of retailing more car brands within a dealership on prices and profits is likely to be ambiguous. On the one hand, if a firm offers more cars at a dealership, this dealership becomes more attractive for consumers because of the implied economies of search associated with one-stop shopping. This demand effect tends to increase prices and variable profits. However, if a firm chooses to offer more cars at its dealerships then rival firms need to be more aggressive if they wish to enter consumer search sets. This competition effect tends to lower prices and decrease variable profits. For the case of the Dutch market, we have found that if Toyota started to sell Lexus cars in all its dealerships, then prices of Toyota cars would go down on average but demand for Toyota’s products would expand sufficiently so as to increase Toyota’s group variable profits. The picture is quite different if the Renault-Nissan group started to retail Dacia’s cars at all Nissan dealerships. In this case, the prices of Renault-Nissan’s cars would increase but demand fall would be so strong that variable profits of the group would decrease. One of the limitations of our model is that we are mostly ignoring the vertical structure of the market. For instance, our model does not take bargaining between the car dealership and the consumer into account. We only observe list prices in our data and our survey data only allows us to observe whether a consumer visited a dealership of a specific brand, which makes it difficult to infer whether the consumer visited a dealer to learn more about the characteristics of a car or to bargain for a better price. We leave it to future work to focus more on this aspect of the market.47 Another interesting vertical aspect of this market which we leave for future work is how the network of dealerships is determined, especially when search frictions are important. 47 In recent work, D’Haultfœuille, Durrmeyer, and F´evrier (2015) develop a full information BLP-type model that includes bargaining and can be estimated using aggregate data even when transaction prices are not observed.

58

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63

APPENDIX A

Proof of Lemma 1

Rewrite Hif as follows: Z

∞

(z − r)dF (z − δif ).

Hif (r) = r

Using the change of variables t = z − δif , we get Z

∞

(t − (r − δif ))dF (t).

Hif (r) = r−δif

Notice that the right-hand side of this expression is just H0 (r − δif ). Now, recall that rif solves −1 (c). Because Hif (r) = H0 (r − δif ), then rif − δif = H0−1 (c) and the Hif (r) = c, so that rif = Hif

result follows.

B

Derivation of the Probability of Searching Once

We first note that: vi1 =

X

Pr ui0 < max {rik } and max {ui0 , uif } > max {rik } and rif > max {rik } . k6=0

f

=

X

k6=0,f

X

X

Pr ui0 < rif and uif > ui0 and uif > max {rik } and rif k6=0,f

k6=0,f

X

X

Pr ui0 < rif and uif > ui0 and uif > max {rik } and rif k6=0,f

Pr ui0 > uif and rif

f

+

X

X f

> max {rik } k6=0,f

> ui0 > max {rik } k6=0,f

Pr max {rik } < ui0 < rif and uif > ui0 and rif k6=0,f

f

+

k6=0,f

Pr ui0 > uif and rif > ui0 > max {rik }

f

=

> max {rik }

f

+

k6=0,f

f

=

k6=0,f

Pr ui0 > uif and rif > ui0 > max {rik } and rif > max {rik }

f

+

k6=0,f

> max {rik }

Pr ui0 < max {rik } and uif > max {rik } and rif k6=0,f

k6=0,f

64

k6=0,f

> max {rik } . k6=0,f

The sum across f appears because the first searched option can be any of the dealerships. We can simplify this to vi1 =

X

Pr ui0 < rif and max rik < ui0 k6=0,f

f

+

X

Pr ui0 < max rik and max rik < uif and max rik < rif . k6=0,f

f

k6=0,f

k6=0,f

This probability can be written as vi1 =

XZ

r 1 − Fifr (y) Fi,−f (y)f (y)dy

−∞

f

+

∞

XZ f

∞

−∞

r (x)dx, F (x) (1 − Fif (x)) 1 − Fifr (x) fi,−f

r r are the CDF and PDF of maxk6=0,f rik . Note that by equation (10), and fi,−f where Fi,−f

Z

∞

−∞

r (x)dx = F (x) (1 − Fif (x)) 1 − Fifr (x) fi,−f

Z

∞

−∞

r (x)dx, F (x) 1 − Fifw (x) fi,−f

and by integration by parts Z

∞

F (x) 1 − −∞

Fifw (x)

r (x)dx fi,−f

Z

∞

= −∞

r (x) F (x) 1 − Fifw (x) dFi,−f

Z ∞ r (x)d F (x) 1 − Fifw (x) =− Fi,−f Z ∞ Z ∞−∞ r w r (x)f (x)dx, 1 − Fifw (x) Fi,−f = Fi,−f (x)F (x)fif (x)dx − −∞

−∞

where we use w d F (x) 1 − Fifw (x) = f (x) 1 − Fifw (x) − F (x)fif (x). We finally get that vi1 =

XZ f

∞

−∞

Fifw

(y) −

Fifr (y)

r Fi,−f (y)f (y)dy

+

XZ f

∞

−∞

r w Fi,−f (x)F (x)fif (x)dx.

r r where Fi,−f and fi,−f are the CDF and PDF of maxk6=0,f {rik }.

The share of consumers searching only one time is then given by Z q1 =

vi1 dFτ (τi ).

65

(A33)

where τi contain the random coefficients and the Gumbel variables.

C

Market Share Derivatives

Own-price derivatives The market share derivative with respect to price is given by ∂sj = ∂pj

Z

∂sij dFτ (τi ); ∂pj Z ∂sij dFτ (τi ); = −αi ∂δij

The derivative of the buying probability sij with respect to δij is ∂Pij|f ∂Pif ∂δif ∂sij = Pij|f + Pif ; ∂δij ∂δif ∂δij ∂δij ∂Pif 2 P + sij (1 − Pij|f ); = ∂δif ij|f The derivative of Pif with respect to δif is given by ∂Pif = ∂δif

Z

Y

Figw (z)

g6=f

w (z) ∂fif

∂δif

dz.

The density of w is given by c w (Hif (z))(1 − Fif (z))2 + Fifc (Hif (z))fif (z). (z) = fif fif

w with respect to δ Using ∂Hif (z)/∂δif = 1 − Fif (z), the derivative of fif if is given by w ∂fif

∂δif

0c c = fif (1 − Fif )3 + 3fif (1 − Fif )fif + Fifc fif (1 − exp(δif − z)),

c and F c are evaluated at H (z), and f and F are evaluated at z. Note that when the where fif if if if if 0c = f c · (µ − H (z)), where µ is the mean parameter of search cost distribution is normal then fif c c if if

the search cost distribution.

66

Cross-price derivatives The market share derivative of product j with respect to the price of product k is given by ∂sj = ∂pk

Z

∂sij dFτ (τi ); ∂pk Z ∂sij dFτ (τi ); = −αi ∂δik

If product k is sold by firm f , the derivative of the buying probability sij with respect to δik is ∂Pij|f ∂Pif ∂δif ∂sij = Pij|f + Pif ; ∂δik ∂δif ∂δik ∂δik ∂Pif P P − sij Pik|f . = ∂δif ik|f ij|f If product k is sold by another firm, the derivative of the buying probability sij with respect to δik is ∂Pif ∂δih ∂sij = P ; ∂δik ∂δih ∂δik ij|f ∂Pif = P P . ∂δih ik|h ij|f The derivative of Pif with respect to δih is given by ∂Pif = ∂δih

Z

Y

g6=f,h

w

∂Fih (z) w f (z)dz. Figw (z) ∂δih if

w with respect to δ is given by The derivative of Fih ih w ∂Fih c c = −fih (1 − Fih )2 − Fih fih (z); ∂δih w = −fih .

D

Contraction Mapping

Contraction Theorem (BLP). Let f : RJ → RJ be defined as fj (ξ) = ξj + log sj − log σj (ξ) ,

67

j = 1, . . . , J,

where s = (s1 , . . . , sJ ) is the vector of observed market shares and suppose that the market share vector σ (ξ) as a function of ξ = (ξ1 , . . . , ξJ ) ∈ RJ satisfies the following conditions. 1. σ is continuously differentiable in ξ and ∂σj ∂σj (ξ) ≤ σj (ξ) , (ξ) < 0 for any j, k 6= j and ξ ∈ RJ , ∂ξj ∂ξk (the former is equivalent to the fact that the function σ j : RJ → R, σ j (ξ) = σj (ξ) exp (−ξj ) is decreasing in ξj ) and J X ∂σj k=1

∂ξk

(ξ) > 0 for any ξ ∈ RJ .

2. The share of the outside alternative σ0 (ξ) = 1 −

PJ

j=1 σj

(ξ) is decreasing in all its arguments

and it satisfies that for any j and x ∈ R the limit lim

ξ−j →−∞

σ0 (ξ1 , . . . , ξj−1 , x, ξj+1 , . . . , ξJ ) ≡ σ e0j (x)

is finite and the function σ e0j : R → R obtained as the limit satisfies that lim σ e0j (x) = 1 and

x→−∞

lim σ e0j (x) = 0,

x→∞

where ξ−j → −∞ means that ξ1 → −∞, . . . , ξj−1 → −∞, ξj+1 → −∞, . . . , ξJ → −∞. 3. The function σ j defined in Condition 1 satisfies lim σ j (ξ) > 0.

ξ→−∞

J Then there are values ξ, ξ ∈ R such that the function f : ξ, ξ → RJ defined by f j (ξ) = J J min ξ, fj (ξ) has the property that f ξ, ξ ⊆ ξ, ξ , is a contraction with modulus less than 1 with respect to the sup norm k(x1 , . . . , xJ )k = maxj |xj |, and, in addition, f has no fixed point J outside ξ, ξ . Here we verify that conditions 1, 2, and 3 of this theorem are satisfied for σ equal to the market R share vector function s = (s1 , . . . , sJ ), where sj = sij dFτ (τi ), j = 1, . . . , J, in the case specified 68

in Section 3.4. Note that equation (21) implies that si0 =

1 1+

PJ

k=1 exp (δik

(A34)

− µig )

and the derivatives ∂sij ∂ξj ∂sj ∂ξj

∂sij ∂si0 = (1 − sij ) sij , = −sij si0 , = −sik sij for j 6= k, ∂ξk ∂ξj Z Z Z ∂sj ∂s0 = (1 − sij ) sij dFτ (τi ), = − sij si0 dFτ (τi ). (A35) = − sij sik dFτ (τi ), ∂ξk ∂ξj

Condition 1. Clearly the market share vector s is continuously differentiable in ξ. We can see R ∂s ∂s ∂s that ∂ξjj ≤ sj holds because ∂ξjj − sj = − s2ij dFτ (τi ) ≤ 0. The inequality ∂ξkj < 0 holds obviously. P ∂s The third inequality, Jk=1 ∂ξkj > 0 follows by observing that J X ∂sj k=1

∂ξk

=

J X ∂sk k=1

∂ξj

=−

∂s0 , ∂ξj

which is positive by equation (A35). Condition 2. The fact that the share of the outside alternative s0 = 1 −

PJ

j=1 sj

is decreasing

in all its arguments follows from equation (A35). Next we compute the limit lim

ξ−j →−∞

s0 (ξ1 , . . . , ξj−1 , x, ξj+1 , . . . , ξJ ) ≡ sej0 (x) .

From equation (A34) we see that sej0 (x) =

1 1 + exp (δij (x) − µig )

,

where δij (x) denotes the expression δij where ξj is replaced by x. From this it is straightforward to obtain that limx→−∞ sej0 (x) = 1 and limx→∞ sej0 (x) = 0. Condition 3. We show that limξ→−∞ sj (ξ) exp (−ξj ) > 0. We have Z lim sj exp (−ξj ) =

ξ→−∞

lim sij exp (−ξj ) dFτ (τi ).

ξ→−∞

69

Further, from equation (21) we have

sij exp (−ξj ) =

exp αi pj + x0j βi − µif 1+

J X

,

exp (δik − µig )

k=1

so the numerator does not depend on ξj for any j = 1, . . . , J. Therefore, lim sj exp (−ξj ) = exp αi pj + x0j βi − µif ,

ξ→−∞

which is strictly positive. In conclusion, the contraction property holds.

E

Micro Moments

In order to describe the computation of the micro moments it is useful to introduce some notation. Suppose that we observe the demographic characteristics and purchase decisions of N consumers. Let i ∈ {1, . . . , N } and for simplicity maintain the notation vi for the vector of consumer i’s unobserved and observed characteristics (i.e., Vi = diag (vi )). Denote by ai ∈ {0, 1, . . . , J} the choice of i, yi the income of i and ri a discrete demographic characteristic of i out of the vector di of all demographic characteristics, like age or family size. In order to be general we use a generic demographic characteristic qi for either yi or ri , and let R be a partitioning of the possible values of qi into a few (two or three) subsets. Let T denote a certain group of products, like family car. We consider micro moments based on the following type of conditional expectations: E [1 (ai ∈ T ) |qi ∈ Rk ] , k = 1, 2 where R = {R1 , R2 } . For specific examples we refer to Section 5. Let R ∈ R. Since we observe the choice of each consumer i ∈ {1, . . . , N }, the micro moments boil down to aggregation of the choice aiT of i regarding T over those consumers i whose demographic characteristic satisfies that qi ∈ R, where

aiT

1 = 0

if ai ∈ T otherwise.

70

Note that aiT is a Bernoulli random variable with success probability siT (θ) = P (aiT = 1|p, x, θ, ξ, vi ) = P (ai ∈ T |p, x, θ, ξ, vi ) =

X

P (ai = j|p, x, θ, ξ, vi ) =

j∈T

X

sij

j∈T

and independent across i conditional on (p, x, θ, ξ, vi ). Therefore, E [aiT |p, x, θ, ξ, vi ] = siT (θ) //var [aiT |p, x, θ, ξ, vi ] = siT (θ) (1 − siT (θ)) .

(A36)

Aggregation over i s.t. qi ∈ R yields the moment N 1 X (aiT − siT (θ)) , = NR

gqR (θ)

(A37)

i=1 qi ∈R

where NR is the number of consumers i for which qi ∈ R. This is just the sample counterpart of the moment condition E [aiT − siT (θ) |p, x, θ, ξ, vi ] = 0 over the sample of consumers i with qi ∈ R.

F

The Weighting Matrix

The optimal choice of Ξ is a matrix proportional to

//var g θ

0

−1

h i−1 0 0 0 = E g θ g θ ,

where θ0 is the true value of the parameter vector θ. Since the micro moments depend on the demand unobserved characteristics ξ, this weighting matrix is not a block diagonal in general. Several components of this matrix can be computed exactly; for example, the variances of the micro moments (see equation (A36)). However, several other components cannot be computed exactly. Therefore, in order to obtain a positive definite weighting matrix, we propose this matrix to be approximated as Ξ=

VJ θˆ 0

71

−1 0 , VN θˆ

where θˆ is a previously obtained consistent estimator of θ0 , VJ θˆ =

2J 0 1 X 0 ˆ 0 ˆ − gJ θˆ ˆ Z ψ θ − g θ Z ψ θ , j j J j j (2J)2 j=1

and VN θˆ is a diagonal matrix whose main diagonal contains the variances of the micro moments computed as in equation (A36). Alternative choices for Ξ are Ξ = I (the identity matrix) or Ξ=

(Z 0 Z)−1

0

0

IM

where IM is the identity matrix of dimension M , which is the number of micro moments.

72

Consumer Search and Prices in the Automobile Market∗ Jos´e Luis Moraga-Gonz´alez† Zsolt S´andor‡ Matthijs R. Wildenbeest§ November 2017
Abstract In m...