# Proving the Fix: Damages

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## Introduction

In antitrust litigation, the issue of damages seems relatively straightforward – the injured party should be compensated for the harm it suffered as a result of the defendant’s illegal and anticompetitive conduct.^{[2]} While the basic concept underlying antitrust damages may seem rudimentary, measurement of damages can be complex.^{[3]} This is because damage analysis requires consideration of a hypothetical economic environment – an environment that would have existed ‘but for’ the anticompetitive conduct, which in all other, important ways, was the same as the actual economic environment. For example, if a group of competitors conspires to raise prices to its customers, the customers may sue for price-fixing and claim damages based on the difference between the actual prices they paid and the prices they would have paid, had there been no conspiracy. The hypothetical environment is commonly referred to as the ‘but-for world’, and the prices the customers would have paid in that but-for world are referred to as ‘but-for’ prices. Measurement of the but-for prices, and therefore measurement of damages, requires an analysis of what would have occurred in the hypothetical world that would have existed without the conspiracy, but all other important factors that affect prices would have been the same as in the actual world. Therefore, in the example of the conspiracy, measurement of but-for prices must be done as if all of the other important supply and demand factors that affect prices were the same as in the actual world.

There are a number of other reasons quantification of antitrust damages can be complex. Not only do the antitrust laws relate to a variety of different types of conduct – including conduct involving multiple firms such as price-fixing or other types of conspiracies, as well as conduct involving a single firm such as tying, or exclusionary conduct – but the way in which that conduct may affect a plaintiff can be different and be affected by the particular market circumstances at the time of the violation.^{[4]} A proper assessment of damages must consider the way in which the conduct caused harm as well as the important economic factors that may be relevant. Further, damage analyses will be different depending on the type of plaintiff involved in the litigation. While buyer-plaintiffs may suffer from overcharges in the prices they pay, competitor-plaintiffs may suffer lost profits as a result of foreclosed business opportunities.^{[5]} The type of buyers may also vary and require different damage analyses. For example, an overcharge analysis for customers who purchase directly from an antitrust defendant will be different from an overcharge analysis for buyers who purchase indirectly from an antitrust defendant. In addition, there are a host of other issues that potentially must be taken into account, including, for example, the scope of the damages period and whether the plaintiff’s injury ended at some point in the past or will continue into the future and if so, what factors affect the length of the future period. The scope of the geographic area and how to measure sales in a particular area in which harm was suffered may be an additional potential consideration for damage analysis.

In this chapter, the key principles of quantifying damages associated with the measurement of price overcharges, generally paid by buyers, are summarised. We also attempt to address some of the significant challenges associated with developing damage models. The next section describes the primary focus of antitrust damages – the price overcharge – that is, the difference between the amount the buyer actually paid and the amount the buyer should have paid absent the conspiracy. Thereafter, we describe a common approach used in measuring price overcharges: the before-during-after approach. We then describe alternative approaches to the measurement of price overcharges.

## The price overcharge in antitrust damages

Damages to buyers harmed from a horizontal price-fixing conspiracy are generally measured as the dollar amount buyers paid as a result of the violation. This amount is a transfer from the buyer to the antitrust violator and the intent of the damage analysis is to transfer that amount back to the buyer. It is measured as the price overcharge, which is measured either on a per unit basis and multiplied by the number of units purchased in the actual world, or as a percentage of sales and multiplied by the dollar sales paid in the actual world. The price overcharge, on a per unit basis, is the difference between the price a buyer paid that was affected by an antitrust violation – the ‘actual price’ paid in the ‘actual world’ – versus the price a buyer would have paid absent the antitrust violation – the ‘but-for price’ paid in the ‘but-for world’. Generally, the number of units purchased by the buyer is a matter of record;^{[6]} however, there is no actual data related to the but-for price. The but-for price is a hypothetical price; it is the price that would have been charged had the conspiracy not taken place. Because the but-for price is not observable, it must be estimated by experts using economic and financial theories, industry analyses, and evidentiary data and information.

Notably, there are two possible price overcharges considered in price-fixing cases, depending of the type of buyer harmed – the overcharge paid by the customer of the antitrust defendant (e.g., the direct purchaser) and the price overcharge paid by a buyer downstream from the antitrust defendant (e.g., the indirect purchaser).^{[7]} An indirect purchaser may pay the full overcharge – if the antitrust defendant’s customer passes through the overcharge to the indirect purchaser in full; or it may pay only a portion of the overcharge – if the antitrust customer absorbs some of the overcharge and passes through only a portion of the overcharge to the indirect purchaser. In some cases, there is evidence that direct purchasers do not pass through any of the overcharge, and the indirect purchaser is not harmed.^{[8]} In any of these cases, to measure damages to the indirect purchaser, an estimate of the direct overcharge is necessary and so is an estimate of the relevant pass-through rate (or rates). Below, the discussion of the price overcharge reflects the overcharge paid by a direct or first purchaser.^{[9]}

## Measurement of the price overcharge: the before-during-after approach

There are two general approaches to measuring price overcharges. The first approach, discussed in this section, compares prices paid during the time of the violation with prices paid during a period of time when there was no violation – for example, prices before the anticompetitive conduct, prices after the anticompetitive conduct, or, in some cases, both before and after the anticompetitive conduct. This approach is often referred to as the ‘before-during-after’ approach to calculating damages.^{[10]} To the extent that the difference between prices during the period the violation occurred and prices before (or after) the period the violation occurred can be attributed to the conduct at issue, that difference is a price overcharge and can be used in the damage calculation.

This approach can be and has been used in price-fixing cases brought by purchasers.^{[11]}

## Price comparisons in the damages and but-for periods

The before-during-after approach may require more analysis than a comparison of prices charged in a period unaffected by the conspiracy (e.g., the before or after period) with prices charged during the damages period. The particular period of time used as the but-for period must be considered. In addition, if there are factors that are unrelated to the anticompetitive conduct and that affected prices differently in the but-for period and the damages period, then those factors may warrant consideration. Ideally, the but-for period should resemble the damages period in all important aspects, except for the violation itself.^{[12]} In reality, market circumstances that affect prices change over time, and it may be difficult to find a but-for period that is both free from the effects of the conspiracy and resembles the damages period. For example, the product at issue may change and evolve over time, and thus the cost of producing the product may vary over time and possibly be higher in the damages period than in the but-for period. A simple comparison of prices before to prices during the conspiracy, ignoring the changes in the product and the effect of cost on price, would find an overcharge when, in fact, the price difference could be due, in whole or in part, to the change in cost. There may be multiple other factors that affect the supply and demand of the product, and consequently affect the price of the product. In order to use the difference between prices in the damages and but-for periods as a price overcharge, then, it can be necessary to evaluate whether such factors exist and, to the extent they do exist and play an important role in price determination, control for changes in those factors.

## Use of regression in before-during-after overcharge analysis

Regression analysis is a tool used by economists to measure the relationship between variables while statistically controlling for the effects of other factors. For example, a regression analysis can be used to measure the relationship between the price of a product (one variable) and its cost (another variable), while controlling for other market factors such as changes in demand. In this way, it allows a researcher to sort out which variables have an impact on price and which do not, and it provides a quantitative measure of that impact. Regression is a tool that is commonly used to find estimates of average price overcharges and at least theoretically, provides a means to control for factors unrelated to the conspiracy.^{[13]}

There are two different types of regression analysis used in before-during-after estimation of price overcharges: dummy variable regression and the forecasting regression. In both, the variable of interest is the price of the product allegedly overcharged. In this context, the price is called the ‘dependent variable’ in the regression. That is, the price depends on other variables – when one of those other variables changes, the price of the product changes. The other variables are referred to as ‘independent variables’, or ‘explanatory variables’ and include factors that affect the price, such as the cost of producing the product, the cost of shipping the product, the prices of substitute products, and others. Regression analysis requires the collection of data points for the price of the product as well as the explanatory variables.

## Dummy variable regression

In the dummy variable approach, data points for price as well as all of the explanatory variables are collected for both the but-for period and the damages period. So, for example, if the conspiracy existed from 2000 to 2005, data may be collected from 1990 to 2005 to capture a period prior to the conspiracy (e.g., 1990–1999) and the damages period (e.g., 2000–2005). Regression analysis typically requires a substantial number of data points, so, for example, prices could be collected on a daily basis or even a transaction-level basis. In addition to the explanatory variables, the regression model also includes a ‘dummy variable’. The dummy variable takes on the value of ‘0’ during the but-for period (e.g., the 1990–1999 period) and the value of ‘1’ during the damages period (e.g., 2000–2005). The dummy variable thus separates the data sample into the two periods. The regression model produces results for each of the variables in the model, including the dummy variable. The result for the dummy variable indicates the average difference between the price of the product in the damages period and the but-for period, adjusting or controlling for the other variables that are included in the model. That result is an estimate of the average price overcharge, or is an estimate that can be used to find the overcharge, depending on the particular way the regression model is specified.^{[14]}

Consider the simplified example of a regression model that attempts to estimate a price overcharge where the price of the product is assumed to depend on the cost of manufacturing the product (a supply variable) and the price of a close substitute (a demand variable). Data is collected for the price of the product, the cost and the price of the substitute. The data is collected over both time periods: the damages period and the but-for period. A conspiracy dummy variable is added to the equation to separate the data into the but-for period and the damages period. The regression analysis produces estimates of the relationship between the price of the product and cost, and the price of the product and the price of the substitute. In addition, the regression analysis produces an estimate attached to the dummy variable. If that estimate is positive, the regression indicates that the price of the product was on average higher during the conspiracy period, after controlling for the effects of cost and the price of the substitute. Importantly, the dummy variable, as the name implies, does not prove that the conspiracy caused the price to be higher – only that the price was on average higher, for some reason, even after controlling for the explanatory variables that have been included in the regression model.

A subtle, but sometimes important, assumption underlying the dummy variable approach is that the model provides an unbiased result only if the relationship between price and the explanatory variables is the same in the damages period and the but-for period.^{[15]} For example, one of the most common independent variables in a pricing regression is the cost of product. The coefficient associated with the cost variable in the regression model is a measure of the cost ‘pass-through’ rate. The pass-through rate measures how much of the supplier’s input cost increases are passed on to the buyers or consumers in the form of higher prices. It is not a priori clear that the pass-through rate is the same during a price-fixing period and a but-for period. If the pass-through rate is affected by the conspiracy and is therefore different across the two periods, then the damages estimate from the dummy variable approach will be biased.^{[16]} In general, when the time periods being scrutinised are lengthy, it is more likely that market circumstances and, possibly, the relationships between price and market factors change over those time periods. Whether the changed relationships are due to the conspiracy or not, it can be important to consider whether the relationship between price and explanatory variables are the same in the but-for period and the conspiracy period, and to the extent that the relationships do differ alter the methodology to account for such differences.

## Forecasting regression

A forecasting regression analysis is an alternative approach that provides a means to allow for differing relationships between price and the explanatory variables in the damages period versus the but-for period. In particular, a forecasting regression may be useful when there is evidence that the conspiracy caused the relationships between price and the explanatory variables to be different than what those relationships would have been absent the conspiracy. The forecasting approach is similar to the dummy variable approach in that price is still the dependent variable of the regression and the regression still includes the important explanatory variables. However, the regression utilises data only for the but-for period, for example, the period before the conspiracy, and therefore the relationships between price and the explanatory variables are relationships estimated from data only in the but-for period. To the extent that the conspiracy caused changes in the relationships between price and explanatory variables, the forecasting regression will produce an overcharge estimate that does not account for such an effect. There is no dummy variable since the sample of data underlying the regression covers only the period prior to the conspiracy. The regression finds the relationship between price and the explanatory variables in the but-for period. The regression results that summarise these relationships between price and the independent variables are combined with data for the conspiracy period to find but-for prices. The regression results are essentially used to ‘forecast’ what the price would have been in the damages period given the relationships between price and the explanatory variables that existed in the but-for period, without the conspiracy, but with the actual values of those explanatory variables during the damages period. So, for example, the regression results for the relationship between price and cost, estimated with data for the period when there was no conspiracy, are used with the cost data during the period of conspiracy to find what the price would have been absent the conspiracy.

A number of studies have compared the advantages and disadvantages of the dummy variable regression versus the forecasting regression.^{[17]} As noted above, since the forecasting approach only uses pre-conspiracy data, that model will not be tainted by any effects that the price-fixing agreement might have had on the explanatory variables. In addition, the forecasting approach is usually implemented by selecting explanatory variables on the basis of statistical criteria. The criteria are generally designed to include explanatory variables based on their ability to improve the forecast. Variables that may improve the in-sample fit of the model (e.g., give a higher R-square) but also reduce the forecasting power of the model are excluded.^{[18]} This approach in choosing the explanatory variables makes it less susceptible to ‘cherry picking’ and ‘over-fitting’ – the practice of including irrelevant variables that are correlated with prices to explain price differences and lead to lower or no damages.

On the other hand, one drawback of the forecasting approach can occur if the relationships between the independent variables and the dependent variable in the pre-conspiracy period are not the same as those relationships in the conspiracy period, for reasons unrelated to the conspiracy. For example, if markets are highly dynamic and the industry changes over relatively short periods of time, the relationships between price and the explanatory variables in the but-for period may not resemble those relationships during the conspiracy period. Hence, the regression model of the relationship of price to other explanatory variables estimated using data before the conspiracy could lead to incorrect estimates of this relationship in the but-for world.^{[19]}

## Issues to consider in a regression analysis

Assuming the data exists, some regression with the price as the dependent variable and with various independent variables can be estimated and some estimate of an average price overcharge can be found. However, that does not mean the result is necessarily reliable. There are a number of issues that must be considered in evaluating any regression analysis.

In some circumstances, the prices at issue in a conspiracy case can be quite complicated – the prices may differ for different types of products, for different types of customers, for different geographic areas, and change frequently over time. Diverse and complex prices may also reflect differences in supply and demand factors, or the fact that individual customers negotiate prices and therefore may be affected differently by a conspiracy. The complexity associated with separating the factors that affect prices may not be limited to the complexity in the prices themselves, but also extend to the factors that affect those prices. For example, the cost of the product may change frequently over time or be different for different suppliers. Accounting for these complications is not trivial and regression models that depend on highly simplified assumptions, such as using average prices and average costs, may reduce the complications associated with developing a regression model but may also cause the results to be imprecise.

Aside from those complications, there are other issues that must be considered in evaluating the results of any regression model. These issues include, for example, whether the important variables that affect price have been included in the model, as well as the statistical properties of the results.

## Including all the important independent variables

A key issue in the evaluation of any regression analysis is whether the important variables that explain the dependent variable have been included in the regression. If one or more important variables are omitted, the regression results, including the estimate of the price overcharge, will be biased – that is, the result from the regression, on average, will be different from the true overcharge. In the case of a dummy variable regression, if a variable is omitted and that variable affects price and is correlated with the dummy variable, the estimate of the price overcharge will capture not only the impact of the conspiracy, but in addition, the impact from that omitted variable. For example, if the damages period occurs at or around the same time as a supply event (e.g., a hurricane that reduces capacity to produce the product in question and leads to price increases as a result), and there is no separate variable included in the regression for that supply event, then the estimate of the price overcharge will include both the effect of the conspiracy and the effect of the supply event.^{[20]} As noted above, a regression model that includes a conspiracy dummy variable is not capable of proving that a conspiracy caused prices to be higher. When the conspiracy dummy variable coincides in time with some other factor that causes prices to be higher, the dummy variable is merely indicating that prices are higher during that time period.

A forecasting regression model will suffer in a similar way from the exclusion of an important variable. A forecasting regression does not include data for the damages period and does not include variables that affect prices only during the damages period. So, if, as described above, some factor other than the conspiracy caused prices to increase during the damages period, a forecasting regression model will not include that variable and cannot capture its effect. The forecasted but-for prices will include the impact of the conspiracy as well as the impact of that other, unrelated, variable.

One way to assess whether the important variables are included in the regression model is to compare actual prices paid, either during the damages period and accounting for the overcharge, or during the but-for period without the overcharge, to the prices that the regression would ‘predict’ given the supply and demand variables that are included in the model. If prices are complicated and determined by many factors, then a model based on a relatively limited number of explanatory variables is likely to produce large differences between actual prices and prices predicted by the model. Large differences mean that the regression model might not reliably be explaining actual prices and that there are likely other factors, not included in the model, that are important determinants of price. That problem can extend to the model’s ability to isolate the effect of the conspiracy.

## Statistical significance

Another factor to consider in evaluating the reliability of the price overcharge from a regression analysis is the certainty of the result. Economists use hypothesis testing and tests of statistical significance to determine the probability that chance was the cause of the estimated overcharge rather than a systematic factor, such as a conspiracy. These issues are commonly reduced to discussions of ‘statistical significance’. Economists, as well as others, typically rely on fixed significance levels – usually 5 per cent, but sometimes 1 per cent or 10 per cent – to make inferences from regression analyses.^{[21]} The most common hypothesis-testing method is to identify a ‘null hypothesis’, and, in the language of statistics, either reject or fail to reject that hypothesis based on a fixed level of statistical significance – usually 5 per cent. The null hypothesis in this context is that the average price overcharge is equal to zero; in other words, any difference in prices during the damages period, compared to the but-for period, is due to random chance rather than a systematic factor, such as a conspiracy. That hypothesis is either not rejected – which would indicate the difference in prices is due to random chance and there is no systematic factor such as the conspiracy causing an observed difference – or rejected – which would indicate that the observed difference is not random but instead owing to a systematic factor, such as a conspiracy. The basis for rejection or failure to reject is the level of statistical significance. As noted, the typical level of statistical significance is 5 per cent, but can be 10 per cent or 1 per cent.

Determining whether the null hypothesis should be rejected can be the subject of highly technical debates among economists and statisticians. Drawing inferences based on standard statistics generated from the regression may be called into question depending on issues related to the specification of the regression model as well as the underlying data.^{[22]} Any damages calculation that relies on a regression analysis will be subjected to this type of scrutiny, and if the statistics from that regression do not show appropriate levels of statistical significance, the results will be called into question.^{[23]}

## Identifying the damages period

Identifying the damages period as well as a period unaffected by the conspiracy may require some empirical analysis. While conspiracy periods are often identified by plaintiffs based on documentary evidence, such as communications among competitors initiating contact or perhaps ending participation in a cartel, those dates may not coincide with the dates during which the conspiracy impacts prices and causes damage. The period during which a conspiracy is effective should take into account that the conspiracy may not take effect immediately. It may start and then stop as firms join the conspiracy and then cheat on the conspiracy, and its effect can outlast litigation in order to conceal its effects.^{[24]}

Properly identifying the conspiracy period assures that only data from unaffected periods are used in the measurement of but-for prices. If the damages period includes times during which the conspiracy is not effective and prices are not impacted, the before-during-after method can understate price overcharges. The dummy variable regression described above would, for example, measure an average amount that prices during the conspiracy period were different compared to the but-for period, which would include times when the conspiracy was effective as well as times when there was no overcharge. The resulting estimate of the average price overcharge then would be an average of the actual overcharge and zero, and thus be lower than the actual overcharge.

Correctly identifying the damages period is particularly important if there are plaintiffs that purchase only during certain time periods. Some of those plaintiffs may not have been impacted at all because they purchased during times when the conspiracy was not effective. Others who purchased only when the conspiracy was effective have an interest in correctly identifying the damages period and the appropriate overcharge.

## Other damage methods

## Yardstick approach

An alternative method for the estimation of damages is based on a comparison of the affected product with some other product in another product market or the same product in another geographic market.^{[25]} Often this method is referred to as the yardstick or benchmark method.^{[26]}

The yardstick and before-during-after approach are both based on a comparison of the price-fixed product with some benchmark. In the before-during-after approach, the benchmark is a period of time not affected by the conspiracy; in the yardstick approach, the benchmark is some other product or geographic area not affected by the conspiracy.^{[27]} Regardless of which approach is taken, it may be important to control for as many differences between the price-fixed product and the chosen benchmark to isolate the effect of the anticompetitive conduct. The before-during-after approach has the benefit of, at least potentially, controlling for some factors. It essentially involves the same market, with potentially the same participants and the same supply and demand characteristics; while damage estimation based on the yardstick method requires the selection of a benchmark product or geographic market that is sufficiently comparable to the price-fixed product. The particular product or geographic market that satisfies this requirement is case-specific, and while the markets do not have to be identical, market conditions of supply and demand must be sufficiently similar across the two markets to allow one to use a different geographic or product market as the hypothetical competitive market that would have resulted absent the price-fixing behaviour. The yardstick method is sometimes used when the before-during-after method is not available, for example, if the price-fixed product was affected at the time of its introduction – so there is no ‘before’ period – and the effects of the conspiracy continue or linger into the present – so there is no ‘after’ period (or the after period is not sufficiently long to use as a benchmark period).

## Combining before-after and benchmark methods: the diff-in-diff approach

A potentially superior alternative to both the before-during-after approach and the yardstick approach would be one where both those two approaches are combined in what is called the differences-in-differences (diff-in-diff) method. The approach, generally, compares outcomes (e.g., prices), before and after a change (e.g., a conspiracy) for the group affected by the change (e.g., buyers of price-fixed products) to a group not affected by the change (e.g., buyers not affected by the conspiracy), or when available if there are comparable geographic markets, one affected by the conduct and one not.

The diff-in-diff method is well-known in economics and has been used for many years in a wide variety of applications.^{[28]} The analysis, for example, would involve a price regression with two dummy variables. The first dummy variable would be 1 if the observation is from the market affected by the conspiracy and 0 otherwise, and the second dummy variable would be 1 if the observation is from the period of the affected conspiracy and 0 otherwise. Furthermore, there is an interaction term between the two dummy variables, which is equal to 1 when an observation is both in the conspiracy market and during the conspiracy period, and 0 otherwise. The estimated coefficient of the interaction term gives the estimated overcharge. Intuitively, the procedure is computing two differences: the difference in the average price between the conspiracy period and the pre-conspiracy period in the affected market (difference A); and the difference in the average price between the conspiracy period and the pre-conspiracy period in the unaffected market (difference B). The measure of overcharges is the difference between A and B – hence the name ‘difference-in-difference’.

In the context of damage estimation due to price-fixing, the diff-in-diff method could potentially allow for a more precise estimation of the price overcharge by comparing prices in the price-fixed market to prices in some other market both before and during the conspiracy. However, the diff-in-diff method is often hard to implement because the data necessary to make such comparisons is hard to come by.

## Notes

^{1} Michelle M Burtis is a senior consultant and Keler Marku is a senior associate at Charles River Associates.

^{2} Assessing damages based on the harm to the plaintiff not only makes up for the injury caused to the plaintiff, but also provides appropriate incentives for deterrence. Harm-based penalties are recognised in the economics literature as being ‘optimal’, in the sense that they force firms to fully internalise the costs of decisions to violate the law. See e.g., Gary S Becker, ‘Crime and punishment: An economic approach,’ in *The economic dimensions of crime* (London: Palgrave Macmillan, 1968); and William M Landes, ‘Optimal sanctions for antitrust violations’, in *The University of Chicago Law Review* 50, no. 2 (1983): 652–678. In the US, measured damages to a plaintiff are trebled to reflect that not all antitrust violations are detected and multiplying actual harm by three will incentivise plaintiffs to bring cases. See e.g., Franklin M Fisher, ‘Economic analysis and antitrust damages,’ in *World Competition* 29.3 (2006): 383–394. (‘ . . . The most notable feature of US damage awards in antitrust cases is that of treble damages . . . it provides a disincentive to engage in antitrust violations. But the real purpose here is to provide an incentive to potential private plaintiffs to bring private antitrust actions, thus contributing to antitrust enforcement through the actions of “private attorneys general”.’) The effect of trebled damages on incentives to sue and settle are widely discussed in the economic literature. For a summary see Ilya R Segal and Michael D Whinston, ‘Public vs. private enforcement of antitrust law: A survey’ (2006).

^{3} See, for example, William H Page, ed., *Proving Antitrust Damages: Legal and Economic Issues* (Chicago: American Bar Association, 1996); Daniel L Rubinfeld, ‘Econometrics in the Courtroom’, in *Colum. L. Rev*. 85 (1985): 1048; Daniel L Rubinfeld and Peter O Steiner, ‘Quantitative methods in antitrust litigation’, in *Law & Contemp. Probs*. 46 (1983): 69; Jonathan B Baker and Daniel L Rubinfeld, ‘Empirical methods in antitrust litigation: Review and critique,’ in *American Law and Economics Review* 1, No. 1/2 (1999): 386–435; Herbert Hovenkamp, ‘A Primer on Antitrust Damages,’ in *University of Iowa Legal Studies Research Paper* (2011). (‘But the law of damages has the much more difficult task of quantifying injury; the difference between saying that a certain practice is harmful and quantifying the amount of harm can be significant.’)

^{4} The notion that antitrust liability and damage must flow from the anticompetitive aspect of an unlawful practice is embedded in US antitrust law. See e.g., *Brunswick Corp. v. Pueblo Bowl-O-Mat, Inc.*, 429 U.S. 477 (1977). See also, *Comcast Corp. v. Behrend*, 569 U.S. 27 (2013) (‘The first step in a damages study is the translation of the legal theory of the harmful event into an analysis of the economic impact of that event’ and ‘[t]he District Court and the Court of Appeals ignored that first step entirely’); Amy W Ray, Christopher D Wall, ‘Antitrust,’ in *Litigation Services Handbook*, eds. Roman L Weil, Daniel G Lentz, and Elizabeth A Evans (New Jersey: Wiley, 2017). (‘A plaintiff seeking damages for an antitrust violation must not only show that the damages would not have occurred but for the antitrust violation, but also that the violation was the proximate cause of antitrust injury.’)

^{5} The focus of this chapter is damages from horizontal price-fixing, which are generally measured as price overcharges. Other conduct, for example, conduct that causes harm to a competitor, such as monopolisation, is focused on the competitor’s lost profits. In those circumstances, the damage analysis is also based on the construction of a hypothetical but-for world, but but-for profits, rather than but-for prices, are measured.

^{6} Economics recognises that assuming the number of units purchased in the actual and but-for world understates harm because it does not include the amount buyers lost when, as a result of the higher price caused by the violation, they reduced purchases of the product affected by the violation and purchased some other product instead. That amount is referred to by economists as a ‘deadweight’ loss and is not typically included in a damage calculation due, primarily, to the difficulties associated with its calculation. See e.g., Martin F Hellwig, ‘Private damage claims and the passing-on defense in horizontal price-fixing cases: an economist’s perspective’, in *MPI Collective Goods Preprint* 2006/22 (2006); and Leonardo J Basso and Thomas W Ross. ‘Measuring the true harm from price fixing to both direct and indirect purchasers’, in *The Journal of Industrial Economics* 58, No. 4 (2010): 895–927.

^{7} In the US, only direct or ‘first’ purchasers are allowed to bring federal antitrust claims. See *Illinois Brick v. Illinois* 431 U.S. 720. In the US, indirect purchasers are able to bring antitrust claims only under state laws. In Canada, the legal regime does not eliminate indirect purchasers as well. See James Brander and Thomas Ross, ‘Estimating Damages from Price-Fixing’, in *Canadian Class Action Review*, ed. Stephen GA Pitel Vol. 3 Issue 1 (Irwin Law, 2006). Recently, the US Supreme Court defined a first purchaser as any party with a direct contractual relationship with the defendant, which depending on the nature of the relationship may require consideration of pass-through issues in the estimation of damages. See *Apple, Inc. v. Pepper*, 587 U.S. ___ (2019).

^{8} For example, an overcharge that is small relative to the costs of changing prices may cause a reseller not to change a price and absorb the overcharge. See e.g., Dennis W Carlton, ‘The theory and the facts of how markets clear: is industrial organization valuable for understanding macroeconomics?’ in *Handbook of industrial organization* 1 (1989): 909-946 at footnote 3; Goldberg, Pinelopi and Rebecca Hellerstein. ‘Sticky prices: why firms hesitate to adjust the price of their goods,’ in *Current Issues in Economics and Finance *13, No. 10 (2007).

^{9} While determination of a pass-through rate, which is necessary to find the price overcharge paid by an indirect purchaser, may involve the same type of tools used to find direct overcharges (e.g., regression analyses), the focus of that analysis is different. Pass-through analysis is mainly focused on the actual relationship between prices and costs, and the extent to which a cost increase affects prices. In the context of damages, a price overcharge is treated as a cost to the direct purchaser and it is assumed that to the extent the direct purchaser passes through cost changes to its buyers, it would pass through the anticompetitive overcharge.

^{10} Justin McCrary and Daniel L Rubinfeld, ‘Measuring benchmark damages in antitrust litigation’, in *Journal of Econometric Methods* 3, No. 1 (2014): 63-74, describe the ‘before-during-after’ methodology as the most commonly used method of measuring damages. The method is also referred to as the before-and-after or before-and-during approach. While appropriate care should be taken when choosing the pre or post conspiracy period, or both, as the but-for world, the general econometric techniques of estimating but-for prices are similar and broadly follow the same principles.

^{11} See, Brander and Ross, ‘Estimating Damages from Price-Fixing’; and John M Connor, Global Price Fixing: Our Customers are the Enemy (Boston: Kluwer Academic Publishers, 2001). See also, United States District Court for the Northern District of California; MDL No. 1917 (N.D. Cal. 8 July 2015); *In Re Cathode Ray Tube (CRT) Antitrust Litig.* N.D. Cal. United States District Court for the Northern District of California MDL No. 1917 Master Case No. CV-07-5944-SC Individual Case No. CV-14-2058-SC 07-08-2015 *In Re: Cathode Ray Tube (Crt) Antitrust Litigation*: ‘This Order Relates To: All Direct Purchaser Actions Order In Re Class Certification With Respect To The Thomson And Mitsubishi Defendants,’ available at www.govinfo.gov/content/pkg/USCOURTS-cand-3_07-cv-05944/pdf/USCOURTS-cand-3_07-cv-05944-351.pdf at paragraph 33. (‘The difference between prices actually charged for CRTs during the Class Period and prices in a “but-for” world is sometimes called the “usual measure” of damages. This is a common damages calculation method.’)

^{12} It is a misconception that the but-for price should be the ‘perfectly competitive’ price where firms are pricing at marginal cost. In economics, the perfectly competitive price results from a particular set of market circumstances including, for example, that there are many firms offering a product at a price equal to marginal cost. These circumstances are rarely observed and would not necessarily exist absent some anticompetitive conduct. For example, if a group of firms in an oligopoly conspired to fix prices, the but-for price would not be the perfectly competitive price, but instead the price resulting from the oligopolists competing instead of conspiring. Lawrence J White, ‘Lysine and Price Fixing: How Long? How Severe?’ *Review of Industrial Organization* 18, No. 1 (2001): 23–31.

^{13} Regression analysis, generally, is a common tool used by economists for a variety of purposes. Used appropriately, the statistical method can provide valuable insights into economic relationships. See, for example, James H Stock, and Mark W Watson.* Introduction to econometrics*. Vol. 104. Boston: Addison Wesley, 2003, at 3. Regression analysis to estimate prices is the most common statistical method used in antitrust litigation; see Baker and Rubinfeld, ‘Empirical methods in antitrust litigation: Review and Critique.’ 391.

^{14} See Rubinfeld, ‘Econometrics in the Courtroom’ 1090; and Daniel L Rubinfeld, ‘Reference Guide on Multiple Regression,’ in *Reference Manual on Scientific Evidence: Third Edition *(Washington, DC: The National Academies Press, 2011). (‘The intercept of the straight line is the average value of the dependent variable when the explanatory variable or variables are equal to 0 . . . Similarly, the slope of the line measures the (average) change in the dependent variable associated with a unit increase in an explanatory variable.’)

^{15} Bias is a statistical concept. The technical definition of statistical bias is that the expected value of the estimator is different from the true value of the parameter being estimated. In this context, that means that if it was possible to obtain many different sets of data and run the regression many times, the average value of the estimated overcharge would be different from the true value of the overcharge. See, for example, Jeffrey M Wooldridge, *Introductory Econometrics: A Modern Approach*, 5th Edition (Cengage Learning, Mason, 2013) at 88–92.

^{16} Whether this bias leads to an overestimate or underestimate of overcharges depends on the nature of competition and the nature of cooperation as well as differences in the variability of inputs across the two periods.

^{17} See McCrary and Rubinfeld ‘Measuring benchmark damages in antitrust litigation’, at footnote 3 for a list of such studies.

^{18} ibid., 67.

^{19} This problem still exists in the dummy variable regression, although the relationships are typically measured as averages across both periods.

^{20} See, e.g., Daniel L Rubinfeld, ‘Quantitative methods in antitrust,’ in *Issues in Competition Policy*, ABA Antitrust Section (2008), at 726: ‘the omission of relevant variables can bias the results. If, for example, costs were high during those periods of alleged wrongful behavior because of the influence of variables not included in the regression model, or if demand grew more inelastic during that period in ways not captured by the included demand-side variables, then a dummy variable reflecting the likely effect of wrongful behavior might have a large positive coefficient for reasons unrelated to the existence of the alleged conspiracy.’ Detecting whether important variables have been omitted requires analysing information about how prices are determined. That is, there is no simple statistical result that will necessarily indicate whether the problem exists. Relying on, for example, an R-squared statistic that provides information regarding the percentage of the variation in price that is explained by the variables in the regression does not necessarily provide information about whether an important variable has been omitted. See, e.g., Peter Kennedy, *A guide to econometrics*, 5th edition, (MIT press, 2003), 254 (‘Care must be taken in evaluating models containing dummy variables designed to capture structural shifts or seasonal factors, since these dummies could play a major role in generating a high R2, hiding the fact that the independent variables have little explanatory power.’)

^{21} See for example, James H Stock and Mark W Watson, *Introduction to Econometrics*, 3rd Edition (Boston: Pearson, 2011) at 77–78 (‘In many cases, statisticians and econometricians use a 5% significance level.’); Jeffrey M Wooldridge, *Introductory Econometrics*, 2nd Edition (Mason: South-Western, 2002) (‘Suppose we have decided on a 5% significance level, as this is the most popular choice.’) See also Stephen T Ziliak, and Deirdre N McCloskey, *The Cult of Statistical Significance: How the Standard Error Costs Us Jobs, Justice, and Lives*, (Ann Arbor: University of Michigan Press, 2008) (discussing the history of significance tests). Some courts have criticised the use of fixed significance thresholds in antitrust cases. The court in* Re Photochromic Lens Antitrust Litigation*, 2014, U.S. Dist. LEXIS 46107 (2014) found that ‘[t]here is not, however, any “precise level in the law” at which statistical significance is sufficient to permit the inference derived from a correlative study. And most courts have rejected the arbitrary application of a 5% threshold’.

^{22} See, for example, Larry B Hedges and Christopher H Rhoads, ‘Correcting an analysis of variance for clustering’, in *British Journal of Mathematical and Statistical Psychology*, (2011), 64, pp. 20–37 at p. 20. (‘A great deal of educational and social data arises from cluster sampling designs where clusters involve schools, classrooms, or communities. A mistake that is sometimes encountered in the analysis of such data is to ignore the effect of clustering and analyze the data as if it were based on a simple random sample. This typically leads to an overstatement of the precision of results and too liberal conclusions about precision and statistical significance of mean differences.’)

^{23} See, for example, William H Page, 'Proving Antitrust Damages: Legal and Economic Issues', 2nd ed. *Antitrust Practice Guide*. (Chicago, Ill.: Section of Antitrust Law, American Bar Association, 2010) at 141–144. (‘Correct statistical inference requires not only good estimates of the coefficients of the model, but also good estimates of the standard errors of these coefficient estimates . . . Testing a hypothesis about a coefficient requires a measure of the statistical precision of the estimate of the coefficient. If there is a great deal of statistical noise so that a coefficient estimate is highly imprecise, it would provide relatively little information about the value of the true underlying coefficient . . . The 5 percent level of significance (and the corresponding 95 percent confidence interval) is often used by economists and statisticians when conducting hypothesis tests, but other levels of significance, such as 1 percent or 10 percent, are also sometimes used.’)

^{24} See, e.g., Edward J Green, and Robert H Porter, ‘Noncooperative collusion under imperfect price information’, in *Econometrica: Journal of the Econometric Society* (1984): 87–100; Joseph E Harrington Jr, ‘Post cartel pricing during litigation’, in *The Journal of Industrial Economics *52, no. 4 (2004): 517–533.

^{25} Such an approach, for example, was used by the plaintiffs’ experts to estimate damages in consumer class action lawsuits against Microsoft. See John E Lopatka, ‘Overcharge damages for monopolization of new economy markets’, in *Antitrust Bulletin* 51 (2006): 453.

^{26} Some authors refer to the before and after method as the benchmark method (see McCrary and Daniel L Rubinfeld, ‘Measuring benchmark damages in antitrust litigation’, for example), and use the term ‘yardstick method’ to describe the method where a different geographic market or product market is used as the but-for world. However, most sources, use the terms ‘benchmark’ and ‘yardstick’ interchangeably to describe the use of another geographic or product market as the but-for world. We adopt that convention here.

^{27} A benchmark does not necessarily need to be another market. It could just be another individual firm or another product of the same firm.

^{28} For example, one early and well-known example is a study of whether a change in the minimum wage affected employment. In that study, wages of workers in areas where the minimum wage increased were compared to the wages of other workers, both before and after the minimum wage change. See e.g., Orley Ashenfelter and David Card, ‘Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs’, in *The Review of Economics and Statistics* 67, No. 4 (1985): 648–60.