Measuring the Welfare of Intermediaries
Abstract
We investigate the welfare of intermediaries in oligopolistic markets where intermediaries offer additional services. We exploit the unique circumstance that in the empirical setting studied, outdoor advertising, consumers can purchase from manufacturers or intermediaries. Intermediaries provide additional services to the consumers and charge a margin for them. Intermediaries provide the following additional services: search services (information about products), purchaseaggregation services (access to quantity discounts), and consulting services. We specify an equilibrium model and structurally estimate it using marketlevel data. The demand includes consumers with costly search and channelspecific preferences. The supply includes two distribution channels. One features bargaining about wholesale prices between manufacturers and intermediaries and downstream price competition. The other is vertically integrated. We show how Google search data can be used to identify the searchcost parameters. We use the estimated model to simulate counterfactual scenarios where intermediaries do not offer additional services. We find that the three services considered provide value to consumers, with search playing a prominent role. Our analysis helps explain why intermediaries are ubiquitous in modern economies despite the double marginalization.
This paper was accepted by Matthew Shum, marketing.
Funding: The authors acknowledge the allocation of computing time from the Ohio Supercomputer Center [Grant PAS13502]. This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. This work was also supported by Fundação para a Ciência e a Tecnologia [Grant UIDB/00315/2020].
Supplemental Material: The data files and online appendix are available at https://doi.org/10.1287/mnsc.2021.4266.
1. Introduction
Intermediaries play an important role in contemporary economies. In the United States, they represent over onethird of the value added to the economy.^{1} They provide a wide variety of services to consumers. Intermediaries often add value by transforming products (adding transportation, packaging, or assembling services) or by providing information and consulting services about the characteristics of the products sold by the manufacturers (Spulber 1996). Intermediaries improve welfare to consumers by reducing search frictions, thus improving the coordination of the actions of consumers and manufacturers (Rubinstein and Wolinsky 1987). When negotiating with a manufacturer, intermediaries centralize transactions of multiple consumers, thus supplanting consumers’ decentralized bargaining with the manufacturer. The resulting increase in intermediaries’ bargaining power translates into lower marginal costs for the intermediaries, which results in lower prices for the consumers. In the absence of market power, intermediaries improve consumers’ welfare when they provide these additional services (Spulber 1999). However, as noted by Salinger (1988), when market power is present intermediaries may also lead to double marginalization, whereby the product is marked up above the marginal cost of production twice: once by the manufacturer and once again by the intermediary.^{2} In such cases, intermediaries may reduce welfare. A natural question arises: What are the welfare implications of intermediaries in oligopolistic markets where intermediaries offer additional services to differentiate their products from the ones of the manufacturers?
There is a vast literature studying the role of intermediaries. Two major explanations why intermediaries arise are to facilitate the matching of buyers and sellers and to guarantee quality. There is also a large empirical literature studying specific roles of intermediaries in many markets, such as online markets, twosided platforms, financial markets, banking, asset pricing, labor markets, and facilitating trade. However, there has been little empirical work to address the central question of what are the overall welfare implications of intermediaries when they offer additional services to differentiate their products from the ones of the manufacturers. Yet, ignoring these additional services has significant consequences on the theoretical and empirical predictions for the determination of prices and consumer choices in these markets.
We provide empirical estimates of the welfare of intermediation in vertical markets when intermediaries simultaneously provide consulting, search, and purchaseaggregation services. There are two major challenges to identifying the value of intermediaries in such cases. The first challenge arises because of the nonexistence of a counterfactual scenario without intermediaries in industries where intermediaries are present.^{3} It precludes evaluating the performance of the market without intermediaries. The second challenge arises because of the difficulty of observing all the transactions between manufacturers, intermediaries, and consumers in the industry. It may introduce a selection problem when evaluating the behavior of the unobserved participants. Recovering consumer demand preferences in both cases requires strong assumptions about market participants.
To address these issues, we collected a novel data set with all meaningful transactions among manufacturers and intermediaries in the Portuguese outdoor advertising industry for the year 2013. These data allow us to exploit two unique features of the industry to quantify the welfare effects of intermediaries. First, there are two distribution channels in the outdoor advertising industry. Consumers may purchase the product directly from manufacturers or through intermediaries. This feature helps us overcome the first challenge by comparing instances where the same combination of display format—the physical products in the industry studied—and manufacturer is sold in both distribution channels. We then use a model of conduct to compute the counterfactual value that the consumer would have obtained had the purchase been made in a distribution channel different from the one observed. Second, we collected marketlevel data directly from all the meaningful manufactures and intermediaries in the industry. The data encompass more than 95% of the volume of transactions in the industry. This feature helps us overcome the second challenge.
To quantify the value of intermediation we develop an econometric model of the industry. The model features two distribution channels where consumers may buy advertising: the direct sales channel (DSC), where consumers purchase directly from the manufacturers, and the vertical sales channel (VSC), where consumers purchase using the intermediaries. On the demand side, consumers have preferences that are specific to each distribution channel and engage in costly search. We use a randomcoefficient nestedlogit model with costly search. Crucially, our model allows for consumers to endogenously choose which channel they prefer to use, based on their idiosyncratic characteristics, such as price sensitivity and unobserved channelspecific shocks. The latter is introduced via withinchannel correlation of the different productlevel utility shocks. It captures, for example, that some customers—firms that demand advertising to promote their products in the industry studied—may have larger inhouse marketing departments and, therefore, obtain less value from the services provided by intermediaries to design the advertising campaign. On the supply side, the industry consists of two vertical layers modeled using a twostage game. In the top layer, manufacturers produce display formats for the display of outdoor advertising (manufacturer products) that they sell to the intermediaries at wholesale prices. Manufacturers and intermediaries bargain over wholesale prices through Nash bargaining. We call the top layer the manufacturer game. In the second layer, manufacturers and intermediaries sell the display formats (final products) to the consumers, competing on prices. We call the bottom layer the retail game. The distribution channels are represented by two types of retailers: DSC and VSC retailers. The DSC retailers are the manufacturers who sell final products to the consumers charging DSC prices. The VSC retailers are the intermediaries who charge VSC prices to the consumers.^{4}
We estimate the model in two steps. First, we estimate the parameters that characterize demand without using the supplyside model. To identify the price coefficient and the heterogeneity parameters we rely on instruments with exclusion restrictions. To identify the searchcost parameters, we construct additional micro moments using Googlesearch data. We then estimate the parameters that characterize supply conditional on the demand estimates from the first step. To identify the supplyside parameters, we use the equilibrium conditions from the model and additional restrictions using the vertical structure in our empirical setting. We use the firstorder conditions from the manufacturer and retail games and assume that the manufacturer marginal costs are the same for display formats sold to VSC retailers and consumers.
Our strategy to estimate the welfare implications of intermediaries consists of comparing circumstances where the same combination of display format and manufacturer is sold by DSC and VSC retailers and using the model to estimate the value to consumers of each of the additional services provided by the VSC retailers. The VSC retailers provide three additional services to consumers. They charge a margin for them. The first additional services are search services, whereby VSC retailers provide information to consumers about display formats from multiple manufacturers, thus decreasing consumers’ search costs. The second are purchaseaggregation services, whereby consumers benefit from quantity discounts that VSC retailers obtain because they aggregate purchases from multiple consumers. The third are consulting services, defined as the residual gross utility of buying from VSC retailers relative to a DSC retailer. The market structures in the vertical layers determine the prices and margins charged by the manufacturers and retailers.
We use the estimated equilibrium model to simulate four counterfactual scenarios to quantify the value of intermediaries. First, we simulate the equilibrium of an industry where retailers do not offer consulting services. Second, we simulate the equilibrium of an industry where retailers do not offer search services. Third, we simulate the equilibrium of an industry where retailers do not offer purchaseaggregation services. Finally, we remove simultaneously the three types of services to evaluate the total impact on welfare due to the intermediaries.
We report the following findings: (1) removing consulting services reduces consumer surplus by one Euro per square meter; (2) removing search services increases the overall cost of the search by 35%, which translates into a reduction of consumer surplus of 12 Euros per square meter; (3) removing purchaseaggregation services increases retail prices, which translates into a reduction of consumer surplus of two Euros per square meter; and (4) removing simultaneously the three services provided by intermediaries increases consumer surplus by 14 Euros per square meter. Overall, we find that the presence of intermediaries increases welfare because the value of their services outweighs the additional margin charged.
In summary, we make three main contributions. First, we combine a novel data set with a new econometric equilibrium model to estimate consumer demand preferences and marginal costs in the presence of intermediation, consumers’ costly search, and bargaining between manufacturers and intermediaries. The model includes consumers who have preferences that are specific to each distribution channel and engage in costly search on the demand side, and two layers of activity with two distribution channels on the supply side. Second, we quantify the value of intermediaries in oligopolistic markets where intermediaries offer these additional services to differentiate their products from the ones of the manufacturers. Finally, from a normative perspective, our estimates show that the presence of intermediaries in the outdoor advertising industry is welfare improving because the benefits to consumers from the additional services provided by the intermediaries outweigh the additional margin charged by the intermediaries.
1.1. Related Literature
We contribute to the literature that studies intermediaries. Spulber (1999) presents a comprehensive study of intermediation, including how intermediaries alleviate problems associated with search costs and a detailed discussion of additional services provided by intermediaries. The role of firms as intermediaries has been studied extensively. Articles include, for example, Yanelle (1989), Gehrig (1993), Rust and Hall (2003), Hagiu and Jullien (2011), Wright and Wong (2014), and Edelman and Wright (2015). Some explanations why intermediaries arise are to facilitate the matching of buyers and sellers as in Rubinstein and Wolinsky (1987), to guarantee quality as in Biglaiser (1993) and Spulber (1996), and, recently, as rent extraction (Farboodi et al. 2017). Our case is closest to that in Rubinstein and Wolinsky (1987) and Spulber (1995, 1999) in that intermediaries create value by reducing search costs and by providing additional services to the consumers.
The role of intermediaries has been studied in many markets. There is a large literature studying the role of intermediaries in online markets (Brynjolfsson and Smith 2000, Morton et al. 2001, Brown and Goolsbee 2002, Brynjolfsson et al. 2003, Baye et al. 2003, Ellison and Ellison 2009, Quan and Williams 2016),^{5} and in financial markets, banking, and asset pricing (Diamond 1984, James 1987, He and Krishnamurthy 2013, Brunnermeier and Sannikov 2014, Gavazza 2016).^{6} Intermediation also plays an important role in labor markets (Stanton and Thomas 2016), agrifood chains (Lee et al. 2012), facilitating trade (Ahn et al. 2011), and certifying information in markets with adverse selection (Biglaiser 1993, Lizzeri 1999, Biglaiser et al. 2017). Relative to these articles, our contribution is to estimate the welfare implications of intermediaries in the industry, accounting for the change in the market structure created by the presence of the intermediaries and the additional services that intermediaries offer to consumers which differentiates their products from the ones of the manufacturers. The literature studying outdoor advertising is nonexistent. The only articles that we are aware of are Pereira and Ribeiro (2018), who study capacity divestitures in this industry, and Donna et al. (2021), who study how a directtoconsumer channel enhances the manufacturer’s bargaining power; these articles do not study intermediation.
Our demand model is related to the literature that uses models of discrete choice between differentiated products with costly search.^{7} Our demand model is closest to De los Santos et al. (2012), Honka (2014), and MoragaGonzález et al. (2015).^{8} They develop discretechoice models of demand in which consumers engage in costly search with fixedsample size.^{9} None of these papers consider preferences specific to the distribution channel, which is the main focus of this article.^{10} We incorporate these preferences using the distribution assumptions of the nested logit that we embed into a randomcoefficient discretechoice demand model with costly search.^{11} For the estimation of the demand, we use an adapted version of the procedure proposed by MoragaGonzález et al. (2015). This procedure adapts the nested fixedpoint algorithm from Berry (1994) and Berry et al. (1995) to account for the additional term in the choice probability introduced by the distributionchannel preferences. It modifies the computation of the market share function in the estimation algorithm.
On the supply side, our model is related to the literature about vertical relations between manufacturers and intermediaries/retailers. Our model features two layers of activity (manufacturers and VSC retailers) and two distribution channels, where consumers can purchase (VSC and DSC retailers). The two layers of activity are related vertically as in, for example, Brenkers and Verboven (2006), Mortimer (2008), Bonnet and Dubois (2010), VillasBoas (2007), and Dubois and Sæthre (2016). The main difference between these articles and ours is that in our model, manufacturers and VSC retailers bargain over wholesale prices through Nash bargaining.^{12} Our bargaining model is similar to, for example, Crawford and Yurukoglu (2012), Draganska et al. (2010), Grennan (2013), Crawford et al. (2021), and Noton and Elberg (2018). The main difference between the bargaining models in these articles and ours is that in our model the retailers in both distribution channels can sell their products to the consumers. Such sales occur in our model after the bargaining process, where prices are set to consumers through Bertrand competition. Thus, the instruments and identifying assumptions to recover equilibrium margins as a function of the demand primitives, and bargaining power of VSC retailers and manufacturers are different. As in Grennan (2013), we do not estimate all bargaining and cost parameters because we do not have enough information. Similar to our article, the model in Donna et al. (2021; DPTY) features both directtoconsumer sales by manufacturers and bargaining between manufacturers and retailers. The main focus of DPTY, however, is the supply side. The central feature in the model of DPTY is that a directtoconsumer channel enhances the manufacturer’s bargaining power, which can harm retail consumers. In contrast, our main focus here is the demand side to estimate the value of intermediaries to consumers.
The rest of the article is organized as follows. Section 2 describes the industry, the data, and presents stylized facts about the industry. Section 3 presents the model. Sections 4 and 5 discuss identification and estimation of the demand and supply, respectively. Section 6 presents the estimation results. The welfare analysis is performed in Section 7. Section 8 presents the concluding remarks. Appendix A extends the search model to allow for unobserved searchcost heterogeneity. Robustness analysis, extensions, and details about the data and the model are in the online appendix.
2. Portuguese Outdoor Advertising Industry
2.1. Industry Overview
2.1.1. Agents.
There are three main economic agents in the Portuguese outdoor advertising industry: manufacturers, retailers, and consumers. A manufacturer, also called media owner, is a firm that installs and commercially exploits equipment for the display of outdoor advertising. Examples include J.C. Decaux Group, Cemusa, and Mop. A retailer, also called media group, is an intermediary that buys advertising from the manufacturer on behalf of the consumer. Examples include Omnicom Media Group, WPP Plc., and Power Media Group Inc. Retailers offer consumers additional services such as consulting services, advertising planning campaigns, and information about the display formats of several manufacturers.^{13} All manufacturers and retailers operate in the same geographic market. This feature follows from Portugal being a small country, where the population is concentrated along the coast.^{14} A consumer, also called advertiser, is a firm that demands advertising to promote its products. Consumers in this industry are firms that buy exposure in the manufacturer’s advertisement network.^{15} For example, consumers buy 200 panels of 2m^{2} panels (called faces) distributed in the national network of J.C. Decaux Group. They cannot choose, however, specific 2m^{2} panels located at a particular place. Most of the purchases are in the national network, which is the focus of this article. The exposition is similar across manufacturers.
2.1.2. Vertical Relations.
Consumers make 85% of their purchases from the retailers and the remaining 15% directly from the manufacturers (Table 1). There are two active distribution channels. In the VSC, consumers purchase manufacturers’ display formats through the intermediation of retailers. In the DSC, consumers purchase manufacturers’ display formats directly from the manufacturers. We refer the manufacturers that sell directly to consumers in the DSC as DSC retailers and to the retailers in the VSC as VSC retailers. We refer to the price charged to the consumers by the DSC retailers (VSC retailers) as DSC price (VSC price or retail price). Figure 1 displays the vertical relations in the industry. Advertisers’ choice of the distribution channel is determined by their advertising needs, which may or may not be related to the size of their firm. The two channels offer different services. The direct channel offers a basic service. The intermediated channel offers the basic service plus additional services, such as consulting. Firms that advertise only occasionally or that make simple campaigns typically use the direct channel. Firms that advertise frequently or make elaborate campaigns, that require complex planning, typically use the intermediated channel.

Sales Percentage to Consumers by Manufacturer, Retailer, and Product
Panel A: Sales to consumers by manufacturer and retailer (as percentage of total sales)  

Seller  Manufacturer  Total  
m_{1}  m_{2}  m_{3}  m_{4}  
VSC retailers  ${r}_{4}^{v}$  1.06  2.34  0.63  2.34  6.36  
${r}_{5}^{v}$  0.54  1.24  0.66  0.96  3.41  
${r}_{6}^{v}$  3.31  5.35  1.26  5.32  15.25  
${r}_{7}^{v}$  1.43  4.61  1.68  13.53  21.25  
${r}_{8}^{v}$  0.18  1.36  0.37  –  1.91  
${r}_{9}^{v}$  6.97  23.86  5.86  0.30  37.00  
DSC retailers  ${r}_{1}^{d}$  1.51  –  –  –  1.51  
${r}_{2}^{d}$  –  8.79  –  –  8.79  
${r}_{3}^{d}$  –  –  4.52  –  4.52  
Total  15.01  47.56  14.98  22.45  100.00 
Panel B: Sales to consumers by manufacturer, retailer, and display type (as percentage of total sales)  

Seller  2m^{2} panel  Senior  Other  Total 3  Total 4  
m_{1}  m_{2}  m_{3}  m_{4}  m_{1}  m_{2}  m_{3}  m_{4}  m_{1}  m_{2}  m_{3}  m_{4}  
VSC retailers  ${r}_{4}^{v}$  1.06  0.94  0.24  –  –  1.40  0.10  –  –  –  0.29  2.34  6.36  85.18  
${r}_{5}^{v}$  0.54  1.10  0.28  –  –  0.14  0.22  0.17  –  –  0.16  0.79  3.41  
${r}_{6}^{v}$  3.31  3.20  0.97  1.39  –  2.15  0.19  –  –  –  0.10  3.93  15.25  
${r}_{7}^{v}$  1.43  3.42  0.68  0.28  –  1.06  0.45  –  –  0.13  0.55  13.25  21.25  
${r}_{8}^{v}$  0.18  0.22  –  –  –  1.10  0.16  –  –  0.04  0.21  –  1.91  
${r}_{9}^{v}$  6.93  17.55  3.79  0.10  0.03  5.82  0.53  0.15  0.01  0.49  1.55  0.06  37.01  
DSC retailers  ${r}_{1}^{d}$  1.51  –  –  –  –  –  –  –  –  –  –  –  1.51  14.83  
${r}_{2}^{d}$  –  5.10  –  –  –  3.49  –  –  –  0.21  –  –  8.80  
${r}_{3}^{d}$  –  –  1.61  –  –  –  0.21  –  –  –  2.70  –  4.52  
Total 1  14.97  31.54  7.56  1.77  0.03  15.17  1.86  0.32  0.01  0.87  5.56  20.36  100  
Total 2  55.84  17.37  26.80  100 
Notes. Each cell in Panels A and B corresponds to the percentage of sales to consumers (relative to the total sales’ volume to consumers sold in year 2013 in the whole sample) by the corresponding combination of (1) Manufacturer and Seller in Panel A and (2) Manufacturer, Seller, and Display Format in Panel B. Thus, in each panel, all the numbers sum to 100 (excluding the rows and columns labeled as “Total”). A cell displays the symbol “–” when no sales are observed for such combination. In Panel B, there are a total of 57 cells with positive sales (i.e., without the symbol “–”), that corresponds to the 57 inside products (see Endnote 16). In Panel B, “Total 1” refers to the total sum by manufacturer m_{i}, $i=1,\dots ,4$, “Total 2” refers to the total by display format (2m^{2} panel, Senior, and Other), “Total 3” refers to the total sum by retailer ${r}_{j}^{v},\hspace{0.17em}j=4,\dots ,9$ and ${r}_{j}^{d}$, j = 1, 2, 3, “Total 4” refers to the total by VSC retailers (i.e., sum over ${r}_{j}^{v},\hspace{0.17em}j=1,\dots ,6$) and by DSC retailers (i.e., sum over ${r}_{j}^{d}$, j = 1, 2, 3). “DSC” stands for Direct Sales Channel. “VSC” stands for Vertical Sales Channel. See Figure 1 for definitions of prices and vertical relations in the industry.
2.1.3. Retailers’ Services.
Retailers provide three main services to the consumers in this industry. First, they provide consulting services. Retailers assist consumers with their advertisement campaigns by helping them to make decisions such as the type and number of display formats to buy (i.e., type and the total number of panels) and the duration of the advertising campaign. Second, retailers provide purchaseaggregation services to the consumers. Retailers negotiate rebate scales with manufacturers. Retailers aggregate the purchases from multiple consumers when buying from the manufacturers. These discounts are partially transferred to the consumers (Section 2.3). Retailers aggregate the purchases of many advertisers. It gives retailers larger bargaining power to negotiate with the manufacturers, enabling them to obtain lower prices per unit relative to the consumers (i.e., quantity discounts as defined in Section 2.3). A retailer attains a larger volume of purchases, and thereby of rebate levels, than individual advertisers. Therefore, buying through a retailer gives consumers access to larger rebate opportunities than they could obtain by themselves. Finally, retailers provide search services to consumers. Retailers provide information about the prices available for the display formats of multiple manufacturers in the industry. Retailers collect this information once per period (e.g., month) and use it for the orders of multiple consumers. Retailers benefit from economies of scale relative to the consumers (we document this in Section 2.3). Retailers have more experience than consumers collecting this information. It allows them to do it more efficiently (i.e., lower search costs due to better search technology).
2.1.4. Display Formats.
There are three main display formats: 2m^{2} panels (mupis), seniores, and others. Panels of 2 m^{2} include city information panels, bus shelters, kiosks, etc. A senior is an advertising panel with an area between 8 and 24 m^{2}. The last category, others, encompasses transports and special formats. A transport includes panels on moving vehicles (e.g., buses, trains, taxis) or transport hubs (e.g., airports, railway’s stations, subways’ stations). Finally, a special format is a large panel typically made by special request to be displayed, for example, on buildings’ gables. We define a product as a combination of display format, manufacturer, and retailer. Examples of products are as follows: J.C. Decaux Group’s 2m^{2} panels sold by Havas Media Group, Cemusa’s seniores sold by WPP Plc., and J.C. Decaux Group’s 2m^{2} panels sold directly by J.C. Decaux Group.
See Online Appendix B.1 for a discussion about product differentiation, payment schedules, productive capacity, and market concentration.
2.2. Data
2.2.1. Data Set.
The data were obtained from various sources. We obtained administrative data from all the meaningful manufactures and retailers in the industry for the year 2013 aggregated at the monthly market level. By meaningful, we mean that our data encompass more than 95% of the volume of transactions in the industry. We consider three display formats: 2m^{2} panel, senior, and an additional category aggregating the remaining formats that have negligible weight individually. We consider four manufacturers: the three main manufacturers in the industry (J.C. Decaux Group, Cemusa, and Mop) and an additional manufacturer that aggregates the smaller manufacturers. We consider nine retailers: the five main VSC retailers in the industry (Omnicom Media Group, WPP Plc., Power Media Group Inc., Havas Media Group, and Interpublic Group of Companies), one additional VSC retailer that aggregates the smaller VSC retailers, and three DSC retailers representing the direct sales of each of the three larger manufacturers (J.C. Decaux Group, Cemusa, and Mop). There are no direct sales from the other manufacturers. Henceforth, for confidentiality reasons, we refer to the three main manufacturers as m_{1}, m_{2}, and m_{3}, not necessarily in the order above, to the additional manufacturer as m_{4}, to the retailers in the DSC as ${r}_{1}^{d},\hspace{0.17em}{r}_{2}^{d},\hspace{0.17em}{r}_{3}^{d}$, by the same order as the three main manufacturers, to the five main VSC retailers as ${r}_{4}^{v},\dots ,{r}_{8}^{v}$, not necessarily in the order above, and to the additional VSC retailer as ${r}_{9}^{v}$. Figure 1 summarizes this information. See Online Appendix B.2.1 for details about the procedures to clean the data.
Characteristics of the manufacturers and retailers were collected by inspecting their websites. Google search data—used to construct micro moment conditions to identify the searchcost parameters on the demand side—were obtained from Google Trends Portugal. See Online Appendix B.2.2 for details.
In each month and for each triplet of display format, manufacturer, and retailer, we observe the total sales, measured in Euros; the total quantity of advertising sold, measured in advertising faces and square meters; the wholesale prices charged from the manufacturers to the retailers, measured in Euros; the commissions, fees, and quantity discounts paid to the manufacturers, measured in Euros; and the installed capacity, measured in advertising faces. We also observe characteristics for each manufacturer and retailer, such as the number of offices.
2.2.2. Products.
We define a product as a combination of display format, manufacturer, and retailer (including DSC and VSC retailers). Panel A in Table 1 shows the percentage of sales to consumers by each combination of manufacturerretailer in the sample. Panel B in Table 1 shows the percentage of sales of each of the 57 inside products in the sample. The total number of inside products in the sample is 57. This number is lower than the total possible products in the market: 81.^{16} This feature is because some VSC retailers only sell a subset of display formats from certain manufacturers (the subset with which they contracted; for example, Panel B in Table 1 shows that retailer ${r}_{8}^{v}$ does not sell 2m^{2} panels manufactured by m_{3}), and some DSC retailers do not sell certain display formats directly to consumers (e.g., Panel B in Table 1 shows that retailer ${r}_{1}^{d}$, which corresponds to manufacturer m_{1} selling directly to consumers, does not sell seniores in the DSC). All VSC retailers contract with all of the three largest manufacturers. This feature rules out the possibility that some retailers do not negotiate with some of the manufacturers because of selection based on unobservables.
2.2.3. Wholesale and Retail Prices in the VSC.
Table 2 reports summary statistics on wholesale and VSC prices for each display format. VSC prices, that is, retail prices, are higher than wholesale prices. Panel B shows large differences in prices across both manufacturers and retailers holding constant the display format. These price differences and the differences in the observed market shares suggest that differentiation is important. Table A1 in the Online Appendix compares wholesale and retail prices in the VSC by manufacturer and by retailer for the display format 2m^{2} panel. There are substantial differences in VSC and wholesale prices across VSC retailers holding constant the display format and the manufacturer. For example, retailer ${r}_{9}^{v}$ is the most expensive retailer, including DSC retailers, for 2m^{2} panels manufactured by m_{2}, but the cheapest retailer for seniores manufactured by m_{2}. Table 2 and Table A1 show that differences in wholesale and VSC prices are small. They suggest that most of the differences in VSC prices are explained by differences in wholesale prices. The profit margins of VSC retailers are small.

Wholesale and Retail Prices in the VSC
Display format  Wholesale price  VSC price (retail price)  

Median  Mean  Standard deviation  Minimum  Maximum  Median  Mean  Standard deviation  Minimum  Maximum  
Panel A: All manufacturers and all VSC retailers  
2m^{2} panel  8.34  12.05  12.75  0.81  93.38  9.05  13.14  13.94  0.86  99.39  
Senior  12.93  17.23  18.21  0.81  158.06  13.71  18.30  19.46  0.83  165.80  
Other  24.79  28.67  26.07  0.34  148.60  27.04  31.76  29.52  0.37  171.99  
Wholesale price  VSC price (retail price)  
Display format  Manufacturer  Median  Mean  Standard deviation  Minimum  Maximum  Median  Mean  Standard deviation  Minimum  Maximum 
Panel B: By manufacturer and all VSC retailers  
2m^{2} panel  m_{1}  8.11  9.39  7.35  1.42  51.64  8.75  10.61  8.26  1.50  56.18 
m_{2}  10.50  11.99  9.52  2.33  64.80  11.31  13.06  11.33  2.41  83.22  
m_{3}  6.26  8.64  11.74  1.04  79.45  6.79  9.40  12.73  1.09  81.52  
m_{4}  12.38  19.80  18.88  0.81  93.38  13.29  21.10  20.22  0.86  99.39  
Senior  m_{1}  16.09  14.95  4.39  9.07  24.13  16.78  15.67  4.49  9.46  25.17 
m_{2}  6.27  10.77  14.22  0.81  98.39  6.42  11.12  14.59  0.83  100.57  
m_{3}  9.01  21.76  27.55  2.09  158.06  10.06  23.95  29.69  2.17  165.80  
m_{4}  18.71  21.07  10.25  6.11  46.45  19.40  22.03  10.85  6.49  53.85  
Other  m_{1}  48.69  42.41  24.94  3.61  83.26  52.58  48.05  29.76  5.09  106.60 
m_{2}  34.39  37.18  17.99  0.34  117.09  37.97  39.31  18.77  0.37  120.03  
m_{3}  12.98  28.50  33.93  0.45  148.60  14.66  32.55  39.33  0.64  171.99  
m_{4}  13.48  15.44  14.73  0.38  57.28  14.44  17.59  16.88  0.41  66.93 
Notes. Panel A reports summary statistics of wholesale and VSC prices (i.e., retail prices) for each display format (2m^{2} panel, Senior, and Other) across manufacturers (m_{1}, m_{2}, m_{3}, and m_{4}) and VSC retailers (${r}_{4}^{v},{r}_{5}^{v},\dots ,{r}_{9}^{v}$), respectively. Panel B reports summary statistics of wholesale and VSC prices across all VSC retailers for each combination of display format and manufacturer. See Table A1 in the online appendix for a comparison of summary statistics of wholesale and VSC prices by manufacturer and by VSC retailer for the display format 2m^{2} panel. “DSC” stands for Direct Sales Channel. “VSC” stands for Vertical Sales Channel. See Figure 1 for definitions of prices and vertical relations in the industry.
2.2.4. Sales to Consumers in the VSC and DSC.
Panel A in Table 1 shows that 85.2% of the sales to consumers are made through VSC retailers The remaining 14.8% of the sales are made through DSC retailers. There is substantial variation across months in the market shares of VSC and DSC sales (see Figure 2 and Online Appendix B.3.2). Monthly sales in the DSC range between 13.9% and 42.6% (Figure 2). DSC prices are higher than wholesale prices holding constant the manufacturer and the display format. It is the result of manufacturers offering quantity discounts to retailers. It suggests that manufacturers use direct sales as a price discrimination mechanism in the DSC.
Table 3 shows that the median price paid by consumers is higher in the DSC than in the VSC. Occasionally, prices in the DSC are lower than in the VSC (e.g., senior manufactured by m_{1} in Panel B in Table 3). There are two effects at play. On the one hand, VSC retailers aggregate the purchases of several consumers. It allows them to obtain lower prices per unit (because of quantity discounts) when negotiating with the manufacturers (see Section 2.3). This effect lowers VSC prices and increases VSC price dispersion relative to the DSC prices.^{17} On the other hand, VSC retailers offer additional services to the consumers that are not offered by DSC retailers. VSC retailers charge a price for the additional services. This effect increases VSC relative to DSC prices.

Price Paid by Consumers to in the DSC and VSC
Display format  Manufacturer  Sales’ channel  Median  Mean  Standard deviation  Minimum  Maximum 

Panel A: By display format, all manufacturers  
2m^{2} panel  DSC  10.16  12.79  12.29  1.67  66.90  
VSC  9.05  13.14  13.94  0.86  99.39  
Senior  DSC  13.61  13.38  4.54  6.30  22.98  
VSC  13.71  18.30  19.46  0.83  165.80  
Other  DSC  9.15  14.81  16.36  1.36  63.62  
VSC  27.04  31.76  29.52  0.37  171.99  
Panel B: By display format and by manufacturer  
2m^{2} panel  m_{1}  DSC  11.71  12.28  2.88  9.19  19.04 
VSC  8.75  10.61  8.26  1.50  56.18  
m_{2}  DSC  14.71  19.41  19.07  1.67  66.90  
VSC  11.31  13.06  11.33  2.41  83.22  
m_{3}  DSC  6.85  6.64  2.23  2.67  10.16  
VSC  6.79  9.40  12.73  1.09  81.52  
Senior  m_{1}  DSC  14.64  14.61  2.65  11.84  19.04 
VSC  16.78  15.67  4.49  9.46  25.17  
m_{2}  DSC  14.68  14.56  3.93  7.87  21.31  
VSC  6.42  11.12  14.59  0.83  100.57  
m_{3}  DSC  9.80  11.32  5.52  6.30  22.98  
VSC  10.06  23.95  29.69  2.17  165.80  
Other  m_{2}  DSC  15.84  22.89  20.57  1.36  63.62 
VSC  37.97  39.31  18.77  0.37  120.03  
m_{3}  DSC  5.46  7.31  4.36  1.87  16.58  
VSC  14.66  32.55  39.33  0.64  171.99 
Notes. The table reports summary statistics of the price paid by consumers on sales made in the DSC and in the VSC (column labeled “Sales’ channel”). Panel A reports the summary statistics by display format (2m^{2} panel, Senior, and Other). DSC prices refer to the prices over all sales from manufacturers to consumers in that display format. VSC prices refer to the prices over all sales from retailers that are not manufacturers for that display format. Panel B reports the summary statistics by display format and by the manufacturer. DSC prices in Panel B refer to the manufacturer in each cell (i.e., there is only one manufacturer in each of these cells). VSC prices refer to the prices over all sales from retailers that are not manufacturers for the display format and manufacturer in the relevant cell. Manufacturer m_{4}, that corresponds to the additional manufacturer that aggregates smaller manufacturers, is not included because it does not perform any sale to the consumers directly (i.e., manufacturer m_{4} does not participate in the DSC). Similarly, manufacturer m_{1} is not included for the display format “Other” because it does not perform any sale to the consumers directly. “DSC” stands for Direct Sales Channel. “VSC” stands for Vertical Sales Channel. See Figure 1 for definitions of prices and vertical relations in the industry.
2.2.5. Market Shares.
We use the described data to build a data set of products sold in the DSC and VSC for each month of the year 2013 and their characteristics. Market shares are defined by dividing volume sales by the total potential sales in a given month. These potential sales (or market size) were assumed to be 20% greater than the maximum observed total monthly sales of the year 2013. The market share of the outside good was defined as the difference between one and the sum of the market shares of the inside goods in each month. The outside good can be conceptualized as including goods outside the sample (e.g., special request panels), outdoor advertising sold by other manufacturers and retailers (e.g., small manufacturers and retailers that operate locally), and not buying outdoor advertising. An observation in this data set represents a market share of a product as defined above in a given month. We define a market as a month. We consider 12 markets, one for each month of the year.
2.3. Three Stylized Facts
The Portuguese outdoor advertising industry is characterized by quantity discounts in the VSC, seasonal effects and large variation in the market shares, and substantial price dispersion conditional on quantity discounts and seasonal effects.
2.3.1. Quantity Discounts in the VSC.
Consumers’ purchases exhibit quantity discounts in the VSC but not in the DSC. By quantity discounts we mean that the price paid per square meter decreases with the volume purchased. Table 4 presents evidence about quantity discounts. It displays Ordinary Least Squares (OLS) regressions of the price paid by consumers per square meter of advertising on the total volume of advertising in a logarithmic scale, denoted by “Log(m^{2}).” Column 1 shows that the price paid by consumers per square meter of advertising decreases nonlinearly with the volume purchased of advertising. In column 2, we include an interaction between “Log(m^{2})” and “VSC.” The variable “VSC” is a dummy variable that equals one if the consumer performed the purchase through a VSC retailer and zero if the consumer performed the purchase through a DSC retailer. The interaction term is negative and statistically different from zero, whereas the coefficient on “Log(m^{2})” is no longer statistically different from zero. The purchases made by consumers in the VSC exhibit quantity discounts while the ones made in the DSC do not. Columns 3 and 4 show similar results when we include fixed effects for manufacturers, retailers, display formats, and months. Columns 2 and 4 show that the effect of quantity discounts is only present in the VSC.^{18}

Quantity Discounts in the VSC but Not in the DSC
Price paid by consumers per m^{2}  (1)  (2)  (3)  (4) 

Log(m^{2})  −7.0708***  −1.8348  −6.9948***  −1.5502 
(0.4472)  (1.2105)  (0.4511)  (1.1810)  
Log(m^{2}) × VSC  −6.0297***  −6.2510***  
(1.2990)  (1.2576)  
Manufacturers fixed effects  Yes  Yes  Yes  Yes 
Retailers fixed effects  Yes  Yes  Yes  Yes 
Display formats fixed effects  No  No  Yes  Yes 
Months fixed effects  No  No  Yes  Yes 
Adjusted R^{2}  0.4081  0.4291  0.4493  0.4723 
Number of observations  570  570  570  570 
Notes. All regressions are OLS specifications. The sample is the same sample used for the structural estimation. It corresponds to all purchases of all display formats made by the consumers in the industry. The dependent variable is the price paid by consumers per square meter of advertising in a given month, labeled as “Price paid by consumers per m^{2}.” The variable “Log(m^{2})” corresponds to the total square meters of advertising purchased by consumers in that month on a logarithmic scale. The variable “VSC” is a dummy variable that equals 1 if the consumer performed the purchase through a VSC retailer and 0 if the consumer performed the purchase through the DSC retailer. “DSC” stands for Direct Sales Channel. “VSC” stands for Vertical Sales Channel. Standard errors are in parentheses.
*p < 0.10; **p < 0.05; ***p < 0.01.
2.3.2. Seasonalities and Monthly Variation.
Seasonal variations are substantial. The total volume purchased increases during the summer. See Online Appendix B.3.2 for details. For the estimation, we use monthly indicator variables to account for these seasonal effects.
2.3.3. Price Dispersion and Returns to Consumer Search.
There is substantial price dispersion: (i) across retailers holding constant the display format (product heterogeneity), the month of the year (seasonal effects), and the volume percentile (quantity discounts); and (ii) across months holding constant the display format, the manufacturer, the retailer, and the volume percentile. This feature indicates that the returns to consumers’ search (for product’s prices) are high in this market.
Figure 3 shows that price dispersion is lower in the VSC than in the DSC conditional on quantity discounts. The top panel displays the distribution of the coefficient of variation of prices (CV) holding constant the display format, the month, and the volume percentile. That is, each CV is computed within the unit of analysis in the tuple $(\text{Display}\text{Format},\text{Month},\text{Volume}\text{Percentile}$).^{19} The mean CV is 45% (pooling together sales in the VSC and DSC). The mean CV for sales made in the VSC is 43% and for sales made in the DSC is 54%. This result indicates that returns to consumers’ search for product’s prices vary substantially by distribution channel.^{20}
The bottom panel in Figure 3 shows that the empirical CDF for sales made in the DSC firstorder stochastically dominates the one for sales made in the VSC. It indicates that consumers who buy in the VSC face lower price dispersion consistently. Buying in the VSC can provide substantial returns to consumers with large search costs in this market. Figure 3 is consistent with VSC retailers providing search services to the consumers. The covariates included in the model explain more than 90% of the price variation in the data (adjusted ${R}^{2}=0.927$ of regressing prices on covariates). We interpret this fact as products being relatively homogeneous after accounting for these covariates and in favor of using a randomcoefficient demand model with costly search to account for the remaining unobserved product heterogeneity.
3. Model
3.1. Consumers
We use a randomcoefficient nestedlogit model with costly search. Consumers know the products available in each market but do not know the price nor the realization of the random shock associated with each product. To learn this information, consumers engage in costly search for retailers.
Consumer’s choice is a twostep process. In the first step, the consumer chooses the subset of retailers to search. After searching for a retailer, the consumer learns the information of the products sold by that retailer, prices, and realizations of the random shocks. This step determines the consideration set of each consumer type. The consideration set is given by the subset of products sold by all the retailers searched and the outside product. In the second step, after observing the prices and random shocks of the products sold by the retailers searched, the consumer chooses the product to purchase; that is, the consumer chooses among the subset of products from the retailers searched. This step is a standard discretechoice problem similar to, for example, Berry et al. (1995) and Nevo (2001). The difference is that the choice set for each consumer is endogenously determined in the first step. We refer to the first step as the search step and the second step as the purchase step. Because we solve for the equilibrium by backward induction we describe, first, the purchase step and, then, the search step.
We assume that there are $t=1,\dots ,T$ markets, each with a continuum of rational, utilitymaximizing consumers. Consumers have different preferences for different products. A market is defined as a month. In each market t, there are J_{t} horizontally differentiated and mutually exclusive inside products, indexed by $j=1,\dots ,{J}_{t}$. We index with j = 0 the outside product. It allows consumers not to purchase any of the inside products. In each market, each consumer purchases one inside product or the outside product.
3.1.1. Step 2: Purchase Step.
Consider consumer i who searched R_{i} retailers in the search step in market t.^{21} The indirect utility of consumer i for inside product j in market t, denoted by U_{ijt}, is:
In each market t, we normalize the characteristics of the outside product, j = 0, such that ${p}_{0t}={x}_{0t}={\tau}_{0}^{D}={\xi}_{0t}=0$ for all t. Denote by ${\overline{U}}_{i\widehat{j}t}\equiv {\alpha}_{i}{p}_{\widehat{j}t}+{x}_{\widehat{j}t}\beta +{\tau}_{d}^{D}+{\tau}_{m}^{D}+{\tau}_{r}^{D}+{\tau}_{t}^{D}+{\xi}_{\widehat{j}t}$ the indirect utility of consumer i for product $\widehat{j}\in {\widehat{J}}_{t{R}_{i}}$ in market t, net of the stochastic term, ${\widehat{\epsilon}}_{\mathit{ijt}}$. We model the distribution of consumers’ preferences for price as ${\alpha}_{i}=\alpha +{\sigma}_{\nu}{\nu}_{i}$ with ${\nu}_{i}\sim {P}_{\nu}({\nu}_{i})=\mathcal{N}(0,1)$, where α and ${\sigma}_{\nu}$ are parameters, ν_{i} captures unobserved, by the econometrician, individual characteristics, and ${P}_{\nu}(\xb7)$ is a parametric distribution assumed to be a standardized Normal, $\mathcal{N}(0,1)$, for the estimation. Denote by ${\delta}_{\widehat{j}t}\equiv \alpha {p}_{\widehat{j}t}+{x}_{\widehat{j}t}\beta +{\tau}_{d}^{D}+{\tau}_{m}^{D}+{\tau}_{r}^{D}+{\tau}_{t}^{D}+{\xi}_{\widehat{j}t}$ the mean utility for product $\widehat{j}$ in market t; that is, the portion of the utility that is constant across consumer types. Then ${\overline{U}}_{i\widehat{j}t}={\delta}_{\widehat{j}t}{\sigma}_{\nu}{\nu}_{i}{p}_{\widehat{j}t}$ for all i, $\widehat{j}$, and t.
Consumers have preferences that are specific to each distribution channel (or retailer type) and the outside product. We capture it by decomposing the stochastic term, ${\widehat{\epsilon}}_{\mathit{ijt}}$, using the distributional assumptions of the nested logit with a factor structure: ${\widehat{\epsilon}}_{\mathit{ijt}}={\zeta}_{\mathit{igt}}+(1\lambda ){\epsilon}_{\mathit{ijt}}$. The subindex $g\in \{0,1,2\}$ define three groups (or nests) of nonoverlapping products for the outside product (denoted by g = 0, with only one product), the products sold by the DSC retailers (denoted by g = 1), and the products sold by the VSC retailers (denoted by g = 2). The random variable ζ_{igt} has a unique distribution such that ${\widehat{\epsilon}}_{\mathit{ijt}}$ is extreme value (Cardell 1997). The parameter λ is a nesting parameter such that $0\le \lambda <1$. A larger value of λ corresponds to a greater correlation in preferences for products in the same distribution channel and the outside product. A larger value of λ is, therefore, associated with less substitution between products in different distribution channels and the outside product. When λ = 0, the model in the second step collapses to a standard randomcoefficient mixedlogit model (Berry et al. 1995, Nevo 2001) with no preference heterogeneity for distribution channels or the outside product but with an endogenous choice set selection from the search step.
For the estimation, it is convenient to write the nestedlogit choice probability as the product of two standard logit probabilities. Denote by ${\mathbb{P}}_{i\widehat{j}t{R}_{i}}$ the nestedlogit probability that individual i chooses product $\widehat{j}$ in period t conditional on the searched retailers, R_{i}. Then:^{23}
3.1.2. Step 1: Search Step.
Consumers know the products available in each market but do not know the price, p_{jt}, or the realization of the random shocks, ${\widehat{\epsilon}}_{\mathit{ijt}}$, associated with each inside product. Before searching consumers only know the distributions of the prices, ${\tilde{F}}_{p}(p)$, and random shocks, ${\widehat{\epsilon}}_{\mathit{ijt}}$.^{24} Consumers can purchase an inside product only if they collect information about its price and random shock. They can engage in costly search to collect this information. A consumer who does not search can only buy the outside product. Let $S{C}_{{R}_{i}}$ be the cost of consumers of collecting information about prices and random shocks of retailer R_{i}.^{25} We assume that if consumers search a retailer, they collect information about all the products sold by that retailer. Our search costs are, therefore, the cost of searching for a retailer, not the cost of searching for a product. VSC retailers sell the products from multiple manufacturers. Searching for a VSC retailer allows consumers to collect information about a larger set of products than searching for a DSC retailer. It allows us to rationalize the lower price dispersion observed in the VSC relative to the DSC.
We consider a fixedsample stochastic search process. First, consumers commit to searching a fixed number of retailers. The number could be zero, in which case the consumer buys the outside product in the purchase step. This commitment is done before beginning the search. The search finishes after consumers searched all the retailers they committed to even if they obtain a favorable search outcome early on.^{26} The expected net value for consumer i of searching a subset of retailers R_{i} in market t, denoted by ${V}_{t{R}_{i}}$, is the difference between the expected maximum utility of buying the most preferred product in that subset and the cost of searching for these retailers, denoted by $S{C}_{{R}_{i}}$:^{27}
Before searching, consumers only know the distribution of prices of the inside products available in market t, ${\tilde{F}}_{p}(p)$. We assume that consumers know the true empirical distribution of prices disaggregated by distribution channel (or type of retailer). This assumption is equivalent to say that consumers know two distributions of prices: the distribution of prices for the DSC retailers and the distribution of prices for the VSC retailers. Consumers learn the prices of the set of products sold by each retailer when they search for such retailer.^{28} We model the cost of searching a subset R_{i} of retailers in t, $S{C}_{{R}_{i}}$, as:
We model the search problem of the consumer from a stochastic point of view. We add a random shock to the subset of searched retailers, ${\tilde{\epsilon}}_{it{R}_{i}}$ in Equation (3), as in De los Santos et al. (2012) and MoragaGonzález et al. (2015). We do this for two reasons. First, the variance of the shock can be interpreted as measuring the degree of heterogeneity in the errors that consumers make when evaluating the net expected gain of a subset of retailers (De los Santos et al. 2012). Alternatively, by positing the random shock directly in the searchcost equation, one can interpret it as a shock to the total cost of searching a subset of retailers. The latter is our preferred interpretation. Second, solving for a consumer’s optimal search strategy is a difficult problem. The consumer must simultaneously choose among a set of ranked stochastic options. Each choice is costly and only the bestrealized option is exercised. When there are many alternatives available in the market, finding the optimal choice set is extremely complex because there are many choice sets to be evaluated. By approaching this problem from a stochastic perspective, we smooth the choiceset probabilities of choosing a given subset of retailers. Therefore, we do not need to solve the search problem of every consumer. Instead, we compute the probability that a given subset of retailers is searched by a consumer. We assume that the term ${\tilde{\epsilon}}_{it{R}_{i}}$ is drawn independent and identical distributed (i.i.d.) (across individuals, markets, and sets of retailers) from a type I extreme value distribution with location parameter ${\mu}_{\tilde{\epsilon}}=0$ and scale parameter ${\sigma}_{\tilde{\epsilon}}>0$.^{29} Denote by $\mathrm{\Psi}\equiv (\overline{S},{\sigma}_{\tilde{\epsilon}})$ the vector of searchcost parameters.
Consumer i chooses the subset of searched retailers, R_{i}, that maximizes the expected net benefit of searching, ${V}_{t{R}_{i}}$. The probability that consumer i finds optimal to sample the subset of retailers R_{i} in market t, denoted by ${\mathbb{P}}_{{R}_{i}}$, is:
3.1.3. Choice Probabilities and Market Shares.
The unconditional choice probability of consumer type i for product j in market t is:
Intuitively, Equation (6) says that the unconditional probability that consumer type i chooses product j in market t is the weighted average of the conditional choice probability of each consideration set, where the weight of each consideration set is given by the unconditional probability that the consumer finds it optimal to sample that subset of retailers, ${\mathbb{P}}_{{R}_{i}^{\prime}}$. This weighted average of probabilities (Equation (6a)) can be written as the product of three standard logit formulas that are linked (Equation (6c)): (i) the conditional probability of choosing product j given that it belongs to group g and is sold by the subset of searched retailers R_{i} (${\mathbb{P}}_{\mathit{ijt}g{R}_{i}^{\prime}}$); (ii) the conditional probability of choosing a product in group g given that it is sold by the subset of searched retailers (${\mathbb{P}}_{\mathit{igt}{R}_{i}^{\prime}}$); and (iii) the unconditional probability that the consumer finds optimal to sample the subset of retailers (${\mathbb{P}}_{{R}_{i}^{\prime}}$). The probabilities in (i) and (ii) are linked through the inclusive value ${I}_{ig{R}_{i}}$. This inclusive value is the expected utility of consumer i from choosing a product among the ones in nest g. When λ = 0, the probabilities in (i) and (ii) collapse to a standard randomcoefficient logit model. Similarly, these probabilities are linked to the probability in (iii) through the consideration sets. These subsets of retailers, ${R}_{i}^{\prime}$, enter into the value ${\overline{V}}_{t{R}_{i}^{\prime}}$, and in the inclusive values ${I}_{ig{R}_{i}^{\prime}}$ and ${I}_{g{R}_{i}^{\prime}}$. The parameters in the search costs, $S{C}_{it{R}_{i}^{\prime}}$, determine the probability that the consumer finds it optimal to search ${R}_{i}^{\prime}$ retailers. When all search costs are zero, the consumer searches all retailers with probability one and ${\mathbb{P}}_{{R}_{i}^{\prime}}=0$ for any other subset ${R}_{i}^{\prime}$ of retailers. Therefore, Equation (6) collapses to ${\mathbb{P}}_{\mathit{ijt}}={\mathbb{P}}_{\mathit{ijt}g}\times {\mathbb{P}}_{\mathit{igt}}$, a standard randomcoefficient nestedlogit model without search.^{30}
The market share function for product j in market t, denoted by s_{jt}, is obtained by integrating over the distribution of consumer types:
In Appendix A, we generalize the search model by allowing correlation between the stochastic shocks to the consideration sets of retailers R_{i}.
3.2. Manufacturers and Retailers
The supplyside model has two main characteristics. First, the industry consists of two layers of activity that are related vertically. Second, there are two distribution channels (or retailers’ types), where consumers can buy advertising: the DSC and the VSC. The game unfolds in two stages. In the first stage, manufacturers and VSC retailers bargain over wholesale prices through Nash bargaining. In the second stage, VSC and DSC retailers set retail prices to consumers through Bertrand competition.
Consider an industry with a twolayered vertical structure: the manufacturer layer and the retail layer. In the manufacturer layer, multiproduct firms, called manufacturers, produce basic production factors, called display formats, that they sell either to the VSC retailers or directly to the consumers if they have a DSC channel. A production factor (display format) from a given manufacturer sold to different VSC retailers generates different manufacturer products. In the retail layer, multiproduct firms, called VSC retailers, combine manufacturer products with their retail production factors to produce retail products, also called display formats, that they sell to final consumers. Retailers have free access to all the information regarding the products that they carry in their portfolios.
There are $d=1,\dots ,\mathcal{D}$ basic production factors, $m={m}_{1},\dots ,{m}_{\mathcal{M}}$ manufacturers, and $r={r}_{1},\dots ,{r}_{\mathcal{R}}$ retailers. Each manufacturer may sell their product through one of the retailers or directly to the final consumer. There are potentially $\mathcal{J}=\mathcal{D}\times \mathcal{M}\times (\mathcal{R}+1)$ final products.^{31} Not all the manufacturers have a DSC channel. It is, therefore, convenient to divide them into pure manufacturers (those who sell only in the VSC) and hybrid manufacturers (those who sell in both the VSC and DSC). Denote by ${\mathrm{\Omega}}_{m}^{V}$ the set of products that manufacturer m sells to VSC retailers and by ${\mathrm{\Omega}}_{m}^{D}$ the set of products that manufacturer m sells to consumers directly. Denote by Ω_{r} the set of products that retailer r sells to the final consumers. Denote by ω_{j} the wholesale price of manufacturer product j, by $\mathbf{\omega}$ the $\mathcal{J}\times 1$ vector of manufacturer wholesale prices, by ${c}_{j}^{m}$ the marginal cost of manufacturer product j, and by ${\mathbf{c}}^{\mathbf{m}}$ the $\mathcal{J}\times 1$ vector of manufacturer marginal costs. Denote by p_{j} the price of retail product j, by p the $\mathcal{J}\times 1$ vector of retail prices, by ${c}_{j}^{r}$ the marginal cost of retail product j, and by ${\mathbf{c}}^{\mathbf{r}}$ the $\mathcal{J}\times 1$ vector of retail marginal costs. The profit function of hybrid manufacturers contains two terms: the profits from selling the products in the VSC and the DSC. For the profit of hybrid manufacturers in the DSC, we assume that the marginal cost is the manufacturer cost plus a retail cost: ${c}_{j}^{m}+{c}_{j}^{r}$. Denote by M the market size, by ${s}_{j}(\mathbf{p})$ the market share of product j given by Equation (7), and by $\mathbf{s}(\mathbf{p})$ the $\mathcal{J}\times 1$ share vector.^{32}
The profit of a VSC retailer r is:
The profit of a pure manufacturer m is:
The profit of an hybrid manufacturer m is:
Our model allows for economies of scale because a product is a combination of display format, manufacturer, and retailer and because retailers have different marginal costs; that is, larger retailers may have lower marginal costs than smaller ones.
To account for the dual channel, but keep the equations compact, we define ${\tilde{\omega}}_{k}$ as:
3.3. Equilibrium
We construct the equilibrium by working backward. The game unfolds in two stages. In the first stage, manufacturers and VSC retailers bargain over manufacturer prices (i.e., wholesale prices of display formats) in a Nash bargaining game. The equilibrium concept is Nash equilibrium in Nash bargains. We call this the manufacturer game. In the second stage, VSC and DSC retailers set retail prices to the consumers, through a Nash Bertrand game. We call this the retail game. The equilibrium concept is subgame perfect equilibrium (henceforth, equilibrium). We solve for the equilibrium by backward induction, starting with the retail game. Equilibrium prices are denoted with asterisks.^{33}
3.4. Stage 2: The Retail Game
The standard equilibrium firstorder necessary conditions for p_{j} are:
The system of Equations (8) defines retail prices implicitly as a function of wholesale prices, ${\mathbf{p}}^{\ast}=\mathcal{P}(\mathbf{\omega})$ by applying the implicit function theorem to (8).
3.5. Stage 1: The Manufacturer Game
Manufacturers and VSC retailers bargain bilaterally and simultaneously over wholesale prices, ω_{j}, as in Horn and Wolinsky (1988). The equilibrium concept is Nash equilibrium in Nash bargains: no manufacturerretailer pair would like change their agreement given all other agreements.^{34} Motivated by our empirical setting, where VSC retailers negotiate with manufacturers each display format separately, we assume that all manufacturerretailer pairs negotiate each wholesale price separately, as in Draganska et al. (2010) and Bonnet et al. (2016).^{35} If the negotiations over ω_{j} fail, manufacturer and retail products j are not sold. If the negotiations over ω_{j} succeed, the profit of manufacturer m from manufacturer product j is ${\mathrm{\Pi}}_{mj}(\mathbf{\omega})=\left({\omega}_{j}{c}_{j}^{m}\right)M{s}_{j}(\mathcal{P}(\mathbf{\omega}))$, and the profit of retailer r from retail product j is ${\mathrm{\Pi}}_{rj}(\mathbf{\omega})=\left({p}_{j}^{\ast}{\omega}_{j}{c}_{j}^{r}\right)M{s}_{j}(\mathcal{P}(\mathbf{\omega}))$. Denote by ${\mathrm{\Pi}}_{r,j}$ and ${\mathrm{\Pi}}_{m,j}^{}$ the disagreements payoffs of retailer r and manufacturer m, respectively, when they bargain over ω_{j}. Denote by ${\nu}_{\mathit{rmj}}^{}$ the bargaining weight of retailer r when it bargains with manufacturer m over ω_{j} and define ${\delta}_{\mathit{rmj}}^{S}\equiv \frac{\left(1{\nu}_{\mathit{rmj}}\right)}{{\nu}_{\mathit{rmj}}}$. The Nash product of manufacturer m and retailer r for ω_{j} is:
Denote by ${\mathrm{\Omega}}_{x}\backslash \{j\},\hspace{0.17em}x=r,m$, the set of products that firm x sells without product j. Denote by ${\mathbf{\omega}}_{j}$ the $\left(\mathcal{J}1\right)\times 1$ vector of manufacturer prices without element ω_{j}. Denote by $\mathrm{\Delta}{s}_{k}^{j}(\mathcal{P}({\mathbf{\omega}}_{j}))$ the change in the market share of product k if product j is not offered. We assume that the disagreement profits for manufacturer m and retailer r when they bargain over ω_{j} are the maximum profits each could earn if product j was not offered, where the parties assume that other contracts would not be renegotiated if they did not reach an agreement. The disagreements payoffs are ${\mathrm{\Pi}}_{r,j}{\sum}_{k\in {\mathrm{\Omega}}_{r}\backslash \{j\}}\left({p}_{k}{\omega}_{k}{c}_{k}^{r}\right)M{s}_{k}^{j}(\mathcal{P}({\mathbf{\omega}}_{j}))$ and ${\mathrm{\Pi}}_{m,j}^{}{\sum}_{k\in {\mathrm{\Omega}}_{m}\backslash \{j\}}\left({\tilde{\omega}}_{k}{c}_{k}^{m}\right)M{s}_{k}^{j}(\mathcal{P}({\mathbf{\omega}}_{j}))$. The bargaining game takes place only over products that are sold in the VSC. However, when hybrid manufacturers bargain with retailers, the Nash product expression includes profits from both the VSC and DSC because a change in the wholesale price that the parties negotiate also affects sales in the DSC channel.
The firstorder necessary equilibrium conditions for ω_{j} with $j=1,\dots ,\mathcal{J}$ are:
4. Demand: Identification and Estimation
Demand and searchcost parameters enter the purchase probability in different ways. To identify the price coefficient and heterogeneity parameters, we rely on instruments with the exclusion restrictions discussed later. We identify the value to consumers of the services provided by the VSC retailers by using the model and comparing instances where the same combination of display format and manufacturer is sold by DSC and VSC retailers. We describe a procedure where we use ratios of searched retailers that do not depend on the demand parameters. Then, we show that certain ratios of Google searches can be used to estimate the ratios of probabilities. We estimate the demand and searchcost parameters by Generalized Method of Moments (GMM) without using the supplyside model. For the estimation, we use an adapted version of the procedure proposed by MoragaGonzález et al. (2015) with the modifications described later.^{36} We then construct micro moments using the ratios of Google searches and incorporate them into the GMM objective.
4.1. Identification of Demand Parameters
We rely on instruments with exclusion restrictions to identify the price coefficient and the heterogeneity parameters. Identification of these parameters requires at least one instrument for price and each heterogeneity parameter.
4.1.1. Price Parameter α.
At least one instrument is needed to identify α because of price endogeneity concerns (Berry 1994, Berry et al. 1995, Nevo 2001). The error term may be correlated with prices because retailers make their pricing decisions with knowledge about the valuations of the consumers in each market, conditional on the search step. In our case, the error term is the unobserved monthspecific deviation from the overall mean valuation of the product. The supplyside model assumes that retailers in the industry observe this deviation. It enters into the marketspecific markup term in the pricing equation, thus introducing a bias in the estimate of the price sensitivity α. To address price endogeneity, we use prices of the same product in other markets as instruments for the price of the product in the current market (Hausman 1996, Nevo 2001).^{37} The identifying assumption is that monthspecific valuations for a product are independent across time after accounting for display format, manufacturer, retailer, and months fixed effects. The prices of the same product are correlated across months because of the common marginal cost. They are uncorrelated with monthspecific valuations because of the exclusion restriction. We use average retail and average wholesale prices in all months (excluding, in both cases, the price of the product in the month being instrumented) and lagged wholesale prices.
4.1.2. Heterogeneity Parameters ${\sigma}_{\nu}$ and λ.
The parameter ${\sigma}_{\nu}$ governs the distribution of the random coefficients (or heterogeneity in consumer preferences) for price. An instrument is needed to identify this parameter due to the endogeneity problem arising from the unknown parameter ${\sigma}_{\nu}$ interacting with the endogenous variables, $({s}_{jt},{p}_{jt})$. We use a variation of the differentiation instruments proposed by Gandhi and Houde (2019). We construct instruments defined by a proximity measure counting the number of competitors located within one standard deviation of product j. We use the count of other products whose predicted prices lie within five Euros of the own price and the interaction of this variable with product and manufacturer dummy variables.^{38}
The nestedlogit parameter, λ, governs the substitution within and between subgroups of products (or nests) sold by the retailers in the DSC, VSC, and the outside product. An instrument is needed due to the unknown parameter, λ, interacting with the endogenous withingroup share. We use the number of products in the market within each distribution channel as an instrument. The identifying assumption is that the error term is uncorrelated with the number of products in the market within each distribution channel. The power of the instrument comes from the number of products in the market within each distribution channel being negatively correlated with the share of the products within that distribution channel.
4.1.3. Value of VSC Retailers.
The identification problem arises because of the nonexistence of a counterfactual scenario without the VSC retailers. We evaluate the performance of the market without the VSC retailers by constructing such a counterfactual scenario using our model and the fact that, in the outdoor advertising industry, goods can be purchased by the final consumer from either VSC or DSC retailers. We compare instances where the same combination of display format and manufacturer is sold by a DSC and a VSC retailer and compute the counterfactual value that the consumer would have obtained had the purchase been made in a distribution channel different from the one used. Consider consumer i and suppose that a given combination of display format and manufacturer is sold by a DSC and a VSC retailer in a given market and that both types of retailers are part of the consideration set of the consumer. The value of a VSC retailer to consumer i is determined by the extent to which the consumer purchases from a VSC retailer rather than from a DSC retailer. There are three nonmutually exclusive channels for such consumer decision according to the model. The first is that the access to quantity discounts by the VSC retailer may bring its retail prices down relative to where they would have been if those quantity discounts were not present. The second is that the VSC retailer reduced the search costs to the consumer because of its access to the display formats of multiple manufacturers (search services). The third is that the gross utility to the consumer of purchasing from a VSC retailer is larger than the gross utility of purchasing from a DSC retailer (consulting services). The model decomposes the value of VSC retailers to consumer i into the three channels by constructing counterfactual scenarios where we remove each of these channels at a time.
4.2. Identification of SearchCost Parameters
To identify searchcost parameters, we rely on an exogenous variation of product availability across markets within retailers in the VSC, the searchcost specification in our setting, and availability of search data with information about ratios of the subset of searched retailers. We show that the searchcost parameters can be written as a function of the ratios of subset searched retailers using Equation (5). Then, we show under which assumptions one can use the Googlesearch data to construct sample analogs of these ratios. Intuitively, if the search costs are high, consumers search only for the more preferred retailers. Thus, the prices of the products sold by the less preferred retailers would likely not affect the market shares of the products sold by the more preferred retailers because the consumers are not aware of possible lower prices from the less preferred retailers. In contrast, price reductions of less preferred retailers can affect the market shares of most preferred retailers when search costs are low. In general, consumers have more incentives to search, the larger is the variance from the distribution of prices of the inside products available in the market, denoted by ${\tilde{F}}_{p}(p)$ in the model, which is known by the consumers ex ante. Thus, the correlation between prices of less preferred retailers and market shares of more preferred retailers is larger when this variance is large.
We proceed in four steps. First, we present the three assumptions that we use to identify the searchcost parameters. Second, we present the main identification argument assuming that search data are available (Assumption 3a). Third, we extend the previous argument to the case in our setting with Googlesearch data (Assumption 3b). In Online Appendix C.4, we discuss the validity of the assumptions in our empirical setting. See Appendix A for a generalization of the search model allowing for correlation between the stochastic shocks to the consideration sets of retailers.
We use the following assumptions to identify the searchcost parameters.
(Exogeneity and Full Support). There is an exogenous variation of product availability across markets within retailers in the VSC with full support conditional on the other variables.
(SearchCost Specification). Consumers search for retailers but pay a search cost for each manufacturer sold by the retailer.
(Search Data). There is availability of search data with the ratios of probabilities of the searched retailers for any pair of retailers.
(GoogleSearch Data). The ratio of Google searches of two retailers converges in probability to the ratio of consumers who searched the retailers for any pair of retailers such that the denominator is positive.
Assumption 1 says that the number of products offered by each retailer varies exogenously across markets. The main restriction from Assumption 2 is that consumers search for retailers but pay a search cost for each manufacturer sold by the retailer. For the estimation, we use the linear specification of search costs in Equation (4).^{39} There are two alternative versions of Assumption 3. Assumption 3a simply says that there is availability of data about ratios of the subset of searched retailers. We use Assumption 3a to show the economic argument to identify the searchcost parameters and how the argument can be generalized by relaxing Assumptions 1 and 2. Assumption 3b shows how we use readily available Google search data to identify searchcost parameters.
We start discussing identification of the searchcost parameters using Assumptions 1, 2, and 3a. Consider a consumer type who bought a given product $j\in (\widehat{g}\cap {\widehat{J}}_{\tilde{t}}\backslash \{0\})$ in $\tilde{t}\in \{t,t\prime \}$. Denote by ${R}_{\tilde{t}}$ the subset of retailers searched by this consumer in $\tilde{t}\in \{t,t\prime \}$ and by $\widehat{r}$ the retailer who sold product j. Choose t such that ${R}_{t}=\{\widehat{r}\}$ is singleton and that retailer $\widehat{r}$ has only availability of products from a single manufacturer. Such choice is always possible because of Assumption 1 and observability of products available in a given market. For example, using the full support variation from Assumption 1, pick t such that only the products of retailer $\widehat{r}$ are available and $\widehat{r}$ has only products from the manufacturer of j. We focus on the case where ${R}_{t}=\{\widehat{r}\}$ is singleton to ease the exposition. Recall from Section 3 that search is costly, and consumers know the products available in the market in the search step. The argument can be extended to the case where $\widehat{r}$ is the only retailer in the VSC channel. In such case, one can use a weaker version of Assumption 1: exogenous variation of product availability across markets within distribution channels with full support conditional on the other variables. Note that ${R}_{\tilde{t}}=\{\widehat{r}\}$ does not imply that the consideration set, ${\widehat{J}}_{\tilde{t}}$, is singleton, because $\widehat{r}$ may sell multiple products from the same manufacturer. Similarly, choose $t\prime $ such that product $j\in (\widehat{g}\cap {\widehat{J}}_{t\prime}\backslash \{0\})$ is available, ${R}_{t\prime}=\{\widehat{r}\}$ is singleton, and that retailer $\widehat{r}$ has availability of products from two manufacturers. Then, using Equation (5):
Similarly, by choosing $t\u2033$ such that product $j\in (\widehat{g}\cap {\widehat{J}}_{t\u2033}\backslash \{0\})$ is available, ${R}_{t\u2033}=\{\widehat{r}\}$ is singleton, and that retailer $\widehat{r}$ has availability of products from three manufacturers:
Using Assumption 3a, the lefthand side in equations (11) and (12) is observed. Thus, these equations jointly identify the searchcost parameters, $\overline{S}$ and ${\sigma}_{\tilde{\u03f5}}$.
Assumption 2 and Equation (4) posit linearity for the SC. Such linearity can be generalized by positing, for example, a polynomial function. In the case of a polynomial function of degree two with two parameters, one can use a similar argument as above with an additional ratio of probabilities in $t\u2033\prime $ to jointly identify the two parameters of the seconddegree polynomial function and ${\sigma}_{\tilde{\u03f5}}$ using a system of three equations. It is straightforward to generalize the argument to allow for additional parameters. We suspect that this argument may also be used to nonparametrically identify the curvature of the search costs under certain assumptions, although we have not proved it.
For the remaining of analysis in this subsection, denote with a hat “$\widehat{}$” variables that are not function of model parameters (i.e., data). Let ${\widehat{G}}_{rt}$ be number of Google searches for retailer r in t, ${\widehat{M}}_{rt}$ be the number of consumers who searched for retailer r in t, ${\widehat{M}}_{t}$ be the size of the market, and ${\widehat{\mathbb{P}}}_{rt}\equiv {\widehat{M}}_{rt}/{\widehat{M}}_{t}\in (0,1)$ be the share of consumers who searched for retailer r in t. For the estimation, we are interested in ${\widehat{\mathbb{P}}}_{rt}$. The identification problem is that we observe ${\widehat{G}}_{rt}$ but we do not observe ${\widehat{M}}_{rt}$ nor the ratio of probabilities in Assumption 3a. We provide conditions under which ${\widehat{G}}_{rt}$ can be used as proxy for ${\widehat{M}}_{rt}$ to compute the ratios of probabilities ${\widehat{\mathbb{P}}}_{rt}$.
Denote by ${\mathbb{P}}_{rt}$, without hat, the prediction of the model for the share of consumers who searched for retailer r in t. This variable is calculated from the model and is a function of the parameters. Define the set of consumers who searched for retailer r in t as ${A}_{rt}=\{({\zeta}_{\mathit{igt}},{\epsilon}_{\mathit{ijt}},{\nu}_{i},{\tilde{\epsilon}}_{it{R}_{t}}):r\in {R}_{it}\}$, where R_{it} is the set of retailers searched by consumer i in t, and ζ_{igt}, ${\epsilon}_{\mathit{ijt}}$, ν_{i}, and ${\tilde{\epsilon}}_{it{R}_{t}}$ are defined in Section 3. Then:
Then, for any retailers r and k with ${\mathbb{P}}_{kt}>0$:
Finally, ${R}_{\tilde{t}}$, with $\tilde{t}\in \{t,t\prime ,t\u2033\}$, is singleton in Equations (11) and (12). With the Google search data, we proceed in similar form as before. Choose t such that ${R}_{t}=\{\widehat{r}\}$ is singleton. For example, pick t such that the only products available in the market are the products sold by retailer $\widehat{r}$ from a single manufacturer, the manufacturer of j. Again, the exogeneity and full support variation from Assumption 1 ensures this is always possible. Thus, ${\mathbb{P}}_{{R}_{\tilde{t}}}={\mathbb{P}}_{r\tilde{t}}$ and the ratio of Google searches in (13) can be replaced in the lefthand side in Equations (11) and (12), provided ${\mathbb{P}}_{kt}>0$.
See Online Appendix C.4 for a discussion of Assumptions 1–3.
4.3. Estimation
We estimate the demand model adapting the procedure used by MoragaGonzález et al. (2015; MSW). The procedure by MSW adapts the nested fixed algorithm used by Berry et al. (1995; BLP) by allowing for an endogenous choice set for each consumer type i, which is the outcome of the search step. There are four major differences in our procedure relative to the one by MSW. First, because of our research question, we account for consumers’ preferences for the two distribution channels. The additional distribution channel introduces the multiplicative term, ${\mathbb{P}}_{\mathit{igt}{R}_{i}^{\prime}}$, to the choice probability in Equation (6c), which enters into the marketshare Equation (7). Second, we estimate the parameters on the demand side without specifying a functional form for the supply side, whereas the estimation in MSW relies on the functional form of a supply equation, similar to BLP. Third, we use micro moments to identify the search parameters. Finally, the instruments and identifying assumptions are different because of the previous points.
The model is estimated by GMM and relies on the moment condition $\mathbb{E}[Z\prime \xb7\omega ({\theta}^{*})]=0$, where Z is a matrix of instruments, $\omega (\xb7)$ is an error term defined later, and ${\theta}^{*}=(\alpha ,{\sigma}_{\nu},\lambda ,\mathrm{\Psi})$ is the true value of the parameters. The GMM estimate is:
For each candidate parameter vector, we use Equation (7) with the choice probability in Equation (6c) to compute the market shares as a function of the parameters.^{40} We define the error term as the unobserved products’ characteristics and compute it by solving for the mean utility level, δ_{jt} that equates:
4.3.1. Google Search Micro Moments.
For the estimation with Google search micro moments, we add one additional moment condition defined as follows.^{41} First, for each retailer $r=1,\dots ,R$, we compute the difference between the ratio of probabilities across consecutive months predicted by the model and the Google search measure observed in the data, $\frac{{\mathbb{P}}_{rt}(\theta )}{{\mathbb{P}}_{r,t+1}(\theta )}\frac{{\widehat{G}}_{rt}}{{\widehat{G}}_{r,t+1}},$ where ${\mathbb{P}}_{rt}(\theta )$ is the model’s prediction of the share of consumers who searched for retailer r in t and ${\widehat{G}}_{rt}$ is the number of searches for retailer r in t from the Googlesearch data. We define by ${\mathcal{P}}_{t}(\theta )$ the ($R\times 1$) rowvector with such differences, one for each retailer. Finally, we define the micro moment as $m({\theta}^{*})\equiv \mathbb{E}\left[{\mathcal{P}}_{t}({\theta}^{*})\prime {\mathcal{P}}_{t}({\theta}^{*})\right]=0$. For the estimation, we use its empirical analog:
We add the moment condition in (16) to the GMM objective in (14) and use the inverse of the sample variance of the empirical moments as the weighting matrix. We compute the standard errors for the estimates using the standard procedures (Hansen 1982, Newey and McFadden 1994), correcting them to account that the simulation draws are the same for all of the observations in a market.
5. Supply: Identification and Estimation
5.1. Identification
The parameters from the supply side are the vector of retail marginal costs, ${\mathbf{c}}^{\mathbf{r}}$, the vector of manufacturer marginal costs, ${\mathbf{c}}^{\mathbf{m}}$, and the vector of bargaining weights, ${\mathbf{\delta}}^{S}$. We observe the vector of retail prices, ${\mathbf{p}}^{\ast}$, the vector of wholesale prices, ${\mathbf{\omega}}^{\ast}$, the vector of market shares, s, and size of the market, M. Using the previously described procedure, we have an estimate of the demand system, $\left(\mathbf{s}({\mathbf{p}}^{\ast}),{\nabla}_{p}\mathbf{s},\overline{s}\right)$.
The firstorder conditions from the retail game in Equation (8) provide a system of $\mathcal{J}$ equations that just identifies the $\mathcal{J}$vector of retail marginal costs, ${\mathbf{c}}^{\mathbf{r}}$. The firstorder conditions from the manufacturer game in Equation (10) also provide a system of $\mathcal{J}$ equations. Thus, in general, without additional restrictions, Equation (10) cannot be used to identify both the vector of manufacturer marginal costs ${\mathbf{c}}^{\mathbf{m}}$ and bargaining weights ${\mathbf{\delta}}^{S}$, which jointly has dimension $2\times \mathcal{J}$.
We obtain these additional restrictions using the vertical structure in our empirical setting. Namely, manufacturers sell the same display format to both consumers (charging DSC prices) and VSC retailers (charging wholesale prices). A natural set of restrictions justified by this structure is that the manufacturer marginal cost of a given display format in a given month is the same whether it is sold to the consumer or to a VSC retailer. In terms of the model, this implies that the manufacturer marginal costs, ${\mathbf{c}}^{\mathbf{m}}$, can be recovered using the firstorder conditions from the retail game (system in Equation (8)), without using the firstorder conditions from the manufacturer game (system in Equation (10)), because the manufacturers are DSC retailers. Therefore, in the first step, we use the firstorder conditions from the retail game in Equation (8) to identify the vector of retail and manufacturer marginal costs using that manufacturer marginal costs are the same for a display format sold to a VSC retailer and the consumer. In other words, ${\mathbf{c}}^{\mathbf{m}}$ is contained in ${\mathbf{c}}^{\mathbf{r}}$. Then, in the second step, we use the firstorder conditions from the manufacturer game in Equation (10) to identify the bargaining weights. The $\mathcal{J}$vector of bargaining weights, ${\mathbf{\delta}}^{S}$, is just identified using the system in Equation (10) conditional on the estimated manufacturer marginal costs, ${\mathbf{c}}^{\mathbf{r}}$, from the retail game. Our identification arguments exploit the vertical structure in our empirical setting and, thus, are different from the ones used previously in the literature (Draganska et al. 2010, Grennan 2013).^{42}
5.2. Estimation of Marginal Costs and Bargaining weights
To estimate the vector of marginal costs, we need to compute the element $\frac{\partial {s}_{kt}(\mathbf{p}\ast )}{\partial {p}_{jt}}$ in the matrix ${\left[{\nabla}_{p}\mathbf{s}\right]}^{\prime}$ in the retail game Equation (8), which is:
Applying the envelope theorem and simplifying the firstorder conditions from the manufacturer game in (10), we obtain the following expression used to recover the bargaining weights (see Online Appendix D):
We parameterize the manufacturers’ marginal costs, ${c}_{jt}^{m}$, as:
Rearranging terms, write the supply unobservable error term as:
For the estimation, we assume that the unobservable determinants of costs are $i.i.d$ across products, j and markets, t. We set the retailers’ marginal cost to zero, ${c}_{jt}^{r}=0$$\forall $(j,t). We believe these are sensible assumptions in our empirical setting for two reasons: first, because manufacturers and retailers’ marginal costs are quite low in this industry and vary little across markets (see subsection 6.2); and second, because our interest in the supplyside parameters is as inputs for counterfactual scenarios without intermediaries’ services in Section 7.2.^{43} We perform the estimation by choosing the value of the parameters, $(\gamma ,{\mathbf{c}}^{\mathbf{r}},{\mathbf{\delta}}^{S})$, that minimize the sum of squared errors given by Equation (20), subject to the demand estimates, ${c}_{jt}^{m}\in [0,{p}_{\mathit{mjt}}],\hspace{0.17em}{c}_{jt}^{r}=0$, and ${\delta}^{S}\in (0,1)$.
6. Estimation Results
6.1. Demand Estimates
Table 5 displays estimates from the following specifications of the model: (1) a simple logit model (without random coefficients for the price, without channelspecific preferences, without search); (2) a mixed logit model (without channelspecific preferences and without search); (3) a mixed logit model with channelspecific preferences (without search); and (4) a mixed logit model with channelspecific preferences and with costly search. The latter specification corresponds to the full model described Section 3.1. Model 4 uses the additional Google micro moments implemented using Equation (16). All the specifications include a set of dummy variables for manufacturers, retailers, display formats, and months fixed effects. The instruments used in the GMM specifications are described in Section 4.

Demand Estimates
Logit  Mixed logit  Mixed logit with channelspecific preferences  Mixed logit with channelspecific preferences and costly search  

(1)  (2)  (3)  (4)  
Coefficient  Standard error  Coefficient  Standard error  Coefficient  Standard error  Coefficient  Standard error  
Price  
Mean (α)  0.050  (0.001)  0.168  (0.004)  0.057  (0.001)  0.118  (0.002) 
Standard deviation (${\sigma}_{\nu}$)  0.071  (5.8e05)  0.024  (0.007)  0.057  (0.002)  
Firm dummy variables  
Manufacturer 1  −0.672  (0.117)  −0.416  (0.198)  −0.142  (0.076)  −0.275  (0.134) 
Manufacturer 2  0.930  (0.103)  1.005  (0.169)  0.336  (0.065)  0.609  (0.115) 
Manufacturer 3  −0.382  (0.096)  −0.493  (0.162)  −0.147  (0.062)  −0.338  (0.110) 
Retailer 1  0.193  (0.257)  0.459  (0.437)  −0.683  (0.168)  0.063  (0.297) 
Retailer 2  −0.659  (0.117)  −0.836  (0.196)  −0.262  (0.075)  0.008  (0.133) 
Retailer 3  −0.909  (0.107)  −0.541  (0.181)  −0.224  (0.069)  0.314  (0.123) 
Retailer 4  2.728  (0.119)  0.128  (0.267)  −0.784  (0.103)  −0.291  (0.182) 
Retailer 5  −0.424  (0.113)  −0.874  (0.186)  −0.257  (0.072)  −0.106  (0.126) 
Retailer 6  0.242  (0.161)  0.129  (0.272)  −0.877  (0.105)  −0.228  (0.185) 
Retailer 7  −0.505  (0.109)  −0.494  (0.179)  −0.164  (0.069)  −0.360  (0.121) 
Retailer 8  −1.867  (0.118)  −1.603  (0.203)  −0.456  (0.078)  −0.525  (0.138) 
Product dummy variables  
2m^{2} panel  0.911  (0.085)  0.336  (0.143)  0.156  (0.055)  0.270  (0.097) 
Senior  −0.652  (0.086)  −0.848  (0.145)  −0.194  (0.056)  −0.406  (0.099) 
Channelspecific preferences  
Nesting parameter (λ)  0.495  (0.002)  0.373  (0.025)  
Search parameters  
Search cost ($\overline{S}$)  0.182  (0.021)  
Scale of $\tilde{\epsilon}$ (${\sigma}_{\tilde{\epsilon}}$)  0.116  (0.023)  
Model specification  
OLS  Yes  No  No  No  
GMM  No  Yes  Yes  Yes  
Random coefficients for price  No  Yes  Yes  Yes  
Channelspecific preferences  No  No  Yes  Yes  
Costly search  No  No  No  Yes  
Google search micro moments  No  No  No  Yes  
Value of GMM objective  –  26.762  4.800  29.375  
Number of observations:  570  570  570  570 
Notes. Estimates of selected parameters from the structural demand model. All specifications include dummy variables for manufacturers, retailers, display format, and months fixed effects. The model with search uses the following information structure for ${\tilde{F}}_{p}(p)$: consumers know two distributions of prices, the distribution of prices for the DSC retailers and the distribution of prices for the VSC retailers (see Endnote 16). See Section 2.2 for details about the data used in the estimation. A description of the demand model is in Section 4. Details about the estimation procedure are in Section 3.1. See Section 6.1 for details about the specifications of the models in the different panels. The Google search micro moment is implemented using Equation (16). See Section 4.2 for details. Standard errors are in parentheses.
We apply the estimation procedure from Section 4 with the obvious modifications. For example, for the simple logit, model 1, the error term in the system of Equations (15) has a closedform expression, the search step in Section 3 is skipped, and the model is estimated by OLS. For models 2 and 3, we solve for the error term using the contraction mapping and skip the search step. The demand estimates do not impose the equilibrium conditions from the supply side.
The estimated parameters have the expected signs and are sensible in magnitude. Three conclusions emerge from this table. First, by comparing the estimates from models 1 and 2, one can see the role of accounting for price endogeneity and unobserved price heterogeneity. The estimated mean price coefficient in model 2 is three times higher in absolute terms than the one in model 1 ($0.168/0.050$). The coefficient for the standard deviation of the random coefficients for the price is statistically different from zero. Consumer heterogeneity is important in this industry. Not accounting for these features may bias the estimated absolutevalue mean price elasticity downward.
Second, by comparing the estimates from models 2 and 3, one can see the role of accounting for preference heterogeneity for the distribution channels. Model 3 allows for such preference heterogeneity. The null hypothesis that there is no preference heterogeneity for the distribution channels, $\widehat{\lambda}=0$, is rejected. Model 2 precludes correlation in consumer preferences for the products in the same distribution channel. In model 3, consumers selfselect into the distribution channels based on their preferences. They are less responsive (lower α in absolute value) and more homogeneous (lower ${\sigma}_{\nu}$) in their taste for price for products in the same channel, relative to model 2. Overall, these results indicate that ignoring channelspecific preferences may overestimate price sensitivity and price heterogeneity.
Finally, by comparing the estimates from models 3 and 4, one can see the role of accounting for consumer search. The searchcost parameters, $\overline{S}$ and ${\sigma}_{\tilde{\epsilon}}$, are precisely estimated. The estimate of the searchcost parameter, $\overline{S}$, implies that the cost of searching one additional retailer is 1.54 Euros on average ($0.182/0.118$). This search cost represents 8% of the mean price paid by consumers across all display formats in the setting ($1.54/19.64$, where 19.64 Euros is the mean price of all display formats across both distribution channels in Table 3). For 2m^{2} panels, the most popular product in the industry, with 56% of the sales, the cost of searching one additional retailer represents 12% of the mean price ($1.54/13.09$). The estimate of the scale parameter of the consideration sets, ${\sigma}_{\tilde{\epsilon}}$, is about nine times smaller than the scale parameter of the utility function shock, which is normalized to one ($1/0.116$). This result indicates that unobserved factors affecting consumer choice of the consideration sets, although statistically different from zero, play a relatively small role in the empirical setting studied. The estimated searchcost parameters imply that consumers search, on average, for 5.8 retailers to collect information about their prices, p_{jt}, and the realization of their random shocks, ${\widehat{\epsilon}}_{\mathit{ijt}}$, associated with their products. In other words, consumers sample approximately 60% of the subset of all retailers available in the market when performing their search ($5.77/9=0.64$). This finding indicates that the restriction to consumers’ consideration sets is substantial due to search costs: around 40% of the overall retailers do not belong to the consideration set of a given consumer.
Next, compare the price sensitivity of the models with and without search. Table 6 presents the consumerlevel, ownprice elasticities. The last column shows the ratio of elasticities computed from the model without search (model 3) relative to the elasticity of the model with search (model 4). For the median elasticity, the ratio is 0.5. Consumers are more sensitive to price in model 4 with search. These results are consistent with prior findings in Draganska and Klapper (2011) and De los Santos et al. (2012). They indicate that ignoring consumer search (i.e., incorrectly assuming that consumers have full information) may bias the estimated absolutevalue price elasticities downward. The explanation is simple, as emphasized by De los Santos et al. (2012, p. 2977): “[…] the price changes we—as econometricians—observe in the data are not observed by consumers who sample only a subset of the stores. A full information […] model assumes that all prices are observed, thus ascribing unresponsiveness to price changes to low price elasticity.” Finally, compare the ratio of elasticities between DSC and VSC retailers. For DSC retailers, the ratio ranges between 0.5 and 0.8; for VSC retailers, it ranges between 0.2 and 0.7. In other words, the bias is larger for VSC retailers. By allowing consumers to have access to multiple manufacturers, VSC retailers decrease consumer search costs relative to DSC retailers. Ignoring search generates a greater bias in the estimated price elasticities of VSC retailers than the ones of DSC retailers because VSC retailers provide better search services. These demand elasticities are important by themselves, as they directly translate into pricecost margins and affect merger simulations and merger analyses.^{44}

ConsumerLevel OwnPrice Elasticities
Breakout  Statistic  No search model  Full model  Ratio 

Mixed logit with channelspecific preferences  Mixed logit with channelspecific preferences and costly search  (No Search/Full)  
(3)  (4)  (5)  
Panel A: All retailers, manufacturers, display formats, and markets  
All pooled  25th Percentile  −3.49  −11.08  0.31 
50th Percentile  −1.04  −2.12  0.49  
75th Percentile  −0.35  −0.87  0.40  
Panel B: By DSC retailers (all manufacturers, display formats, and markets)  
${r}_{1}^{d}$  50th Percentile  −0.70  −0.87  0.80 
${r}_{2}^{d}$  −0.81  −1.62  0.50  
${r}_{3}^{d}$  −1.80  −3.56  0.51  
Panel C: By VSC retailers (all manufacturers, display formats, and markets)  
${r}_{4}^{v}$  50th Percentile  −0.89  −1.49  0.59 
${r}_{5}^{v}$  −0.51  −1.10  0.46  
${r}_{6}^{v}$  −0.84  −1.22  0.68  
${r}_{7}^{v}$  −1.04  −2.25  0.46  
${r}_{8}^{v}$  −2.66  −12.77  0.21  
${r}_{9}^{v}$  −1.28  −3.31  0.39  
Panel D: By manufacturer (all DSC and VSC retailers, display formats, and markets)  
m_{1}  50th Percentile  −0.95  −1.93  0.49 
m_{2}  −1.13  −1.76  0.64  
m_{3}  −0.83  −2.08  0.40  
m_{4}  −1.58  −3.53  0.45 
Notes. Consumerlevel, ownprice elasticities from the structural model. Models 3 (mixed logit with channelspecific preferences) and 4 (mixed logit with channelspecific preferences and costly search) correspond to models 3 and 4 in Table 5, respectively. The table presents the consumerlevel, ownprice elasticities across all display formats and markets disaggregated by type of retailer or manufacturer. The elasticities for all models and panels are the percent change in market share of the product j with a 1% change in the price of product j. Panel A displays 25th, 50th, and 75th percentiles of the elasticities across all manufacturers, VSC and DSC retailers, display formats, and markets. Panel B displays 50th percentile of the elasticities for the DSC retailers across all manufacturers, display formats, and markets. Panel C displays 50th percentile of the elasticities for the VSC retailers across all manufacturers, display formats, and markets. Panel D displays 50th percentile of the elasticities by manufacturer across all VSC and DSC retailers, display formats, and markets. The last column shows the ratio of elasticities computed from the model without search (model 3) relative to the elasticity of the model with search (model 4). “DSC” stands for Direct Sales Channel. “VSC” stands for Vertical Sales Channel.
The demand estimates in Table 5 and the elasticities in Table 6 show that consumer search plays a relatively large role in the empirical setting studied. By facilitating search, intermediaries increase consumer welfare, a result that will be reflected in the counterfactual analysis.
6.2. Supply Estimates
Table 7, Panel A, displays the estimates of selected parameters of the manufacturers’ marginal cost from Equation (19). Panel B displays summary statistics of the distribution of manufacturers’ marginal costs. Panel C displays the mean bargaining weights.

Supply Estimates
Estimate  

Panel A: Marginal costs estimates  
Manufacturers  
Constant (γ_{0})  0.383 
2m^{2} panel  0.431 
Senior  0.127 
Manufacturer 1  0.604 
Manufacturer 2  0.508 
Manufacturer 3  0.063 
Retailers  
Constant  0 
Panel B: Distribution of manufacturers’ marginal costs  
Mean  0.872 
Standard deviation  0.353 
Minimum  0.383 
Median  0.877 
Maximum  1.418 
Panel C: Bargaining weight estimates (mean)  
Bargaining weight retailers (${\overline{\nu}}_{\mathit{rmj}}$)  0.240 
Bargaining weight manufacturers (1 − ${\overline{\nu}}_{\mathit{rmj}}$)  0.760 
${\overline{\delta}}_{\mathit{rmj}}^{S}$  0.806 
Notes. Estimates of selected parameters from the structural supply model. The supply estimates use the estimated demand model 4 from Table 5. A description of the supply model is in Section 3.2. Details about the estimation procedure for the supply model are in Section 5. See Section 6.2 for details about the estimates. The estimates in Panel C refer to the mean (across retailers, manufacturers, and display formats) of the variables as defined in Sections 3.2 and 6.2 and are denoted with upper bars.
The estimated parameters are sensible in magnitude. Two patterns stand out. First, Panel B shows that manufacturers’ marginal costs are relatively low in this industry, consistent with expert industry reports as in, for example, U.K. Office of Fair Trading (2011). For example, for 2m^{2} panels, the median wholesale price is 8.34 Euros per square meter (Table 2), and the median estimated marginal cost is 1.30 Euros per square meter ($0.877+0.431$). Marginal costs vary little across firms, display formats, and markets. The coefficient of variation is 0.4 ($0.353/0.872$). Second, Panel C shows that the VSC retailers have relatively low bargaining power, 0.24 on average, compared with the bargaining power of the manufacturers, 0.76 on average. These numbers are consistent with the large concentration at the manufacturer level and the low retail margins in the empirical setting. The largest manufacturer, m_{2}, has nearly 50% of the sales. VSC retailers have little bargaining power when negotiating with manufacturer m_{2}. Retail margins for the VSC retailers are low. The median (mean) margin of the VSC retailers is 0.57 (1.72) Euros per square meter.^{45}
We use the supplyside parameters to simulate the counterfactual scenarios in Section 7.2.
6.3. Robustness
We performed several robustness tests of our model. First, in Table 5 we performed the estimation of the demand model using different specifications, where we build up the full demand model starting from a simple logit model. We also tested different specifications of the supply model, as discussed in Endnote 43. Second, we tested for different information structures for the specification of the empirical distributions of prices, ${\tilde{F}}_{p}(p)$, in Table A2 in the Online Appendix, discussed in Endnote 28. Third, in unreported results, we tested for different specifications of the Google search micro moments using ratios of probabilities of different retailers in a given market (instead of ratios of probabilities of the same retailer in different markets as implemented in Table 5) and using the same specifications of the micro moment as in Table 5 but with the different definitions of Google searches in Online Appendix B.2.2. Fourth, also in unreported results, we estimated the model using different instruments (using a different definition of the differentiation instruments as discussed in Endnote 38, using wholesale prices or lagged wholesale prices to address price endogeneity, and using interactions of the latter variables with product availability in the previous months). Sixth, we tested for different functional form specifications of the search cost in the demand model (e.g., using an exponential function) and the counterfactual (see Section 7). Seventh, we tested increasing/decreasing the market size (to, respectively, 50% and 10% greater than the maximum observed total monthly sales). Finally, we tested using different nonlinear programming solvers, starting values, number of simulated consumers, and seeds to control the generation of random numbers. The estimated parameters did vary sometimes across some of these robustness tests. However, the implications discussed in Sections 6.1, 6.2, and 7.3 are robust in the cases examined.
7. Welfare
7.1. Welfare Measures
The expected consumer surplus, in Euros, for consumer type i is given by (see Online Appendix C.5):
Consumer welfare for type i is defined as the change in the consumer surplus, or compensating variation, CV, that results from a change in the services offered by the retailers. We compute the difference between the consumer surplus before and after such change. We consider four changes in the services offered by the retailers that are described in Section 7.2. We compute the total consumer surplus calculated as the weighted sum of $\mathbb{E}(C{S}_{i})$ using the weights reflecting the number of consumers who face the same representative utilities as the sampled consumer. That is:
7.2. Counterfactual Scenarios
Three channels through which VSC retailers affect consumers’ welfare are by providing consulting, search, and purchaseaggregation services. We consider three counterfactual scenarios where we turn off each of these channels and an additional one where we turn off all three simultaneously. For each counterfactual scenario, we compute the compensating variation using Equation (22).
For each scenario, we follow the following three steps. First, we compute the optimal prices by solving the system of retail and bargaining equations using the initial matrix of elasticities. Second, we use the vector of prices from the supply side to form the consumer’s price expectations. We do this step by taking multiple draws with replacement from the optimal price vector and integrating them numerically. This step guarantees that the price expectations are rational. Finally, we solve the consumerdemand problem using the price expectations.
7.2.1. No Consulting Services.
In this scenario, consumers may use the VSC, but VSC retailers do not offer consulting services, defined as the gross utility of a given display format from the retailer. In Section 3.1, the gross utility of the consumer of purchasing a display format from a given manufacturer differed according to whether it was purchased through the VSC or DSC. We define the difference in gross utilities between the VSC and DSC retailers as the consulting services provided by the VSC retailers.
We implement this counterfactual by imposing that the gross utility of consuming a display format from a given manufacturer (purchased through the VSC) to be the gross utility of consuming the same display format of the same manufacturer purchased through the DSC. According to Equation (1), the gross utility for display format d, produced by manufacturer m, and sold by retailer r, in market t, is given by ${\tau}_{\mathit{dmrt}}\equiv {\tau}_{d}^{D}+{\tau}_{m}^{D}+{\tau}_{r}^{D}+{\tau}_{t}^{D}$. The noconsultingservice scenario, denoted with the superscript c_{1}, is implemented by changing each component of the vector that corresponds to purchases made through the VSC, such that ${\tau}_{\mathit{dmrt}}^{{c}_{1}}={\tau}_{\mathit{dmmt}}$, for every m, r, and t.^{47}
7.2.2. No Search Services.
In this scenario, consumers may use the VSC, but VSC retailers do not offer search services. According to our model, VSC retailers reduce consumers’ cost of searching. We implement this counterfactual by increasing the search cost of consumers as follows. In Equation (4), consumers pay $\overline{S}$ for each manufacturer sold by the searched retailer. In this counterfactual, consumers pay $\overline{S}$ for each retailermanufacturer combination carried by the retailer searched.^{48}
This counterfactual leaves constant the number of “stores” and display formats. It only eliminates the searchcost advantage of buying through a retailer instead of a manufacturer. We then simulate the choice outcomes predicted by the demand model.
7.2.3. No PurchaseAggregation Services.
In this scenario, we recompute the equilibrium prices using the supply side. According to the model, the initial observed prices were set following, first, the bargaining game and, then, the retail (or Nash Bertrand) game. In this counterfactual, we use the estimated supply parameters to remove the purchaseaggregation services by recomputing prices assuming that they are generated by two successive Nash Bertrand.
We follow the following four steps. First, we compute the optimal retailprice function (as a function of any wholesale price) given by Equation (8). Second, we use the result from step 1 to solve numerically for the passthrough matrix defined by $\partial {p}_{k}/\partial {\omega}_{r}$ for all k, r, similar to equation (9) in VillasBoas (2007, p. 634). Third, we solve for the optimal wholesale prices in the twomargin model using Equation (10) with ${\nu}_{\mathit{rmj}}^{}=0$ and step 2 to get ${\nabla}_{w}\mathbf{s}\equiv \partial \mathbf{s}/\partial {\mathbf{\omega}}^{\prime}=\partial \mathbf{s}/\partial \mathbf{p}\times \partial \mathbf{p}/\partial \mathbf{\omega}$. Finally, we solve for the optimal wholesale prices, $\mathbf{\omega}$, using Equation (10) from step 3, which is similar to equation (9) in Draganska et al. (2010, p. 62).
This procedure gives an expression that is a function of $\mathbf{\omega}$ and p that can be solved for $\mathbf{\omega}$ using the implicit function theorem applied to (10) because ${\mathbf{p}}^{\ast}=\mathcal{P}(\mathbf{\omega})$. We then use the new price vector and the estimated demand system to recompute the purchase decisions of the consumers.
7.2.4. No Intermediaries’ Services.
In this scenario, both VSC and DSC retailers operate, but VSC retailers do not offer consulting, search, nor purchaseaggregation services, as defined previously. We implement it by simulating a new counterfactual where we implement the three previous counterfactuals simultaneously. To evaluate the welfare under the different scenarios, we simulate the choice outcomes predicted by the demand model.
7.3. Counterfactual Results
Table 8 reports the results from the previous counterfactual scenarios. Columns 1–4 compare the results relative to the baseline predictions (model 4 in Table 5 labeled as baseline). We report the following outcome variables: the inside share (fraction of the market with purchases of inside products), DSC as fraction of inside (fraction of inside purchases made through the DSC), mean posted prices, mean paid prices (mean posted prices weighted by the quantities purchased), number of retailers searched, count paid of search costs (number of times that a search cost was paid), and the total change in the consumer surplus.

Counterfactual Results
Outcome variables  Baseline  Intermediaries do not provide  

Consulting services  Search services  Purchaseaggregation services  Consulting, search, nor purchaseaggregation services  
(1)  (2)  (3)  (4)  
Inside share (percentage)  70.63  69.61  67.45  65.33  61.98 
DSC sales as a fraction of inside sales (percentage)  18.25  19.91  18.31  25.92  28.01 
Mean posted price (Euros per square meter)  8.29  8.47  8.28  11.81  12.03 
Mean paid price (Euros per square meter)  8.73  8.71  8.73  10.98  11.01 
Number of retailers searched  5.77  5.79  5.47  5.74  5.50 
Count of search costs  5.77  5.79  7.79  5.74  7.77 
Change in consumer surplus (Euros per square meter)  —  −0.95  −11.60  −1.79  −14.28 
Notes. Counterfactual results using model 4 from Table 5 and the supply estimates from Table 7. The row labeled “Inside share” reports the fraction of the total potential size of the market that resulted in purchases of the inside products. The row labeled “DSC as fraction of inside” reports the fraction of those purchases of the inside products made through the DSC. The row labeled “Mean posted price” reports the mean price posted for the inside products. The row labeled “Mean paid price” reports the mean price weighted by the quantity purchased. The row labeled “Number of retailers searched” reports the mean number of retailers searched by the consumers (both in the DSC and VSC). The last row labeled “Change in consumer surplus” reports the change in the total consumer surplus of each column, relative to the baseline, computed using the weighted sum across types of consumers of the compensating variation using Equation (22). The column labeled “Baseline” reports the previous measures for the baseline model 4 from Table 5. Columns 1 to 4 reports the previous measures for each of the counterfactual scenarios defined in Section 7.2. In column 4, the change in consumer surplus is computed by simulating simultaneously the counterfactuals in columns 1, 2, and 3, which is not equivalent to the sum of the change in consumer surpluses in these columns. See Section 7 for details.
In column 1, we remove the consultingservice differential between the VSC and the DSC. We observe a small decrease in the total purchases. There is an increase in the sales fraction from the DSC. The number of searched retailers exhibits little variation. This finding is consistent with the search costs not being affected in this counterfactual. The total consumer surplus decreases by one Euro per square meter. These results reflect the estimated demand system, which shows a larger gross utility for purchases in the VSC. It is consistent with intermediaries providing additional services besides the advertising space, such as assistance with the advertising design and brand recognition for intermediaries.
In column 2, we remove intermediaries’ search services. The cost of searching increases for consumers. There is a decrease in the amount purchased of inside products. The increase in search costs decreases the number of retailers searched by 5% ($5.47/5.771$). The overall cost of the search increases substantially, by 35% ($7.79/5.771$), even when the overall level of prices is similar to the baseline. That is, removing the intermediaries’ searchcost advantage results in consumers paying substantially higher search costs: now consumers pay the search cost for each retailermanufacturer combination carried by the searched retailer relative to paying such cost for each manufacturer sold by the searched retailer. Although the increase in the search cost decreases the number of searched retailers, the total amount spent on searching increases. In sum, consumers search less, pay more search costs, buy less inside products, and pay similar prices relative to the benchmark. The consequence is a large decrease in the total consumer surplus, 12 Euros per square meter. This number is 33% higher than the mean paid price in the baseline ($11.6/8.731$). These outcomes reflect the estimates of the search parameters in the demand system. Search frictions are substantial. Intermediaries reduce them by providing consumers access to the display formats of multiple manufacturers. The removal of the intermediaries’ search advantage generates a decrease in the consumer surplus comparable to a large increase in market power.
In column 3, we remove the intermediaries’ purchaseaggregation services. Wholesale prices paid by the VSC retailers increase because of the elimination of the intermediaries’ bargaining power, thus partially transferring the increase to the consumers. Prices to the consumers increase by 42% ($11.81/8.291$). This increase reflects the rise of VSC prices. DSC prices decrease. The increase in relative VSC prices induces consumers to substitute away from the intermediaries to the DSC retailers. It also generates a decrease in the amount purchased of inside products. These two effects mitigate the large increase in VSC prices. As a consequence, total consumer surplus decreases only two Euros per square meter.
In column 4, we simultaneously remove all services provided by the VSC retailers. There is a relatively large increase in prices, 45% on average ($12.03/8.291$). This increase is driven by the rise in DSC prices because of the removal of the purchaseaggregation services of the VSC retailers. On the one hand, higher prices induce consumers to search more and to substitute to the DSC retailers, as in column 3. On the other hand, the higher search costs induce them to search less and to pay more search costs, as in column 2. Column 4 shows that the net effect is a decrease in the number of searched retailers and an increase in the fraction of DSC purchases by 53% ($28.0/18.21$). There is also a decrease in the total purchases of inside products by 12% ($62.0/76.61$).
The consumer surplus decreases by a large amount, 14 Euros per square meter.^{49} The decrease in the consumer surplus is 64% higher than the mean paid price in the baseline ($14.28/8.731$). The decrease in the consumer surplus can be decomposed in terms of the contribution of the services provided by the intermediaries. The consulting services explain approximately 7% of the raw decrease in the consumer surplus in column 4 ($0.93/14.28$), whereas the search services explain approximately 81% ($11.58/14.28$), and the purchaseaggregation services explain the remaining 12% ($1.77/14.28$). In other words, providing search services is the most prominent mechanism for intermediaries’ welfare enhancement in the empirical setting studied, followed by purchaseaggregation and consulting services.
We interpret the welfare results from column 4 as the impact that VSC retailers have on consumer welfare, holding constant the market structure. In column 4 we remove the three channels through which the VSC retailers (intermediaries) affect consumers’ welfare without affecting the downstream level of competition or the vertical structure in the marketplace: VSC and DSC retailers continue to operate, but VSC retailers do not offer consulting, search, or purchaseaggregation services.^{50}
8. Concluding Remarks
We proposed an empirical framework to quantify the welfare effects caused by intermediation. We use structural econometric techniques in demand and supply estimation to isolate the channels through which intermediaries affect welfare. We apply our empirical framework to the outdoor advertising industry, recover the primitives of the industry, and simulate counterfactual scenarios to quantify the welfare of the services offered by the retailers. The presence of intermediaries increases the welfare in this industry. The value of their services outweighs the additional margin charged.
Our model combines features that are typical of a vertical industry. These features include consumers who have unobserved preferences that are specific to the distribution channel and engage in costly search on the demand side, and two layers of activity—where manufacturers and intermediaries bargain over wholesale prices—with two distribution channels—that compete on downstream prices—on the supply side. The empirical setting studied, outdoor advertising, looks similar to other vertical markets in several dimensions. Recent examples in the United States include disputes between Tesla and Automobile Dealer Association and the proposed merger between Aetna and CVS.^{51} Our framework may be used to evaluate the implications of vertical mergers when intermediaries, or retailers, offer additional services relative to the ones of the manufacturers.
Two main conclusions arise from our analysis. First, the presence of intermediaries increases welfare. This finding is not surprising because consumers made 85% of the purchases through the intermediaries in the setting studied. However, similar canals to the ones analyzed here may be present in other industries and sectors, where the counterfactual scenario without intermediaries may not be observable; that is, where consumers do not buy directly from the manufacturers. Measuring the welfare of intermediaries for merger evaluation, for example, may also require quantifying the value of the services provided by the intermediaries to consumers. In such cases, our framework may provide new insights for regulators, competition authorities, and antitrust agencies. Ignoring the retailers’ searchcost advantage or the resulting increase in final prices because of the removal of the retailers’ bargaining advantage may generate effects comparable to a large increase in market power with significant consequences for horizontal and verticalmerger evaluation. Second, we find that the three services considered provide value to consumers, with search playing a prominent role. This finding is, no doubt, specific to the empirical setting investigated. However, our approach shows the importance of specifying a flexible model that may allow for such quantification.
It is well known that vertical integration often eliminates double marginalization and may generate efficiencies gains.^{52} Our analysis complements such literature. It helps to explain why intermediaries are ubiquitous in modern economies despite the double marginalization, a subject that has received little empirical work.
Discussions with Jason Blevins, Franco Cattaneo, Chris Conlon, Pierre Dubois, Daniel Ershov, Paul Grieco, Doris M. D. GrilloGonzález, Fabio Miessi, José Luis Moraga González, Aviv Nevo, Ariel Pakes, Mathias Reynaert, Tiago Ribeiro, Michelle Sovinsky, Matt Weinberg, Kevin Williams, and Renan Yoshida, as well as seminar participants at University of California Los Angeles (UCLA) Anderson, Toulouse, Getulio Vargas Foundation Graduate School of Economics (FGV/EPGE), Nova School of Business and Economics, University of Porto, the Ohio State University, Colegio Universitario de Estudios Financieros (CUNEF), the Barcelona Graduate School of Economics (GSE) Summer Forum (Consumer Search and Switching Costs Workshop), the 15th and 16th International Industrial Organization Conference (IIOC), the 12th Competition and Regulation European Summer School and Conference (CRESSE), the 11th Portuguese Economic Journal (PEJ) annual meeting, the 2018 Society for Economic Dynamics (SED) meeting, the 2017 North American Summer Meeting (NASAM) of the Econometric Society, the 2018 Research Office (GEE) of the Portuguese and Nova School of Business and Economics (SBE) conference, the 45th European Association for Research in Industrial Economics (EARIE) Conference, the 23th Jornadas de Economía Industrial, the 2nd Bogota Workshop on Structural Industrial Organization, and the 2017 Triangle Microeconomics Conference in honor to Tiago Pires have greatly benefited this work. The opinions expressed in this article reflect only the authors' views and in no way bind the institutions to which they are affiliated. First version of the manuscript: March, 2016.
Appendix A. Search Model with Correlated Consideration Sets of Retailers
In this appendix, we extend the search model to allow for unobserved searchcost heterogeneity. We generalize the search model in step 1 by allowing correlation between the stochastic shocks to the consideration sets of retailers, R_{i}. The idiosyncratic unobserved search costs may be correlated between the consideration sets of DSC and VSC retailers. For instance, a consumer i who has a idiosyncratic search cost that makes it more likely to search the subset of VSC retailers ${R}_{i}=\{{r}_{4}^{v},{r}_{5}^{v},{r}_{6}^{v}\}$, may be more likely to search for the subset of VSC retailers ${R}_{i}^{\prime}=\{{r}_{4}^{v},{r}_{5}^{v}\}$ than the subset of DSC retailers ${R}_{i}^{\u2033}=\{{r}_{1}^{d},{r}_{2}^{d}\}$. In the baseline search model, the idiosyncratic shocks to the consideration sets are independent across R_{i}, ${R}_{i}^{\prime}$, and ${R}_{i}^{\u2033}$. We now extend the baseline model to allow for correlation between the shocks to R_{i} and ${R}_{i}^{\prime}$; that is, between the shocks to the consideration sets of retailers in the same distribution channel.
We allow consumers to have searchcosts shocks that are specific to consideration sets of retailers in the same distribution channel and consideration sets with retailers in both distribution channels and the nosearch option. We capture this correlation by decomposing the stochastic term, ${\tilde{\epsilon}}_{it{R}_{i}}$ in Equation (3) using the distributional assumptions of the nested logit. It is straightforward to extend the approach using other distributions. For example, one can also obtain closedform solutions for the search probabilities using the generalized extreme value (GEV) distribution.
Let $\vartheta \in \{0,1,2\}$ define three groups (or nests) of nonoverlapping consideration set of retailers for: (i) consideration sets with retailers in both distribution channels and the nosearch option denoted by $\vartheta =0$ (henceforth, mixed consideration sets), (ii) consideration sets with retailers in the DSC denoted by $\vartheta =1$ (henceforth, DSC consideration sets), and (iii) consideration sets with retailers in the VSC denoted by $\vartheta =2$ (henceforth, VSC consideration sets). Let $\varkappa $ be a nesting parameter, such that $0\le \varkappa <1$. A larger value of $\varkappa $ corresponds to a greater correlation in idiosyncratic search costs for consideration sets in DSC, VSC, and mixed consideration sets. A larger value of $\varkappa $ is, therefore, associated with less search for consideration sets in DSC, VSC, and mixed consideration sets. When $\varkappa =0$ the search model collapses to the baseline search model with no searchcost heterogeneity for consideration sets of retailers. Consumer i chooses the subset of searched retailers, R_{i}, that maximizes the expected net benefit of searching, ${V}_{t{R}_{i}}$. The probability that consumer i finds optimal to sample the subset of retailers ${\widehat{R}}_{i}$ in market t, ${\mathbb{P}}_{{\widehat{R}}_{i}}$ in Equation (5), is:
The unconditional choice probability of consumer type i for product j in market t is:
Allowing for the unobserved searchcost heterogeneity discussed in this section adds an additional search parameter to the estimation routine, $\varkappa $. The demand nesting parameter, λ, and the search nesting parameter, $\varkappa $, enter the unconditional choice probability, ${\mathbb{P}}_{\mathit{ijt}}$ in Equation (A.2), in different ways through the net indirect utility, ${\overline{U}}_{\mathit{ijt}}$, and the net expected value of searching, ${\overline{V}}_{t{R}_{i}}$, respectively. Under Assumptions 1, 2, and 3b in Section 4.2, the parameter $\varkappa $ is identified using an additional ratio of probabilities in $t\u2034$ yielding to a system of three equations in $\overline{S},\hspace{0.17em}{\sigma}_{\tilde{\u03f5}}$, and $\varkappa $.
^{1} See U.S. Bureau of Economic Analysis (2017). The estimate corresponds to the year 2016 using the definition by Spulber (1996) in Table 1, whereby intermediation includes retail trade (5.9% of gross domestic product (GDP) for the year 2016), wholesale trade (5.9%), finance and insurance (7.3%), business services (12.4%), and other services (2.3%). This estimate assumes that intermediation activities in all other sectors are zero. It is a conservative estimate.
^{2} This is the wellknown result when there are successive monopolies at two layers of production and goes back to Lerner (1934) (for further references, see Spengler 1950 and Tirole 1988, pp. 174–176). When the manufacturer and intermediary layers are both oligopolistic and vertically integrated and unintegrated manufacturers coexist the presence of intermediaries may increase or decrease the price of the final good (Salinger 1988). With consumer search, the double marginalization problem is worsened, resulting in higher wholesale and retail prices because of manufacturer’s demand being more inelastic (Janssen and Shelegia 2015).
^{3} Alternatively, the counterfactual scenario with intermediaries is unobserved in industries where intermediaries are not present.
^{4} We use the terms intermediaries, retailers, and VSC retailers interchangeably.
^{5} Some references in the growing literature on twosided platforms as intermediaries include Bernard and Jullien (2003), Evans (2003), Rochet and Tirole (2003), Armstrong (2006), Galeotti and MoragaGonzález (2009), and Boik (2016).
^{6} See O’Hara (1995), Freixas and Rochet (2008), and Frankel et al. (2009) for surveys.
^{7} For studies about the formation of consideration sets with fixedsample search, see Roberts and Lattin (1991) and Mehta et al. (2003) in the marketing literature.
^{8} We refer to the working paper by MoragaGonzález et al. (2015), which uses a nonsequential search model. The 2018 (and subsequent) version(s) of their paper with the same title uses a different—a sequential search—model to the one in this article.
^{9} See also Goeree (2008), Ershov (2018), and Murry and Zhou (2020).
^{10} The information structure is also different in our model relative to these papers. In our model, consumers face uncertainty over both the price and the realization of the random shock of each product (similar to Pires 2016), whereas in De los Santos et al. (2012), consumers only face uncertainty about the price of the product (not about the realization of the random shock) and in MoragaGonzález et al. (2015), consumers only face uncertainty about the realization of the random shock (not about the price of the product).
^{11} For other recent applications of the randomcoefficient nestedlogit model, see Grennan (2013), Ciliberto and Williams (2014), and Miller and Weinberg (2021). None of these articles incorporate costly search.
^{12} Nash bargaining is a way to generate quantity discounts or nonlinear pricing schemes. In a Nash bargaining model, the larger the value of the bargaining parameter and the larger the value of the outside option, the better the terms a party can negotiate. In our setting, when negotiating with a VSC retailer, the outside option of a manufacturer is the profit if its products are not sold by the VSC retailer. For a given manufacturer, the larger is the VSC retailer that is negotiating with, the smaller is the value of its outside option and the smaller is the wholesale price it is willing to charge the VSC retailer. There are no volumes/quantities explicitly involved in our bargaining game. However, the volumes/quantities define how large is the VSC retailer and, thus, determine its outside option in the Nash bargaining game. The bargaining model does not generate quantity discounts per se. It rather rationalizes the observed quantity discounts in the setting through larger estimated outside options for larger VSC retailers. The quantity discounts between manufacturers and VSC retailers are then partially transferred to the consumers by the VSC retailers. There is a large body of literature studying quantity discounts and nonlinear pricing (Miravete 2002; Miravete and Röller 2004a, b; Busse and Rysman 2005; McManus 2007; Cohen 2008; Chu et al. 2011; Donna and Pires 2016; Nevo et al. 2016).
^{13} A retailer is a set of media agencies and a central purchasing agency with a common owner. Media agencies plan and buy advertising campaigns. The central purchasing agency aggregates purchases of media agencies and places orders to the manufacturers. A retailer might own several media agencies either because they specialize in different industries or to avoid confidentiality issues with advertisers.
^{14} In 2014, in a merger review case on the outdoor advertising industry—case Ccent. 15/2014 JCDecaux/Cemusa—the Portuguese Competition Authority considered that the geographic market for this industry is Portugal. We follow that same approach in this article.
^{15} The advertisement network refers to the location of the display formats of the manufacturers.
^{16} From Table 1, the total possible number of products to the consumers in the market is:
^{17} Conditional on quantity discounts, however, the distribution of prices in the VSC is less disperse than in the DSC, as discussed in subsection 2.3.
^{18} We obtain similar results by regressing the price paid by consumers per square meter using a polynomial function of square meters of advertising purchased.
^{19} We obtain similar results using other measures of price dispersion such as percentile differences (e.g., the difference between the 95th and the 5th price percentiles, the difference between the 90th and the 10th price percentiles), range, and price gap. Substantial price variation is explained by quantity discounts. Ignoring quantity discounts, one would incorrectly conclude that the price distribution is more disperse for sales made in the VSC than for sales made in the DSC (bottom panel in Figure 2).
^{20} VSC retailers offer additional services to consumers (e.g., consulting services, advertising planning campaigns, information about the products of all manufacturers) that are not offered by DSC retailers. Figure A1 in the online appendix shows similar patterns to the ones in Figure 3 when we measure price dispersion across months holding constant the display format, the manufacturer, the retailer, and the volume percentile (i.e., identical products sold by the same seller holding constant the volume percentile). The additional services provided by VSC retailers shift the distribution of prices charged by each VSC retailer but do not affect price dispersion in the market.
^{21} The set of searched retailers is market specific. To simplify the notation, we omit the market subscript, and we refer to the set of searched retailers as R_{i} instead of R_{it}.
^{22} Heterogeneity in the value to consumers within product (e.g., because of the specific location of the billboard) is of horizontal nature (e.g., some consumers may prefer space near a school, whereas others may prefer it close to a highway). This feature is captured in our model by ${\widehat{\epsilon}}_{\mathit{ijt}}$.
^{23} See Online Appendix C.2 for details.
^{24} See Section 3.1.2 and Endnote 28 for details.
^{25} The search cost includes the time spent to find and collect information about retailers, and processing costs (e.g., investigating in the retailer’s web page). Our definition of search costs encompasses the cost of including a product at the purchase occasion and an evaluation cost (Hauser and Wernerfelt 1990).
^{26} In our model, consumers are firms demanding advertisement. The decision of how many retailers to contact is typically made ex ante. The fixedsample search assumption in our model is intended to capture such practice.
^{27} See Online Appendix C.3 for details.
^{28} We have also performed the analysis using the following information structures for ${\tilde{F}}_{p}(p)$. (i) Consumers only know the overall distribution of prices. That is, consumers only know one distribution with the prices for all the products in the market. (ii) Consumers know the distribution of each product in the market disaggregated by distribution channel and by product. That is, consumers know 57 distribution of prices, where the number 57 corresponds to the number of inside products in the sample (see Endnote 16). Under the information structure in (i), consumers have less information than in the benchmark. Under the information structure in (ii), consumers have more information than in the benchmark. We obtained similar results in terms of the welfare analysis under the benchmark, (i), and (ii). Models 2 and 3 in Table A2 in the online appendix shows the results under (i) and (ii), respectively. For the estimation and for each information structure in the benchmark, (i), and (ii), we pool the relevant prices across all markets to compute the empirical distribution observed by the consumers before searching, ${\tilde{F}}_{p}(p)$.
^{29} The scale parameter, ${\sigma}_{\tilde{\epsilon}}$, is identified because we have already normalized the scale of the ordinal utility of the consumer. The latter was done by normalizing the scale parameter of the stochastic term ${\widehat{\epsilon}}_{\mathit{ijt}}$ in Equation (1) to ${\sigma}_{\widehat{\epsilon}}=1$. Here, we make the assumption that the shocks are i.i.d across consideration sets of retailers because of the nature of our data, that is aggregated at the market level. In Appendix A, we extend the search model to allow for unobserved searchcost heterogeneity. The cumulative distribution function for the shocks ${\tilde{\epsilon}}_{it{R}_{i}}$ is $F({\tilde{\epsilon}}_{\mathit{ijt}})={e}^{{e}^{{\tilde{\epsilon}}_{\mathit{ijt}}/{\sigma}_{\tilde{\epsilon}}}}$.
^{30} If the nesting, price heterogeneity, and searchcost parameters equal zero (i.e., if $\lambda ={\sigma}_{\nu}={\overline{S}}_{t}={s}_{rt}^{D}=0$ for all D, t), then the demand model collapses to a standard logit model, and ${\mathbb{P}}_{\mathit{ijt}}={e}^{{\delta}_{jt}}/{\displaystyle {\sum}_{\widehat{j}=0}^{{J}_{t}}{e}^{{\delta}_{\widehat{j}t}}}$ in Equation (6). Similarly, our randomcoefficient nestedlogit model with search collapses to the nestedlogit model if ${\sigma}_{\nu}={\overline{S}}_{t}={s}_{rt}^{D}=0$ for all D, t.
^{31} Some of these products may not be offered because some VSC retailers may not carry the products of all manufacturers. The total number of inside products in our data is 57 and the total number of possible products in the market is 81.
^{32} We omit the market subscript, t, for the variables in this subsection to simplify the notation.
^{33} Retailers do account for the impact of their retail price choices on the wholesale price negotiations. Given any wholesale prices, retailers independently choose retail prices. At a Nash equilibrium of the second stage game, each retailer’s strategy is the best response to the rivals’ strategies. Anticipating the equilibrium of the second stage game, retailers and manufacturers bargain over wholesale prices.
^{34} Each pair of players maximizes the bilateral gains from trade, modeled by an asymmetric Nash bargaining solution, given the strategies of all other pairs.
^{35} An alternative assumption, followed by Bonnet et al. (2016), is that each pair of manufacturerretailer negotiate all their products jointly.
^{36} They provide conditions under which a combination of aggregate and consumer search data can identify these parameters. Their main insight is to use certain ratios of choice probabilities that do not depend on the searchcost parameters.
^{37} In the setting studied, a market is a month, and a product is a combination of display format, manufacturer, and retailer.
^{38} We use predicted prices, instead of the potentially endogenous prices, as follows. We run a regression of prices on characteristics and predict prices using the estimated parameters from this regression. Then, we use the predicted prices to count the number of products within the 5Euro band. Using such predicted prices generates a valid instrument (even if prices are endogenous) because the characteristics used in the preliminary regression are exogenous. Such regression generates an unbiased estimate of prices in which shocks are removed. The characteristics included in the preliminary regression explain more than 90% of the price variation in the data (adjusted ${R}^{2}=0.927$). We have also experimented with a band of ten Euros and obtained similar results.
^{39} We focus on the linear specification because is the specification used for the estimation in our application. The linearity of search costs, however, can be relaxed, as we discuss later.
^{40} The main difference relative to BLP is that the choice probability and, hence, the market share function incorporates the search step (this is the last term in Equation (6c), denoted by ${\mathbb{P}}_{{R}_{i}^{\prime}}$). Once the market share function is computed, the estimation procedure resembles BLP.
^{41} See Table A2 in the online appendix for a comparison using alternative price beliefs.
^{42} For example, Draganska et al. (2010) use observed prices and quantities to estimate demand parameters. In addition, they have cost data, which they use to estimate marginal costs. Finally, they use the firstorder conditions to estimate the bargaining parameters. Grennan (2013) also uses observed prices and quantities to estimate demand parameters. However, he does not have cost data and cannot estimate all the bargaining and marginal cost parameters. Hence, he imposes restrictions on marginal cost parameters and then uses firstorder conditions to estimate bargaining parameters. We use a somewhat different approach. Prior knowledge of the industry structure allows us to reduce the dimension of the marginal costs parameters (so that manufacturer marginal costs can be estimated with the retailer marginal costs). Then, we use the firstorder conditions from the bargaining game to estimate the bargaining parameters alone.
^{43} Alternatively, one can perform the estimation by using the supplyside moment condition $\mathbb{E}[{Z}^{S}\xb7\widehat{\u03f5}({\gamma}^{*},{\mathbf{c}}^{{\mathbf{r}}^{*}},{\mathbf{\delta}}^{{S}^{*}})]=0$, where Z^{S} is a matrix of supplyside instruments, $\widehat{\u03f5}(\xb7)$ is the error term defined in Equation (20), and $({\gamma}^{*},{\mathbf{c}}^{{\mathbf{r}}^{*}},{\mathbf{\delta}}^{{S}^{*}})$ is the true value of the supply parameters. We also performed the estimation using an expression analog to Equation (19) for retailers’ marginal costs with no unobservable determinants and obtained retailers’ marginal costs that were very close to zero.
^{44} Our estimates imply that the pricecost margins computed from the model without search are substantially lower than those computed from the model with search (50% or more) with a greater bias for VSC retailers. Estimates from a model without search tend to underestimate the effects of a merger because they tend to underestimate the substitution among products. The bias is greater for mergers encompassing VSC retailers that provide better search services.
^{45} The estimated bargaining weights also show that directtoconsumer sales increase the bargaining power of manufacturers when negotiating with retailers. In this article, our main focus is the demand side. We use the supply model to compute the counterfactual prices to investigate the welfare effects to consumers of the services provided by the intermediaries. See Donna et al. (2021) for a supplyside investigation about the impact of directtoconsumer sales on the bargaining power of the manufacturers and the implications for vertical mergers.
^{46} The constant indicates that the absolute level of utility cannot be measured.
^{47} The value τ_{dmrt} represents the gross utility of a display format d, produced by manufacturer m, and sold to consumers by retailer r. In this counterfactual scenario, that product has the gross utility of a display format d, produced by manufacturer m, and sold to consumers by manufacturer m (i.e., a DSC retailer), τ_{dmmt}.
^{48} For example, if the VSC retailer carries products of only one manufacturer, consumers’ search costs do not change in the counterfactual. If the VSC retailer carries products of two (three) manufacturers, consumers’ search costs increase by $\overline{S}$ (2$\overline{S}$). With this specification, the resulting increase in search costs is small. The key insight of this counterfactual is that search costs increase without VSC retailers.
^{49} The change in the consumer surplus in column 4 does not correspond to the sum of the changes in consumer surpluses in columns 1, 2, and 3. The difference is because of interactions between these effects in the counterfactual in column 4, as explained in this paragraph.
^{50} See Donna et al. (2021) for an investigation of the impact of directtoconsumer sales on welfare and the implications for market power and merger evaluation.
^{51} Regarding the U.S. car industry, in 48 states, franchise laws prohibit/limit auto manufacturers from selling directly to consumers. They require the intermediation of car dealers. It has resulted in disputes between Tesla Inc. and state auto dealer associations (Sibilla 2017). Regarding the proposed merger between Aetna and CVS, one of the arguments in its favor is that the merged CVSAetna would not need CVS/Caremark as an intermediary, thus benefiting consumers from the elimination of the intermediaries’ markup (Frakt 2017).
^{52} See, for example, Motta (2004, chapter 6) and the references therein.
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