Abstract
We use the approach of the partial-ownership literature to model the partial sale of a firm’s productive capacity. The framework is applied to the Portuguese outdoor advertising industry. We develop and estimate—with the use product-level data—a differentiated products equilibrium model that: (1) includes a wholesale and a retail level; and (2) allows firms to have several shareholders. The estimated equilibrium model is used to perform several counterfactual exercises that involve the sale to various buyers of parts of a firm’s productive capacity—with and without synergies—instead of the sale of the whole firm to a single buyer, as is usually considered in the literature. The results show that the impact of a divestiture depends on the identity of the buyers and the amount of capacity sold. More interestingly, the results also show that a divestiture may have a net anti-competitive impact.
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Notes
Actually, a media group is set of media agencies and a central purchasing agency with a common owner, where media agencies plan and buy advertising campaigns and the central purchasing agency aggregates the purchases of media agencies and places orders with media owners. A media group might own several media agencies because they specialize in different industries, or to avoid confidentiality issues with advertisers.
Site owners are the landlords of the physical space where the display equipment is installed and include: local authorities, transit authorities, airports, supermarkets, malls, and small private landlords.
Portugal is a small country, where the population is concentrated along the coast. There are three areas that matter for outdoor advertising: Lisbon, Oporto, and the Algarve. All large media owners are present in all of these areas.
The inspection of our data on installed capacity and monthly usage indicates that capacity limits are never attained; and in the case of one of the three largest media owners there is always plenty of free capacity.
Another example are large billboards at the side of highways.
To understand how market power is distributed along the vertical structure, and how changes in the wholesale level affect social welfare, both layers have to be modeled. In industries where wholesalers and retailers are not vertically integrated, ignoring the retail level amounts to assuming that retailers are strategically passive. If the retail level is concentrated, this may be an inadequate assumption. Villas-Boas (2007a) showed that oligopoly equilibrium models that incorporate the strategic interaction between manufacturers and retailers—as compared to and models that do not—may generate very different predictions.
See McFadden (1978) for a complete characterization of functions \( G(\cdot )\).
Or, alternatively, different choices of the joint distribution of components \( \varepsilon _{j}\) lead to different demand models.
A serious analysis of the implications of the separation of ownership and control on firm governance, given the legal and strategic environments, requires a more careful specification of the game between shareholders, and the game between shareholders and managers – or at the very least a more careful specification of managers’ objective functions. That, however, is beyond the scope of our analysis.
We assume, reflecting the industry, that there is no vertical integration. No shareholder owns simultaneously products in \({\mathcal{W}}\) and \( {\mathcal{R}}\).
See Aksoy-Pierson et al. (2013) for conditions for uniqueness in a one stage game. Only local uniqueness is required for our analysis.
From the media owners we obtained data from the first week of each month of the year 2013.
There is a total of 69 possible products. Of these 5 are never sold. Some of the others, with negligible market shares, are not sold every month.
We estimate that the data that we collected correspond in the very least to 95%, and probably 98%, of the industry. Based on this estimate, and on the fact that some of the data received were not usable, due to missing information on some of the variables, we assume that the share of the outside option is about 10%. We performed sensitivity analysis to check that this assumption does not drive our results.
We have sales data from wholesalers and retailers. Wholesale prices are costs for retailers.
All models were estimated with MATLAB.
See McFadden and Train (2000).
It is well known that the Mixed Multinomial Logit model can approximate arbitrarily well any discrete choice model that is derived from random utility maximization. However, a parsimonious approximation requires a judicious choice of a specific mixing distribution. One possible adaptive approach to building such a parsimonious mixing distribution is to use specification tests to identify the presence of certain mixing components. See McFadden and Train (2000). The failure to reject the insignificance of the mixing coefficients on discrete dummy variables for the groups that are associated with the nests is consistent with the nest structure used in the NL model, and can be seen as providing evidence for these models. Mixture models that emphasize the correlations that are associated with the nests can be seen as mimicking these models. Alternatively, one can interpret the NL model as a mixture model with a particular choice of mixing destitutions that captures the same pattern of correlations between alternatives. See Berry (1994).
The F statistic from the first stage is 17.8, which is well above the rule of thumb of 10, and rejects the weak instruments hypothesis with the use of the tables of Stock and Yogo (2005).
In the context of competition policy, this characteristic of the estimators is desirable.
More precisely, a divestiture is the sale by a media owner to another media owner, of a particular contract with a site owner. The purpose of the exercise is to illustrate the impact on the industry’s equilibrium and welfare of different forms of carving out the installed capacity of the acquired firm. We do not model the third firm’s decision of whether to acquire capacity. Instead, we assume that additional capacity is valuable. This assumption is justifiable because the total industry capacity is fixed. Expanding capacity is possible—but hard—because it involves the agreement of landlords, such as municipalities. Media owners own a given number of display panels, where advertisements can be placed. The sum of these panels represents a firm’s installed capacity. For convenience, we will express the number of units to be divested as a percentage of the firm’s installed capacity.
The Lerner indices of retailers would decrease from 41 to 37%, and and the Lerner indices of wholesalers would increase from 57 to 61%.
An application of the equilibrium price increase version of the small but significant and non-transitory increase in price test—as in, e.g., Pereira et al. (2013)—would have shown that \(2\, \mathrm{m}^{2}\) panels are a relevant product market, in the sense of competition policy. See the “1984 Merger Guidelines of the U.S. Department of Justice”, or the “2010 Merger Guidelines of the U.S. Department of Justice”. Both versions are available on the internet. For other versions of the test, see Pereira et al. (2013).
In addition, to convey better the intuition of the remedies and their impact, in the analysis of the divestitures we will adopt a language that suggests a sequential flow of actions. However, the model is static.
Labeling the entrant as “\(S_{4}\)” is obviously an abuse of notation. However, it enables the presentation of the two reference cases, as well as the intermediate situations, in a unified way. The entrant could be a shareholder that is currently out of the industry, or one of the atomistic shareholders that we aggregate in \(S_{4}\).
Case (R1) is equivalent to shareholder \(S_{4}\) leaving the industry, selling \(1-\tau _{2}\) of the equity capital of \(W_{4}\) to shareholder \(S_{3}\), and the remainder \(\tau _{2}\) to shareholder \(S_{2}\).
Case (R2) is equivalent to shareholder \(S_{4}\) leaving the industry, selling \(1-\tau _{4}\) of the equity capital of \(W_{4}\) to shareholder \(S_{3}\), and the remainder \(\tau _{4}\) to a shareholder that has just entered the industry, similar to \(S_{4}\). Alternatively, it is equivalent to shareholder \(S_{4}\) selling \(1-\tau _{4}\) of the equity capital of \(W_{4}\) to shareholder \(S_{3}\), keeping \(\tau _{4}\).
I.e., compared with the case where \( \varLambda ^{\mathcal{W}}=I_{4}\).
The previous discussion applies more generally to a sale, or a purchase, of an asset, or a part of an asset, that belongs to a portfolio of imperfectly substitute assets to another party, that also has a portfolio of imperfectly substitute assets.
By full collusion we mean that each firm, in its profit maximization problem, gives the same weight to the rivals’ profits than it gives to its own profit. By partial collusion we mean that each firm, in its profit maximization problem, gives a positive weight to the rivals’ profits, but less weight than it gives to its own profit.
If after the merger the owner sells all of the recently acquired firm to the third rival, the impact of the merger may, or may not, be mitigated.
From Table 9, if \(S_{3}\) buys all of the equity capital of \(W_{4}\), on average, the equilibrium retail prices of \(2\, \mathrm{m}^{2}\) panels increase by 11.8%. This illustrates the case of full collusion between two firms: \(W_{3}\) and \(W_{4}\). If \(S_{3}\) buys all of the equity capital of \(W_{4}\), and afterwards sells 30% of \(W_{4}\) to \(S_{2}\), on average, the equilibrium retail prices of \(2\, \mathrm{m}^{2}\) panels increase by 13.6%. This illustrates the case of partial collusion between three firms: \(W_{2}\), \(W_{3}\) and \(W_{4}\).
The 10% value is the one that is usually considered in the literature. To understand the result, consider the following. First, wholesale marginal costs are very low. Hence, a 10% reduction of these values leads to a small variation of these marginal costs. Second, changes of wholesale marginal cost have first to be transmitted to wholesale prices: and thus to retailers’ marginal costs. Only afterwards are these changes transmitted to retail prices. With a small wholesale pass through and a small retail pass through, the impact of wholesale marginal cost reductions on retail prices ought to be small.
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We thank the editor, L. White, two anonymous referees, W. Beckert, T. Pires, R. Ribeiro, M. Schwartz, Y. Spigel and S. Villas-Boas for useful comments. The opinions expressed in this article reflect only the authors’ views and in no way bind the institutions to which they are affiliated. Pedro Pereira is pleased to acknowledge financial support from Fundação para a Ciência e a Tecnologia and FEDER/COMPETE (Grant UID/ECO/04007/2013).
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Pereira, P., Ribeiro, T. Evaluating Partial Divestitures When Vertical Relations are Important. Rev Ind Organ 53, 321–345 (2018). https://doi.org/10.1007/s11151-018-9619-y
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DOI: https://doi.org/10.1007/s11151-018-9619-y