Measuring unilateral effects in partial horizontal acquisitions

International Journal of Industrial Organization 33 (2014) 22–36 Contents lists available at ScienceDirect International Journal of Industrial Organization journal homepage: www.elsevier.com/locate/ijio Measuring unilateral effects in partial horizontal acquisitions☆ Duarte Brito a,e, Ricardo Ribeiro b,⁎, Helder Vasconcelos c,d,f a Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Portugal Faculdade de Economia e Gestão, Universidade Católica Portuguesa, Porto, Portugal c Faculdade de Economia, Universidade do Porto, Portugal d Centre for Economic Policy Research, United Kingdom e Center for Advanced Studies in Management and Economics, Universidade de Évora, Portugal f Center for Economics and Finance, Universidade do Porto, Portugal b a r t i c l e i n f o Article history: Received 10 February 2013 Received in revised form 24 December 2013 Accepted 26 December 2013 Available online 7 January 2014 JEL classification: D12 C54 L13 L41 L66 a b s t r a c t Recent years have witnessed an increased interest, by competition agencies, in assessing the competitive effects of partial acquisitions. We propose an empirical structural methodology to examine quantitatively the unilateral impact of partial horizontal acquisitions. The acquisitions may be direct or indirect, and may or may not correspond to control. The proposed methodology simulates the effects on prices, market shares, firm profits and consumer welfare. It can deal with differentiated product industries and nest full mergers as a special case. We provide an empirical application to several acquisitions in the wet shaving industry. © 2014 Elsevier B.V. All rights reserved. Keywords: Antitrust Unilateral effects Partial acquisitions Oligopoly Differentiated products Demand estimation 1. Introduction Recent years have witnessed a phenomenal growth of privateequity investment that formed a perfect storm in which firms often hold partial ownership interests in competing firms (Wilkinson and White, 2007). This led competition agencies to take an increased interest in assessing the competitive effects of partial acquisitions. For example, in 2007, the European Commission assessed and rejected a request by Aer Lingus to order Ryanair to divest its 29.4% shareholding in the Irish flag carrier. Also in 2007, the UK Competition Commission assessed ☆ We would like to thank the Editor, Pierre Dubois, and two anonymous referees for their thorough and thoughtful reports. We would also like to thank Stephane Caprice and Natalia Fabra, as well as numerous participants at the XXVII Jornadas de Economía Industrial and seminars participants at Toulouse School of Economics and Universidade Católica Portuguesa, for helpful comments and suggestions. We are grateful to the James M. Kilts Center for Marketing, University of Chicago Booth School of Business for sharing the data and to Fundação para a Ciência e a Tecnologia for financial support (PTDC/EGE-ECO/ 099784/2008 and programme FEDER/POCI 2010). All remaining errors are of course our own. ⁎ Corresponding author at: Faculdade de Economia e Gestão, Universidade Católica Portuguesa, Rua Diogo de Botelho, 1327 4169-005 Porto - Portugal. Tel.: +351 22 619 62 00. E-mail addresses: dmb@fct.unl.pt (D. Brito), rribeiro@porto.ucp.pt (R. Ribeiro), hvasconcelos@fep.up.pt (H. Vasconcelos). 0167-7187/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ijindorg.2013.12.003 the BskyB's acquisition of a 17.9% shareholding in ITV (with no board representation) and found that it would substantially lessen competition in the UK TV market. More recently, in 2008, the European Commission assessed and approved subject to conditions, the acquisition by News Corporation of an approximately 25% shareholding in Premiere. This paper proposes an empirical structural methodology to assess quantitatively the unilateral competitive effects of partial acquisitions in a differentiated products setting, distinguishing two distinct ownership rights: financial interest and corporate control. Financial interest refers to the right of the (partial) owner to receive the stream of profits generated by the operations and investments of the target firm, while corporate control refers to the right of the (partial) owner to influence the decisions of the target firm. We need to identify and distinguish the two rights because partial horizontal acquisitions that do not result in effective control present competitive concerns distinct from partial acquisitions involving effective control. When a firm acquires a partial financial interest in a rival, it acquires a share of its profits. Such acquisition can lessen competition by reducing the incentive of the acquiring firm to compete aggressively because it shares in the losses thereby inflicted on that rival. On the other hand, when a firm acquires corporate control in a rival, it acquires the ability to influence the competitive D. Brito et al. / International Journal of Industrial Organization 33 (2014) 22–36 conduct of the target firm. Such influence can lessen competition because it may be used to induce the rival to compete less aggressively against the acquiring firm. The proposed methodology relates to two strands of the literature. The first strand of literature examines the unilateral impact of partial competitor ownership on competition. In one of the earliest contributions, Reynolds and Snapp (1986) analyze the unilateral competitive effects of partial financial interests and small joint ventures in the context of a Cournot homogeneous-product model. They show that, in markets where entry is difficult, partial financial interests (even if relatively small) could result in lower equilibrium market output and higher equilibrium market prices. They quantify such effects using a summary measure of the state of competition: an adjusted Herfindahl–Hirschman index (HHI). Bresnahan and Salop (1986) build on Reynolds and Snapp (1986) by introducing the distinction between financial interest and corporate control. They evaluate the unilateral competitive effects of a joint venture among competitors, considering different financial interest and control arrangements and proposing a set of modified HHIs to quantify the effects of each alternative arrangement. O'Brien and Salop (2000) extend Bresnahan and Salop (1986)'s modified HHI to a richer set of corporate control scenarios and multiple, overlapping, joint ventures. Furthermore, they propose an extension of the analysis to the context of a Bertrand oligopoly model with differentiated products, building on Shapiro (1996)'s diversion ratio approach. They quantify the effects of partial ownership interests on competitive incentives in this context using a summary measure of the economic pressure to change prices in response to a change in the corporate control scenario or joint venture. They refer to this measure as a Price Pressure Index (PPI). Reynolds and Snapp (1986), Bresnahan and Salop (1986), and O'Brien and Salop (2000) confine their analysis to direct partial ownership interests. Flath (1992) builds on Bresnahan and Salop (1986) and extends the literature by treating the more general case in which indirect partial ownership interests are also present. Firm A has an indirect partial ownership interest in firm C if it holds a partial ownership interest in firm B and, in turn, firm B holds a partial ownership interest in firm C. This issue is particularly important for antitrust purposes because indirect partial ownership interests may constitute a way of evading antitrust rules that limit direct ownership in rivals. Dietzenbacher, Smid and Volkerink (2000) extend this analysis to the context of a Bertrand oligopoly model with differentiated products. Brito et al. (2013a, hereafter BCV) incorporate such indirect partial ownership interests to investigate what the best way is to implement a divestiture of control rights in a context where firms compete in prices and prices are strategic complements, which encompasses the case of a Bertrand oligopoly model with differentiated products. They contribute to the literature by proposing sufficient statistics for the effects of partial ownership (and divestiture of partial ownership) within a duopoly on consumer welfare. The second strand of literature relates to merger simulation. The models within this second strand of the literature simulate the unilateral price effects of mergers in differentiated product markets. These unilateral effects flow from the incentive to increase prices after a merger, an incentive that results from the internalization of consumer substitution among the products of the merging firms. The procedure typically involves the identification of the patterns of consumer substitution, which are then used with a Nash–Bertrand equilibrium assumption to simulate (either explicit or implicitly recovering unobserved marginal costs) the unilateral price effects of mergers. The identification of the patterns of consumer substitution is key and creates a dimensionality problem. In an industry with J differentiated products, this requires the estimation of at least J2 demand price elasticities, a formidable task. In one of the earliest contributions, Baker and Bresnahan (1985) propose an econometric procedure to analyze the unilateral price effects of a merger by considering that the effects of all non-merging firms in the industry can be summed together. The 23 proposed procedure reduces the dimensionality of the problem since it involves the estimation of a partial residual demand system consisting only of the products of the merging firms, rather than the J products in the industry. However, the reduction of the dimensionality is only apparent since each partial residual estimating equation must still include all cost and demand shift control variables for all non-merging products (for which no demand equation is estimated). Hausman et al. (1994, hereafter HLZ) propose to analyze the unilateral price effects of a merger by using Gorman (1995)'s approach to multi-level demand. This approach reduces the dimensionality of the consumer's utility maximization problem (that involves J different products) by modeling it as a sequence of separate, but related decision problems. At the top level, the consumer decides the overall category demand. At a middle level, the consumer decides the demand for specific sub-groups (segments) of products. And finally, at a bottom level, the consumer decides the demand for particular products within each subgroup (or segment). This solves the dimensionality problem because, at each level, the decision involves only a reduced number of options (products or sub-groups). Furthermore, this multi-level procedure is rich enough in parameters to allow flexible substitution patterns and it can be shown to be equivalent to solving a single one-level consumer's utility maximization problem. As a consequence of the latter, it constitutes a structural procedure in the sense that it can be empirically estimated and used not just to simulate the unilateral price effects of mergers, but also to analyze the corresponding change in consumer welfare. However, the procedure cannot be used to identify the patterns of consumer substitution from markets with significant entry and exit of products, which substantively limits its empirical applications. Froeb and Werden (1994) address the limitation of HLZ by analyzing the unilateral price effects of a merger in the context of a random utility model: McFadden (1974)'s standard multinomial Logit model. The procedure is also fully structural and can be used also to analyze the corresponding change in consumer welfare. Consumers are assumed to make a discrete choice among the set of J product alternatives (plus an additional outside option), selecting the alternative yielding the greatest utility. The framework builds on Lancaster (1966) and postulates that consumers derive utility from the properties or characteristics of the products, rather than directly from the products themselves. This setting can deal with markets with significant entry and exit of products, and solves the dimensionality problem by reducing the relevant size from J2 to the (typically smaller) dimension of the space of characteristics. However, the substitution patterns of consumers implied by this standard model tend to be model- instead of data-driven. Nevo (2000) overcomes this drawback by considering a random-coefficients multinomial Logit model in the lines of McFadden and Train (2000) that introduces unobserved consumer heterogeneity in order to allow flexible substitution patterns. We specify a methodology that attempts to link these two strands of the literature. The general strategy models supply competition in a setting similar to O'Brien and Salop (2000) and BCV, and uses a procedure similar to Nevo (2000) to simulate the unilateral effects of actual and hypothetical partial acquisitions: demand side estimates are used jointly with a Nash–Bertrand equilibrium assumption to recover (unobserved) marginal costs, which are then used to simulate the unilateral impact of partial acquisitions on prices, market shares, firm profits and consumer welfare. The acquisitions may be direct and indirect, and may or may not correspond to control. Furthermore, it nests full mergers (100% financial and control acquisitions) as a special case. This structural approach to partial acquisitions has not been, to our knowledge, examined in any other academic study and it may be a preferable method for competition policy issues to the current indirect methods in the literature of using summary measures like modified HHIs or PPIs suitable or relevant only in certain particular economic conditions. Extensions of this methodology to measure (i) the coordinated effects of partial acquisitions, and (ii) the unilateral and 24 D. Brito et al. / International Journal of Industrial Organization 33 (2014) 22–36 coordinated effects of partial acquisitions that involve firms in the vertical chain are provided in two companion papers (Brito et al., 2013b,c). We also provide an empirical application of the methodology to several acquisitions in the wet shaving industry. On December 20, 1989, the Gillette Company, which had been the market leader for years and accounted for 50% of all razor blade units sales, contracted to acquire the wet shaving businesses of Wilkinson Sword in the United States (among other operations) from Eemland Management Services BV (Wilkinson Sword's parent company) for $72 million. It also acquired a 22.9% of the nonvoting equity shares of Eemland for about $14 million. On January 10, 1990, the Department of Justice (DoJ) instituted a civil proceeding against Gillette. The complaint alleged that the effect of the acquisition by Gillette may have been substantially to lessen competition in the sale of wet shaving razor blades in the United States. Shortly after the case was filed, Gillette voluntarily rescinded the acquisition of Eemland's wet shaving razor blade business in the United States, but went through with the acquisition of 22.9% nonvoting equity interest in Eemland. The DoJ approved the acquisition after being assured that this stake would be passive. On March 22, 1993, the Warner-Lambert Company acquired Wilkinson Sword (full merger) for $142 million from Eemland that had put the razor blade company up for sale the year before. The sale was prompted after the European Commission, in November, ordered the Gillette Company to sell its stake in Eemland because of antitrust concerns. These two acquisitions (one involving a partial interest and the other a full merger), and two additional hypothetical ones, are evaluated below. This paper is organized as follows: Section 2 presents the empirical structural methodology used to evaluate the unilateral effects of partial acquisitions, Section 3 provides the above mentioned empirical application and Section 4 concludes. external to the industry, but also owners from the subset ℑ ≡ {1, …,F} of firms within the industry that can engage in rival cross-shareholding. The implications of partial acquisitions on competition depends critically on two separate and distinct elements: financial interest and corporate control. In order to capture the distinction between these two rights, we consider firm f's total stock is composed of voting stock and non-voting (preferred) stock, with the latter giving the holder a share of the profits but no right to vote for the Board or participate in other decisions. The financial interest of shareholder k in firm f is represented by tkf ≥ 0 which denotes the shareholder's holdings of total stock in the firm, regardless of whether it be voting or non-voting stock. The degree of corporate control of shareholder k over the decision making of firm f is a function of the shareholder's holdings of voting stock in firm f. The larger the holdings of voting stock in a firm, the greater the degree of control over the decision making will typically be. However the relationship may not necessarily be linear. For example, a shareholder holding 49% of voting stock in a firm may have no control over the decision making of the firm if one other shareholder has 51%. In contrast, a shareholder holding 10% of voting stock in a firm may have effective control over the decision making of the firm if each of the remaining shareholders holds a very small amount of voting stock. We denote the degree of corporate control of shareholder k in firm f by γkf ≥ 0, a measure of shareholder k's degree of control over the decision making of firm f that does not necessarily correspond to the corresponding holdings of voting stock. 2.1.2. Firm's operating profit The profits generated by a multi-market and multi-product firm f from its operations are defined over the set of different markets and the subset Γfm of products produced by the firm: 2. Empirical structural methodology πf ¼ This section introduces the empirical structural methodology. We study the implications of partial acquisitions on competition in a setting similar to O'Brien and Salop (2000) and BCV. We provide a structural model that can be empirically estimated and used, unlike O'Brien and Salop (2000)'s, not just to simulate the price equilibrium that would result from several partial acquisition counterfactuals, but also to analyze the corresponding change in consumer welfare, therefore generalizing the duopoly sufficient statistic of BCV. The methodology involves four steps similar to Nevo (2000). Step 0 consists of estimating consumer demand and assessing the degree of substitutability between the competing products. Step 1 models supply competition in a setting similar to O'Brien and Salop (2000) and BCV, where two distinct partial ownership rights are identified: financial interest and corporate control. Step 2 uses a Nash–Bertrand equilibrium assumption jointly with demand side estimates to recover (unobserved) marginal costs, and finally step 3 uses that information to simulate the unilateral effects of actual and hypothetical partial acquisitions. We now move on to describe steps 1–3 in more detail. We defer the description of step 0 to the next section when we introduce the consumer demand model in the context of our empirical application. 2.1. Step 1: model supply competition We introduce here the firm's objective function and the assumptions of the supply side of the model in a setting similar to O'Brien and Salop (2000) and BCV. 2.1.1. The setup There are F firms, indexed by f, each of which produces, in each market m ∈ ϒ ≡ {1, …,M} some subset, Γfm, of the Jm alternative products available in that market. There are also K shareholders, indexed by k, who can own shares in more than one firm. Let Θ ≡ {1, …,K} denote the set of shareholders, which can include not just owners that are X m∈ϒ 2 4 3  X pjm −mcjm Λ m sjm ðpm Þ−C fm 5; ð1Þ j∈Γ fm where sjm(pm) is the market share of product j in market m, which is (by definition of market) a function of the Jm × 1 vector pm of prices for all products available in the market, mcjm is the (assumed constant) marginal cost of product j in market m, Λm is the size of market m, and Cfm is the fixed cost of production of firm f in market m. 2.1.3. Firm's aggregate profit In an industry characterized by rival cross-shareholding, the aggregate profits of firm f include not just the stream of profits generated by the firm from its operations, but also a share in its rivals' aggregate profits due to its ownership stake in these firms. We make the following assumption regarding the distribution of those profits among shareholders: Assumption 1. Each firm's aggregate profit is distributed among shareholders proportionally to the total stock owned, regardless of whether it be voting stock or preferred stock. Under Assumption 1, firm f receives a profit stream from its ownership stake in firm g that corresponds to the percentage tfg of firm g's total stock owned. The aggregate profit of firm f can, therefore, be written as: Π f ¼ π f ðpÞ þ X t fg Π g ; ð2Þ g∈ℑ= f where the first term denotes the operating profit and the second term denotes the returns of equity holding by firm f in any of the other firms.1 This set of F equations implicitly defines the aggregate profit for each firm. 1 The set ℑ/f denotes the set ℑ not including firm f. D. Brito et al. / International Journal of Industrial Organization 33 (2014) 22–36 Let D∗ denote the F × F cross-shareholding matrix with zero diagonal elements, tff = 0, and off diagonal elements tfg ≥ 0 (if f ≠ g) representing the percentage held by firm f on firm g's total stock. In vector notation, the aggregate profit equation becomes:  Π ¼ πðpÞ þ D Π; ð3Þ where Π and π(p) are F × 1 vectors of aggregate and operating profits, respectively. In order to solve for those profits explicitly, we make the following assumption regarding the shareholder structure of the firms in the market: Assumption 2. The rank of (I − D∗) equals the number of firms in the market. Under Assumption 2, matrix (I − D∗) is invertible, which implies that it is possible to solve for the aggregate profit equation:   −1 Π ¼ I−D Þ πðpÞ; ð4Þ where I denotes the identity matrix. 2.1.4. Manager's objective function In a standard oligopoly model with no partial ownership interests, barring any market imperfections that preclude efficient contracting between the shareholders and the manager, the former will typically agree (and give the appropriate incentives) that the latter should maximize profits. However, as O'Brien and Salop (2000) argue: When multiple owners have partial ownership interests, (…) they may not agree on the best course of action for the firm. For example, an owner of firm f who also has a large financial interest in rival firm g typically wants firm f to pursue a less aggressive strategy than the strategy desired by an owner with no financial interest in firm g. In this situation, where the owners have conflicting views on the best strategy to pursue, the question arises as to how the objective of the manager is determined. Ultimately, the answer turns on the corporate-control structure of the firm, which determines each shareholder's influence over decision-making within the firm. (Page 609) We make the following assumption regarding the objective of the manager of the firm: Assumption 3. The manager of the firm maximizes a weighted sum of the shareholders' returns. The formulation implied by Assumption 3 constitutes a parsimonious way to model shareholder influence since it includes a wide variety of plausible assumptions about the amount of influence each owner has over the manager of the firm. Under this formulation, a higher weight on the return of a particular owner is associated with a greater degree of influence by that owner over the manager. Different control scenarios then correspond to different sets of control weights for the different owners. Under Assumption 3, the objective function of the manager of firm f can therefore be written as follows: ϖf ¼ X γkf Rk ; ð5Þ k∈Θ= f where γkf measures (as described above) the degree of control of shareholder k over the manager of firm f, and Rk is the return of shareholder k.2 2 Without loss of generality, we assume the firm does not constitute itself as a shareholder, which translates into the set Θ/f (that denotes the set Θ not including firm f). Some firms do possess own shares. However, because a firm's interests are ultimately their shareholders interests, in these cases, the control weight of those shares is ultimately distributed among the shareholders according to their corresponding control weight. 25 In a setting where each firm's aggregate profit is, under Assumption 1, distributed among shareholders proportionally to the total stock owned and each shareholder can have ownership stakes in more than one firm, the return of shareholder k ∈ Θ can be written as: Rk ¼ (X t kg Π g g∈ℑ ϖk if k∉ℑ : if k∈ℑ ð6Þ Combining Eqs. (5) and (6), the objective function of the manager of firm f becomes: ϖf ¼ X γ kf ϖk þ X k∈Θ k∉ℑ k∈ℑ= f γkf X t kg Π g ; ð7Þ g∈ℑ where the first term involves shareholders that are internal to the industry (k ∉ ℑ/f), rival firms within the industry that engage in crossshareholding, and the second term involves shareholders that are external to the industry (k ∉ ℑ). This set of F equations implicitly defines the objective function for each firm. Let C∗ denote the F × F cross-shareholding matrix with zero diagonal elements, γff = 0, and off diagonal elements γfg ≥ 0 (if f ≠ g) representing the measure of firm f's degree of control over the manager of firm g. Let also C and D denote the (K − F) × F control interest and finance interest shareholding matrices with typical element γkf and tkf, respectively.3 In vector notation, the objective function equation becomes: ′ ′ ϖ ¼ C ϖ þ C DΠ; ð8Þ where ϖ denotes the F × 1 vector of objective functions. In order to solve for those functions explicitly, we make the following assumption regarding the shareholder control structure of the firms in the market: Assumption 4. The rank of (I − C∗ ′) equals the number of firms in the market. Under Assumption 4, matrix (I − C∗ ′) is invertible, which implies that it is possible to solve for the objective function equation:     ′ −1 ′ ′ −1 ′ 
−1 ϖ ¼ I−C C DΠ ¼ I−C C D I−D πðpÞ ¼ LπðpÞ; ð9Þ where I denotes the identity matrix and the second equality is obtained by simple substitution of the aggregate profit Eq. (4). The last equality rewrites the objective function vector in terms of the F × F matrix L = (I − C∗ ′)−1C′D(I − D∗)−1 with typical element lfg, for any f, g ∈ ℑ. 2.2. Step 2: recovering (unobserved) marginal costs 2.2.1. Competitive setting and equilibrium prices Having described the objective function of the manager of the firm, we now address the competitive setting: Assumption 5. Firms compete in prices. Furthermore, a pure-strategy Bertrand–Nash equilibrium exists, and the prices that support it are strictly positive. Assumption 5 is illustrative. The proposed methodology is not constrained to this assumption and remains valid under alternative strategy choices by firms (for example, quantity- or capacity-choice behavior). Finally, the assumption can be tested in the lines of the empirical literature that attempts to evaluate the observed conduct of firms. Recent examples that attempt to test if observed equilibrium prices 3 Note that both C and D matrices are defined only in terms of the set of shareholders external to the industry, since the interests of the set of shareholders ℑ of firms within the industry that can engage in rival cross-shareholding are taken into account in matrices C∗ and D∗. D. Brito et al. / International Journal of Industrial Organization 33 (2014) 22–36 26 are consistent with Nash equilibrium pricing includes Nevo (2001), Slade (2004), Salvo (2010) and Molnar et al. (2013). Furthermore, our methodology can extend this literature by empirically distinguishing between four sources of the true price–cost margins: (i) product differentiation, (ii) multi-product firm pricing in the absence of any crossownership, (iii) multi-product firm pricing with cross-ownership, and (iv) collusion. Let pf denote the set of prices controlled by firm f, i.e., the prices of Γfm, the subset of products produced by the firm in all m ∈ ϒ. Allon et al. (2010) established the conditions under which a Nash equilibrium, in fact a unique equilibrium, exists for the general multi-product price competition model with random coefficients multinomial Logit demand functions (that we consider in step 0), see Theorem 6.1 therein. Following the objective function Eq. (9) and Assumption 5, the manager of firm f solves: 8 2 39 =  X <X X  4 max ϖ f ¼ pjm −mcjm Λ m sjm ðpm Þ−C gm 5 ; lfg lfg π g ¼ pf :m∈ϒ j∈Γ ; g∈ℑ g∈ℑ X gm ð10Þ where the second equality makes use of Eq. (9). ne ne The Bertrand–Nash equilibrium in prices pne = (pne 1 , …,pm , …,pM ) is charaterized by the following system of first-order conditions, for all m ∈ ϒ, j ∈ Γfm and f ∈ ℑ: ne
lff sjm pm þ X lfg g∈ℑ X r∈Γ gm
∂srm ne prm −mcrm pne m ∂pjm
¼ 0; ne
ne ne
Gsm pm −Ωm pm pm −mcm Þ ¼ 0 for all m∈ϒ; ð11Þ ð12Þ where sm(pne m ) and mcm are Jm × 1 vectors of shares and marginal cost in market m, respectively, and G denotes a Jm × Jm diagonal matrix with diagonal elements gjj = lff for j ∈ Γfm. This system of first-order conditions suggests that, even if managers do compete (as stipulated in Assumption 5), cross-shareholding of firms (lfg ≠ 0, for f ≠ g ∈ ℑ) diminishes competition between the products of the firms involved (due to the internalization of consumer substitution). 2.2.2. Recovering (unobserved) marginal costs In order to use the above set of first-order conditions to simulate counterfactual prices, we require information on marginal costs, which are typically unobserved. We propose to use demand side estimates (from step 0) to recover them as follows.
b Let ∂s pne;pre =∂p denote the own- and cross-price effects for any jm m two products r and j estimated in step 0 and evaluated at market m′ subset pne,pre of the pre-partial acquisition observed Bertrand–Nash equilibm rium price vector, pne,pre. Let also lpre fg denote the typical element of matrix Lpre = (I − C∗pre ′)−1Cpre ′Dpre(I − D∗pre)−1, computed under the pre-partial acquisition (both corporate control and financial interest) shareholder's weights. Using the above two elements, we can com^ ne;pre and Gpre, and manipulate the set of conditions (12) pute matrices Ω m to recover each market m′ subset vector of marginal costs: ne;pre ^ ne;pre pne;pre dcpre m −Ω m m m ¼ pm
−1 G pre ne;pre
sm pm 2.2.3. Step 3: post-partial acquisition counterfactual equilibrium prices We now describe how to derive the predicted (counterfactual) post^ ne;pst . The procedure uses partial acquisition equilibrium price vector, p the demand side estimates from step 0, the set of first-order conditions (12), the marginal costs recovered in step 2, and the new post-partial acquisition ownership structure as follows.
ne;pst b Let ∂s =∂pjm denote the own- and cross-price effects for any rm pm two products r and j estimated in step 0 and evaluated at market m′ subset pne,pst of pne,pst. Let also lpst m fg denote the typical element of matrix Lpst = (I − C∗pst ′)−1Cpst ′Dpst(I − D∗pst)−1, computed under the postpartial acquisition (both corporate control and financial interest) shareholder’s weights. Using the above two elements, we can compute ^ ne;pst and Gpst, and solve for each market m′ subset vector of matrices Ω m post-partial acquisition prices that satisfies the first-order conditions (2):       pst ne;pst −1 pst ^ ne;pst p ^ ne;pst ^m ^ ne;pst −Ω p G ^sm p −d mcm ¼ 0; m m m ð14Þ pst which we can re-write in vector notation by defining a Jm × Jm matrix Ωm whose jrth element is given by Ωm,rj = − lfg∂srm(pm)/∂pjm for r ∈ Γgm and j ∈ Γfm: rm cost function using, for example, a method of moments approach. Second, it relies on the ability to consistently estimate the price effects in step 0. We defer an analysis of this latter aspect to the next section when we introduce the consumer demand model in the context of our empirical application. : ð13Þ There are two important aspects about this empirical procedure to recover marginal costs. First, it assumes constant marginal costs. However, it can easily be extended to deal with non-constant marginal costs. In this case, the set of first-order conditions differ slightly from the above and marginal costs can be recovered by estimating a marginal dcm denotes market m′ subset vector of post-acquisition marwhere m ginal costs, which can either be assumed to equal the pre-acquisition pre pst marginal costs (d mcm ¼ d mcm for all m ∈ ϒ) or can incorporate eventual cost efficiencies emerging from the acquisition. Although the description above assumes that the partial acquisition does not alter the competitive setting among firms, the proposed methodology is not constrained to having the same assumption of firm behavior before and after the partial acquisition. If the partial acquisition does alter the competitive setting among firms, the methodology idea remains valid, the only difference being that the post-partial acquisition equilibrium price vector must solve the corresponding (new) set of first-order conditions. In particular, if the partial acquisition changes the manner in which firms in the market interact, increasing the strength, extent or likelihood of coordinated conduct, the methodology needs to be extended to assess coordinated effects antitrust concerns. Brito et al. (2013b) provide this extension. ne;pst ^m After solving for p , we can then use it as input, given that the model is structural, to examine the (unilateral) impact of partial acquisitions on market shares, firm profits and consumer welfare. We defer the description of a measure of change in consumer welfare to the next section when we introduce the consumer demand model in the context of our empirical illustration. 3. Empirical application In this section, we present an illustration of the structural methodology used to evaluate the unilateral effects of partial acquisitions. We apply our framework to several acquisitions in the wet shaving industry. On December 20, 1989, the Gillette Company, contracted to acquire the wet shaving businesses of Wilkinson Sword trademark outside of the 12-nation European Community (which included the United States operations) from Eemland Management Services BV (Wilkinson Sword's parent company) for $72 million.4 It also acquired a 22.9% of the nonvoting equity shares of Eemland for about $14 million. At that time, consumers in the United States annually purchased over $700 million of wet shaving razor blades at the retail level. Five firms supplied all but a nominal amount of these blades. The Gillette 4 Eemland Management Services BV changed its name to Swedish Match NV before adopting the name of Eemland Holdings NV. In antitrust enforcement agencies official documents these names appear often interchangeably. D. Brito et al. / International Journal of Industrial Organization 33 (2014) 22–36 Company, which had been the market leader for years, accounted for 50% of all razor blade units sales. The next closest competitors were BIC Corporation (BIC brand) and Warner-Lambert Company (Shick brand), with Wilkinson Sword Inc. and the American Safety Razor Company (Personna brand) having relatively small pre-acquisition shares. On January 10, 1990, the DoJ instituted a civil proceeding against Gillette. The complaint alleged that the effect of the acquisition by Gillette may have been substantially to lessen competition in the sale of wet shaving razor blades in the United States. Shortly after the case was filed, Gillette voluntarily rescinded the acquisition of Eemland's wet shaving razor blade business in the United States. Gillette said it decided to settle the case to avoid the time and expense of a lengthy trial. However, Gillette still went through with the acquisition of 22.9% nonvoting equity interest in Eemland and of all worldwide assets and businesses of Wilkinson Sword trademark from Eemland, apart from the United States and the European Community. Because Eemland kept the Wilkinson Sword's United States wet shaving razor blades business, Gillette had became one of the largest, if not the largest, shareholder in a competitor. The DoJ (1990) allowed the acquisition provided that: Gillette and Eemland shall not agree or communicate an effort to persuade the other to agree, directly or indirectly, regarding present or future prices or other terms or conditions of sale, volume of shipments, future production schedules, marketing plans, sales forecasts, or sales or proposed sales to specific customers … (page 7) In other words, the DoJ approved Gillette's 22.9% stake in Wilkinson Sword after being assured that this stake would be passive. Indeed, Gillette claimed it was merely making an investment. However, even when the acquiring firm cannot influence the conduct of the target firm, the partial acquisition may still reduce the incentive of the acquiring firm to compete aggressively because it shares in the losses thereby inflicted on that rival. We examine this question by quantifying the unilateral impact of partial acquisitions on prices, market shares, firm profits and consumer welfare of such acquisition. On March 22, 1993, the Warner-Lambert Company acquired Wilkinson Sword for $142 million from Eemland that had put the razor blade company up for sale the year before. The sale was prompted after the European Commission, in November, ordered the Gillette Company to sell its stake in Eemland because of antitrust concerns. A full merger constitutes the extreme case of a partial acquisition, which is nested in our empirical structural methodology. As an illustration, we also examine this acquisition, as well as two additional hypothetical ones, and quantify the corresponding unilateral effects. The paper proceeds by describing the data and performing some preliminary analysis. We then move on to describe the demand model, the estimation procedure and discuss the identifying assumptions. Finally, we present the demand estimation results that we use to recover the marginal costs and then simulate the unilateral effects of the examined acquisitions. 3.1. Data description and preliminary analysis We use scanner data collected from July 1994 to June 1996 by the Dominick's Finer Foods (DFF) chain in the Chicago metropolitan area. The dataset covers 29 different product categories at the store level. It includes weekly sales, prices and retail profit margins for each universal product code (UPC) and store of the chain. We supplement the data with ZIP code (i) demographic information obtained from the Decennial Census 2000, and (ii) industry structure obtained from the Business Patterns 1998 databases. In order to investigate the implications of Gillette's 22.9% nonvoting equity interest acquisition in Eemland and of the Warner-Lambert merger with Wilkinson Sword, we focus on the grooming category. In particular, we focus on disposable razor products to avoid the 27 complications that the tied-goods nature of demand poses for modeling in other razor products. The sample covers 6 brands in 81 stores (across 7 counties in the Chicago metropolitan area) for 104 weeks. Gillette is the dominant brand with an average share of 59.5% of the total number of razors sold in each market, which we define as a store–week combination. DFF private label is the second biggest-selling brand with an average share of 20.6%, followed by Shick (14.0%) and BIC (5.6%). Personna and Wilkinson Sword have very residual average market shares. Although each brand offers several products, the choice set available to consumers is relatively limited. The sample covers 30 products and DFF stores carry an average of 13.2 different products in each market. We define a product to be gender segment-specific so that, for example, Schick Slim Twin and Schick Slim Twin Women are classified as distinct products. Women products account for an average share of 17.3% of the total number of razors sold in each market. In contrast with the substantial brand concentration, at the product level there is slightly more fragmentation. Gillette Good News is the market leader with an average share of 14.2% of the total number of razors sold in each market. Each product is typically offered in several package sizes, with the top four sizes accounting for an average share of more than 99% of the total number of razors sold in each market: 10 razor packages (41.5%), 5 razor packages (41.4%), 12 razor packages (11.3%) and 15 razor packages (5.2%). A product-package size combination defines an UPC. The sample covers 56 UPCs and DFF stores carry an average of 17.3 different UPCs in each market. An important question is obviously whether the dataset is representative of the whole population buying disposable razor products. For purposes of Gillette's equity interest acquisition in Eemland, the DoJ (1990) characterized the industry as follows: Gillette accounts for 50% of all razor blade units (…). The next closest competitor is BIC with 20%, followed by Warner-Lambert with 14%, Wilkinson with 3%, and American Safety Razor with less than 1% of unit sales. (page 9) Because this industry characterization refers to razor products as a whole (and not only to disposable ones) and does not account for private labels, we must be cautious in a straightforward comparison with our dataset. However, it does suggest that our data is reasonably representative, although slightly overrepresenting Gillette and underrepresenting BIC and Wilkinson Sword. We now move on to describe the dataset in more detail. Table 1, Panel A presents summary purchase statistics at the UPC level. Although there is evidence of substantial heterogeneity across markets, the median store in the sample sells 2 packages of 5 men razors per week at a price of $3.10 per package, generating 38.9% gross retail margin. This margin is computed with reference to the average acquisition cost of the items in inventory, an issue we will address in more detail below. Table 1, Panel B presents summary statistics at the store level. 17,539 households visit and purchase something in the median store per week. The potential market size is defined in terms of the number of razor packages purchases and assumed to be proportional to the weekly number of household visits of each store. The proportionality factor is assumed to be the percentage of households buying razor products times the probability of a purchase in any given visit. According to IRI Builders Suite (Bronnenberg et al., 2008), 28.5% of US households purchase razor blades in a year, with an average purchase cycle of 106 days. Furthermore, according to Food & Beverage Marketing (Degeratu et al., 2000), US households visit regular grocery stores about 7.9 times per month on the average. This translates into a median potential market of 181.7 package purchases per store and week, a potential market that a median of 7 grocery stores, 3 convenience stores and 5 pharmacies compete for. We explored the sensitivity of our results to the proportionality factor assumption and all the main 28 D. Brito et al. / International Journal of Industrial Organization 33 (2014) 22–36 Table 1 Summary statistics. Mean Panel A: UPC level Quantity (number of packages) Price ($) Gross retail margin (%) Package size (number of razors) Women segment Panel B: store level Number of household visits (000's) Potential market (number of packages) Number of grocery stores Number of convenience stores Number of pharmacies Panel C: demographic level Age Household size Household income ($ 000's) Median Std Min Max 3.297 3.272 41.108 7.377 0.209 2.000 3.090 38.890 5.000 0.000 3.951 1.393 15.889 3.052 0.407 1.000 0.460 −97.570 1.000 0.000 308.000 6.390 74.910 20.000 1.000 17.481 181.079 9.765 4.296 5.556 17.539 181.684 7.000 3.000 5.000 4.675 48.431 8.784 3.404 3.637 1.686 17.465 1.000 0.000 0.000 30.640 317.395 46.000 16.000 14.000 41.537 2.660 79.544 40.221 2.000 57.457 19.228 1.552 87.337 10.000 1.000 0.002 79.000 9.000 599.999 Panel A statistics are based on 144,325 store–week-UPC observations. Gross Retail Margins denote the margin in percent that DFF makes on the dollar for each item sold. Panel B Number of Household Visits and Potential Market statistics are based on 8346 (store–week) market observations. Panel B competition statistics are based on 81 store observations. Panel C statistics are based on 2000 simulated consumers for each of the 8346 (store–week) markets under analysis. conclusions were found to be robust. Finally, Table 1, Panel C presents summary demographic statistics of each store surrounding area (same ZIP code). The median consumer is 40-year-old within a household consisting of two members and an annual income of $57,457. Having described the main data summary statistics, we now examine in more detail the price variable. Temporary price promotions are important marketing tools in the pricing strategy of many nondurable goods and disposable razors are no exception, as the high price variance and the (occasional) negative gross retail margin reported in Table 1, Panel A suggest. Prices in the sample do display the classic high–low pattern: products have a regular level that remains constant for long periods of time with occasional temporary reductions. High–low pricing allows firms to discriminate between (i) informed and uninformed consumers; (ii) consumers with different inventory holding costs; and (iii) price-sensitive switchers and store-loyal consumers. While the classic high–low pattern is easy to spot, regular price levels are hard to define because they may change over time. Following Dossche et al. (2010), we define a temporary price promotion as any sequence of prices that is below at least 95% of the most left and the most right adjacent prices. In untabulated analyses, we characterize DFF's temporary price promotions. Following the typical pattern of setting regular price levels that remain constant for long periods of time, the median prices set by this supermarket chain across all UPCs, stores and weeks are non-promoted. Occasional temporary reductions account for only 11.5% of all price observations and, although there is evidence of substantial heterogeneity, consist of a median 20.8% discount every 4 weeks. In an environment characterized by temporary price discounts, it is important to examine how consumers respond to price cuts. As Hendel and Nevo (2006a) show, demand estimation based on temporary price reductions may mismeasure the long-run responsiveness to prices. This is of fundamental importance in a setting like ours that relies on the ability to consistently estimate own- and cross-price effects. The first two columns in Table 2 address this issue by comparing, per package size, the percentage of weeks that a UPC was on promotion and the percentage of razors sold during those weeks. The results suggest that consumers do respond to temporary price discounts: the percentage of quantity sold on promotion is larger than the percentage of weeks that the promoted price is available. This is consistent with the hypothesis that consumers respond to temporary price cuts by accelerating (anticipating) purchases and hold inventories for future consumption (i.e. stockpile). The main alternative explanation that consumers simply increase their consumption in response to a price reduction is less valid in the wet shaving setting. In order to avoid mismeasuring the long-run responsiveness to prices due to temporary price reductions, we aggregate the data quarterly. Having characterized the price discrimination induced by temporary price promotions, we now address a second form of discrimination: discrimination induced by price nonlinearity in package size. Nonlinear pricing can be used by oligopolistic firms as a screening mechanism to price discriminate between types of consumers that hold private information about their tastes by nudging consumers to self-select (according to their preferences) into a given price-package size combination. Disposable razors are once again no exception. Prices in the sample display a non-linear schedule in package size, which is also reported in Table 2. The last column of the table presents the quantity discount associated with the biggest-selling package sizes. In a context where not all products are sold in all package sizes and all DFF's stores, we analyzed the nonlinearity in package size in the lines of Hendel and Nevo (2006b), using a regression of the price per 5 razors on size dummy variables, controlling for temporary price promotions as well as product and store fixed effects. The quantity discount of each package size is then computed as the ratio of the coefficient on the corresponding size dummy variable to the constant. The results show that prices do exhibit quantity discounting. As a consequence, price nonlinearity constitutes a feature of the market that must be incorporated into the structural model. Table 2 Temporary price promotions and quantity discount. Package size Weeks on promotion (%) Quantity sold on promotion (%) Quantity discount (%) 5 Razors 10 Razors 12 Razors 15 Razors 11.427 11.967 11.755 6.199 19.027 23.959 15.489 7.875 – 29.635 52.555 61.278 Weeks on Promotion and Quantity Sold on Promotion denote, conditional on package size, the percentage of weeks a promotion was offered and the percentage of number of packages sold on promotion, respectively. Figures are computed across all stores, weeks and UPCs. Quantity discount computed as the ratio of each dummy variable coefficient to the constant, from a regression of the price per 5 razors on size dummy variables, controlling for temporary price promotions as well as product and store fixed effects. D. Brito et al. / International Journal of Industrial Organization 33 (2014) 22–36 3.2. Step 0: model consumer demand The supply-side of our empirical structural methodology outlined in the previous section relies on the ability to consistently estimate ownand cross-price effects in step 0. Here, we introduce the consumer's utility function and the assumptions of the demand side of the model. We model consumer demand using the multinomial random-coefficients Logit model in the lines of McFadden and Train (2000), where consumers are assumed to purchase at most one unit of one of the products available in the market. We consider a differentiated products setting similar to Berry et al. (1995, hereafter BLP). The estimation approach allows for consumer heterogeneity and controls for price endogeneity. 3.2.1. The setup In each market m ∈ ϒ ≡ {1, …,M} there are Im consumers, indexed by i, each of which chooses among Jm UPC alternatives. In the estimation below, we abuse notation (to avoid introducing an additional subscript) and define m as a quarter–store combination. Let j = 1, …, Jm index the inside UPC alternatives to the consumer in market m. The no purchase choice (outside alternative) is indexed by j = 0. 3.2.2. Consumer flow utility The consumer flow utility is expressed in terms of the indirect utility from each of the available alternatives. We begin by specifying the indirect utility from choosing an inside alternative. The utility derived by consumer i from purchasing UPC j in market m is assumed to be of the form: uijm   r ¼ uijm pjm ; q j ; xjm ; wm ; ξjm þ εijm   r ¼ α i pjm þ φ q j þ βi xjm þ τ i wm þ ξjm þ εijm ; α i ¼ α þ ηdi þ γvi ; size and annual household income. For the remaining parameters, we have βi = β and τi = τ. We now move on to specify the indirect utility from not purchasing. The utility derived by consumer i from this outside option in market m is assumed to be of the form: ui0m ¼ ui0m ðξ0m Þ þ ε i0m ¼ ξ0m þ σ 0 vi þ εi0m ; n o Ajm ¼ ðdi ; vi ; εim Þjuijm ≥uilm ∀l ¼ 0; 1; …; J m ; where εim where di is a vector of demographic variables and vi is a vector of random-variables that allows for unobserved heterogeneity. η is a vector of parameters that represents how price sensitivity varies with demographics, while γ is a scaling vector. We allow for the price sensitivity to depend on the age of the consumer, as well as on her household ð18Þ   ¼ εi0m ; …; εi J m m . If we assume a zero probability of ties, the aggregate market share of UPC j at market m is just the integral over the mass of consumers in region Ajm: ð15Þ ð16Þ ð17Þ where ξ0m denotes the mean utility derived from not purchasing in market m and εi0m is a random shock to consumer choice. Because utility is ordinal, the preference relation is invariant to positive monotonic transformations. As a consequence, the model parameters are identifiable up to a scalar, which implies that normalization is required. The standard practice is to normalize the mean utility of the outside option, ξ0m, to zero. Having described the indirect utility from the different alternatives available to the consumer, we now address her maximization problem: consumers are assumed to purchase one unit of the alternative that yields the highest utility. Because consumers are heterogeneous (di, vi, εim), the set of consumers that choose UPC j in market m is given by: sjm ¼ where prjm denotes the retail price of UPC j in market m, qj denotes the number of disposable razors included (package size) in UPC j, xjm denotes a Kx-dimensional vector of observed characteristics of UPC j in market m (observed by the consumer and the econometrician), wm denotes a Kw-dimensional vector of observed characteristics of the competitive environment of each market m to account for variations in the shopping alternatives that consumers have for making their purchases, and ξjm denotes the mean utility derived from the unobserved characteristics of UPC j in market m (unobserved by the econometrician, but observed by the consumer), which may be potentially correlated with price. Finally, εijm is a random shock to consumer choice. αi denotes consumer i's price sensitivity. βi denotes the parameters representing consumer i's preference for the observed characteristics included in the vector xjm, and τi denotes consumer i's valuation of shopping alternatives. Disposable razor products come in several package sizes and prices are typically nonlinear in size. φ(qj) denotes the component of the utility function associated to package size. We assume non-linear functional forms for φ(qj). Following McManus (2007), a linear specification for both price and package size would be inappropriate. If the marginal utility from increasing size is constant, then given that price schedules are typically concave in size, then (if the random shock is omitted from the model) all consumers with sufficiently high valuation to purchase a small size would prefer a larger size to the small one. The estimation approach allows for general parameter heterogeneity. In particular, we allow for observed and unobserved heterogeneity in price sensitivity, αi: 29 Z  Ajm dP ðd; v; εÞ ¼ Z  Ajm   dP d ðdÞdP v ðvÞdP ε ðεÞ; ð19Þ where P∗(d,v,ε) denotes the population distribution function of consumer types (di, vi, εim). We assume d, v and ε to be independent. The last equality is just a consequence of this assumption. Having computed the aggregate market shares, the aggregate demand of UPC j at market m is given by qjm = Λmsjm, where Λm denotes the size of the market (potential market) m. 3.2.3. Estimation procedure Having described the consumer demand model, we address the estimation procedure. We estimate the parameters of the demand model assuming the empirical distribution of demographics for P∗d(d), multivariate independent normal distributions for P∗v(v) and a Type I extreme value distribution for P∗ε(ε). The latter assumption allows us to integrate the εs analytically which implies that the unobserved characteristics, ξ, constitute the only source of sampling error. This gives an explicit structural interpretation to the error term and, thereby, circumvents the critique provided by Brown and Walker (1989) related to the addition of ad-hoc errors and their induced correlations. After integrating the εs, the aggregate market share of UPC j at market m is given by: sjm ¼ Z   3 exp uijm 4X 5dP d ðdÞdP v ðvÞ: Jm Ajm exp ð u Þ ikm k¼0 2 ð20Þ We estimated the parameters of the model by following the algorithm used by BLP and Nevo (2000). The general estimation procedure involves searching for the parameters that equate observed and predicted aggregated market shares at the market level. 3.2.4. Price endogeneity and identification The pricing decision of firms takes into account all characteristics of a UPC. This introduces correlation between prices and UPC characteristics and, in particular, between prices and the unobserved UPC characteristics that constitute the structural error term of the demand model. As a consequence, instrumental variable techniques are required for consistent estimation. We can decrease the requirements on the 30 D. Brito et al. / International Journal of Industrial Organization 33 (2014) 22–36 instruments by modeling ξjm = ξj + ξm + Δξjm and capture ξj and ξm by UPC and market fixed effects, where ξj denotes the (market-invariant) mean valuation for the unobserved characteristics of UPC j and ξm denotes the UPC-invariant market deviation from that mean. However, this procedure does not completely eliminate the need for instrumental variable techniques since UPC and market-specific deviations from those means, Δξjm, are still expected to be correlated with prices. We now provide an informal discussion of identification. We have already noted that because utility is ordinal, the preference relation is invariant to positive monotonic transformations. As a consequence, the model parameters are identifiable up to a scalar, which implies that normalization is required. Without loss of generality, we normalize the mean utility of the outside option, ξ0m, to zero. Given this restriction, the identification of the remaining parameters is standard given a large enough sample. The fixed effects ξj and ξm are identified from variation in market shares across the different UPC and markets, respectively. The taste parameters β and the parameters in φ(qj) are identified from variations in the observed UPC characteristics and package sizes. The mean value of the price coefficient, α, is identified from variation in prices. The competition environment coefficients, τ, are identified from variation in the number of grocery stores, convenience stores and pharmacies across ZIP codes. The parameters in vector η are identified from variation in demographics and, finally, the parameters in vector γ and σ0 are identified from variation in market shares due to unaccounted factors. Because of price endogeneity, it will be appropriate to use instruments rather than the variation in the actual prices to empirically identify the model's parameters. In order for an instrument to be valid, it needs to be simultaneously (1) correlated with the endogenous variable price prjm and (2) uncorrelated with the unobserved UPC characteristic variations Δξjm. We follow Davis and Huse (2010) in using three types of price instruments. First, we instrument the price of UPC j in market m by the median price of that UPC across stores in other counties, in the lines of HLZ. The identifying assumption is that (1) prjm are correlated across counties due to the common marginal cost, and (2) Δξjm are mean independent across counties (which requires, for example, that the advertising and promotion strategies of firms cannot be coordinated across counties, but are allowed to be correlated across stores within a county). Second, we instrument the price of UPC j in market m by the number of other same firm UPCs and the number of rival firms UPCs that are offered in that market, as well as by the sum of package sizes of other same firm UPCs and the sum of package sizes of rival firms UPCs that are offered in that market, in the lines of BLP. Third, we instrument the price of UPC j in market m by the BLP-type instruments above within the same gender segment, in the lines of Bresnahan et al. (1997, hereafter BST): the number of other same segment and firm UPCs and the number of same segment rival firms UPCs that are offered in that market, as well as by the sum of package sizes of other same segment and firm UPCs and the sum of package sizes of same segment rival firms UPCs that are offered in that market. BLP and BST instruments constitute countably additive measures of the distance between UPCs in the product space. The identifying assumption is that (1) prjm are correlated with these distance measures (the literature on oligopoly pricing suggests that isolation in the product space tends to be associated with higher margins), and (2) Δξjm are mean independent of observed UPC characteristics (which requires, for example, that variations in observed characteristics are at least predetermined and do not constitute a reaction to variations in demand). The plausibility of the identifying assumptions above is an empirical issue. The validity of condition (1) can be tested by regressing the endogenous variable on the full set of instruments (the instruments excluded from the demand equation plus all the exogenous explanatory variables in the demand equations). A commonly used statistic is the F-test of the joint significance of the excluded instruments. The validity of condition (2) is more difficult to test and, although, when the demand equations are over-identified (the number of excluded instruments exceeds the number of included endogenous variables), the overidentifying restrictions may be tested via the J statistic of Hansen (1982), there are limits to the extent to which the uncorrelation condition in itself can be tested in an entirely convincingly way. 3.2.5. Consumer welfare The main contribution of the paper is to provide a structural model that can be empirically estimated and used not just to simulate the price equilibrium that would result from several partial acquisition counterfactuals, but also to analyze the corresponding change in consumer welfare. Under the assumptions of the consumer demand model, the expected maximum utility of consumer i in market m, from the available choice set,
prior to observing the vector of random shocks εim ¼ εi0m ; …; εi J m m , is given by McFadden (1981)'s inclusive value: " J # m X expðuikm Þ : ωim ¼ ln ð21Þ k¼0 A partial acquisition in a rival impacts equilibrium prices and, as a consequence, it also impacts the expected maximum utility of consumers. As long as there is no change in the observed and unobserved characteristics of the choice set and the marginal utility of income of each consumer αi is fixed, the expected difference in the maximum utility of consumers before and after the partial acquisition equals the difpre pre pst ference in inclusive values: ωpst im − ωim , where ωim and ωim are computed using the equilibrium prices before and after the aforesaid acquisition, respectively. When the utility is linear in price, as in our discrete choice model setting, we can normalize this difference by the consumer's marginal utility of income and compute the corresponding compensating variation, converting it into the monetary equivalent that compensates consumer i in market m for enduring the ownership change (Small and Rosen, 1981): CV im ¼ pre ωpst im −ωim : αi ð22Þ The average compensating variation is just the integral over the mass of consumers. The aggregate compensating variation in the population of market m is just the product of the average compensating variation and the size of the market:   CV m ¼ Λ m ∫CV im dP d ðdÞdP v ðvÞ; ð23Þ where P∗d(d) and P∗v(v) denote the assumed empirical distribution of demographics and independent normal distributions for unobserved heterogeneity, respectively, and Λm denotes the size of market m. 3.2.6. Consumer demand estimation results Table 3 presents the demand estimation results, with the different columns reporting distinct specifications that vary on both the covariates included, the estimation procedure and the type of price instruments. Specifications (1), (3) and (5) report the results of a generalized method of moments regression of a standard multinomial Logit model using each of the types of instruments described above. These first specifications include price, demographic and competition variables as covariates. Furthermore, we introduce heterogeneity by interacting price with observable demographic characteristics and include UPC fixed effects in order to fully control for ξj.5 The coefficients on the different covariates are all of the expected signs but mostly statistically insignificant. The price coefficient is one example of the latter. 5 Moreover, this captures non-linearities in φ(qj). D. Brito et al. / International Journal of Industrial Organization 33 (2014) 22–36 31 Table 3 Demand estimation results. Logit Logit Logit RC logit IV: HLZ IV: BLP IV: BST IV: BLP (1) (2) Standard coefficients: price, demographic and competition covariates Price −0.921 −1.054 (0.188) (0.124) Price × HH size −0.074 −0.074 (0.083) (0.055) Price × age 0.009 −0.016 (0.115) (0.076) Price × HH income 0.159 0.144 (0.038) (0.021) HH size −0.020 (0.240) Age −0.557 (0.325) HH income −0.171 (0.106) Nearby grocery str. 0.383 (0.406) Nearby conven. str. 2.017 (0.737) Nearby pharmacies −1.556 (0.635) (3) (4) (5) (6) (7) −0.442 (0.487) −0.256 (0.220) −0.083 (0.292) 0.154 (0.085) 0.482 (0.633) −0.299 (0.829) −0.274 (0.256) 0.429 (0.493) 0.886 (0.849) −1.452 (0.671) −2.442 (0.239) −0.187 (0.083) −0.250 (0.135) 0.181 (0.036) −0.627 (0.510) −0.216 (0.233) −0.020 (0.314) 0.082 (0.094) 0.253 (0.665) −0.576 (0.881) −0.065 (0.283) 0.731 (0.482) 0.151 (0.849) −1.568 (0.661) −2.301 (0.232) −0.189 (0.088) −0.135 (0.140) 0.161 (0.041) −2.516 (0.352) Random coefficients: standard deviations Constanta 0.030 (2.501) 0.047 (0.330) Price Random coefficients: demographic interactions Price × HH size Price × age Price × HH income Control parameters No. end. var./instr. R2/Hansen J statistic U– 4/28 146.39 UST 4/28 159.15 U– 4/16 150.59 UST 4/16 18.044+ U– 4/16 154.82 UST 4/16 105.54 −0.189 (0.190) −0.223 (0.222) 0.131 (0.068) UST 6/16 17.398+ Based on 17,745 observations. Standard errors clustered by store-brand in parentheses. HH denotes household. Nearby grocery str. and Nearby conven. str. denote the number of nearby grocery and convenience stores, respectively. No. end. var./instr. denote the number of endogenous variables and the number of instruments, respectively. Specification (1) includes a constant term. U, S and T denote UPC, store and time (quarter) dummy variables. +denotes that the J statistic of Hansen is statistically significant at the 5 percent level. a The constant's standard deviation captures σ0. The interactions with household size and consumer age are mostly statistically insignificant too suggesting that these observed demographics do not explain price sensitiveness. Finally, the coefficients on demographic and competition covariates are also mostly statistically insignificant. This suggests that the utility of purchasing (and not purchasing) is not explained by the observed demographics nor impacted by the number of nearby grocery, convenience stores and pharmacies. Although the first stage F-test of the joint significance of the excluded instruments is statistically significant for all types of instruments, the corresponding tests of over-identification are rejected, suggesting that the identifying assumptions are not valid. In order to reduce the requirements on the instruments, we estimate specifications (2), (4) and (6) that include store- and quarter-fixed effects. Because each market is defined as a store–quarter combination, the fixed effects (partially) control for ξm, UPC-invariant market deviations from the valuation means. Since ξm may be a function of unobserved demographics, if the unobserved demographics are correlated with prices, ξm will be correlated with prices. The inclusion of the store- and quarter-fixed effects increases the absolute value of the price coefficient, which suggests that prices may be positively correlated with ξm, which will underestimate consumer price sensitivity if not accounted for. We interpret the effects on the price coefficient as evidence that controlling for ξm matters. The price coefficient suggests that the average consumer is in fact price sensitive. The interactions with household size and consumer age remain mostly statistically insignificant suggesting that these observed demographics do not explain price sensitiveness. The interaction with household income becomes, however, highly significant suggesting that households with higher income are less price sensitive. The first stage F-test of the joint significance of the excluded instruments is, again, statistically significant for all types of instruments. Controlling for the unobserved demographics via ξm eliminates the omitted-variable bias and improves the corresponding over-identification test statistic. In the case of the BLP type instruments, the improvement is such that the instruments are no longer rejected, suggesting that the BLP identifying assumption is valid. We explored the sensitivity of our results to the inclusion of market fixed effects that (fully) control for ξm. All the main coefficient results were found to be robust. In order to avoid increasing unnecessarily the dimensionality of our problem, we controlled for ξm using store- and quarter-fixed effects. Finally, specification (7) reports the results for the full multinomial random-coefficients Logit model with BLP type instruments. The results suggest that the average consumer is price sensitive. The interaction with household income is, once again, statistically significant confirming that households with higher income are less price sensitive. The remaining interactions with household size and consumer age are statistically insignificant suggesting that these observed demographics do not explain price sensitiveness. The standard deviation coefficients D. Brito et al. / International Journal of Industrial Organization 33 (2014) 22–36 32 Table 4 Median own- and cross-price elasticities. UPC 4 7 9 10 12 13 14 15 16 1. B Lady Shaver 10r 2. B Metal Shaver 5r 3. B Pastel Lady Shaver 5r 4. B Shaver 10r 5. G Daisy Slim 5r 6. G Good News 3r 7. G Good News 10r 8. G Good News Microtrac 5r 9. G Good News Pivot Plus 10r 10. ASR Personna Flicker 5r 11. PL Single Blade 5r 12. PL Twin Blade 5r 13. WL Schick Slim Twin 5r 14. WL Schick Slim Twin 10r 15. WS Colors 5r 16. WS Ultra Glide Twin 5r 0.045 0.036 0.031 −6.439 0.024 0.036 0.032 0.031 0.022 0.032 0.030 0.030 0.027 0.031 0.026 0.023 0.275 0.327 0.301 0.256 0.294 0.325 −12.877 0.346 0.387 0.313 0.246 0.258 0.323 0.305 0.324 0.336 0.009 0.009 0.011 0.010 0.011 0.009 0.010 0.009 −12.761 0.009 0.008 0.008 0.009 0.010 0.011 0.011 0.031 0.033 0.032 0.028 0.051 0.033 0.032 0.035 0.038 −10.221 0.028 0.029 0.034 0.031 0.036 0.033 0.105 0.105 0.105 0.106 0.111 0.114 0.109 0.117 0.111 0.113 0.107 −4.538 0.111 0.110 0.108 0.110 0.045 0.050 0.051 0.046 0.072 0.051 0.051 0.052 0.054 0.053 0.047 0.047 −7.277 0.050 0.056 0.058 0.059 0.149 0.156 0.145 0.228 0.146 0.165 0.181 0.205 0.187 0.135 0.140 0.157 −10.901 0.202 0.205 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 −3.650 0.004 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.007 −4.769 Figures denote the median price elastiticities over the 643 markets. The elasticity in row i and column j represents the percentage change in market share of product i with a 1% change in price of product j. B: BIC, G: Gillette, ASR: American Safety Razor, PL: Private Label, WL: Warner-Lambert, WS: Wilkinson Sword. 3r, 5r and 10r denote package sizes of 3, 5 and 10 razors, respectively. are also statistically insignificant, which suggests that most of the heterogeneity is due to demographics. Further, the point estimates of the price covariate coefficients are very similar to the ones for the standard multinomial Logit model in specification (4), which is indicative that the heterogeneity within each demographic covariate is small. Table 4 reports a sample of the estimated median (across the 643 store–quarter markets) own- and cross-price elasticities, computed according to the estimates from specification (7) in Table 3.6 The average (across the 56 UPCs) of the median of the estimates of the own-price elasticity is − 8.9. While such elasticities may seem relatively high, when one takes into account the fact that there is a large number of UPCs produced by large multiproduct firms, the elasticities seem quite reasonable. If we were to look at own-price elasticities across products or brands, considering the cross-price elasticities of all the other UPCs that the company owns, the magnitudes would be lower. The average of the median of the estimates of the cross-price elasticity is 0.1. By a similar argument as above, while such elasticities may seem relatively low, if we were to look at cross-price elasticities across products or brands, the magnitudes would be higher. 3.2.7. Recovering (unobserved) marginal costs We now move on to recover the (unobserved) marginal costs. Before we do so, we must address two issues. First, in a typical competition policy issue, we would address the pre-partial acquisition marginal costs. It is possible, however, to adjust the methodology to fit the specificities of the data used in the demand estimation (step 0). This is the case of our empirical illustration that uses data from July 1994 to June 1996, the Warner-Lambert's post-acquisition period. As a consequence, we are required to recover the post-partial acquisition marginal costs and perform counterfactuals about prior facts. Second, in the context of our application, we use retail data to infer manufacturer behavior. To do so we rewrite the operating profit of each firm in terms of the retail price. Let the manufacturer's margin w w for a given UPC j in market m be given by mgw jm = pjm − mcjm, where w pw jm denotes the corresponding wholesale price and mcjm denotes the manufacturer's marginal cost of producing an additional pack of UPC j in market m and transporting it from the plant to the retailer store. Let also the margin of the retailer for selling this pack of UPC j in market r r m be given by mgrjm = prjm − pw jm − mcjm, where pjm denotes (as 6 As a robustness check, we computed the own- and cross-price elasticities according to the estimates from specification (4). Given the similarity between the point estimates from specifications (4) and (7), the magnitude of these price elasticities are comparable to the ones presented in Table 4. These results are available from the authors upon request. before) the corresponding retail price and mcrjm denotes the retailer's marginal cost of getting the additional pack to the store shelves and selling it. We can rearrange this margin in terms of the wholesale r r r price (pw jm = pjm − mcjm − mgjm) and use the result to rewrite r the manufacturer's margin in terms of the retail price: mgw jm = pjm − r r w mcjm − mgjm − mcjm. Although we do not model the interaction between manufacturers and retailers explicitly, this is consistent with a wide variety of models of manufacturer–retailer interaction, since we allow the retailer margin to be free floating over markets and UPCs. Furthermore, it implies that, in our application, the recovered marginal cost c pst of each UPC in a given market, mc jm , includes those three elements: c w;pst þ mc c r;pst c r;pst c pst mc jm ¼ mcjm jm þ mg jm : ð24Þ Having addressed the above issues, we now detail the procedure to recover the unobserved marginal costs. It makes use of a slight adjusted version of Eq. (13) that relies on the Bertrand–Nash behavior described in Assumption 5, on the vectors pr,ne,pst and sm(pr,ne,pst ), on the ability to m m consistently estimate own- and cross-price effects, and on the ownership structure established in matrix Lpst. The vectors pr,ne,pst and sm(pr,ne,pst ) are observed in the data. The m m own- and cross-price effects required to compute the elements of mane;pst ^ trix Ω are estimated within the demand model (Table 4 provides a m sample of the estimated price-elasticities). Matrix Lpst is computed, under Assumptions 1–4, using the shareholders' financial interests and corporate control rights in the different firms. The former are easily derived from firm reports. The latter, as discussed above, depend on the relative bargaining power of the shareholders and will typically be a (non-linear) function of their corresponding voting rights. Table 5 presents the distribution of the post-partial acquisition financial interests and voting rights of the different firms (from March 22, 1993 onwards) according to 1994's Schedule 14A (proxy statement) information reported by each firm. In the empirical analysis below, we make the following assumption regarding the measure of each shareholder degree of control over the manager of the firm: Assumption 6. The control weight each owner has over the manager of the firm is equal to the share of voting rights she owns. Assumption 6 constitutes a natural benchmark and it is merely illustrative. Moreover, given the particular ownership structure of our empirical application, it has relatively innocuous implications. In order to see why, recall we recover marginal costs for the post-partial acquisition ownership structure, a structure in which, following the D. Brito et al. / International Journal of Industrial Organization 33 (2014) 22–36 33 Table 5 Principal shareholders and subsidiaries. Shareholders American Safety Razor Company Allsop Venture Partners III, LP Goldman Sachs Group, LP Scudder Stevens and Clarck Equitablea Grantham Mayo Van Otter Leucadia Investors, Inc. Mezzanine Capital and Income Trust 2001 PLC BIC Corporation Bruno Bich Warner-Lambert Company The Capital Group, Inc. Wilkinson Sword, Inc. The Gillette Company Berkshire Hathaway, Inc. Subsidiaries Financial interest Voting right 12.40 7.80 7.00 14.40 5.10 4.10 2.00 12.40 7.80 7.00 14.40 5.10 4.10 2.00 77.70 77.70 5.16 5.16 10.90 Financial interest Voting right 100.00 100.00 10.70 1994's Schedule 14A (proxy statement) information. Financial interest denotes each shareholder's holdings of total stock. Voting right denotes each shareholder's holdings of voting stock. a Equitable denotes the cumulative ownership of Equitable Capital Partners, LP, Equitable Deal Flow Fund, LP, Equitable Capital Partners (Retirement Fund), LP, and The Equitable Life Assurance Society of the United States. distribution of financial interests in Table 5, owners do not have conflicting views on the best strategy to pursue. As a consequence, the recovered marginal costs are invariant to the control weight's distribution among owners. Nevertheless, the proposed methodology is not constrained to Assumption 6. As suggested by Goppelsroeder et al. (2008), we can, alternatively, measure the shareholders' bargaining power by the Shapley–Shubik (1954) power index or the Banzhaf (1965) power index. 7 The first two columns of Table 6 present price and recovered marginal costs for a sample of UPCs. Given that those variables vary by UPC, store and quarter, we present the median for each selected UPC across the 643 store–quarter combinations. The median price and recovered marginal cost is $3.02 and $2.59, respectively. The third column of Table 6 presents the recovered marginal costs as a percentage of price. The median recovered marginal cost to sale price ratio is 85.8%. In order to evaluate the reasonability of our results, we decompose the recovered marginal cost using the gross retail margin prjm − pw jm r,pst (to capture mcr,pst jm + mgjm ), a variable not used in the demand side estimation for exactly this purpose. This decomposition is presented, with the obvious exception of private labels, in columns four and five of Table 6. The median gross retail margin, excluding private labels, corresponds to 36.6% of price, yielding the manufacturer's marginal cost of producing an additional pack and transporting it from the plant to the retailer store corresponds to the remaining 51.6% of the retail price and 79.6% of the wholesale price, which translates into a 20.4% manufacturer's margin to wholesale price ratio. We compare this margin estimate with the accounting estimates supported by 1994's Annual Report of the two biggest-selling brands (excluding private labels). Gillette and Warner–Lambert's operating margin in 1994 was 37.4% (blades & razors business segment) and 24.0% (consumer health care industry segment) of the corresponding wholesale price, respectively, a value reasonably close to our results if we take into account that 7 Although, in our empirical application, the recovered marginal costs are not affected by the control weight's distribution among owners, in general this is not true. In cases involving partial cross-shareholding of voting rights, the owners of a firm can have conflicting views on the best strategy to pursue. Owners that engage in cross-shareholding may use their voting rights to influence the manager to pursue a less aggressive strategy than the strategy desired by the remaining owners. As a consequence, the choice of power index matters and a careful evaluation of the true control weight is essential. If, for instance, the assumed power distribution overestimates the true control weight cross-shareholders have over the manager of a firm, the methodology will infer a less aggressive behavior towards rivals and consequently, for a given observed price level, overestimate marginal costs. disposable razor products typically sell at a lower margin than the remaining razor products, making the accounting estimates above, conservative ones. This seems to suggest the prices (and marginal cost to price ratios) in the industry are consistent with the Bertrand–Nash behavior described in Assumption 5. 3.2.8. Counterfactual analysis After recovering the implied post-partial acquisition marginal costs, dcpst m m , we consider different shareholder and cross-ownership structures and simulate counterfactual equilibria. As discussed above, because of the specificities of our dataset, we aim to perform counterfactuals about facts that occurred prior to 1994. The procedure solves for the prices that satisfy a slight adjusted version of the first-order conditions (14). In particular, we solve for the prices in the baseline (counterfactual) pre-partial acquisition setting in which the shareholder structure of Wilkinson Sword is independent of the remaining firms in the industry (to mimic the industry ownership structure before December 20, 1989) and use them to evaluate the following acquisitions: 1. Gillette acquires a 100% voting equity interest in Wilkinson Sword. This constitutes a hypothetical ownership structure and it is presented to illustrate the counterfactual market outcomes if Gillette did not voluntarily rescinded the acquisition of Eemland's wet shaving razor business in the US (counterfactual). 2. Gillette acquires a 22.9% nonvoting equity interest in Wilkinson Sword. This mimics the industry ownership structure from December 20, 1989 to March 22, 1993 (counterfactual). 3. Gillette acquires a 22.9% voting equity interest in Wilkinson Sword. This constitutes a hypothetical ownership structure and it is presented here to illustrate the differential impact of acquiring a voting and a nonvoting equity interest (counterfactual). 4. Warner-Lambert acquires a 100% voting interest in Wilkinson Sword. This constitutes a full merger and mimics the industry ownership structure from March 22, 1993 onwards (1994's actual situation). Table 7 reports the median simulated percentage variation in equilibrium prices and market shares relative to the baseline case for a sample of UPCs across all DFF stores, using data for the third quarter of 1994. There are three important aspects about these simulated results. First, in the analysis, we assume the recovered marginal costs of each UPC in a given market before and after the shareholder structure change remain constant. This means that the change in ownership does not lead to any efficiency gains or better information. However, as discussed above, the analysis is not constrained to this assumption and can easily D. Brito et al. / International Journal of Industrial Organization 33 (2014) 22–36 34 Table 6 Median recovered marginal costs. mc decomposition UPC pr mc mcw r 2.16 2.09 2.01 2.39 1.89 2.19 4.83 2.89 4.66 3.74 1.01 1.67 2.69 4.03 1.29 1.69 3.02 3.37 1.79 1.73 1.64 2.00 1.48 1.71 4.38 2.41 4.15 3.39 0.62 1.28 2.30 3.65 0.92 1.32 2.59 2.95 mcw mgw w (as a % p ) ($) 1. B Lady Shaver 10r 2. B Metal Shaver 5r 3. B Pastel Lady Shaver 5r 4. B Shaver 10r 5. G Daisy Slim 5r 6. G Good News 3r 7. G Good News 10r 8. G Good News Microtrac 5r 9. G Good News Pivot Plus 10r 10. ASR Personna Flicker 5r 11. PL Single Blade 5r 12. PL Twin Blade 5r 13. WL Schick Slim Twin 5r 14. WL Schick Slim Twin 10r 15. WS Colors 5r 16. WS Ultra Glide Twin 5r Overall Median Median Excluding PL mcr + mgr mc (as a % p ) 83.1 82.4 82.0 84.1 77.9 78.6 90.6 83.6 89.3 90.2 61.8 76.7 85.6 90.7 71.1 78.8 85.8 87.4 27.6 48.3 45.7 34.5 4.20 37.9 35.6 34.5 36.1 61.0 – – 35.6 35.1 61.9 43.8 – 36.6 55.3 34.1 35.2 49.6 68.2 40.9 54.8 48.2 55.0 28.7 – – 49.4 55.7 9.50 34.1 – 51.6 76.2 66.3 66.0 75.4 74.7 65.6 85.4 74.7 84.1 75.8 – – 77.2 86.0 24.9 60.6 – 79.6 23.8 33.7 34.0 24.6 25.3 34.4 14.6 25.3 15.9 24.2 – – 22.8 14.0 75.1 39.4 – 20.4 Figures denote median values over the 643 store–quarter combinations. B: BIC, G: Gillette, ASR: American Safety Razor, PL: Private Label, WL: Warner-Lambert, WS: Wilkinson Sword. 3r, 5r and 10r denote package sizes of 3, 5 and 10 razors, respectively. be adjusted accordingly. Second, although the recovered marginal costs (and the corresponding retailer markups) are allowed to be free floating over markets and UPCs in a manner that is consistent with a wide variety of models of manufacturer–retailer interaction, for the counterfactual analysis, because the interaction between manufacturers and retailers is not modeled explicitly, the procedure assumes the simulated pricing decisions do not impact the retailer markup of each market and UPC. If, as a result of an acquisition, the effect on those decisions is expected to significantly impact retailer markups, the interaction with manufacturers needs to be accounted explicitly. Brito et al. (2013c) model this interaction and extend the methodology for partial acquisitions that involve firms in the vertical chain. Third, in spite of the fact that the recovered marginal costs are, in our empirical illustration, invariant to the choice of power index, the counterfactuals involving partial cross-shareholding of voting rights are not. In our application, such only happens for Gillette's 22.9% voting equity interest acquisition in Wilkinson Sword, which incidentally constitutes a hypothetical acquisition, presented just to illustrate the differential impact of acquiring a voting right over the financial interest. For such purpose, the natural benchmark implied by Assumption 6 seems reasonable. The first two columns of Table 7 examine the impact of the 100% voting equity interest acquisition in Wilkinson Sword initially proposed by Gillette. The DoJ alleged that the effect of this acquisition may have been substantially to lessen competition and shortly after, Gillette voluntarily rescinded the acquisition. The simulated counterfactual price increases are, however, low: 9.3% and 7.2% for WS Colors and WS Ultra Glide, respectively. The next two columns examine the impact of the 22.9% nonvoting equity interest acquisition in Wilkinson Sword by Gillette. The DoJ allowed this acquisition after being assured that this stake would be passive. The results confirm the reasonability of this decision. The simulated price increases are extremely low: smaller than 0.001% for both Table 7 Simulated median percentage change in prices and shares. WS acquired by G 100% voting UPC 1. B Lady Shaver 10r 2. B Metal Shaver 5r 3. B Pastel Lady Shaver 5r 4. B Shaver 10r 5. G Daisy Slim 5r 6. G Good News 3r 7. G Good News 10r 8. G Good News Microtrac 5r 9. G Good News Pivot Plus 10r 10. ASR Personna Flicker 5r 11. PL Single Blade 5r 12. PL Twin Blade 5r 13. WL Schick Slim Twin 5r 14. WL Schick Slim Twin 10r 15. WS Colors 5r 16. WS Ultra Glide Twin 5r price 0.001 0.002 0.001 0.000 0.038 0.053 0.000 0.041 0.027 0.000 0.000 0.000 0.002 0.000 9.283 7.247 share 0.123 0.145 0.067 0.000 −0.114 −0.140 0.000 −0.128 −0.141 0.000 0.000 0.000 0.135 0.000 −28.279 −28.685 G 22.9% nonvoting G 22.9% voting price price share † 0.001 0.001† 0.001† 0.000 0.008 0.012 0.000 0.009 0.006 0.000 0.000 0.000 0.001† 0.000 0.001† 0.001† 0.013 0.015 0.007 0.000 −0.040 −0.052 0.000 −0.048 −0.052 0.000 0.000 0.000 0.014 0.000 0.016 0.016 WL 100% voting share † 0.001 0.001† 0.001† 0.000 0.009 0.012 0.000 0.010 0.006 0.000 0.000 0.000 0.001 0.000 2.673 2.087 0.035 0.042 0.018 0.000 0.023 −0.027 0.000 −0.027 −0.027 0.000 0.000 0.000 0.038 0.000 −9.141 −9.305 price share † 0.001 0.001† 0.001† 0.000 0.001 0.002 0.000 0.002 0.001 0.000 0.000 0.000 0.048 0.000 1.643 1.264 0.027 0.033 0.019 0.000 0.019 0.024 0.000 0.024 0.019 0.000 0.000 0.000 0.027 0.000 −5.638 −5.699 Figures are the median percentage change for each product over 81 stores in the third quarter of 1994. B: BIC, G: Gillette, ASR: American Safety Razor, PL: Private Label, WL: WarnerLambert, WS: Wilkinson Sword. 3r, 5r and 10r denote package sizes of 3, 5 and 10 razors, respectively. † 0.001† denotes percentage changes smaller than 0.001. D. Brito et al. / International Journal of Industrial Organization 33 (2014) 22–36 35 Table 8 Changes in total welfare, consumer welfare, firm's aggregated profits, brand's operating profits. WS acquired by Consumer welfare Firm's aggregated profits BIC Gillette American Safety Razor Private label Warner Lambert Wilkinson Sword Total Brand's operating profits BIC Gillette American Safety Razor Private label Warner Lambert Wilkinson Sword Total welfare G 100% voting G 22.9% nonvoting G 22.9% voting WL 100% voting −20.403 −2.138 −5.835 −4.822 0.914 40.112 0.107 2.865 1.263 – 7.147 0.097 8.749 0.012 0.296 0.135 0.010 0.568 0.261 9.848 0.031 0.820 0.361 −0.146 2.479 0.215 1.460 0.024 0.688 38.224 – 2.497 0.914 3.559 0.107 2.865 1.263 −1.561 −13.256 0.097 0.019 0.012 0.296 0.135 0.010 −1.570 0.261 1.153 0.031 0.820 0.361 −0.146 −3.356 0.215 1.460 0.024 0.688 0.163 −0.054 −2.325 Figures are in thousands of US dollars. The variation in each firm's aggregated profits denotes the variation in the stream of profits from the operations involving its own brand plus the share (corresponding to its financial ownership stake) in the rival's full aggregate profits. For example, for the case in which Gillette acquires 22.9% nonvoting of Wilkinson Sword, the variation in Gillette's aggregated profit includes the variation in the stream of profits from the operations involving Gillette's own brand plus a 22.9% share in Wilkinson Sword's full aggregate profits (not just in the implied variation). The variation in total aggregated profits is equal to the variation in total operating profits and corresponds to the variation in the returns of all external shareholders. WS Colors and WS Ultra Glide. The following two columns examine the differential impact of, in addition to a financial interest, acquiring a voting equity interest. We expect the latter to lessen competition to a greater extent when compared with the sole acquisition of the former. The simulated price increases confirm this expectation: 2.7% and 2.1% for WS Colors and WS Ultra Glide, respectively. Finally, the last two columns examine the impact of the 100% voting equity interest acquisition in Wilkinson Sword by the Warner-Lambert Company, prompted because of antitrust concerns. The concern was focused particularly on Europe where Wilkinson Sword was a stronger player than in the US. Consistently with traditional merger analysis, a merger between firms selling differentiated products may diminish competition by enabling the merged firm to profit by unilaterally raising price. The simulated price increases are however relatively low: 1.6% and 1.3% for WS Colors and WS Ultra Glide, respectively. Interestingly, the quantitative impact of a full merger with a smaller player (Warner-Lambert) on WS's prices is relatively similar to a 22.9% partial voting acquisition by a larger player (Gillette). The main contribution of the paper is to provide a structural model that can be empirically estimated and used not just to simulate the price equilibrium that would result from several partial acquisition counterfactuals, but also to analyze the corresponding change in consumer welfare. Table 8 presents changes in consumer welfare, firm aggregated profits, and total welfare extrapolated for the US economy as a whole (under each of the shareholder and cross-ownership structures considered). The consumer welfare results were calculated as follows. The first step consisted in computing the average compensating variation across the 2,000 simulated consumers for each market m (given that we focus our analysis on the third quarter of 1994, a market is defined here as a store). We then computed the aggregate compensating variation, for each store m, multiplying the corresponding average by the potential size of the store. Finally, we added the aggregated compensating variation across all stores. In order to extrapolate the results for the US economy as a whole, we computed the average compensating variation across the different markets and multiplied by the US economy yearly potential market. The extrapolated results suggest that the 100% voting equity interest acquisition in Wilkinson Sword initially proposed by Gillette, and voluntarily rescinded due to antitrust concerns, would have had the highest negative impact on consumer welfare: approximately $20.4 thousand per year. BVC show that a participation that induces control is more damaging to consumer welfare than a passive participation, though both decrease consumer surplus. Our empirical results are consistent with this theoretical result. The 22.9% nonvoting equity interest acquisition in Wilkinson Sword by Gillette, which was not challenged by the DoJ after being assured that this stake would be passive, has a negative impact on consumer welfare: approximately $2.1 thousand a year, which is indeed smaller than the negative impact of approximately $5.8 thousand per year resulting from the (hypothetical) controlinducing 22.9% acquisition. The aggregated firm profit results were calculated using a procedure similar to the above. The first step consisted in computing the operating profit variation for each store m. We then added the results across all stores to investigate the impact on DFF. In order to extrapolate the results for the US economy as a whole, we computed the average operating profit variation across the different markets and multiplied by the US economy yearly potential market. Finally, we solved for the aggregated firm profits using Eq. (4). We begin the analysis by investigating total profit. The extrapolated results mirror the ones for consumer welfare. The 100% voting equity interest acquisition in Wilkinson Sword initially proposed by Gillette would have had the highest positive impact on total aggregated profits: approximately $7.1 thousand per year, while the 22.9% nonvoting equity interest acquisition had indeed the smallest impact: approximately $0.6 thousand per year. We now address Gillette's perspective. The impact on the extrapolated aggregate profits of Gillette seems relatively low and ranges from approximately $8.7 (case 2) to $40.1 (case 1) thousand per year. This result may not seem unexpected given the very small market share of Wilkinson Sword in the US disposable razor products market. However, it may raise a question as to the motivation of Gillette. The small magnitude of the simulated profit gains does not seem to justify the most likely effort and expense of the acquisition transaction. This is particularly striking since Gillette sought to justify the participation in Eemland on the theory that it was merely making an investment. Nevertheless, the results seem to be consistent with Eemland's management accounts (see Monopolies and Mergers Commission, 1991). At the time of the acquisition, Eemland recorded a negative operating income in the US personal care division. This then seems to suggest that the profitability of Gillette's investment derived solely from the European market, which recorded a substantial positive operating income and it is not accounted for in our analysis. 36 D. Brito et al. / International Journal of Industrial Organization 33 (2014) 22–36 Finally, the total welfare results aggregate the consumer welfare changes with the total profit changes. The 100% voting equity interest acquisition in Wilkinson Sword initially proposed by Gillette would have had an approximate total welfare reduction of $13.3 thousand a year, which indeed exceeds the impact of the 22.9% nonvoting equity interest approved acquisition: −$1.6 thousand a year. Warner-Lambert acquisition of Wilkinson Sword, prompted after the European Commission ordered Gillette to sell its stake in Eemland because of antitrust concerns, was, however, detrimental for both consumer and total welfare: the reduction (comparison between case 4 and case 2) was approximately of $2.9 and $0.8 thousand a year, respectively. 4. Conclusions This paper considers an empirical structural methodology to examine quantitatively the unilateral effects of partial acquisitions involving pure financial interests and/or effective corporate control on prices, market shares, firm profits and consumer welfare. The proposed methodology can deal with differentiated products industries, with both direct and indirect partial ownership interests and nest full mergers (100% financial and control acquisitions) as a special case. The general strategy models supply competition in a setting where partial ownership may or may not correspond to control and use a Nash–Bertrand equilibrium assumption, jointly with demand side estimates, to recover marginal costs, which are then used to simulate the unilateral effects of actual and hypothetical partial acquisitions. This structural approach to partial acquisitions may be a preferable method for competition policy issues to the current indirect methods in the literature of using summary measures like modified HHIs or PPIs suitable or relevant only in certain particular economic conditions. We provide an empirical application of the methodology to several acquisitions in the wet shaving industry. A DoJ challenged’s proposed full acquisition of Wilkinson Sword by Gillette in 1989, voluntarily rescinded due to antitrust concerns in favor of a (not-challenged) partial acquisition of 22.9% nonvoting equity interest in 1990, and finally the full merger between Warner-Lambert and Wilkinson Sword in 1993, prompted after the European Commission ordered Gillette Company to sell its stake in Wilkinson Sword. The results seem to confirm the DoJ challenge of the initial proposal in the sense that it would have induced more damage to consumer welfare than the 22.9% passive final participation. And finally, the results seem also to suggest that the Warner-Lambert and Wilkinson Sword merger prompted for antitrust concerns, was, in fact, detrimental for both consumer and total welfare. This paper leaves many issues yet to be explored. 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