A Comment on Choosing Among Tools for Assessing Unilateral Effects Analysis

By Joseph J. Simons and Malcolm B. Coate *

Note: This article originally appeared in the August 2012 issue of the European Competition Journal published by Hart Publishing.

» Purchase the final PDF of this article

A.  INTRODUCTION

In a recent paper published in the European Competition Journal, Gregory Werden and Luke Froeb (W&F) offer insights into unilateral effects analysis with a particular focus on the Upward Pressure on Price (UPP) model. (Footnote 1)  Their work follows our paper on a similar topic and questions a number of our insights.  In our earlier paper, we provided simple simulations that showed the application of UPP as proposed by Farrell and Shapiro (F&S) could be used to support a dramatic expansion in the universe of mergers subject to challenge. (Footnote 2)  F&S endorse the use of UPP for mergers involving differentiated products, where "differentiated" is defined to encompass most industries in the economy.  In contrast, W&F propose to limit the application of the UPP screen to situations of Bertrand competition, and by imposing an antitrust logit model assumption, to restrict the range of possible margins and diversion ratios. Whereas our analysis shows that UPP analysis, applied as suggested by F&S, would support a dramatic increase in merger enforcement, application as suggested by W&F would reduce merger enforcement significantly from its current level.  Werden and Froeb also contend that merger simulation remains preferable to UPP analysis when price is the key nexus of competition.  The final section of their paper offers some interesting, but controversial, thoughts on the applicability of economic tools to merger analysis.

While we agree with W&F that the usefulness of UPP analysis is limited, in some cases we believe it is more limited and in others less.  First, UPP methodology, as described by F&S, is designed to be agnostic to the underlying competitive process, and applicable in a broader range of situations than just Bertrand competition. (Footnote 3)  Although we believe the UPP methodology has not been demonstrated to be reliable in any situation, our simulations do not over-estimate the extent to which a broad application of UPP could expand merger enforcement.  Second, although UPP simulation shares most of the same draw-backs as game theoretic merger analysis, UPP can be applied with limited data, which allows for easier testing of its ability to reliably predict price effects.   Whether it passes or fails such testing is a different question.  Finally, in a related point, we must stress the importance of verifying the predictions of any theoretical model (including an UPP analysis generalized to predict actual price effects) with empirical evidence.  Whether used for screening or evaluating competitive effects, economic models of unilateral effects must be tied to actual evidence.  Our presentation tracks that of W&F, with an additional section to place UPP simulation in context.

B.  MODELS OF UNILATERAL EFFECTS

Farrell and Shapiro view UPP as "a simple diagnostic test to flag horizontal mergers that are most likely to lead to unilateral anti-competitive price effects for differentiated markets." (Footnote 4)  They see UPP replacing market share as the structural indicator for unilateral effects cases.  As initially formulated, we show that UPP analysis could support a dramatic increase in enforcement activity, because the UPP index will identify potential concerns in a range of mergers currently considered competitively innocuous. (Footnote 5)  F&S also present an analysis of a "pass-though" parameter that would transform an UPP measure into a prediction of a price effect. (Footnote 6)  Following Schmalensee, we take this observation one step further and note that a generalized UPP model would represent a simple merger simulation. (Footnote 7)  However the model is specified, using UPP analysis, as Farrell and Shapiro suggest, to predict price effects could substantially increase merger enforcement.

Werden and Froeb's work serves to place UPP (and merger simulation) in its proper context, as one of many possible models for unilateral effects.  They observe that these models offer three benefits; they set a foundation for the unilateral concern, clarify the nature of the unilateral concern and permit a tradeoff between anticompetitive effects and efficiencies. (Footnote 8)  As W&F recognize, the explicit focus on price imposes structure on the merger analysis, and thus the analyst must determine if a specific price-based model of rivalry is appropriate for the market under review prior to resorting to mathematical modeling.  In section E, we note this is often difficult and thus testing the predictions of the model with empirical evidence will be necessary.

C.  MERGER SIMULATION WITH THE ANTITRUST LOGIT MODEL

Economists offer a wide range of perspectives on merger analysis, with Werden and Froeb preferring simple UPP statistics (the product of the relevant diversion and margin parameters) as "informative diagnostics" for the likely effect of a merger. (Footnote 9)  Of course, the statistic needs a benchmark to be applied; they see the benchmark as the level of required efficiencies to justify the merger.  In effect, it would appear that W&F sign onto the core Farrell and Shapiro methodology; although they restrict the analysis to cases of Nash-Bertrand competition.

In addition, W&F impose an explicit model of the competitive process on the analysis by assuming the number-equivalents version of the Antitrust Logit Model (ALM). (Footnote 10)  With this assumption, they then seek to evaluate our simulations and our conclusion that UPP would support an enormous expansion in the universe of mergers subject to challenge.  To ensure comparability, the ALM technique must impose the implicit F&S benchmark of no price effect after the adjustment for the ten percent merger efficiency and the efficiency effect must be symmetrically imposed on both merger partners. (Footnote 11)  While W&F are correct that the ALM constraint links the diversion variable to the margin variable and thus invalidates a portion of our table (basically high margins are incompatible with the ALM model parameterized with realistic elasticities), there is no basis to think that the ALM assumption is appropriate in any significant number of cases.  They also fail to stress that their application of the ALM model would tighten merger enforcement in differentiated products markets.  Thus, instead of UPP being considered problematic for being too aggressive, the W&F customization would make it problematic for not being aggressive enough.  Moreover, the ALM version of UPP would preclude the existence of high margin industries. (Footnote 12)  Thus, by imposing the ALM structure, Werden and Froeb assume away our result of aggressive UPP-based enforcement.

The particular formulation of the ALM used by W&F assumes a fixed number of equal rivals (ensuring that the initial price and share are identical), sets the efficiency savings to ten percent, allows the analyst to set an exogenous value for the elasticity, and uses the F&S assumption of an 80% diversion within the cluster of competitive firms to generate an endogenous proxy for the substitution parameter.  The fully specified ALM then generates specific diversion and margin values for the specific values of the market elasticity. (Footnote 13)  Thus, for any choice of rivals, it is possible to define a range of margins compatible with a range of market elasticities.  For example, setting the number of rivals to four implies that margins range from 40 percent to 10 percent as the market elasticity changes from -.5 (inelastic) to -2.0 (somewhat elastic). (Footnote 14)  W&F are thus correct that the choice of a controlling structure for competition limits the reasonable values for margins and diversion, although a range of values are possible given the potential for variation in the market elasticity.

Solving for the post-merger price under an ALM structure predicts price increases only where the market elasticity is more inelastic (smaller in absolute value) than -.925.  In effect, by imposing an ALM on the UPP structure, W&F reduce enforcement in four-to-three mergers to a subset of markets with low demand elasticities; we believe four-to-three mergers are currently challenged for a much broader range of market demand elasticities.  Moreover, by employing the ALM assumption, high margins cannot exist; for example, using demand elasticities between -.8 and -1.6 would limit the margin to a range of .25 to .125. (Footnote 15)  In conclusion, imposing this type of theoretical structure seems to adversely affect the ability of the UPP model to screen for competitive concerns.  The ALM may represent the competitive process in an occasional market, but the model lacks the flexibility required for use as a screen.  Our conclusion that UPP analysis could dramatically increase the range of enforcement remains a logical deduction from the structure of the UPP model.

D.  ECONOMIC TOOLS FOR MERGER ANALYSIS

Werden and Froeb present their thoughts on the applicability of economic models to the questions of screening, enforcement actions, and litigation.  While they raise a number of useful points, we believe that they over-value merger simulation as a stand-alone analytical tool.  We discuss the relevant issues in three subsections.

1.   Agency Screening of Mergers

As Werden and Froeb note, early in a merger investigation, the information available to an agency is almost always quite limited.  In the US, parties will usually submit some business planning documents to supplement their formal filing documents, while the agency will interview some customers, competitors, and industry experts.  In addition to the number of significant rivals identified by W&F, killer facts suggestive of substantial fringe expansion, ease of entry, or (for a differentiated market) low diversion is sufficient to allay concerns and avoid the need for a full investigation.  Note, information on market definition is usually required to identify the number of significant rivals, predict fringe expansion, and measure the ease of entry, while it may be possible to evaluate diversion analysis directly.

W&F appear to be overly optimistic that merger simulation is "well suited for use in screening" and "can be performed with crude estimates of diversion ratios." (Footnote 16)  As we have noted, it is necessary to define a benchmark for a possible competitive concern prior to the use of any methodology for screening. (Footnote 17)  With only a subset of consumer goods mergers amenable to simulation, the data needed for benchmarking will be strictly limited and thus it is hard to imagine how a workable simulation screen could be defined.  We agree that W&F could engineer an ALM simulation with minimal data, but such an analysis would only replace the need to measure parameters with the need to identify parameters by assumption. (Footnote 18)  It is hard to see what the simulation technique would offer if the model had to be parameterized via unsupported assumption.  It seems preferable to impose the simpler UPP structure, measure the margin and diversion, and screen for competitive concerns if, as we have noted, a viable benchmark could be defined for UPP.

2.  Agency Decisions after Full Investigations

Werden and Froeb recognize that determining "how and to what extent the merging firms compete" sits at the heart of the full merger investigation. (Footnote 19)  We would add that understanding how ALL the firms in the market compete is crucial to determine the likely effect of the merger, because merger review must consider all possible reactions to the structural change in the market.

After a generic discussion of UPP and simulation, W&F present a few special case models illustrative of the need to customize the competitive effects analysis to the facts in the market.  We heartily agree with this approach but suggest that UPP analysis and merger simulation are simply two additional tools useful in special case circumstances.  Each unilateral effects merger must be carefully studied, with price-based models applied when relevant.  However, in some mergers, analyses of product innovation, promotion, or placement may be more important than simplistic price analysis and thus a naïve price analysis might not predict the likely effect of the merger if repositioning, fringe expansion and entry considerations change in the post-merger environment and affect the competitive process.

3.    Courtroom Presentations of a Merger Case

Litigation rules are likely to affect presentation of an economic study in the courtroom.  In the US, the Supreme Court's Daubert decision (along with the Federal Rules of Evidence) places clear constraints on the ability of an expert economist to apply a unilateral effects model in merger analysis. (Footnote 20)  Under Daubert, all scientific testimony must be both relevant and reliable. (Footnote 21)  Werden and Froeb's approach addresses relevance by ensuring that the testimony is suited to the question under review, but fails to grasp reliability, focusing only on the theory's logical consistency (its basis in economics) and the reasonableness of its application (its application grounded in fact). (Footnote 22)  No attempt is made to show whether application of the theory to the relevant facts leads to reasonably accurate predictions.  W&F reject the importance of testing their theoretical simulation results.  This is a crucial oversight, and is disqualifying under Daubert. (Footnote 23)

In effect, W&F seem to ignore the essence of Daubert and behave as if Frye is still the controlling legal authority. (Footnote 24)  As Parker explained, the Frye standard judged expert testimony based on its general acceptance in the relevant scientific community. (Footnote 25)  However, Parker also implied that Frye was unlikely to promote efficiency in fact-finding, because the standard allowed the fox (the expert witnesses) to guard the chicken house (the rules for evidence).  With the Daubert decision, the Supreme Court rectified this problem and imposed an independent standard of reliability on all expert testimony.  Using Karl Popper's definition of science as a method for the falsification (i.e., testing) of hypotheses about the world, Daubert set up a structure through which expert testimony is judged based on the evidence brought to bear on the relevant theory.  Thus, to be admissible, simulation analysis must provide effects' evidence to substantiate the mathematical prediction of the merger-related price increase. (Footnote 26)

Outside the US, mathematical models of merger effects may be easier to apply, because other nations use different legal structures.  Possibly, the burden of proof would shift with the US expert expected to combine a simulation with evidence, while an expert in some other country could present a simulation analysis but that analysis could be rebutted with effects evidence.  Thus, effects evidence could remain important in all merger reviews.

E.  BENEFITS OF UPP-BASED MERGER SIMULATION

Throughout their text, Werden and Froeb argue for the broad applicability of merger simulation and disparage the idea of UPP-simulation playing much of a role in the merger review process.  Perhaps, this is not surprising given their status as the parents of the merger simulation concept (Footnote 27), but we feel that they fail to fully grasp the special case nature of their baby.  In this section we try to organize our responses to their criticism of the suggestion that UPP models (assuming validation by empirical evidence) could be used as part of a competitive effects analysis.

W&F note that "merger simulation provides a precise, quantitative prediction of the unilateral effects of a merger, …valid only if the model actually does capture the essence of competition in a particular industry and only if the merger itself does not fundamentally change how competitors interact." (Footnote 28)  In effect, if the analyst can prove all the assumptions are true, and show the merger does not change competitive behavior, then they appear to argue that simulation necessarily predicts the price effect of the merger.  While this seems logical, it does not define a generic approach to merger analysis, because no analyst can count on regularly substantiating the  assumptions implicit in any simulation, nor can anyone regularly prove that mergers do not change how competitors interact.  And even if all the assumptions seem reasonable, there must be some basis to believe that the simulation puts them together in a way that reliably predicts competitive behavior in the market at issue.

Instead of emphasizing whether a model is fully specified and all of its assumptions are true, the appropriate approach is to follow Milton Friedman's suggestion and focus on how well the model predicts outcomes. (Footnote 29)  If simulations, carefully applied, successfully predict merger outcomes across a range of industries, then the methodology can be appropriately applied to those industries.  However, with a history of almost 20 years, merger simulation has remarkable little empirical support. (Footnote 30)  Without historical support, simulation analysis only appears applicable when exogenous case-specific evidence serves to confirm its predictions. (Footnote 31)

Once the analyst realizes that the accuracy of the assumptions is of secondary importance to the predictive ability of the model, it becomes obvious why UPP simulation merits consideration.  By transforming the UPP index into a prediction for a price effect, the analyst has a simple theoretical prediction on the likely effect of a merger that is easier to compute than a standard simulation number. (Footnote 32)  In contrast to traditional simulation analysis that requires, at a minimum, evidence sufficient to generate a broad range of elasticities and cross elasticities, a count for the number of rivals, and an efficiency effect, an UPP simulation only requires information on diversions, margins, efficiencies, and pass-through.  Moreover, UPP calculations are transparent so any merger analyst can explore the robustness of the results, while simulation requires complex software to solve for the market equilibrium. (Footnote 33)  Thus, although neither merger simulation nor UPP analysis have been shown to systematically predict competitive outcomes so far, UPP analysis should be easier to test for reliability on a case-by-case basis due to its simplicity. (Footnote 34)

F.  CONCLUSION

Werden and Froeb suggest that UPP analysis should be limited to situations compatible with Nash-Bertrand competition, a restriction that could narrow the applicability of the analysis.  As Farrell and Shapiro have observed, Bertrand competition is a sufficient, but not a necessary condition for their model.  Thus, our simulations, suggesting the UPP screen could dramatically increase the aggressiveness of merger reviews, remain valid.  We also disagree with W&F's preference for the more complex style of merger simulation, noting an UPP-based model offers a simpler prediction.  However, given this potential for UPP analysis to be overly aggressive, we believe that it is absolutely crucial to verify the applicability of the UPP model with empirical evidence, either historical data to establish a benchmark when UPP is used as a screen, or effects' evidence when UPP is used as a simulation to generate a prediction on price.

* Joseph J. Simons is a Partner in Paul, Weiss, Rifkind, Wharton & Garrison LLP and the Director of the Bureau of Competition at the Federal Trade Commission from June 2001 to August 2003.  Malcolm B. Coate is an economist at the Federal Trade Commission.  The analyses and conclusions are those of the authors and do not necessarily represent the views of the Federal Trade Commission, any individual Commissioner or any Commission Bureau.

Footnotes:

1. G. Werden and L. Froeb, "Choosing Among Tools for Assessing Unilateral Merger Effects" (2011) 7 European Competition Journal 155. See also J. Farrell and C. Shapiro, "Antitrust Evaluation of Horizontal Mergers: An Economic Alternative to Market Definition" (2010) 10 The B. E. Journal of Theoretical Economics 1.

2. J. Simons and M. Coate, "Upward Pressure on Price Analysis: Issues and Implications for Merger Policy" (2010) 6 European Competition Review 377.

3.  Werden and Froeb's presentation is somewhat similar to that of Epstein and Rubinfeld.  See, R. Epstein and D. Rubinfeld, "Understanding UPP" (2010) 10 The B. E. Journal of Theoretical Economics and J. Farrell and C. Shapiro, "Upward Pricing Pressure in Horizontal Merger Analysis: Reply to Epstein and Rubinfeld" (2010) 10 The B. E. Journal of Theoretical Economics, at 2.

4. Farrell and Shapiro, supra n 1 at 34.

5. Simons and Coate supra n 2 at 389.  We also note that an UPP analysis may miss a few transactions currently likely to undergo close review due to the use of a 10 percent efficiency allowance.

6. Farrell and Shapiro, supra n 1 at 19-24.

7. Richard Schmalensee, "Should New Merger Guidelines Give UPP Market Definition" (2009) CPI Antitrust Journal at 5; Simons and Coate, supra n 2 at 390-392 and Michael D. Noel, "Upward Price Pressure, Merger Simulation and Merger Simulation Light" (2011) CPI Antitrust Chronicle.

8. Werden and Froeb, supra n 1 at 157.

9. Werden and Froeb choose to label these statistics the aCMCR (the approximate Compensating Marginal Cost Reduction).  Id. at 159-160. This matches the UPP index when the efficiency parameter is set to zero and the prices of the two products are equal.

10. Id at 166-167.

11. Schmalensee, supra n 7 at 5.

12. This result is compatible with firms investing extra resources to sell marginal units of product, thereby increasing marginal cost well above the marginal costs of production and reducing the firm's margin on added sales.

13. As noted in Simons and Coate (supra n 2), margins can range from almost 0 (marginal costs close to price) to almost 1 (marginal costs close to 0).  The gross margin, used to derive the UPP model, subtracts the actual marginal cost from the price to determine the dollar margin earned on a unit sale.  Margin expresses that value as a percentage by dividing by price.

14. The authors would like to thank Dave Schmidt for the excel program that facilitated the logit calculations.

15. Higher margins can be generated by assuming the market recapture ratio falls well below the assumed 80 percent level.

16. Werden and Froeb, supra n 1 at 169.

17. Simons and Coate, supra n. 2 at 380. Werden and Froeb propose a benchmark of 5-10 percent.  Id at 169.

18. The ALM is a classic example of a "black box" methodology. The analyst enters an elasticity, a substitution parameter (or an aggregate diversion rate which fixes the substitution parameter for any value of the elasticity), the number of rivals, and the efficiency savings, and then the model generates the effect of the merger. It is not obvious how changes in the parameters affect the results (although this information could be teased out of the model).   

19. Werden and Froeb supra n 1 at 171 .

20. Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579 (1993).

21. See for example, M. Coate and J. Fischer, "Can Post-Chicago Economics Survive Daubert?" (2001) 34 Akron Law Review 795 and M. Coate and J. Fischer, "Daubert, Science and Modern Game Theory: Implications for Merger Analysis" (2008). Available at SSRN. (forthcoming in the Supreme Court Economic Review).  

22. In an earlier paper, Werden, Froeb, and Scheffman note a model must fit the facts in the industry reasonably well before it is used in merger analysis.  For example, the Lerner index should be able to predict the margin from an estimate of the firm level elasticity.  If the predicted margin is not close to the actual margin, the simulation model should not be used.  See, Gregory J. Werden, Luke M. Froeb, and David T. Scheffman, "A Daubert Discipline for Merger Simulation" (2004) 18 Antitrust 89. 

23. Follow-on decisions include, General Electric v. Joiner, 522 U.S. 136 (1997). Kumho Tire Co. v. Carmichael, 526 U.S. 137 (1999).  Werden and Froeb cite Kumho for the proposition that economics is not "scientific knowledge" but "other specialized knowledge" and thus evaluated based on the standards of the field (an interpretation that could effectively overturn Daubert and return to Frye for classes of expert testimony).  A better reading of Kumho would suggest that the court means "other specialized knowledge" (tire wear expertize) could be used even though the formal scientific trappings are missing from the field.  However, the expert would be expected to apply the basic principles of science.  As for the astounding claim that economics is not "scientific knowledge," we can only note our disagreement and suggest the bulk of the profession believes economics IS a science and economic insights are scientific knowledge.  

24. Frye v. United States, 293 F. 1013 (1923).  Werden and Froeb note that each unilateral model is "grounded in mainstream thinking" and observe that the "only significant admissibility issue is whether the tool fits the facts of the cases."  Werden and Froeb, supra note 1 at 25.  This analysis would be correct if Frye remained relevant, but it is incomplete under Daubert. 

25. Jeffrey Parker, "Daubert's Debut: The Supreme Court, the Economics of Scientific Evidence and the Adversial System" (1994) 4 Supreme Court Economic Review 1, 2-3.

26. Given Daubert is a legal construct, "effects evidence" must be interpreted broadly to include any type of evidence that directly addresses the likely competitive effect of the merger.  This includes a range of natural experiments (including evidence showing the simulation correctly predicts the effects of prior transactions or marketplace impacts other than mergers), informed customer complaints linked to the relevant economic concern or internal documents of the firm that serve to predict the likely effect of the merger.  In light of the very limited appearance of simulation evidence in court, it is not surprising that few Daubert motions have been made.    

27. G. Werden and L. Froeb, "The Effects of Mergers in Differentiated Products Industries: Logit Demand and Merger Policy" (1994) 10 Journal of Law Economics & Organization 407.

28. Werden and Froeb, supra n 1 at 158. 

29. M. Friedman, Essays in Positive Economics (Chicago, University of Chicago Press, 1953).

30. For an overview of the evidence compatible with merger simulation, see D. Carlton, "Use and Misuse of Empirical Methods in the Economics of Antitrust" (2011) CPI ANTITRUST CHRONICLE;   G. Olley, "New Tools for Competitive Effects: Do We Really Know What Works Best?" (2011) CPI ANTITRUST CHRONICLE at 7 and Coate and Fischer, supra n 21.

31. M. Coate, "The Use of Natural Experiments in Merger Analysis" (2011).  Available at SSRN.

32. Simons and Coate, supra n 2 at 390-392.  As a relatively new model, it is unrealistic to expect broad-based empirical support for UPP analysis, although it might be possible to utilize the few studies on merger simulation to generate pro-forma UPP analyses that may or may not match the existing effects' evidence.

33. An UPP simulation is basically mental math, while an ALM requires a spreadsheet to produce results.  Full AIDS simulation requires a complex statistical analysis to estimate elasticities, followed by a computer program to solve for the price effects.

34. And because the UPP analysis is so easy to simulate, it is possible to use the FTC enforcement history to obtain some insights on the relevant parameters compatible with a historical concern.  As detailed in Coate, the FTC enforcement history is compatible with a critical diversion ratio of .30, while variation in the margin does not appear to affect policy.  See, M. Coate, "Benchmarking the Upward Pricing Pressure Model with Federal Trade Commission Evidence" (2011) 7 Journal of Competition Law and Economics 825, 837.