A simple framework for assessing the plausibility of overcharge estimates in litigation

Economic evidence plays a crucial role in antitrust litigation, yet estimates produced by economists are sometimes dismissed by courts as implausible. In extreme cases, the very objectivity of economists has been called into question. In this article, Jorge Padilla, Ben Dubowitz and Roberto Venturini, [1] explore how the presentation of economic evidence can be improved to better inform judicial assessments of plausibility. They argue that plausibility should not be treated as a purely statistical matter. Rather, economists should provide an expert account of the wider economic context alongside “the numbers” to help judges form a coherent view of the plausibility of economic evidence.

Introduction

Courts have relied on expert witnesses for centuries. In 1554, a UK court heard testimony on the proper use of Latin grammar (Buckley v Rice-Thomas).[2] By 1782, experts advised on questions of science and causation – for instance, in Folkes v Chadd, regarding what had plausibly damaged a harbour.[3] Despite this long tradition, the role of economists as expert witnesses in the growing number of antitrust cases feels like it is going through a difficult maturing phase.[4]

In antitrust litigation, economists are essential; estimating the effect of an anticompetitive conduct – typically, the “overcharge” above a counterfactual competitive price – requires sophisticated economic and econometric techniques. However, on occasion, courts in the UK and Europe have rejected the estimates these techniques provide as implausible. Judges have even gone so far as to question whether economists are offering objective assistance.[5]

To help address the issue, this article asks a narrow but important question: how can economic evidence be presented so that it more usefully informs courts’ assessment of the plausibility of an effect when determining liability?[6]

The difficulty with assessing the plausibility of an estimated overcharge is that, while the overcharge is “just a number”, its plausibility depends on a credible account of: (a) the theory of harm that produced that effect; and (b) the competitive counterfactual price that consumers would have otherwise paid.

Neither account is just a quantitative exercise. For instance, where the theories of harm and market contexts differ, the scale of an estimated overcharge may be plausible in one market, and absurd in another.

Our view is that “the numbers” do not speak for themselves: they require context and interpretation. When economists jump straight to the technical detail, or they consider only the statistical plausibility of their estimates – in abstract from the market they are analysing – their contribution is diminished, and their value to the Court constrained.

Demystifying the plausibility of an estimate

Economists tend to agree that the plausibility of an estimate is not just an analytical or statistical question. Ultimately, it boils down to the expectations and a coherent explanation of the relationship between the two – i.e., what “makes sense” given the economic and commercial reality of the market, mechanism, basic logic, and complementary evidence. However, in our experience, the heuristics that inform this assessment in antitrust litigation cases are not always explicit, coherent, or well structured, which risks incorrect inferences and bias.

In the next section, we sketch a framework that helps courts and analysts to form expectations on the range of estimates that could be regarded as plausible from an economic point of view. This helps reduce the temptation to “post-rationalise” explanations to fit the data. However, first we highlight some of the common complications encountered when assessing the plausibility of estimates and illustrate them with examples.

How not to think about the plausibility of estimates

A common difficulty in damages cases is that debates about the plausibility of an estimate and its analytical reliability can become conflated or detached. Analytical reliability concerns whether the statistical or economic methods used are technically sound. Courts and experts often debate which assumptions or modelling choices are most credible.[7] Whether the estimates are “plausible” is a broader question. It considers whether, before digging into technical details and debates, the estimates look credible in light of one’s expectations given, for instance, the economics of the market, the parties incentives, and their particular conduct.

The separation between plausible and analytical reliability is ultimately unhelpful, because the two issues should interact and complement each other. Starting with plausibility provides a benchmark against which the reliability of technical analysis can be judged. This can help courts navigate the complex and technical differences between competing models. It can also help experts avoid errors or unconscious bias. Even when experts use the same dataset, and therefore should avoid statistical noise from sampling (so-called “standard errors”), their estimates can differ, not because they lack objectivity, but because small and seemingly reasonable modelling judgments can accumulate into large divergences (“non-standard errors”). Strong expectations about what is plausible provide a valuable sense-check to reduce these risks.[8]

There are two important caveats to assessing empirical analysis against “plausible” expectations:

• “Plausible” does not mean “common sense”. Common sense may serve as the starting point for plausibility; however, a plausible estimate requires a compelling account of the context and circumstances that determine the effect being estimated, supported by both (a) a credible economic theory of harm and (b) reliable empirical evidence.
• Plausibility guides scepticism; it doesn’t impose it. Plausible ranges of results are not predetermined absolute cutoffs. They provide priors which require strong evidence to overcome. If an estimate diverges from expectations, it may still be accurate. However, a heavier burden of proof is needed to demonstrate accuracy than would be needed in a case where the estimate aligns with expectations.

For instance, as the CAT has observed more broadly in Stellantis v Autoliv, the plausibility of an estimate cannot be detached from the evidence and theory that underpins it: “For an econometric test of this type to provide reliable results, it is essential that the test be formulated in advance in the light of a particular hypothesis (theory of harm) and be used to test that hypothesis. It is not appropriate to reformulate the hypothesis to fit the data.”[9]

Types of implausible estimates

Before setting out the framework, we distinguish between two types of “implausible” estimates in antitrust cases.

Too large and too small

The first type of implausible estimates are those considered implausible in their own right. These are estimates that, at face value, do not align with economic or commercial reality, nor judges’ expectations.

Commonly, they arise in defendants’ submissions that suggest there was no harm, or that the harm was so small that it cannot be empirically distinguished from a “no effect” scenario. For example, in the Trucks litigation, producers argued that damages were negligible. European courts rejected the implication – that a 14-year infringement had no significant effect on prices – as implausible.[10]

Small effects are not impossible. Once an abuse is established, there is a presumption that it had some effect, [11] but that presumption can be rebutted and has been in specific cases.[12] However, the evidential burden to demonstrate that such estimates are plausible is understandably high. First, they only occur in specific circumstances, so there must be strong supporting evidence that market conditions, parties’ incentives, and especially ineffectual mechanisms support the claim there is limited, negligible, or no effect. Second, statistical analysis cannot prove the absence of an effect; at best it can show that no effect has been detected.

At the other extreme, there should also be a ceiling above which estimates are implausible.

To illustrate, consider the same context. The estimates submitted by claimants in the Trucks litigations were typically comparatively high. For instance, in Royal Mail v DAF, the claimant’s expert estimated overcharges of 9-11% on all trucks sold in the UK.[13] Extrapolated across all producers and markets, this implies aggregate damages of nearly €100 billion, significantly greater than the total operating profits for the truck manufacturers during this period.[14] The estimated overcharge therefore implied that, absent the cartel, the industry would have suffered losses greater than the profits it actually earned or that counterfactual costs would have been very substantially lower than they were – a result that strains plausibility.

Too wide a range

The second type of implausibility is related but distinct. Often the parties’ estimates will differ from each other to a great extent. In isolation, either may seem plausible. But as estimates of the same effect of the same conduct in the same context, they cannot both be plausible. At least one must be implausible. And further, proving one is implausible, does not mean the other is necessarily plausible. Therefore, it is vital to establish the range of plausible estimates and rationale for the range in advance to help evaluate the plausibility of estimates in absolute and relative terms.

A framework for informing expectations on plausibility

In the context of a follow-on claim arising from an Article 101 infringement, we propose a framework for establishing an informed expectation of the plausible range of overcharge estimates. This framework sets out three steps:

1. The market context;
2. The parties’ incentives; and
3. The mechanism in question.

The market context

The starting point for assessing plausibility is to ask: What range of overcharges is possible in a particular market?

Artificial monopolies: The bounded range of possible outcomes

In any given market, there is a bounded range of overcharges that a cartel could impose without any constraints.

• Lower bound: An overcharge cannot reasonably be less than zero.[15] It is implausible (if not impossible) that a cartel would reduce prices below the competitive level, since this would defeat the purpose of forming the cartel.
• Upper bound: At the other extreme, overcharges should not reasonably exceed the level a monopolist could sustain. Beyond the monopoly price, further increases would reduce the cartel’s expected profits, as falling sales would more than offset higher margins.

This range is not normally observable, not least because estimating the monopoly price often requires estimating the full demand function. However, this already provides some insight on what is plausible: if there are significant outside market constraints, marginal cost is very low, or demand is very elastic, then monopoly prices may not be significantly above competitive rates.

Estimates falling outside this range should be met with scepticism. Typically, this already happens for estimates that are “small”. However, in our experience, the upper bound is often overlooked or downplayed, but it is crucial in evaluating damages evidence.

A cartel is, in essence, an artificial monopoly; it will not, even in theory, attempt to charge more than a true monopolist could in that market. And for reasons we set out below it may choose to charge significantly less than this rate.

Practical proxies for the upper bound

In practice, simpler metrics such as observed margins can provide useful proxies for the upper bound of possible overcharges. Margins test the plausibility of the counterfactual scenario on which an estimated overcharge depends – as seen in the discussion on Trucks above, and discussed in Nilausen (2020)[16], which looks at how price effects can be translated into profitability within alternative counterfactual scenarios.

Margins are not necessarily a hard constraint. It is possible that the costs, not just prices, would be lower absent a cartel – particularly one with a long life. However, they do stress test the plausibility of an estimate. In a world with 3% margins, one can debate if a 5% overcharge is plausible through counterfactual cost reductions; however, a 20% estimate stretches plausibility beyond breaking point.

Industry specific factors

Ultimately each industry is likely to have very different circumstances which affect what an artificial monopolist could achieve.

To illustrate: suppose the Trucks cartel estimate of a 10% overcharge is judged against meta studies of all cartels. On that benchmark, it looks conservative. Connor (2024) reports a median overcharge of 25% across 709 cartels, and 21% for 2000–2019.[17] Komninos et al. (2011) found a median of 18%.[18] Further, fewer than a quarter of cartels produce overcharges below 10%.[19] By that yardstick, 10% looks modest.

However, judged against the Truck industry, where profit margins can be well into single figures, a 10% overcharge fails a simple sense-check, and the “average” overcharge of 18–25% would be far beyond what this market could plausibly sustain. The range of possible overcharges is therefore market specific. This is both theoretically logical – since it depends on demand conditions, marginal costs, and the counterfactual competitive dynamics – and empirically verified.[20]

It is for this reason that the CAT has cautioned against unhelpful generalisations across industries and across courts: “[it is] wrong in principle to use historical data derived from other findings by other courts and economic studies in relation to other cartels concerning other industries or industrial sectors to prove or assist in answering the empirical question concerning the level of Overcharge in this case.”[21]

Beyond demand conditions, each market is also subject to different vertical relationships with other markets. The effectiveness of a cartel mechanism depends not only on the cartelists’ behaviour but also on the characteristics of their customers. In Stellantis v Autoliv, both the Commission and the CAT considered that car manufacturers, as sophisticated buyers, could resist attempts by suppliers of airbags, steering wheels, and seat belts to impose higher prices. The Commission’s market investigation suggested that in such circumstances, coordinated behaviour would likely have little or no effect.[22]

In such scenarios, even a true monopolist of an upstream input cannot operate unconstrained, but is subject to the same countervailing buyer power discussed extensively in the literature on dominance and mergers.[23]

The parties’ incentives

Once the range of possible overcharges in a market has been identified, the next step is to consider the incentives of the cartelists. This helps establish whether optimal behaviour gives a narrower range of plausible estimates within the possible outcomes.

Economics and logic dictate that a cartel will maximise profitability, and without outside constraints, would seek to approach the monopoly rate. However, unlike a monopolist, cartel members face additional risks that can mean it is rational to target a lower overcharge.

As discussed in a companion paper, [24] two overlapping considerations are especially important which can drive down optimal overcharges:

1. To make the cartel more stable: Like a monopolist, cartelists aim to maximise total expected earnings. But the stability of their arrangement depends on each member perceiving that staying in the cartel is better for them than breaking it. A high overcharge will destabilise the arrangement if the short-term payoff from undercutting rivals – or from defecting and seeking leniency – outweighs the expected long-term benefits of cooperation.
2. To reduce the threat of follow-on damages: Cartelists must also weigh the risk that accumulated overcharges will be reclaimed in damages actions if the cartel is detected. The longer the cartel operates, the larger this potential liability becomes, tipping the balance of risk and reward away from sustaining high overcharge.

The scale of these risks depends on market-specific factors, many of which are observable and verifiable. For example:

• High cost of capital, which diminishes the value of future profits.
• A high probability of cartel breakdown due to regulatory factors (e.g., increased likelihood of detection, fines, or damages) or economic factors (e.g., market changes like mergers, new entrants, demand fluctuations, or technological shifts).
• Slow detection of deviations, which allows a defector to profit longer before retaliation.
• Uncertainty about deviations, making cartelists hesitant to retaliate against price drops.

Taking incentives into account refines the assessment of plausibility. Within the possible range of overcharges, narrower ranges will be plausible or implausible depending on the facts in the relevant market. In some markets, the monopoly rate may be both lucrative and relatively safe. Here, lower-end estimates are less plausible and should be treated with greater scepticism. In other markets, pursuing the monopoly rate would simply increase the risk of collapse. In those circumstances, upper-end estimates are implausible, and the lower part of the range is more consistent with the cartelists’ incentives.

The mechanism in question

The third question is the efficacy of the mechanism that produced the estimated overcharge. Depending on how effective that mechanism is, the overcharge may range from negligible (i.e. no measurable effect) to the maximum level the cartelists had an incentive to pursue.

This highlights the distinction between abuse and harm. At the point of a trial in which quantum is being established, an abuse by object has often been established. This can be either from a preceding EU court decision, [25] or from a prior trial.[26] A finding of abuse by object does not automatically necessitate that harm and damage followed. Just as drunk driving is prohibited regardless of whether an accident happens, a cartel agreement is unlawful even if it has caused little or no economic damage in practice. Damages proceedings, by contrast, focus on the scale of harm actually incurred.

The broad – and intuitive – point that there is a relationship between the scale of damages and the nature of the conduct is described in the economic literature.[27] This is not merely an academic point: courts have recognised that an estimated overcharge must be grounded in and corroborated by the mechanism that led to that effect. Where no link is provided, the mechanism is vague, or is balanced by the presence of efficiencies, it is harder to use it to assess the plausibility of the estimates.[28],[29]

In practice, vague or ineffectual mechanisms are of most interest: where the collusive mechanism is weak, the overcharge is likely to be small – and maybe indistinguishable from having no effect, given available data. The case law reflects this: in T-Mobile (2009), cartel participants met but did not exchange sensitive information.[30] In BIDS (2008), the collusive agreement was never actually implemented.[31]

The efficacy of mechanisms should, whenever possible, be empirically tested. In coordination cases, for example, one would expect to see co-movement of key outcomes (e.g. prices, quantities) that cannot be explained by normal market forces. Such tests should, as all empirical evidence, be subject to robustness and sensitivity analyses, since exogenous shocks (such as tariffs imposed across the sector) can generate similar patterns.

Econometrics through the lens of plausibility

Having established an informed range of plausible overcharges – based on market context, incentives, and mechanism – one is better equipped to evaluate, or demonstrate, the plausibility of a given estimate and the relative plausibility of rival estimates. Econometric analysis is then the final step: it helps determine where, within that range, the actual harm is likely to lie.

Given the complexity of many econometric models, informed expectations help courts and analysts focus scrutiny, direct scepticism, and detect errors. The further an estimate is from the expected range, the stronger the evidence required to show it is nonetheless plausible.

Here we highlight two complementary issues courts must consider when interpreting the plausibility of econometric estimates of overcharge.

Interpreting estimates and uncertainty

Econometric results are usually presented as a point estimate with accompanying statistics on confidence or uncertainty – most often, the estimated statistical likelihood of that estimate being non-zero purely by chance (“statistical significance”). These can be easy to misinterpret in the context of understanding plausibility.

Challenges with interpretation

Statistical significance only tests whether the data allows us to reject the null hypothesis with sufficient confidence (typically, that there is no effect). It does not tell us whether the estimate is consistent with an alternative, economically relevant hypothesis (e.g. a 5% or 10% overcharge). This creates two common interpretive errors:

• Fallacy of rejection: Given the null hypothesis was rejected (i.e. the result is “statistically significant”), assuming that the point estimate is meaningful.
• Fallacy of acceptance: Given a null hypothesis was not rejected (i.e. “not statistically significant”), assuming that the null hypothesis is true – i.e., that there was no effect.

These errors are correlated with the size of the overcharge being estimated.

First, consider a high claimant estimate. A large (but noisy) estimated overcharge may well be statistically significant, but wildly inaccurate. In BritNed, the judge noted that “the estimated mean overcharge was 22% with a 95% chance that the true value lay between 0.32% and 39%, implying overcharge damages of anywhere between €885,000 to €108.7 million”.[32] This, despite rejecting the null, provided no information on whether the model gave useful or plausible results.

Second, consider a low defendant estimate. A small estimate (e.g. 0.5%) will often be statistically insignificant, not because it is less precise than the higher estimate, but because it is so close to the null being tested (i.e. “no effect”) that the data cannot reliably distinguish between the two.

Failure to reject the hypothesis that there is no effect does not prove the cartel had no impact. It means only that, given the available data, one cannot rule out that the observed result might arise even if there were no effect. A “no significant effect” finding therefore usually indicates either (i) the true effect is negligible, or (ii) the dataset lacks the statistical power to detect it. The closer the true effect is to zero, the stronger the data required to distinguish it.

Avoiding misinterpretation

Based on recent CAT decisions, we highlight three ways to avoid misinterpretation of econometric evidence:

• Informed expectations and sense checks: Having clear expectations about whether the overcharge is large or small is likely to help avoid misinterpreting the results of statistical significance. This complements the existing toolkit of basic sense checks and sensitivities courts employ. A model that falls at basic sense checks cannot be relied upon. These encompass the range of possible overcharges captured in the model; [33] negative overcharges; and sensitivity to the period chosen.[34]
• Sufficient data quality: Weak or sparse data cannot deliver reliable point estimates. Courts have pushed back where models relied on poor-quality or very small samples.[35]
• Do not equate “no effect” with “no statistically significant effect”: Defendants sometimes argue that no harm was caused at all. There is an important distinction between a claim that no harm exists, and that the harm incurred is small – even too small to detect. First, a claim that there was no harm at all is, at face value, less plausible. In Trucks, for instance, the CAT found it implausible that a cartel lasting 14 years, and admitted in a Commission settlement, had no effect on prices. Second, empirical evidence cannot prove the absence of an effect.[36] Therefore, there is a very high bar for demonstrating a claim of “no effect” is plausible. The market context and cartelists’ incentives should be consistent with a small overcharge to start with. The causal mechanism must be plausibly ineffectual; and, the empirical estimate must be small or negligible.

Finally, we note that point estimates and significance tests are not the only tools available to economists and the courts. For instance, economists can present the full confidence intervals, which convey the precision and range of possible outcomes. For example, an estimate of 4–6% with 99% confidence is more informative than one between 0.3–17%. In addition, they can employ severity testing, which assesses whether estimates are consistent with alternative hypotheses beyond “zero effect”. For instance, making it possible to evaluate, given the estimated overcharge, whether it is plausible that the true overcharge is 5% or 10%.

Reducing noise and disagreement

A second factor in assessing the plausibility of empirical estimates – and especially the relative plausibility of rival estimates – is the consistency of data and assumptions on which they depend. When parties present very different estimates, the divergence often stems from differences in the data analysed or the assumptions applied.

These differences are not restricted to econometric analysis. In Cabo Concepts Ltd, the CAT rejected damages estimates from both sides. Each party had modelled Cabo’s lost earnings, relative to a counterfactual scenario without the abuse. But the Tribunal found neither counterfactual realistic, and so dismissed both sets of results.[37]

Here too, informed expectations help evaluate and constrain differences in approach, particularly for assumptions. As the expectations must be rooted in the realities and specifics of the relevant market, room for disagreement about the nature of the counterfactual should be restricted.

Our colleagues Haller and Pereiras (2025) have suggested practical ways to improve how econometric evidence is used in court:[38]

• Common dataset. In some jurisdictions sharing data to start from a common basis between the experts is a consolidated procedural tradition. In other jurisdictions, different analyses will start from completely different premises.[39] Independently of the rules, experts should always be invited to share the data and replicate the analysis using the different datasets on the table. They might not agree on which data is best to use, but at least each expert should be able to put forward the preferred range of results using the same data, which will significantly reduce the range of estimates that are on the table.
• Key assumptions. When the underlying data used by the experts is the same, large discrepancies in the results are often the result of one (or a few) crucial assumption(s). For instance, price transformations and inflationary trends can induce very large discrepancies between the results of econometric models that are otherwise very similar. It is, therefore, important that courts assess the plausibility of such assumptions, which is often a much easier task than assessing the plausibility of the resulting counterfactual scenario. This is because the validity of individual assumptions in a model can be easily tested using available factual or witness evidence, or even basic economic logic.

Conclusions

Lord Mackay (quoting Justice Brachtenbach) once warned against using just statistics as a basis for finding harm with the following thought experiment: in a town with four cabs, three blue and one yellow, could we say that a victim of a hit-and-run by an unobserved cab was blue? He argued no: “before any inference that it was a blue cab would be appropriate further facts would be required as, for example, that a blue cab had been seen in the immediate vicinity at the time of the accident or that a blue cab had been found with a large dent in the very part of the cab which had struck the victim.”[40]

Considering this example, the previous Chairman of the CAT said: “My feeling is that lawyers will agree with Justice Brachtenbach and Lord Mackay, but I wonder if economists and statisticians do?”.[41] Setting aside the exact percentages (would lawyers hold the same view if there were 99 blue cabs for every red one?), we agree that economists can be too quick to present statistics alone as enough to identify the most plausible story.

This article has tried to focus on the gap between the legal facts (the large dent) and the econometrics (counting cars) when understanding what is plausible. Economists can and should also provide a wider account of markets, mechanisms, and incentives, in order to help judges reach a coherent view of the evidence, and to be as much of an asset to the court as they can.

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References