Post-merger Price Dynamics Matters, So Why Do Merger Retrospectives Ignore It?

The price effect of past mergers has received increasing attention since the early 1990s. The recent upsurge in the number of such studies generated a considerable body of evidence of the price effect of mergers. Kwoka (2013, 2014) identified more than 60 US studies that looked at the price effect of mergers. Mariuzzo et al. (2016) reviewed another 20 similar European studies.

Methodologically, these studies are relatively homogeneous. They use standard difference in-differences type models, and they vary mainly in the way the counterfactual is constructed. The objective of our paper is to focus on a specific empirical aspect of these studies, the handling of post-merger time-periods. The specification of the estimated model plays a cardinal role in how the results should be interpreted. Most previous studies estimate over-time average post-intervention price-effects; these studies overlook post-merger price dynamics. In general, in many causal inference studies the post-intervention dynamics of the outcome variable would not matter. However, there are equally many situations where evidence on this variation is exactly what the researcher should be aiming to get. Estimating the price effect of mergers is one of these.¹

Estimating the over-time average price effect of mergers is counter-intuitive for two main reasons. First, merger guidelines agree that no intervention is needed if the post-merger price increase disappears within a reasonable amount of time, for example because of new entry. The US Horizontal Merger Guidelines say: “The Agency will consider entry to be timely so long as it would deter or counteract the competitive effects of concern within the two year period and subsequently.”² Similarly, the European Commission’s guidelines on the Merger Regulation state: “The Commission examines whether entry would be sufficiently swift and sustained to deter or defeat the exercise of market power. What constitutes an appropriate time period depends on the characteristics and dynamics of the market, as well as on the specific capabilities of potential entrants. However, entry is normally only considered timely if it occurs within two years.”³ Of course for entry to occur, a potential entrant would have to find such entry profitable, and the extent of entry would have to be such that prices would revert to (or remain at) pre-merger levels. Retrospective studies could verify whether these conditions are fulfilled after a merger. However, entry and its effects are a gradual process (prices might take some time to drop or to increase), which requires looking at the dynamics of post-merger prices in order to identify whether pre-merger expectations about entry—and the effect of entry—were correct.

Second, merger retrospectives are typically conducted to inform policy-makers whether a merger decision was correct or not. For this reason the conclusion as to how prices change post-merger is crucial. The estimation of the average post-merger price-effect requires a different empirical model than estimating annual effects. Is it possible that the two empirical models return different evidence on the price effects of the merger? We show in this paper that the likelihood of making the wrong conclusion is very high if the wrong empirical model is used.

The purpose of this paper is not to stipulate that longer-term studies are better suited for post-merger price evaluations, although given merger policy guidelines, it appears appropriate to include at least two post-merger years in any merger evaluation. Instead we argue that even if the available data are relatively short-spanning (two years), one should still look at the dynamics of price effects (for example the effect in the first and in the second year separately) and not only the over-time average as it is currently done in the majority of studies. The difference is easy to see. Take a merger, that increases prices by 10 percent in the year following the merger but then prices revert to the pre-merger level in the second post-merger year. Currently, only one in five merger retrospectives estimate these annual price effects and would conclude that post-merger prices reverted to pre-merger levels by the end of the second year. Four in five studies would estimate an over time average. In this case this would imply a 5 percent price increase and could lead to the conclusion that the merger was anticompetitive, and that the intervention was insufficient.⁴

There is surprisingly little empirical work on the dynamics of how markets evolve post-merger, and whether the antitrust agency’s expectations at the time of the merger came true (for example, did entry happen as expected and did it reduce prices as predicted?) A notable exception is a set of annually conducted studies by the UK Competition Commission, which used to collect qualitative evidence on how market characteristics (other than just price) evolved over a longer post-merger period.⁵ With regard to specific mergers, Winston et al. (2011) look at the long-run effect of two railroad mergers. They estimate how prices evolved (year-by-year) post-merger and find that despite the short-term increases in price the mergers had no effect in the long-run on prices and welfare. Looking at mergers in the US market for bank deposits Focarelli and Panetta (2003) arrive at similar conclusions: mergers create higher prices in the more immediate aftermath of the merger, but this effect later disappears.⁶

We contribute to the rich body of merger retrospective studies in an important way, by pointing out how inappropriately designed empirical models, irrespective of data availability, will mask important information on the price effect of mergers. First we formalise the problem and argue that pooling together all post-merger time periods will provide price-effect estimates that are the average of the per period (annual) effects with a standard error that is lower than the standard errors of the annual price effects (at least under the assumption of non-positive correlation). This difference in standard errors has an important role to play in our main argument.

We attempt to demonstrate the effect of choosing the wrong model by employing a meta-analysis of more than 600 previous market-level price-effect estimates. Where estimates were available on price dynamics—e.g. where a study estimated annual effects—we were able to show how far off the over-time average estimates would have been. On the other hand, where only over-time average estimates were reported in the studies (this is what we refer to as inappropriate model choice), we could not re-construct the per-period variation in prices, therefore we turned to a set of Monte Carlo simulations and calibrations. These simulations show that models that estimate an average post-merger price effect are more likely to lead to erroneous conclusions (e.g. concluding that the merger increased prices, even when it did not, or concluding that the merger did not increase prices even when it did).

The paper is structured the following way. First, we describe how previous papers have handled post-merger price dynamics and show that this has been typically ignored. We then provide a discussion of the difference between the pooled and unpooled time period models. This is followed by a set of simulations and calibrations to demonstrate the magnitude of the problem, and we conclude with policy recommendations.

We surveyed a large body of retrospective merger studies reviewed by Kwoka (2013) and Mariuzzo et al. (2016).⁷ We focus on one aspect of these studies: the econometric specification for estimating post-merger price effects. The main selection conditions for our sample are: that ex-post percentage price-effect estimates are provided in the study, that their standard errors can be recovered, and that the time span of the data is identifiable. All of the studies in our sample used reduced-form causal inference models (typically difference-in-differences).

Our sample contains price-effect estimates of 68 mergers (which are discussed in 39 papers that are either published or in circulation as working paper at the time of our analysis). Of the 68 mergers, 52 are US mergers, and 16 EU.⁸ Some of the retrospective merger papers report estimates for the effect of the given merger on a range of different product and geographical markets. This gives us a sample of 626 market-level price-effect estimates.⁹

We distinguish between two types of studies. The first, and by far the most common, treats the post-merger period as a single period, and pools all post-merger price observations, and thus estimates the average effect of the merger over the post-merger period. We call this set of studies “pooled studies”. The second group controls for price observations year by year, and estimates annual post-merger price changes (“unpooled studies”).

More than 80% of the 68 merger studies have pooled the post-merger time periods and estimated an average price effect for the entire post-merger period. Similarly most of the product/geographic market-level price effects—558 out of 626—are estimated by pooling the post-merger period data. The remaining 68 market-level estimates—10 merger studies that were published in 5 papers—are from unpooled studies. More detailed description of the data is given in the “Appendix”.

Another striking figure in the data is that more than 80% of these merger studies have estimated the average price effect within less than two years of the merger. There are two problems with this. First, estimating an over-time average completely masks the dynamics of post-merger prices, and as such is inadequate for evaluating the effectiveness of merger control. Second, it does not allow for a full assessment of how prices evolve over time. Both the EU and the US guidelines emphasise that a merger may not be considered problematic if appropriate entry happens within two years of the merger, therefore the knowledge of how prices changed within two years cannot fully answer the question of whether a merger decision was effective.

Table 1 shows the number of mergers that have been evaluated in retrospective studies published in the most frequent outlets (two or more mergers covered). The American Economic Review (including Papers and Proceedings) published the largest number of merger studies, most use the pooled model. The Journal of Law and Economics has the highest propensity of studies that use the unpooled model.

An interesting question—although somewhat tangential to our main story—is whether the choice of the model (pooled or unpooled) is random with respect to the type of mergers. As a simple test, we compare the distribution of price effect estimates for the two groups. A comparison at the market/product level of estimates (626 estimates), using a two-sample Kolmogorov-Smirnov (KS) equality-of-distributions test, provides evidence that the two distributions differ. However, when we collapse the samples to merger-level estimates (68 estimates) and repeat the two-sample KS test we find that the null hypothesis of equality-of distributions is not rejected. The focus of this paper is on the dynamics of price changes and not on their general distribution, however the evidence that the pooled and unpooled distributions do not differ at the merger level could be interpreted as a sign that the mergers in the two groups are roughly comparable. Again, this is not required for our main point about using the right estimation model, but it helps illustrate our point.

For each market m and time t, let \(p_{mt}\) denote the price of a unit (product or firm) and \(W_{m}\) the treatment dummy variable (firm/product involved in the merger). \(T_L\) periods are recorded before—and \(T_R\) after—a merger that takes place in period 0. Let \(d_{k}\) represent a dummy variable that takes the value 1 every kth period after the merger, and zero otherwise. The sum of the post-treatment dummy variables is used in the pooled model, and is denoted as \(D_{T_R}\equiv \sum _{k=1}^{T_R}d_{k}\). Furthermore, indicate with \(\tau =1,\ldots ,T\) fragments of time within a period k; for example \(\tau\) could measure days and k years–when we have daily price data but are estimating yearly price effects post treatment. Examining the yearly effects for \(T_R\) periods following the merger and one period pre-merger (\(T_L=1\)), we can express the unpooled linear econometric equation for prices as: where \(\delta _{k}\) are the difference-in-differences (DiD) estimators for each year after the merger; \(\alpha _{m}\) is a market-specific unobservable variable; and \(\lambda _{\tau }\) is a set of controls that capture possible seasonality in the data. If we assume that the dataset is balanced, the total time observations are \(T\times (T_R+1)\).

As was discussed earlier, what is typically estimated in most merger retrospective studies is a slightly different model, with time-period post-merger dummy variables replaced by a pooled period post-merger dummy:where the DiD estimator for a pooled period of length \(T_R\) is denoted with \(\Delta _{T_R}\). Equation (1b) is what we refer to as the pooled model. Equation (1b) can be seen as a restricted version of Eq. (1a) once we impose \(\gamma _{1}=\gamma _{2}=\cdots =\gamma _{T_R}=\varGamma _{T_R}\) , along with the further restriction \(\delta _{1}=\delta _{2}=\cdots =\delta _{T_R}=\Delta _{T_R}\); but as we will show later, even in this case standard errors may differ.

If we consider an analysis that is restricted to only two years after the merger (\(T_R=2\)) and one year before the merger (\(T_L=1\)), and use the unpooled model, we have that the DiD coefficient for the second year from the above equation, when separate time period dummy variables are included, can be written as: For two periods after the merger the pooled model DiD estimator is:What are the implications, for the ex-post merger analysis, of using a period-by-period dummy variable (unpooled) version rather a pooled period dummy variable model?

Continuing with the simplifying example where we focus only on the two periods that follow the merger, let us assume that there is a price increase in the first period—\(\delta _{1}>0\)—but then prices revert to pre-merger levels in the second period: \(\delta _{2}=0\). This is an example of a merger that would be considered unharmful because the price effect would have vanished after one year, perhaps because of entry.

Suppose that we have estimated the parameters \({\widehat{\Delta }}_{2}\), \({\widehat{\delta }}_{1}\), and \({\widehat{\delta }}_{2}\) with the use of the two different specifications. In “Appendix B” we show that the restricted estimator \({\widehat{\Delta }}_{2}\) is equal to the average of the yearly time period parameters, \(({\widehat{\delta }}_{1}+ {\widehat{\delta }}_{2})/2\). Then, on the assumption that the central limit theorem holds, the time period estimators for a sample of size \(N=T\times (K+1)\times M\) have the following probability distributions: \({\widehat{\delta }}_1 \sim N\left( \delta _1, \sigma _{\delta _1}^2/N\right)\), \({\widehat{\delta }}_2 \sim N\left( \delta _2, \sigma _{\delta _2^2}/N\right)\), which leads to \({\widehat{\Delta }}_2 \sim N\left( (\delta _1+\delta _2)/2,\sigma _{\Delta _2}^2/N\right)\), with \(\sigma _{\Delta _2}^2=1/4\left( \sigma _{\delta _1}^2+\sigma _{ \delta _2}^2+2\sigma _{\delta _1\delta _2}\right)\). With the use of the pooled model, a merger retrospective could conclude that a merger was harmful and that intervention was insufficient, if \(\Delta _{2}>0\). With the use of the unpooled model one can identify the dynamics of post-merger prices, and would only conclude that the merger was harmful if prices are still above the pre-merger level by the second period: if \(\delta _{2}>0\). Both cases can be tested empirically. Given the asymptotic normality of the parameters, which follows the central limit theorem, the probability values are: Assume a simple case, where in both periods we have a small, 1 percent price increase (\({\widehat{\delta }}_{1}=0.01\), \({\widehat{\delta }}_{2}=0.01\)), and standard deviations \({\widehat{\sigma }}_{\delta _{1}}={\widehat{\sigma }} _{\delta _{2}}=0.1\). Assume also that our sample size is \(N=200\). Under the assumption of independence between \({\hat{\delta }}_{1}\) and \({\hat{\delta }}_{2}\) , \(\sigma _{\delta _{1}\delta _{2}}=0\), we would conclude that the merger increases prices under the pooled, but not the unpooled model:The purpose of this simple, back of the envelope example, is to highlight the importance of carefully choosing which model to use. To demonstrate further how much it matters, we examined all of the studies in our sample, where the unpooled model was used to ex-post identify the effect of mergers.¹⁴ Using the above method we then re-estimated these merger effects but now using the pooled model. The purpose of this exercise is to demonstrate the prevalence of making an erroneous conclusion on the evaluated merger, where the researcher (wrongly) chooses the pooled model.

For each merger that was analysed in each paper we report in Table 3 the effect that was estimated in the original paper for the first and the second year following the merger (relative to the pre-merger price), together with their standard errors (columns \(\delta _{1}\) and \(\delta _{2}\)). As was mentioned earlier, where more than one models was estimated for each merger (different treatment and control groups, or different specifications) we report an average (unweighted) effect and standard error.¹⁵ The table also shows what the price effect and its standard error would have been had the authors of the respective studies (wrongly) used a pooled model (column \(\Delta _{2}\)). Not having access to the original data, to calibrate the ‘pooled’ standard errors, we rely on the assumption that the annual estimates are independent (their covariance is zero).¹⁶

The table shows (dark grey) that in four out of the ten studies, the final conclusion of the study would have been different under the pooled model. For example, Winston et al (2011) estimated that post-merger prices would have reverted to pre-merger levels by the second year after the merger. Had the authors used the pooled model (column \(\Delta _2\)), they would have wrongly concluded that the merger led to a price-increase. In Kemp et al. (2012) and in Hosken et al. (2011) the authors estimated that after an initial price drop after the merger, prices increased back to pre-merger levels in the second post-merger year. Had they used a pooled model, they would have wrongly concluded that both mergers would have reduced post-merger prices. We also highlight (in lighter grey) the studies, where using the pooled model would have produced estimates with higher statistical power (become more significant). For example Schumann et al (2011) estimated a drop in post-merger prices both in the first and the second year after the merger. This was significant at 95%. Had the authors used a pooled model, their results would have shown significance at 99%.

The main message of this simple exercise was to highlight that using the wrong model (pooled instead of unpooled) would have led to the wrong conclusion about the merger in 40% of the cases. Of course the best way to show the implications of using a pooled model would be to examine all of the studies that use the pooled model and re-estimate them using the unpooled model. The problem is, that we do not have any knowledge on the per-period price variation in these papers (and have no access to the data used). For this reason we turn to a set of Monte Carlo simulations to demonstrate the gravity of the problem.

In the following we simulate a set of cases, where we know how prices evolve post-merger. The objective of this exercise is to gauge how likely it is that using the pooled model leads to the wrong conclusion on the effect of the merger. We consider the following hypothetical cases. (1) Where following an initial post-merger price increase, prices revert to pre-merger levels; (2) Where post-merger prices do not increase immediately after the merger but they do within a reasonable amount of time; (3) Where the merger is followed by an immediate price drop, which then disappears; and (4) Where the post-merger price change is constant over multiple periods.

Merger retrospectives are typically conducted to inform policy-makers about the fitness of merger control for filtering and remedying price increasing mergers. For this reason the conclusion as to whether a merger increased prices is crucial. We showed above that the probability of making the wrong conclusion is high if the wrong empirical specification is used. If the antitrust agency predicted that the merger would lead to a temporary price hike, but prices would eventually (within a reasonable length of time) revert to pre-merger levels, then it would probably refrain from intervention. Therefore the retrospective study should not only examine how prices change on average, instead, the study should also estimate whether (and how quickly) prices revert to pre-merger levels.

We find that more than 85% (58 mergers) of previous studies estimate post-merger average price effects (pooled sample), and per-period (annual) effects were estimated for only 10 mergers (unpooled sample). We argue that this is a mistaken approach as it masks information on post-merger price dynamics that would be crucial for the assessment of the merger. By running a set of Monte Carlo simulations we show that estimating the mean post-merger price effect might lead to erroneous conclusions on the effect of the merger. Our simulations demonstrate that potentially all studies (using the pooled sample) that concluded that the merger led to a price increase, could have been wrong, and that the price increase actually disappeared within a reasonable time. This is more likely where the studies had large samples (for example daily price data over large cross-sections). Similarly, up to half of the studies that concluded—based on the pooled sample—that the merger did not increase prices might have been wrong, and in actuality after a short period of unchanged prices, prices went up. Finally, studies that estimate that the merger reduced prices can potentially all be wrong in their conclusion on the merger if the merger was eventually followed by a price increase, but this was preceded by a sufficiently large price drop.

In our view, where data are available to estimate the pooled sample, it should be equally available to estimate yearly effects—this is not about getting longer-spanning data but using a different model specification—and thus gather evidence on how prices evolve post-merger. Not only could this more accurately inform the researcher whether the antitrust authority’s intervention was appropriate, but accumulating a large mass of these studies could tell us more about the dynamics of post-merger market self-correction.

An estimation that uses the unpooled sample does much more than just show whether the merger significantly increased prices in the K-th period. It gives the researcher highly valuable information on the dynamics of post-merger prices. This is important not only because one cares about whether prices eventually revert to pre-merger levels, but it also allows the identification of whether prices remain stable or unstable over time. These two outcomes can have very different welfare implications and would lead to different policy conclusions. The literature on the welfare implication of price stability can offer us more general insights, starting with simplistic models of Waugh (1944), and followed by the highly influential work of Newbery and Stiglitz (1979) and Stiglitz (1981). From this tradition we can find a rich body of works that examine the effect of price stability with realistic assumptions about consumer utility functions and introducing risk-attitude (Turnovsky et al. 1980). These models show that—depending on consumers’ risk-averseness—stable prices may mean lower or higher associated consumer surplus than do volatile prices. However, the important point is that the welfare implications of stable and volatile post-merger prices are likely to be different, therefore it matters which empirical model is used for estimating the effect of mergers on these prices.