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  • Writer's pictureDan O'Brien

The Good, The Bad and The Ugly of Vertical Merger Analysis: Fixing It

Updated: Jun 22

Two posts ago I discussed the state of modeling vertical merger effects in antitrust cases. In this post, I raise three points related to fixing the situation that I will emphasize in an upcoming talk on the subject at CRESSE.

I. Analysis should be as simple as it can be, but not simpler.

In the endless search for simplicity, often driven by the need to persuade decision-makers untrained in economics, practitioners take short-cuts that generate frameworks that cannot possibly answer the ultimate question, which in the context of vertical mergers is whether the merger is pro-competitive or anticompetitive on net. That's a pretty damning statement. What are some examples?

  1. Simple foreclosure arithmetic that asks whether the merged firm would profit from refusing to sell to unintegrated downstream firms effectively assumes that the merged firm is limited to two choices for the input price post merger: the pre-merger price, or infinity. Seriously? Since when do mergers remove a giant piece of the merged firm's choice set? Doesn't removing this part of the choice set affect answers? Of course it does. (It's actually worse than this, because the merged firms prices are also fixed.)

  2. Simple foreclosure arithmetic, simple first-order price pressure analysis (e.g., vGUPPIs), and simple bargaining variants of the latter conclude that vertical mergers are worse when upstream profit shares are low. Really? What if upstream profit shares are low because there is a lot of upstream competition or other constraints on upstream prices that would make it a real stretch for the upstream firm to profitably foreclose rivals using its "upstream market power?" This issue is frequently ignored or shifted to the background by plaintiffs in complaints and expert analysis in recent vertical merger cases. Doing so amounts to assuming the answer! This egregious error is similar to ignoring the implications of pre-merger margins in critical loss analysis, a practice we saw repeatedly in the 80s and 90s in horizontal merger analysis. (See these papers by O'Brien and Wickelgren and Katz and Shapiro for a discussion.) In any coherent economic model, pre-merger margins and profit shares reflect the competitive constraints firms face. These implications cannot be ignored, and doing so has large adverse effects on the analysis.

  3. As part of simple foreclosure arithmetic, arguments about post-merger quality degradation at pre-merger prices fail to consider whether a more profitable strategy for the merged firm would be to leave quality alone and raise the input price charged unintegrated rivals by an amount that has the same effect on downstream strategies but transfers money to the merged firm. The answer is that quality degradation often is not a profitable strategy when prices are flexible and the merged firm can commit to quality in its offers to downstream firms, because quality degradation throws away profit.

  4. Simple foreclosure arithmetic frequently ignores that ff the merged firm cannot credibly commit to refrain from quality degradation, rational firms understand that this will affect downstream outcomes, including prices, which in turn will affect the input prices downstream firms are willing to pay. Why don't these obvious effects appear in the analysis? Because it's too hard to do? Too hard for a judge to understand? (...Simple as possible, but not simpler... ...)

  5. Rigorous analysis shows that it can be profitable in some economic environments for an upstream firm to commit to stop selling an input to one or more downstream firms, but simple foreclosure arithmetic ignores this can happen with or without a merger. I don't recall ever seeing a rigorous foreclosure analysis in a merger case analyzing how the merger changes the incentive to make such a commitment. Why not? Because it's too hard? Too hard for a judge to understand? (...Simple as possible, but not simpler... ...)

  6. The list goes on and on and on.

This list is a sample of simplifications that make the analysis simpler than it can be to answer relevant questions, and this is even before we bring in the internalization of complements externalities (e.g., EDM effects), discussed below. These over-simplifications lead vertical merger analysis into an abyss.

I am cognizant of the criticism that all models are abstractions and require simplification, and I certainly agree with this view. However, much of the analysis happening in vertical merger cases today takes the argument for simplicity to levels that would garner a failing grade in an undergraduate IO course. That should not happen.

Note that I haven't said anything about the conclusions reached when these errors are corrected. It is well-known that vertical mergers can have procompetitive or anticompetitve effects. The point is that much of the analysis being done today has no hope of distinguishing between the two, except by luck.

II. It is not possible to analyze the effects of vertical mergers without a calibrated equilibrium model that at least sits in the background of the analysis.

  1. "Economists are model-builders." Those were the first words of my undergraduate intermediate microeconomics professor in class. Yes, we are. Without models, we've got almost nothing. Physicists, chemists, biologists, other scientists are no different. Without their models, they've got almost nothing. We need to use our models.

  2. The issues raised in point I above are all addressed by using an economic model that describes optimal strategies in the but for world absent the merger, the optimal strategies in the post-merger world, and an analysis of the consequences of how the optimal strategies change. Economists call this kind of analysis "comparative statics" analysis, as it involves comparing the predictions of a model in a but for world (e.g., pre-merger) with its predictions in a different world (e.g., post-merger). (For sticklers about the potential endogeneity of mergers, I certainly get that point, but I don't think it materially affects most of what appears in this post.)

  3. Because (i) vertical mergers can create both downward and upward forces on prices and investments, and (ii) the way these forces interact to produce net effects depends on details, it is not possible to evaluate net effects without a model that reflects these details. If such a model is not used, we might as well throw darts.

  4. As observed two posts ago, if marginal transfer prices exceed marginal cost, a vertical merger internalizes what Tirole calls the basic vertical externality associated with double marginalization. The elimination of double marginalization ("EDM") through vertical merger puts downward pressure on prices. Vertical mergers can also generate upward pressure on prices by raising input prices charged unintegrated rivals ("raising rivals cost," or "RRC effects;" sometimes called "partial foreclosure" effects.). There can also be customer foreclosure effects, but I focus on input foreclosure in this post. Net effects--how EDM and RRC effects net out--can only be predicted with a model that accounts for both effects. Net effects cannot be determined (except by accident) by examining these effects in isolation and simply adding or averaging two numbers.

  5. Under some modeling assumptions, pre-merger margins are small or even non-existent, in which case EDM may be small or non-existent. (For examples, see Hart & Tirole,1990; O'Brien & Shaffer, 1992; McAfee & Schwartz, 1994; O'Brien (1988; 2014). In these cases, RRC effects are more likely to outweigh EDM effects, although the merger is also more likely to enhance investment, an effect rarely taken into account in antitrust cases. (See, e.g., Yang, 2020 and Israel and O'Brien, 2022 for analyses of investment effects and conditions under which they tip the balance.) If it is believed that empirical reality and appropriate modeling assumptions are that upstream competition is weak, EDM effects are small and dominated by RRC effects, and investment benefits do not tip the balance in the other direction, these factors and conclusions need to be sorted carefully using an economic model.

III. Allowing simplicity to interfere with rigor is a big mistake.

  1. In analyses of recent vertical mergers presented in trial and before other decision-makers, plaintiffs make claims with either no economic model or what purports to be an economic model but would not be considered as such in any economic seminar room. Because decision-makers do not understand the "would not be considered as such" part of the preceding sentence, defendants naturally attack plaintiffs' analysis by showing that different results occur under different assumptions within the same incomplete framework. The decision-maker is left with deciding between claims made using a half-baked framework with different assumptions. This is not how vertical merger analysis should proceed.

  2. Tremendous damage is done when bad precedent is established in antitrust decisions. When endless debate occurs within a framework that is incapable of answering the question, this may leave the impression that the framework can provide answers where it can't. As an example of the harmful effects of bad argument and precedent and argument, look no further than the antitrust treatment of the close cousin to vertical mergers: vertical restraints. The per se illegality of RPM lasted 100 years before economic analysis done in the middle of that 100-year period was finally incorporated into the legal framework. The reason the wrong precedent was established is that someone concluded, without rigorous supporting analysis, that agreements over price are bad regardless of whether they are between vertically-related firms or horizontal competitors. Debates raged in RPM cases for 100 years over whether there was an "agreement" on price, which is not the main issue, but it became the issue. Most economists and many lawyers though this was silly, for decades. Setting aside the fact that rigorous analysis shows that RPM can in certain environments harm competition, the economic literature did not support per se treatment of RPM for at least 50 of the 100 years the rule was in place because a bad precedent and flawed arguments were made in court for 100 years.

  3. As alluded to two posts ago, the relegation of EDM to a tack-on efficiency in vertical merger analysis is a simplification that is doing tremendous damage. It amounts to relegating economics 101 effects to the background because someone apparently thinks that other economics 201 effects are more relevant. Both effects are relevant. Neither effect should be relegated to the background. Doing so makes zero sense.

  4. Rigorous economic models that consider all effects are hard to develop, but we have the tools to do so. Such models require taking stands on factors that can be are hard to confirm empirically, but that's where robustness analysis comes in. And such models can be hard to explain to decision-makers, but that is the role of experts. We have to accept that judges and other decision-makers untrained in economics simply will not understand in detail all of what goes into an economic model and all the reasons it makes the predictions it does. That's just how it is. The modeling required to get Elon Musk's biggest rocket to Mars is hard, requires taking a stand on unknowns, and is hard to explain to the FAA, NASA, and certainly judges. Does that mean it shouldn't be done? Of course not. Unless one wants crash after crash after crash, which is not far from what we are seeing in vertical merger analysis as I type..

  5. When I say "economic model," I mean an "equilibrium model." Equilibrium effects that arise from conflicting partial effects cannot be sorted without an equilibrium model. There are no short cuts that work on this point, at least none that are known at present.

  6. Economics is mostly about two things: (i) optimization (consumers and firms try to the best for themselves), and (ii) equilibration (we all try to do the best for ourselves at the same time, which leads to equilibrium outcomes). Economic frameworks that fail to incorporate these two core ideas are not economic frameworks.

Happy modeling.

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