Upward Pressure on Price Analysis: Issues and Implications for Merger Policy

By Joseph J. Simons and Malcolm B. Coate *

Note: This article originally appeared in the August 2010 issue of the European Competition Journal published by Hart Publishing.

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Farrell and Shapiro's Upward Pressure on Price (UPP) framework is an innovative and elegant technique designed to evaluate mergers in differentiated product markets.  The authors advance their approach primarily as a screen for unilateral effects cases, although others suggest that UPP might be implemented to create a presumption of anticompetitive effect.  We raise two concerns with the methodology. First, there is no empirical evidence confirming that the method can reliably predict whether a merger is likely to increase price and second, UPP analysis screens or presumes as anticompetitive a very large universe of mergers.  We develop simple simulations illustrating that a UPP- based approach would identify mergers as potentially problematic at levels that have not attracted serious scrutiny from any major antitrust authority in decades. Farrell and Shapiro's UPP methodology also has potential as an alternative to merger simulation.  Here, we are cautiously optimistic that UPP analysis can replace the complex simulation models introduced by economists over the last 20 years.  However, simulation analysis should not be used in any particular case without exogenous evidence confirming the basic predictions.
 
A.    INTRODUCTION

For over fifteen years, analysts have searched for a better method to evaluate the potential competitive effects from anticompetitive mergers involving differentiated products. (Footnote 1)  The traditional analysis involves the definition of a relevant market and the use of concentration statistics adapted to the evaluation of unilateral effects. (Footnote 2)  Some economists, however, have suggested dropping the concept of the market from the antitrust lexicon and directly estimating the unilateral competitive effect. (Footnote 3)  Instead of applying a structural market analysis, merger simulation would predict the price increase likely to stem from the merger under review.  Within this approach, other types of evidence might rebut the simulation results, but, absent sufficient immunizing evidence, the simulation results would prove the violation. 

These economic models have not been very successful for multiple reasons. (Footnote 4)  Even the simplest simulation requires detailed parameterization, involving for example, reasonably precise estimates of a demand system including own and cross price elasticities along with predicted marginal cost savings.  Thus, the methodology does not give rise to a viable initial screening structure to separate innocuous from potentially problematic mergers.  Moreover, even with a full investigation, parameterization is often problematic.  Unless rich data sets are available, simulation offers little insight.  Finally, even for retail consumer products where rich data sets are available, simulation models have not been shown to reliably predict price effects from mergers and thus, standing alone, likely would not pass a Daubert test in the United States. (Footnote 5)

In 2008, Farrell and Shapiro (F&S) introduced the Upward Pressure on Price (UPP) index to evaluate the potential for competitive concerns in differentiated products markets. (Footnote 6)  In its simple form, the technique purports to identify mergers that might lead to higher prices.  In a more complex form, UPP analysis seems to address some of the problems presented by merger simulation.

The basic UPP index focuses on measuring the upward pressure that a merger would place on price as a function of diversion ratios, margins, and efficiencies.  Farrell and Shapiro expect the analyst to be able to estimate diversion ratios and price-cost margins, and illustrate how the calculation will work with 10 % marginal cost savings.  Mergers with a positive UPP coefficient would require a more detailed investigation of their likely anticompetitive effects or as others have suggested, a material increase in UPP would create a presumption of illegality. (Footnote 7) 

Proposed revisions for both the United Kingdom (UK) and the United States (US) Merger Guidelines integrate UPP-related variables into the merger review process. (Footnote 8)  The UK draft notes the diversion ratio is "a useful measure of the ability of the second product to constrain the prices of the first product" (at 4.88a) and identifies high profit margins as an indicator variable for the likelihood of a price increase (at 4.88b).  These two variables, diversions and margins, sit at the core of the UPP analysis.  The US draft Guidelines raise similar issues.  Higher diversion ratios are expected to predict a greater probability of anticompetitive unilateral pricing (at Section 6.1, on page 21).  The US discussion then mentions the margin between price and cost as a variable that measures the lost profits from a price increase.  The Upward Pressure on Price construct is noted as one of the factors that can be considered in a merger review.  While both Guidelines detail other variables likely to affect the competitive analysis, it appears that the UPP construct could play an important role in merger analysis on both sides of the Atlantic.

We have serious concerns with Farrell and Shapiro's screen and even greater concerns with suggestions that the UPP methodology be used to create a presumption of anticompetitive effect.  Absent efficiencies, the UPP index predicts that every horizontal merger has an anticompetitive effect and thus every horizontal merger could appear to be illegal. (Footnote 9)  Farrell and Shapiro recognize this result as extreme and propose using a "standard deduction" for efficiencies, which tends to offset the price increasing effect. (Footnote 10)  As an example, they discuss a very generous 10% marginal cost efficiencies deduction. 

Most antitrust enforcement authorities, however, have historically been skeptical, if not hostile to efficiency defenses, so that permitting such a large standard deduction for efficiencies would be quite a departure from current practice. (Footnote 11)  Moreover, the use of a standard deduction does not change the fact that the UPP index has not been proven to generate reliable predictions.  Using a standard deduction that itself has no empirical basis would not be much different than just adding a fudge factor to hide the fact that otherwise, the approach always produces a price effect.  Finally, in our experience, Federal Trade Commission (FTC) recognition of merger specific marginal cost savings in the range of 10% is rare, if not unprecedented.  As we show below, even assuming such a high level of efficiencies, the approach suggested by Farrell and Shapiro would identify as potentially problematic a large number of mergers that have not attracted serious scrutiny from the antitrust enforcement authorities in decades.  
 
With respect to a more fully-parameterized version of Farrell and Shapiro's UPP model, it may be able to function as a simple simulation for the competitive effects of a merger. (Footnote 12)  The methodology, parameterized with diversions, margins, efficiencies, pass-through coefficients, and benchmarks for tolerable price increases, is a more transparent method of evaluating post-merger price effects than pre-existing simulation techniques.  Moreover, the simulation concept is generalizable to other models that purport to measure upward pressure on price.

Although UPP based simulation represents a significant improvement over the pre-existing simulation methodologies, it suffers from the same fundamental verification problem that undermines all merger simulation structures. That is, UPP analysis lacks a history of successful prediction of post-merger price effects needed to scientifically predict the price effects of mergers.  Accordingly, absent a showing that the UPP analysis is likely to predict price effects correctly in the industry in question, the methodology would be unscientific and thus should not be admissible in court.  In cases where other evidence (e.g. natural experiments) can be used to demonstrate the likelihood of a specific price effect, however, it may be possible to calibrate a UPP simulation based on that other evidence and enable the model to balance the impact of structural change with merger-related efficiencies.   

The rest of the paper is organized as follows.  It starts with some background material to tie the UPP methodology to the better known tool of merger simulation.  The limitations on simulation are introduced to highlight why an alternative approach would be of value.  The third section provides an overview of Farrell and Shapiro's UPP screen.  Tables are generated to illustrate the link between the results of an UPP analysis and diversions or market structure, given first, no efficiencies and then, ten % marginal cost savings.  If used as a screen for investigative purposes only, we show the approach would tag a very large universe of mergers as potentially problematic, thus failing to isolate the mergers most appropriate for further review.  Alternatively, if used to create a presumption of anticompetitive effect, the UPP model could support a dramatic increase in merger challenges, marking a stark contrast with enforcement over the last several decades.   Section D addresses the ability to use UPP models to simulate the competitive effects of a merger in a differentiated products business.  We conclude that UPP-based simulation holds limited promise as a technique for balancing clearly demonstrated efficiencies and empirically-demonstrated anticompetitive effects.  Section E summarizes our observations.

B.    BACKGROUND ON THE THEORY

The UPP model is grounded in the standard Nash-Bertrand differentiated products analysis that has become prevalent in the economics literature over the last twenty years.  These theoretical models impose a tight mathematical structure on the competitive process in an industry and then generate implications for the effect of a merger by re-optimizing the equilibrium given the change in structure caused by the merger. (Footnote 13)  Parameters include coefficients of the relevant demand system (sufficient to give rise to own and cross elasticities and the associated diversion ratios), pre-merger prices, and merger-related marginal cost efficiencies.  Once parameterized, a relatively straight-forward optimization scheme generates predictions on the price increases caused by the merger. (Footnote 14)  Absent sufficient efficiencies, these models predict price increases for all horizontal mergers no matter how fragmented the market.  As a general proposition, the price of the product sold by the smaller of the merging parties will increase by more than the price of the product sold by the larger of the merging parties. (Footnote 15)  Prices of third parties increase by significantly less than the prices of the merged parties.  Cost efficiencies exert downward pressure on the merged firm's price, and if the efficiencies are large enough, prices will fall. 

Nash-Bertrand simulation models can be implemented in a range of situations.  Economists can estimate the necessary coefficients by imposing Logit structures when minimal data is available or more general AIDS assumptions when much more detailed pricing data can be obtained.  Current cost conditions fall out of the pre-merger equilibrium calculation, but are expected to match the empirical evidence as part of the technical validation of the model. (Footnote 16)  Predictions for post-merger price increases often depend on the particular demand structure chosen, but the robustness of these price effects can be examined by changing the specification of the model and/or tweaking the parameters of the model.  Of particular interest is the effect of cost changes on the magnitude of the post-merger price changes.  It is generally recognized that merger simulation represents one approach to balance the anticompetitive effects of a structural change with the pro-competitive benefits of merger-specific efficiencies.  Merger analysts know simulations must be followed with an evaluation of repositioning and entry impediments to ensure that these considerations do not trump the prediction of a competitive concern. 

Although the methodology was fully developed in the 1990s, merger simulation has not caught on in the United States.  While Budzinski and Ruhmer report merger simulation is one of the tools used by the enforcement agencies, (Footnote 17) no court has accepted the analytical approach. (Footnote 18)  This failure is not surprising, because simulation analysis suffers from a number of draw-backs. (Footnote 19)

First, the black box nature of the modeling structure limits the ability of even experienced antitrust lawyers to actually understand the analysis.  The computations start with a set of assumptions and derive a vector of price increases linked to the change in market structure caused by the merger.  Unless the price changes are trivial or obvious evidence rebuts the presumption of concern, the merger is seen as anticompetitive. (Footnote 20)  Moreover, the magnitude of the price effect can change substantially as the analyst imposes different modeling structures on the data. (Footnote 21)

Second, simulation analysis is often divorced from the concept of a relevant market.  While theorists argue demand simulation generates price effects without the need to define markets, failure to ground the simulation in a relevant market makes it particularly difficult to fully evaluate the price predictions.  If the simulation model does not represent a relevant market, can the analyst complete the market-based repositioning and entry analyses needed to support the final conclusion that the merger substantially lessens competition within some (undefined) area of rivalry?
 
Third, all simulation models impose substantial data requirements on the analyst.  This significantly limits the applicability of the analysis to markets in which rich sources of data are available.  While the analyst can impose structure to reduce data requirements, these structural assumptions run the risk of introducing error into the analysis. (Footnote 22)  Moreover, to the extent that data limitations introduce estimation error into the analysis, the price predictions may not be accurate. (Footnote 23)

Fourth, by focusing the competitive analysis on the price set by each firm, the simulation methodology appears to ignore more complex competitive processes.  For example, non-price competition with respect to the design, promotion, or placement (distribution) of the products sold in the market may have a significant effect on customer decisions.  Dynamic links between price and the other variables are also assumed away, regardless of the factual situation.  Finally, and most importantly, prices may be set through direct customer-supplier negotiation, suggesting producers do not have the ability to set a single price for their differentiated product. (Footnote 24)  While the simulation methodology could be adjusted to address some of these problems, the analysis would become even more dependent on the assumed parameters. (Footnote 25)

All these problems likely contribute to the inability of most simulation models to predict post-merger prices. (Footnote 26)  In effect, these models are not generalizing scientific theories, because their lack of broad empirical support implies simulation modeling fails the "market test" of science.  Instead, these models are possibility (or exemplifying) theories of economics, defining what might happen, rather than predicting what will happen.  Of course, simulation may still remain useful on a case-by-case basis, when natural experiment evidence is compatible with the predictions of the model. 
 
C.    UPP ANALYSIS OF MERGERS

Farrell and Shapiro introduced UPP analysis to focus on the pressures for unilateral price effects while avoiding both the need for market definition and the much greater data requirements of traditional merger simulations.  As noted below, if the merging firms can be considered symmetric, UPP analysis can be undertaken with just evidence on diversion ratios and price-cost margins, along with an assumption for efficiencies.  While diversions interact with margins to create pressure to raise prices, efficiencies serve to reduce the upward pressure on price.  Once accounting for efficiencies, it is possible to compute the net upward pressure on price. (Footnote 27)

The F&S UPP technique observes that every horizontal merger in a differentiated product market exerts upward pressure on price, because the merged firm is able to recover the margin on sales gained by one of the merged entities when the other entity raises price.  Likewise, if one entity lowers price to gain share, the merger makes that price decrease more costly, because the merged firm recognizes the loss in margin to the partner entity caused by the price decrease. (Footnote 28)  Farrell and Shapiro focus on this cannibalization effect and estimate the initial effect (tax, in their terminology) of a one unit increase in output as the diversion rate to the merger partner multiplied by the gross margin of a unit of production by the merger partner.

Farrell and Shapiro note the cannibalization effect will be at least partially offset by the merger-specific efficiencies achieved by the entity changing price.  Here, F&S propose 10 % cost savings as an example of the "standard deduction" for cost savings achieved by the firm.  Thus, what-ever upward pressure that exists to raise price will be offset to some degree by the marginal cost reductions.   Equation 1 follows Farrell and Shapiro and combines the cannibalization effect with the efficiency allowance and an assumption of Nash-Bertrand competition to define an inequality that determines whether the firm faces upward pricing pressure.

1)    D12 * (P2 - C2) > E1*C1

where the diversion ratio from firm 1 to firm 2 is D12, the P's and C's are the prices and marginal costs of firms 1 and 2 and E1 is firm 1's standard deduction for efficiencies.
 
Schmalensee, following the original Werden analysis, suggests a slightly different equation reproduced below as equation 2. (Footnote 29)  Because costs fall after the merger for both merger partners, the margin of firm 2 must be adjusted to reflect the lower post-merger costs.  Here, E will be used to represent marginal cost savings (as both firms are credited with the same standard deduction for efficiencies).  While Farrell and Shapiro prefer their equation, we agree with Schmalensee that efficiency adjustments should be made on both sides of the equation. 

2)    D12 * (P2 - (C2 - E*C2)) > E*C1

An analogous equation exists for the other merged entity.  Imposing symmetry assumptions on the firms, along with cost and price equality justifies Equation 3, with D considered the diversion parameter and M considered the pre-merger price-cost margin relevant to both firms. (Footnote 30)

3)    D > E * (1-M)* (1-D)/M

To explore the implications of this model, we rearrange terms to obtain a slightly adjusted equation for the percentage upward pressure on price (UPP*/P).  If equation 4 is met, then the merger is considered to exert upward pressure on price after correcting for efficiencies and thus would trigger the screen for anticompetitive effect.  A comparable calculation is made for Farrell and Shapiro's UPP model and it is given in the Appendix.  Table 1-b and Table 2, introduced below, are re-estimated in the appendix to show the choice of UPP* or UPP has little effect on the outcome of the analysis.

4)    UPP*/P = M * D - E * (1-M) * (1-D) > 0
 
Equation 4 defines a very simple formula for the UPP model.  Tables 1-a and 1-b evaluate the model for given values of the margin and diversion parameters, first when the efficiency index is set to 0 and then when it is set to Farrell and Shapiro's example of 10 % savings. (Footnote 31)

Table 1-a shows all mergers in differentiated products result in a positive UPP, placing upward pressure on price.  This illustrates that the approach always predicts the merger will lead to higher prices when efficiencies are not present. (Footnote 32)  Given the symmetry assumption, the merger would generate the same upward price pressure for both merger partners.  Thus, without efficiencies, merger enforcers could be very active in differentiated products markets. 

Table 1-a:  UPP* Model by Margin and Diversion, No Efficiencies

Table 1-b:  UPP* Model by Margin and Diversion, 10 % Efficiencies

Table 1-b adds the standard deduction for efficiencies to the simulation.  A quick review of the table shows that enforcers could still be much more active than would be consistent with current practice. (Footnote 33)  UPP would be positive for all mergers involving firms with 50% margins or higher and for substantial number of mergers with margins of over 30%. 

 Table 2 links the F&S results to market structure.  The analyses take assumptions on the number of competitors and translate them into diversion ratios that would result assuming each competitor is equally situated (i.e., volume diverts equally to each other competitor assuming a price increase by one of the firms). For example, a 20% diversion ratio implies that there would be six equally situated pre-merger competitors. A merger would reduce the number of competitors by one. (Footnote 34)  Table 2-a illustrates that (without efficiencies) all horizontal mergers are predicted to raise price under this approach.  For example, there would be a positive UPP of 1.1 % for situations involving a merger in a market with ten rivals when the firms have margins of only 10%. (Footnote 35)

Table 2-a:  UPP* Model by Margins and Rivals, No Efficiencies

Table 2-b:  UPP* Model by Margins and Rivals, 10 % Efficiencies

Table 2-b shows the results assuming a substantial 10% standard deduction for efficiencies.  Even with this deduction, however, enforcers could still be extremely active.  For example, a merger involving two of ten firms  produces a positive UPP as long as the margins are 50% or higher.  UPP would be positive for instances involving six equally situated pre-merger entities with margins as low as 30%.  This approach could essentially condemn six-to-five mergers where margins would be considered moderate at best. (Footnote 36)  For higher margins, (those usually applied in differentiated products markets) the approach would be much more aggressive.  Table 2 makes clear that the UPP approach even with the 10% standard efficiencies deduction would mark a substantial break with historical enforcement patterns over the last two decades (Footnote 37), let alone the outcome of recently litigated US merger cases. (Footnote 38)

Tables 1 and 2 both illustrate a fundamental concern with the Farrell and Shapiro screen - it identifies as potentially problematic far more mergers than would be challenged or even investigated under the enforcement standards that have existed for more than 20 years.   Perhaps these enforcement standards have not been appropriate and merger policy has been far too lenient over this time period.  But if that were the case, we should expect to see a very large universe of consummated mergers that produced price effects over that time.  At least for now, no such evidence exists.

Simply tweaking the Farrell and Shapiro structure to impose a threshold tolerance level in addition to (or as a replacement for) the efficiency defense does not solve the problem, because such a model would still lack empirical verification. (Footnote 39)  This problem also precludes others from using UPP to establish a presumption.  While it is premature to conclude that is it impossible to define an UPP based approach that could reliably predict the price effects of certain mergers, such a model does not exist today. Thus, a basis to support the use of UPP to create a generalized screen for anticompetitive effects is lacking, as is its use to create a presumption of anticompetitive effect.

D.    UPP-BASED MERGER SIMULATION 

Farrell and Shapiro's generic UPP methodology also represents a new tool that can address the problems faced by merger simulation models when trying to illustrate competitive concerns. (Footnote 40)  Equation 5 defines a variant of the Farrell and Shapiro model (UPP-FS) with G considered the requirement for a significant price increase and R taken as the pass-through rate.  In addition to estimating both the price-cost margin (M) and the symmetric diversion (D), the analyst must measure both efficiencies (E) and pass-through (R).  Only the tolerance level for the price increase is assumed. (Footnote 41) 

5)    UPP*/P = M * D - E * (1-M) * (1-D) > G/R

Upward pressure on price can be transformed into a price effect by multiplying both sides of the UPP equation by the pass-through R.  Equation 6 presents a representative model with R set at the linear demand pass-through of one half.

6)    % Price Simulation Effect = ½ * (M * D - E * (1-M) * (1-D))

This formula is much simpler than any existing market simulation structure.  While the UPP model is unable to match a standard simulation by predicting the price responses of competitors, these price changes are generally small second-order effects and thus probably not material.  The core UPP formula focuses on estimating the two price increases imposed by the merging firm from the available information.  And the effects of different pass-through rates can be considered by simply setting parameter R- to a different value.   While the required material price effect (G) needed to evaluate the simulation must be assumed, the standard merger simulation has the same problem. Simulations only generate post-merger price levels, leaving the analyst to determine if the change is material. (Footnote 42)  

Schmalensee suggests another UPP formulation (UPP-S), by dividing equation 6 by one minus the diversion ratio. (Footnote 43)  The basic difference between these two UPP methodologies is that Farrell and Shapiro model the merger's initial impact on price, while Schmalensee presents a post-merger price effect after all the merged firm's sequential responses occur.  Farrell and Shapiro recognize that the full effect of the upward pressure on price may be higher than their model suggests, but prefer the simpler, more intuitive approach. (Footnote 44)  While the simulation results are quite similar for small values of diversion, the results may differ materially for close competitors with large diversion ratios.  For example, setting margins to .5, efficiencies to 10 %, pass-through to .5, and diversion to 25 % generates a 4.38 % price effect for UPP-FS and a 5.84 % price effect for UPP-S. (Footnote 45)  Thus, choosing a modeling structure can easily impose a 33 % difference in the predicted price effect.  Higher values for margins or diversions increase the potential variance in the prediction. (Footnote 46)  Overall, to make accurate predictions, analysts need evidence to suggest that they use both the correct simulation structure and parameters.

UPP simulation does have significant advantages over the standard simulation analysis.  Any form of UPP-based simulation serves to eliminate the black box concerns associated with the complex merger simulation models, and simplifies the data required for simulation.  Moreover, the relative ease at which this structure can be applied makes it more feasible to "test-drive" the model prior to completing the detailed industry study needed to show the model is applicable.  To determine if the UPP simulation is likely to aid in the evaluation of a merger, it is necessary to understand the dynamics of competition in the market.  While price competition might be controlling in some differentiated product markets, product innovation is likely to be the essence of competition in others.  When innovation is controlling, the pricing decision becomes much more complex, thus precluding the use of a simple Lerner index based simulation analysis. (Footnote 47)

When price is the controlling competitive consideration, UPP simulation merits attention.  However, this paper identifies two possible UPP simulation methodologies and we are certain that economists can create many more.  Thus, the analyst faces a serious problem in applying the analysis, due to the need to choose a specific model.  Moreover, within any model, the predicted price effects depend on the choice of the pass-through parameter (R).  In effect, UPP simulation can predict a very broad range of price increases.  Without some exogenous evidence to eliminate a large number of model-parameter combinations, UPP simulation is simply not scientific.  Thus, we believe it is necessary to exogenously confirm the results of any UPP simulation with natural experiment data, thus demonstrating reliability. (Footnote 48)  Both the UK and US draft Guidelines touch on the importance of this evidence in predicting post-merger performance. (Footnote 49)  And, in cases when evidence confirms the specific price predictions of the relevant simulation, the model may prove extremely valuable in balancing potential anticompetitive and efficiency effects.  Of course, simulation analysis will always need to be supplemented with repositioning and entry analysis, because these factors are exogenous to the simulation methodology. (Footnote 50) 
 
E.    CONCLUSION

Farrell and Shapiro have introduced an innovative and elegant methodology to move the economic analysis of mergers in a more practical direction.  Based on merger simulation concepts, F&S focus their analysis on a few reasonably observable variables and define a merger screening algorithm designed to identify situations in which anticompetitive effects may be likely.  Because screening mechanisms purport to highlight general results, they need empirical support to show the methodology actually predicts concerns relatively well.  This empirical support is not available at this time.  Moreover, our simple simulations suggest that the UPP methodology will identify concerns with a large class of mergers generally considered innocuous or even pro-competitive.  Until the model is shown to predict relatively well, it is premature to put the UPP screen to work.
   
Farrell and Shapiro's methodology also defines a useful algorithm that can be used to improve merger simulation analysis.  UPP-based analysis significantly reduces the black box nature of simulation and minimizes the data requirements.  Issues remain with evaluating when the price technique is best applied and calibrating the simulated price increase to reflect reality.  As a possibility (exemplifying) model of economic science, simulation requires some exogenous natural experiment evidence (broadly defined) to confirm their predictions.  Estimates of exact price effects require more comprehensive support.  If these science-related requirements can be met, UPP analysis defines a useful structure with which to balance likely anticompetitive effects and efficiencies.  Over time, analysts are likely to gather experience with UPP methodology and more fully understand the insights and limitations of the general model.

* Joseph J. Simons is a Partner in Paul, Weiss, Rifkind, Wharton & Garrison LLP and Director of the Bureau of Competition at the Federal Trade Commission from June 2001 to August 2003 and Malcolm B. Coate is an economist at the Federal Trade Commission.  The authors would like to thank Jeffrey Fischer and Thomas Krattenmaker for helpful comments.  The analyses and conclusions set forth in this paper are those of the authors and do not necessarily represent the views of the Federal Trade Commission, any individual Commissioner, or any Commission Bureau.

Appendix A:  Calculations for the Farrell and Shapiro UPP  Structure

In the text, we slightly changed the specification of Farrell and Shapiro's UPP model to reflect the merger-specific efficiencies captured by the merger partner in the analysis.  Here, we return to exact Farrell and Shapiro specification and present alternative values for the simulations in Table 1-b (Table 1-a is invariant to the change, because the efficiency coefficient is set to zero.).  Table 2 includes a second modification; and all the results change, when we directly allow for diversion of sales outside the market of concern as part of the numerical simulation.

To start, we replicate Farrell and Shapiro's equation 6 below.

A-1)  D * M/(1-M) > E

Where D is the diversion for the symmetric firms, M is the margin, and E is the exogenous efficiencies.  Equation A-1 can be rearranged to obtain the UPP equation.

A-2)  UPP/P = D * M - E * (1 - M)
   
Other than the adjustment in the efficiency effect required to reflect the impact of the merger partners' efficiencies on the opportunity cost of a price change (captured by multiplying the weighted efficiency savings by (1-D)), the UPP* equation is identical to the UPP equation.  Thus, Farrell and Shapiro's specification should show relatively less upward pressure on price, especially when the Diversion ratio is high.

Table A-1 presents the results of the UPP model for specific margins and diversions.  The effect on the UPP index for small diversions is minimal.  For example, for a diversion of .1 and a margin of .6, the UPP index is reduced from 2.4 % in Table 1-b to 2.0 % in Table A1.  Somewhat larger effects are observed for higher values of the diversion ratio.  Moving across the table to a diversion of .4 (with the same margin of .6) shows an UPP value of 21.6 % in Table 1-b and 20 % in table A1.  Given the values of the UPP index increase significantly with diversions, we find that even though the absolute differences in the UPP values increase with diversion, the percentage differences decline.  Overall, the implications of the two UPP specifications are similar.

Table A1:  F&S UPP Model by Margin and Diversion, 10 % Efficiencies

When moving from measured diversions to counts of competitors, the presentation becomes slightly more complex.  Farrell and Shapiro suggest using a market recapture ratio (REC in their paper) to identify the aggregate level of diversion retained by the set of firms being modeled.    Thus, the share-based diversion would be reduced by the REC coefficient (here, also .8) and the UPP values calculated.  The number of rivals could be considered to represent the number of significant competitors in the market. 

Table 2 is  re-calculated in its entirety in Table A2, because the market recapture rate lowers all the implicit diversions (here, by 20 %) and thus reduces the upward pressure on price.  When no efficiencies exist, the value for UPP falls exactly 20 %, while when efficiencies are considered, two adjustments are imposed.  In addition to the same 20 % reduction in upward pricing pressure, a larger efficiency effect is imposed (because the Farrell and Shapiro methodology does not reduce efficiencies for the diversion effect (1-D)).

Table A2-a:  F&S UPP Model (.8 REC) by Margins and Rivals, No Efficiencies

Table A2-b:  F&S UPP Model (.8 REC) by Margins and Rivals, 10 % Efficiencies

While the calculations generate lower results when the Farrell and Shapiro model is used in place of the UPP* model introduced by Werden and advocated by Schmalensee, they are still substantial enough to generate a UPP index of 5 % or more for a broad range of market structures.  With margins set at .5, nine-to-eight mergers would be problematic if efficiencies were ignored (see, Table A2-a, above) and five-to-four mergers would be flagged with an aggressive finding of 10 % efficiencies (see, Table A2-b, above).  Thus, both versions of the UPP analysis would identify potential concerns in a broad collection of mergers.

Footnotes

1.  For the EU, see Council regulation (EC) No 139/2004 of January 20 2004 on the control of concentrations between undertakings.  The formal documents and extensions are available at:  http://ec.europa.eu/competition/mergers/legislation/regulations.html (accessed on 27 June 2010). In the United States (US), the controlling legal authority for structural merger analysis can be found in Philadelphia National Bank, U. S. v. Philadelphia National Bank, 374 U.S. 321 (1963),which created a presumption of prime facie illegality for mergers involving firms controlling "an undue percentage share of the relevant market and results in a significant increase in concentration…"  Id at 335.  During the late 1960s, the Supreme Court applied the presumption of illegality to firms with very small shares.  Over the next several decades, however, lower courts significantly reduced the strength of the presumption and have tended to apply it only for mergers involving very high market shares. ABA SECTION OF ANTITRUST LAW, ANTITRUST LAW DEVELOPMENTS (6th ed. 2007) at 346-48.

2.  Post-merger market share is generally the key statistic in the EU, because dominant firms hold large shares.  Unilateral concerns, other than dominance, have only been actionable in the EU since 2004 under the more general substantial lessening of competition standard.  M Bergman, M Coate, M Jakobsson, and S Ulrick  "Merger Enforcement in the European Union and the United States: Just the Facts" (2010), available at SSRN. Two statistics (the number of significant rivals and the change in the Herfindahl) are commonly used in the US.  For significant rivals, see M Coate, "Unilateral Effects under the Guidelines:  Models, Merits, and Merger Policy" (2009), available at SSRN.  And for the change in the Herfindahl, see G Werden and L Froeb, "Simulation as an Alternative to Structural Merger Policy in Differentiated Products Industries", in M Coate and A Kleit (eds), The Economics of the Antitrust Process, (Boston, Kluwer Acad, 1996), 75.

3.  See, for example, J Baker and C Shapiro, "Reinvigorating Horizontal Merger Enforcement that has Declined as a Result of Conservative Chicago Analysis", in R Pitofsky (ed), Where the Chicago School Overshot the Mark, (New York, Oxford University Press, 2008), 235.

4.  While simulation structures have been applied by the US enforcement agencies, the models have had no success in the courts.  See for example. U.S. v. Oracle, 331 F. Supp. 2nd 1098 (N.D. Cal. 2004).  Likewise, simulation models influence EU-related enforcement agencies, but appear not to play a role in the court cases. O Budzinski and I Ruhmer, "Merger Simulation in Competition Policy: A Survey" (2008), available at SSRN.

5.  M. Coate and J. Fischer, "Daubert, Science and Modern Game Theory: Implications for Merger Analysis" forthcoming, Supreme Court Economic Review.  Also available at SSRN.  Legal standards in the EU are less clear, see. I. Lianos, "Judging Economists: Economic Expertise in Competition Law Litigation", in Lianos and Kokkoris (eds), New Challenges in EC Competition Law Enforcement, (Dordrecht, Kluwer, 2009).

6.  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.  A closely related version is available at SSRN.

7.  Ibid, 14 and 22;  For the discussion of UPP-based presumptions, see S Moresi, "The Use of Upward Price Pressure Indicies in Merger Analysis" (2010), Antitrust Source, and S Salop and S Moresi, "Updating the Merger Guidelines: Comments," (2009).

8.  For the most recent document in United Kingdom. see "Review of Merger Assessment Guidelines," April 14, 2010. For the United States, see, "Horizontal Merger Guidelines," April 20, 2010.

9.  A quick look at equation 2 in Farrell & Shapiro (supra n. 6) is illustrative.  If we put efficiencies to the side (i.e. set them to zero), then any positive diversion from product 1 to 2 (i.e. any positive cross-elasticity) produces a positive UPP.

10.  Ibid, 9-10 and 22.

11.  In the US, efficiencies must be carefully vetted and only extraordinary efficiencies would be expected to offset a particularly large anticompetitive effect (US Merger Guidelines, 1997, section IV.)   In the EU, efficiencies are rarely considered in the final merger review decision.  See, Bergman et al. supra n. 2, 35-37.

12.  Farrell and Shapiro (supra n. 6) suggest that their technique serves "a very different role than merger simulation" (29), but also note their screening analysis could be revised as part of the full analysis on the merits (22-23).

13.  Examples include G Werden and L Froeb, "The Effects of Mergers in Differentiated Products Industries: Logit Demand and Merger Policy" (1994) 10 Journal of Law, Economics and Organization 407, J Hausman, and G Leonard, "Economic Analysis of Differentiated Products Mergers Using Real World Data" (1997) 5 George Mason Law Review 321, and G Werden, "Simulating the Effects of Differentiated Products Mergers: A Practical Alternative to Structural Merger Policy" (1997) 5 George Mason Law Review 363.  

14.  Ibid, Hausman and Leonard, 331-334 and Werden and Froeb, 412-413.

15.  Werden and Froeb, supra n 2, 72.  Of course, this result depends on the assumptions for the relevant diversions.

16.  Hausman and Leonard, supra n 13, 331.

17.  Budzinski and Ruhmer, supra n 4, 17-24.  The US Merger Commentaries also endorse simulation. Federal Trade Commission and U.S. Department of Justice, Commentary on the Horizontal Merger Guidelines (2006): http://www.ftc.gov/os/2006/03/ CommentaryontheHorizontalMergerGuidelinesMarch2006.pdf at 14.

18.  See for example, the simple Lerner index model is rejected by the court in FTC v. Swedish Match 131 F. Supp 2nd 151 (D.D.C. 2000) and the limitations of more complex simulations addressed in U.S. v. Oracle, 331 F. Supp. 2nd 1098 (N.D. Cal. 2004).  EU courts do not appear to have addressed the issue.  Budzinski and Ruhmer, supra n 4.

19.  For another list of draw-backs see, Budzinski and Ruhmer, Ibid, 25-30

20.  In effect, simulation has a benchmarking problem, because it is unclear when the price effect is large enough to be material.  One interesting approach would benchmark with social welfare.  Werden and Froeb (supra n 13, 419) note all hypothetical mergers in their long distance service market would improve social welfare, except for a deal between AT&T (long-distance) and MCI.  In effect, small price increases would be tolerated, because society is better off with the merger.  Large increases in average industry prices would be problematic. 

21.  As Farrell and Shapiro recognize, simulation results depend crucially on the assumed structures for demand (which give rise to specific pass-through values).  See, Farrell and Shapiro supra n 6, 19-21 and P Crooke, L Froeb and S Tschantz, "Effects of Assumed Demand Form on Simulated Postmerger Equilibria" (1999) 15 REVIEW OF INDUSTRIAL ORGANIZATION 205.

22.  For example, Logit analysis requires less data than AIDS analysis, but imposes assumptions on the demand structure that may not be accurate.

23.  For a discussion of estimation problems in data rich environments, see D Hosken,  D O'Brien, D Scheffman, and M Vita, "Demand System Estimation and its Application to Horizontal Merger Analysis", Federal Trade Commission Working Paper, (2002). 

24.  These problems are discussed with respect to critical loss analysis in M Coate and J Simons, "Critical Loss: Modeling and Application Issues" (2009).  Available at SSRN.  

25.  For an initial attempt to suggest modeling structures to address the impact of current decisions on future returns, see J Farrell and C Shapiro, "Improving Critical Loss" (2008) Antitrust Source.  When the inter-relationships are customer-specific and each customer faces its own time series of inter-related prices, mathematical "fixes" would require much more assumed structure and therefore simulation-related tools offer little, if any insight. 

26.  This evidence is summarized in Coate and Fischer, supra n 5, 39-43.

27.  See Farrell and Shapiro, supra n 6, 11-13.

28.  This intuition also helps to explain why the model predicts that any horizontal merger will raise price absent the presence of sufficient efficiencies. 

29.  R Schmalensee, "Should New Merger Guidelines Give UPP Market Definition" (2009) 12 CPI ANTITRUST CHRONICLE 1 and G Werden,   "A Robust Test for Consumer Welfare Enhancing Mergers Among Sellers in Differentiated Products"  (1996) 44 Journal of Industrial Organization 409.

30.  Farrell and Shapiro derive firm-specific equations for use when market conditions preclude the symmetry assumption.  Farrell and Shapiro, supra n 6, 13.  Our paper imposes symmetry assumptions for ease of exposition.  At this point, it retains the standard assumption that diversion remains constant when rivals raise price.

31.  Mathematically, the simulation multiplies the price-cost margin and diversion for each cell and then subtracts the product of the efficiency savings multiplied by both, one minus the price-cost margin and one minus the diversion ratio.  The impact of a smaller "standard deduction" for efficiencies can be computed by interpolating between the results of the two tables.  For example, given a price-cost margin of .5 and a diversion ratio of .2, efficiencies of 5 % would lower the UPP by 2 percentage points (.02) for Table 1-a and raise it by 2 percentage points for Table 1-b.

32.  Technically, prices will not change if the pass-through parameter equals zero.  Thus, special case situations may exist where positive UPP values will not result in higher prices.  Farrell and Shapiro provide a formula for the pass-through and that formula can not be zero if the demand curve is convex (the type of curve most economists use).  Farrell and Shapiro, supra n 6, 21.

33.  Using simulated data and a market definition concept that assumes firms are in the same market if the diversion ratio exceeds 5 %, Das Varma shows the UPP structure will generate concerns in 78 % of the sample, while the 35 % critical share (implicit in the US Merger Guidelines) creates a concern in only 35% of the sample. Using a higher critical share to reflect an EU concept of dominance would generate even fewer concerns.  G Das Varma, "Will the Use of the Upward Pricing Pressure Test Lead to an Increase in the Level of Merger Enforcement" (2009) 24 Antitrust 27.

34.  Our computation assumes all product is diverted to the firms' rivals.  Diversion to products outside the market can be represented by defining one rival to be a composite good for consumer choices outside the market.  In the Appendix, an alternative approach is used, as we allocate 20 % of the diversion to products outside the market and assign 80 % of the diversion by market share.  The two methods can be compared by matching any column in Table A2-a with the column from Table 2-a associated with one fewer rival.  (Table A2-b is not directly comparable to Table 2-b.)   

35.  Although it is conceivable that not all equally situated competitors would be included in a market technically defined under the Merger Guidelines, we are aware of no instances where this has occurred in practice.  Accordingly, we believe the simulations in Table 2 provide valuable insight and allow for good comparisons with historic levels of enforcement.  To the extent that the analyst can estimate actual diversions, the simulations in Table 1 can be used directly.

36.  Bailey et al. focus on the 35 % dominance standard and find that for share-based diversions, the UPP policy could be more aggressive for margins above 32 % and less aggressive for margins below 32 %.  They also suggest an UPP test could be difficult to implement.  E Bailey, G Leonard, S Olley, and L Wu, "Merger Screens: Market Share-Based Approaches and 'Upward Pricing Pressure' (2010) Antitrust Source.  

37.  For the EU, very few matters were enforced when post-merger share fell below 40 % (equivalent to 5 equal pre-merger firms).  See Bergman et al, supra n 2, Table 6.  Interestingly, the proposed UK guidelines seem to address this problem by noting enforcement will be rare, when either the merger can be characterized as 5-to-4 transaction or the firm's post-merger share falls below 40 %.  See, UK Guidelines, supra n 8, 4.79. For details on the US policy, see Coate, supra note 2, 38 (Table 2). Only 5 of the roughly 180 investigations focused on markets with 7 or more pre-merger rivals (one actually enforced), hence these matters should not be presumed problematic.  Likewise, only 8 six-to-five transactions were investigated, with enforcement in only two matters.  Core unilateral effects enforcement affects three-to-two and two-to-one mergers.  No rival-based or share based restrictions were in the draft US Guidelines, supra n 8. 

38.  In addition to Oracle, see FTC v. Arch Coal, Inc, et al. 329 F. Supp. 2nd 109 (D.D.C., 2004) and FTC v. Foster, 2007-1, Trade Cas. (CCH) ¶ 75,725 (D. N.M., 2007).

39.  Farrell and Shapiro present a formulation of Salop and Moresi's UPP methodology which would eliminate the efficiency standard deduction but replace it with a deminimis tolerable level for a price effect.  Farrell and Shapiro, supra n 6, 23. 

40.  Farrell and Shapiro are reluctant to consider their methodology to be a form of simulation.  Farrell and Shapiro, Ibid, 29.  However, the methodology, once generalized for pass-through rates, easily generates a prediction of the mergers' price effect.  Epstein and Rubinfeld also see UPP as a special case of simulation.   R Epstein and D Rubinfeld, "Understanding UPP" (2010) 10 The B. E. Journal of Theoretical Economics.

41.  Farrell and Shapiro observe that estimation of the pass-though might be extremely difficult and thus the analyst might end up assuming a value.  Ibid, 20-23.   (The formula in equation 5 is adjusted to (1) represent symmetry and (2) consider efficiencies captured by the merger partner in the analysis as detailed in Section III, above.  Thus it is not technically a Farrell and Shapiro model, but follows Farrell and Shapiro in declining to track the full equilibrium price and thus we feel it is appropriate to keep the designation.)

42.  If the other parameters of the model could be defined for a sample of cases, it might be possible to estimate G from historical enforcement data.

43.  Schmalensee, supra n 29, 5. Consider Schamalensee's PCAL to equal Farrell and Shapiro's G and then rewrite one half as R and divide it across the equation to basically obtain the Farrell and Shapiro result.  The only difference is the inverse of the difference between one and the diversion ratio.  Schmalensee cautions against a naïve application of his simulation formula.  And he notes that he assumes away effects driven by responses from other competitors.  It is unclear if Schmalensee sees the formula as a useful structure for merger simulation.
 
44.  Farrell and Shapiro, supra n 6, 24.  Farrell and Shapiro trace the alternative analysis to Werden, supra n 29. 

45.  The result for UPP-FS can be read off of Table 1-b, although it will be necessary to divide by two to adjust for the pass-through parameter.  The UPP-S result will be 33 % higher when the margin is set at .5.  In the symmetric model, both the merged firms will raise price by these amounts.  This result requires the assumption that diversion ratios do not change when both firms raise price.  If this assumption is not acceptable, the simulation should focus on a single firm price increase.

46.  Different analysts can also generate different results by using different pass-through statistics. 

47.  For a discussion on the implications of dynamic competition for market definition, see Coate and Simons, supra n 24.

48.  As discussed in Coate and Fischer, supra n 5, merger simulation models merely present what might happen after a merger.  Without some type of evidence to confirm the prediction, the model merely states a hypothesis.

49.  The UK draft appears to touch on natural experiments at 4.12 (and 4.89), while hot documents seem covered at 4.8 and customer complaints at 4.9.  For the US, natural experiments show up at 2.1.1 and 2.12, while hot documents are relevant at 2.2.1 and customer complaints at 2.2.2.  See Draft Guidelines, supra n 8. 

50.  Some insights on this issue can be drawn from FTC data.  Coate identifies a sample of 75 analyses (with three or more pre-merger significant rivals) in which the FTC undertook a unilateral effects investigation.  (M Coate, "The Enhanced UPP Screen, Merging Markets into the UPP Methodology" (2010), 17, available at SSRN.  Of these matters, 31 were closed.  A review of the files indicates that repositioning was an issue in nine of these 31 closed matters.  Three of the nine cases also exhibited findings of relatively easy entry and another four had six or more pre-merger rivals.  Thus, standing alone, repositioning is rarely used to justify closing a unilateral effects investigation.