Evaluating a Decade of Mobile Termination Rate Regulation

We re�?consider the impact that regulation of call termination on mobile phones has had on mobile customers’ bills. Using a large panel covering 27 countries, we find that the ‘waterbed’ phenomenon, initially observed until early 2006, becomes insignificant on average over the 10�?year period, 2002–11. We argue that this is related to the changing nature of the industry, whereby mobile�?to�?mobile traffic now plays a much bigger role compared to fixed�?to�?mobile calls in earlier periods. Over the same decade, we find no evidence that regulation caused a reduction in mobile operators’ profits and investments.

Mobile (or cellular) communications markets have been growing at an impressive rate over the last two decades, with worldwide subscriptions increasing from a few million in the 1990s to seven billion users in 2013 on all continents. 1 Competition in the industry has been quite vigorous and regulators have not interfered much with the workings of the market. In particular, and contrary to fixed telephony networks, retail prices directly set by regulators are virtually unknown in mobile telephony.
This view is possibly too simplistic, as regulators have also dealt extensively with matters related to mobile telephony but in a way which is less visible to end users. An important question is whether the design of regulation of the early days is still valid in the light of the dynamic development of this industry. 2 Regulators in particular worry about inter-network (termination) charges for calls to mobile networks and, starting in the early 2000s, have repeatedly intervened over the years to cut these charges with the aim to improve competition and reduce prices to final consumers. However, both academics and mobile operators have argued that reducing the level of mobile termination rates (MTRs) can potentially increase, instead of decrease, the level of prices for mobile subscribers, causing what it was termed as the 'waterbed' effect. In our earlier work (Genakos and Valletti, 2011), using data for the period 2002-6, we showed that, indeed, countries that introduced regulation that cut the termination rates caused a significant waterbed effect, whereby a 10% reduction in MTRs led to a 5% increase in mobile retail prices, varying between 2% and 15% depending on the estimate. In other words, cuts in termination rates before 2006 had led to the possibly adverse consequence of increasing the yearly bill per mobile subscriber by roughly 25 euro (varying from 10 to 82 euro), or some 750 million euro (varying from 300 to 2,400 million) extra in total in our sample.
The introduction of the New Regulatory Framework for electronic communications by the European Commission in 2002, where mobile termination was defined as a relevant market, meant that over time all EU countries imposed various differential cuts to termination rates. The debate among regulators and mobile operators on the likely benefits and costs of termination rate regulation became even more intense, with our work being featured as a 'weapon' against any tightening of such regulation. 3 At the same time though, the telecommunications market was undergoing a fundamental change, whereby mobile voice traffic had overcome fixed line call volumes, changing the economic forces that gave rise to the waterbed effect in the previous years.
In this article, we summarise these new theoretical arguments related to the underlying changes in mobile-to-mobile (M2M) and fixed-to-mobile (F2M) traffic volume; we empirically revisit our earlier analysis, using an extended data set covering 27 countries from 2002 until the end of 2011. Our new results demonstrate that the waterbed effect is not present anymore on average across the whole sample. Delving deeper into the possible channels, we uncover, in line with theory, that the distinguishing feature for this change is the importance of calls made from and to mobile phones relative to calls made to mobile phones from fixed lines. The ratio of mobile to fixed traffic is key in our findings. Countries that introduced termination rate regulation when mobile traffic was high did not experience any waterbed effect. On the contrary, countries that introduced the same regulation at a time of low mobile traffic experienced the waterbed effect overall: retail prices first increased substantially, as we found in Genakos and Valletti (2011), but then this effect considerably decreased over time due to the growing importance of M2M traffic. Finally, we do not find any evidence that profits of mobile operators have been affected by regulatory cuts in termination rates.
Our results have important policy consequences. The fact that mobile penetration nowadays is very high in most developed countries and that M2M traffic far exceeds F2M traffic volumes, means that regulators should now be less worried about possible adverse or unintended short-run consequences of regulatory cuts to mobile termination charges. The absence of the waterbed effect now implies that further termination charges cuts will decrease the price of calls to mobile phones, which will benefit consumers. Nor there is any strong indication that these cuts have considerably weakened the mobile operators' position to survive or to compete by making new investments.
The rest of the article is organised as follows. In Section 1, we describe the main issues related to mobile interconnection. In particular, we highlight how results from the extant literature differ when calls are made from fixed to mobile networks, as opposed to calls within the mobile industry. Section 2 presents the empirical framework, while Section 3 describes our data. Section 4 discusses the empirical results, split between the effects that regulation had on customers' bills and on mobile operators' profits. Section 5 concludes.

Interconnection and Call Termination
Telecommunications networks sell wholesale services (also called 'termination') to each other, as a call which is initiated on a network must obviously also be answered, and not necessarily on the same network. These termination services are not directly visible to end users but have an impact on their bills.
In the early days of mobile telephony, the largest amount of traffic directed to mobile phones would come from fixed networks. The economics literature highlighted how, even in settings where mobile operators compete against each other vigorously, competition does not help to keep F2M termination rates low (Gans and King, 2000;Armstrong, 2002;Wright, 2002). This situation has been called one of 'competitive bottlenecks': mobile operators have the ability and incentives to set monopoly prices in the market for F2M calls (as the price there is paid by callers on the fixed line, not by own mobile customers) but the rents thus obtained might be exhausted via cheaper prices to mobile customers in case competition among mobile operators is vigorous.
The intuition for the monopoly pricing result for the F2M market is simple: imagine F2M termination rates were set at cost; then one mobile operator, by raising its F2M termination rate, would be able to generate additional profits that it could use to lower subscription charges and attract more customers. While the mobile sector would therefore not necessarily be making any excess profits overall, an inefficiently low number of F2M calls would be made.
Given the strong case for regulatory intervention, it is not surprising that many countries have decided to intervene to cut these rates. Indeed, all EU member states, as well as several other countries, have done so, to the benefit of consumers calling mobile phones. The 'market analysis' performed under the European Regulatory Framework for Communications adheres to this logic: each mobile network is a monopolist on termination of calls to its own customers and therefore has the market power to raise wholesale prices significantly above cost.
By cutting termination rates, regulators have benefited those fixed users calling mobile phones from the fixed networks. However, reducing the level of F2M termination rates can potentially increase the level of prices for mobile subscribers, causing what is known as the 'waterbed' (or 'seesaw') effect. The negative relationship between F2M termination rates and prices paid by mobile consumers is a rather strong theoretical prediction that holds under many assumptions about the details of competition among mobile operators (Armstrong, 2002;Wright, 2002;Genakos and Valletti, 2011). These predictions, though, are only valid for F2M calls. Over the last decade, most countries have witnessed a strong growth of the mobile sector that has now overtaken fixed telephony. Given these developments, it is worth asking if the economics of M2M calls are the same and whether the rationale for intervention has changed or not.
The economics literature has analysed those issues in detail. To make the analysis sharper, a large part of the literature on competition between mobile networks is concerned primarily with their interconnection and the setting of the corresponding wholesale prices, therefore ignoring calls received from the fixed network, which were instead the focus of the earlier studies. The seminal works of Armstrong (1998) and Laffont et al. (1998) considered the question of whether mobile networks could achieve collusive outcomes in the retail market by jointly choosing the M2M termination rate. This research question should be seen in the light of the broader issue of whether competition between firms owning communications infrastructures should involve only minimal regulation, such as an obligation to give access and negotiate over the respective charges, or whether wholesale prices should be regulated directly. A concern is that wholesale rates might be set in such a way as to relax competition in the retail market, i.e. that termination rates could be used as an instrument of 'tacit' collusion.
What the more recent literature found is that the answer depends on several nuances of the models employed. A reduction in M2M termination causes directly a reduction in the costs for all calls made to customers belonging to a different mobile network (the so-called 'off-net' calls). But there are also subtle strategic effects, often depending on the types of tariffs used: with linear tariffs, i.e. tariffs that only charge for each call made, networks would co-ordinate on termination rates above cost in order to raise the cost of stealing each other's clients. In this case, lowering M2M termination rates would actually make the industry more competitive, therefore reducing bills. In this scenario, one would expect a positive relationship between termination rates and customers' bills. This is in stark contrast with the unambiguous waterbed effect that would arise from F2M calls.
Hence, the economics of F2M termination are quite different from the economics of M2M termination. But, in practice, the two are related. A relation arises in two ways: either both M2M and F2M termination rates are forced by regulation to be set at the same level, or 'arbitrage' possibilities force them to be so, as discussed in Armstrong and Wright (2009).
This has important consequences for the way customers' bills would change as a consequence of regulations that cuts termination rates. In Appendix A, we present a simple Hotelling model of duopoly competition in the mobile industry, alongside calls being received from the fixed network and show that the total bill of a mobile customer can be summarised as follows: The first term on the RHS refers to the total cost of supplying mobile telephony services to a user. The second term is a standard term reflecting the intensity of (horizontal) competition between networks. The third and fourth terms are what we discussed above; both depend on termination rates. The lower the termination rate, the lower the termination rent from F2M calls, therefore causing a waterbed effect: the bill should increase as a consequence of a regulatory cut in termination rates. However, this very same cut will also impact on the last term. While in general its sign depends on model details, it suffices here to say that there are plausible circumstances that make the last effect opposite to the waterbed prediction. An example was given above (competition in linear tariffs) but there are several other mechanisms that generate the same predictions. 4 Since regulation affects both the last two terms, our aim is to try to capture the overall effect on the total bill coming from regulatory cuts in MTRs.

Empirical Framework
For our empirical analysis, we employ an instrumental variable regression framework, similar to our earlier research (Genakos and Valletti, 2011): (2) Equation (2) tests the impact of regulation of MTRs on customers' bills, while (3) tests the impact regulation has on mobile operators' profits. In more detail, the dependent variable in (2) is the logarithm of (euro PPP adjusted) retail prices (ln P ujct ) paid by a customer with the usage profile u = {low, medium, high} and subscribing to mobile operator j in country c in quarter t. The dependent variable in (3) is the logarithm of earnings before interest, taxes, depreciation and amortisation (EBITDA), which is defined as the sum of operating income and depreciation and is our proxy for profits (ln Π jct ). Time fixed effects (a t ) and usage-operator-country fixed effects (a ujc ) control for time-invariant global trends and for usage-operator-country characteristics respectively. The main variable of interest, ln(MTR) jct , is the logarithm of the (euro PPP adjusted) MTRs charged by mobile operators for terminating calls on their networks.
The key idea is to use termination rate regulation as an instrument that directly impacts only on MTRs and not customers' bills. In our earlier work (Genakos and Valletti, 2011, pp. 10-14) we argue extensively on the exogeneity of regulation with respect to mobile bills. We recall here the important point that regulators do not have any legal power to intervene on retail prices in the mobile industry and conduct a wholesale market analysis of mobile call termination only. Hence, both retail prices and termination rates were freely chosen by mobile operators before the introduction of regulation and should be considered endogenous. After the introduction of regulation though, MTRs were capped by regulators through glide paths that were always binding for mobile operators. In other words, after regulation is applied, the MTR becomes exogenous as it is set by the regulators and not the mobile operators themselves. 4 An expression akin to (1) can be found, e.g. in the model of Armstrong and Wright (2009) that we take as a reference point (see their equation (12)). Other models that would generate a similar prediction on bills include those of Hoernig et al. (2014) who model calling circles, Hurkens and Lopez (2014) who consider customers' expectations, and Jullien et al. (2013), who deal with heterogeneous mobile calling patterns. For surveys on the existing literature, see Armstrong (2002), Gans et al. (2005) and Hoernig and Valletti (2012).
As an example, consider the MTRs set by the telecommunications regulator in France (ARCEP; http://www.arcep.fr/index.php?id=8080). Regulation was introduced in 2004, when mobile termination to the two largest firms (Orange and SFR) was capped at 14.94 €cent/min, while the latest entrant in the market (Bouygues) was capped at 17.89 €cent/min. All operators indeed set their termination rates at the maximum level allowed by the cap. In every year since then, the regulator has further cut MTRs, allowing some differentiation between the largest incumbents and the smallest entrant, until 2011Q3 when all operators' MTRs were capped at the same rate of 2 €cent/min. This is a huge change in just seven years, showing an example of how the binding glide paths set by the regulators have been decreasing fast over time. We exploit both differences in the timing of the enactment and also differences in the toughness of the implementation of the regulation across and within countries. 5 First, we use a binary indicator (0/1) to signify the exact timing of the start of regulation for every operator in each country (Regulation jct ). The impact of regulation on prices through the MTR is identified from countries that introduced the regulation and measures the effect of regulation in reforming countries compared to the general evolution of prices in non-reforming countries. This simple indicator is very powerful when examining the years around the change in regulation. However, its identification power deteriorates towards the end of our data set when all the countries have introduced such regulation. For instance, in the French case illustrated above, a binary variable equal to one over the seven-year period 2004-11 would not be able to capture the actual toughness of regulation at the intensive margin. Using the binary indicator is not enough because prices do not simply respond to the initial step decrease in MTRs but also to a continuous and fast sliding path. To capture this underlying phenomenon, we also employ an index of regulation that varies over time depending not only when each country introduced this regulation but also how 'tough' the regulatory authorities were in cutting MTRs. Our index of regulation is defined as: where MaxMTR c is the highest MTR allowed in country c one quarter before the introduction of regulation, capturing the level that MTRs would achieve in the absence of regulatory interventions. The absolute level of the index is not of particular concern when comparing countries, as we control for time-invariant country-operator-usage fixed effects, as well as time fixed effects that account for common global trends.

Data
We matched three different data sources for our analysis. First, we used Cullen International to get information on MTRs. Using this source and various other industry and regulatory publications, we were also in a position to identify the dates in which regulation was introduced across countries and operators, and the level of regulated rates (see , Table 1). Second, we used Teligen to obtain quarterly information on the total bills paid by consumers across operators and countries (2002Q3-2011Q4). Teligen collects and compares all available tariffs of the two largest mobile operators for thirty OECD countries. It constructs three different consumer usage profiles (large, medium and low) based on the number of calls and messages, the average call length and the time and type of call. 6 A distinction between pre-paid (pay-as-you-go) and post-paid (contract) tariffs is also accounted for, as this is an important industry characteristic. These consumer profiles are then held fixed when looking across countries and time. Third, we used quarterly information taken from the Global Wireless Matrix of the Bank of America Merrill Lynch data set (henceforth, BoAML). BoAML compiles basic operating metrics for mobile operators in 46 countries. For our purposes, we used the reported earnings

2015]
A margin before interest, taxes, depreciation and amortisation (EBITDA). 7 Table 2 provides some key summary statistics. The Teligen data set has two main advantages. First, by fixing a priori the calling profiles of customers, it provides us with information on the best choices of these customers across countries and time. Second, the prices reported in this data set include much of the relevant information for this industry, such as inclusive minutes, quantity discounts, discounts to special numbers, etc. (although it does not include handset subsidies). However, this richness of information comes at the cost of having data for only the two biggest operators of every country at each point in time. This reduces the variability and makes identification of our variables of interest harder. 8 Moreover, examining a decade long of consumer behaviour in such a dynamic industry such as the telecommunication industry, would perhaps call into question the stability of the customer profiles throughout the whole period. Indeed, 7 All consumer prices, termination rates and revenue data were converted to euros using the purchasing power parities (PPP) currency conversions published by the OECD to ease comparability. None of our results depends on this transformation. 8 The BoAML data set, which gathers information from companies' accounts, includes instead every mobile operator in a country.
Teligen adjusted the calling profiles of its customers in 2006 and we also use this data set to examine the robustness of our results.

Results
Results from our baseline model (2) are reported in Table 3. In column (1) we replicate our earlier results: for the period 2002Q3-2006Q1, we found a statistically significant waterbed effect when employing the binary indicator for regulation (Genakos and Valletti, 2011, Table 1, column 1). Column (2) applies the same approach to the whole sample (2002Q3-2011Q4). The picture now changes quite dramatically, despite a trebling of the sample size. The waterbed effect is now statistically indistinguishable from zero. Most importantly though, the binary indicator of regulation does not seem to be a valid instrument in the first stage. This is somehow expected since, as argued above, the identification power of the binary indicator diminishes over time as all the countries become regulated and underestimates the tightening of regulatory cuts over time. For this reason, in the next two columns, we employ the MaxCountry index of regulation. In column (3), looking at the period 2002-6, there is a positive and significant waterbed effect, in line with our earlier Notes. The dependent variable is the logarithm of the euros PPP adjusted total bill paid by consumers with different usage at every quarter. The instrumental variable Regulation is a binary indicator that takes the value one in the quarters when mobile termination rates are regulated. The instrumental variable MaxCountryMTR is an index that takes larger values, the more regulated a mobile operator is compared to the MTR prior to regulation in that country. p-values for diagnostic tests are in brackets. Standard errors clustered at the country-operator-usage level are reported in parenthesis below co-efficients: *significant at 10%; **significant at 5%; ***significant at 1%. Source. Authors' calculations based on the Teligen data corresponding to the best deals available at every quarter.

D E C A D E O F M T R R E G U L A T I O N
F39 results, thus reassuring on the validity of the MaxCountry index of regulation. The effect becomes insignificant when looking at the whole sample in column (4). Notice that the first-stage co-efficient is in both cases negative and significant, capturing the continuous tightening of the regulation. We conclude that a decade of regulation has cut termination rates, but did not have any adverse impact on mobile bills to final customers on the whole. 9 In Table 4 we conduct several robustness checks. 10 First, Teligen updated in 2006 the way it calculates baskets of services. In particular, from 2006Q2, Teligen reports Notes. The dependent variable is the logarithm of the euros PPP adjusted total bill paid by consumers with different usage at every quarter. The instrumental variable Regulation is a binary indicator that takes the value one in the quarters when mobile termination rates are regulated. The instrumental variable MaxCountryMTR is an index that takes larger values, the more regulated a mobile operator is compared to the MTR prior to regulation in that country. p-values for diagnostic tests are in brackets. Standard errors clustered at the country-operator-usage level are reported in parenthesis below coefficients: *significant at 10%; **significant at 5%; ***significant at 1%. Source. Authors' calculations based on the Teligen data corresponding to the best deals available at every quarter.
information both about a 'new' basket that it found more relevant for market comparisons, as well as the 'old' basket employed in earlier periods. Hence, in the second half of our data (2006Q2-2011Q4), we can see if differences might arise by employing different weights in the customers' profiles. The answer is no: results persist in both cases; see columns (1) and (2). Employing both the 'old' and the 'new' Teligen baskets produces very comparable results, whereby the first stage coefficient is negative and significant but the second stage impact on MTRs is statistically not different from zero. Second, in the expanded data set, new countries not previously monitored are included. These correspond to Estonia, Finland and Slovenia (about 200 observations in total). To check if results are driven by a composition effect, we exclude these countries. Results in column (3) are virtually identical to those in Table 3, column (4). Hence, the vanishing of the waterbed effect does not seem to be driven by having included a particular set of countries.
As a third exercise, we consider the extent to which results are driven by the treatment group. In Genakos and Valletti (2011), we had a set of countries that were always regulated, a set that were always unregulated and a set of countries that experienced a change of regulation during the period. The latter set of countries is the treatment group in our earlier work. 11 In the new data set, all countries get regulatedsooner or later. In column (4), we compare the set of countries that got regulated post-2006 ('new treatment group') 12 with the control group that was always regulated throughout the periodhence excluding the treatment group of Genakos and Valletti (2011). Results indicate that the waterbed effect is not present for this set of countries. Finally, in column (5), we compare the evolution of prices in countries that introduced the MTR regulation before 2006 ('old treatment group') to the evolution of prices in countries that were regulated, hence excluding the countries that were unregulated until 2006. Results seem to indicate that the waterbed effect is still present for this set of countries, even though it has been reduced significantly over time. 13 Hence, there seems to be a distinctive behaviour between countries that introduce termination rate regulation earlier to the countries that did that later on. In line with the theoretical arguments presented above, our conjecture is that this difference is not random, but stems from the increasing importance of M2M relative to F2M calls. We explore this hypothesis below.

Industry Evolution
The picture in the telephony market that emerges in recent years is very different from the one in earlier years, where we had found in our previous work the existence of a waterbed effect. The evolution of the UK market provides an interesting case study. According to Ofcom, the UK's regulator, in 2005 the volume of F2M calls was 15.7 billion minutes, comparable with 16 billion minutes of M2M off-net calls. By 2012, F2M calls were 9.4 billion minutes, less than one quarter of the 43 billion minutes of M2M off-net calls ('Communications Market Report: UK', Ofcom 2013). From these figures, it is also immediately apparent how relevant the stakes are: a cut in termination rates of 1 penny per minute, when multiplied by several billions of minutes of communications every year, produces large transfers of money in the industry. Therefore, according to the theoretical predictions summarised by (1), what should matter for the overall effect of regulation of termination rates on mobile customers' bills, is the relative weight that F2M calls have compared to M2M calls. The larger the share of M2M calls, the lower the waterbed effect that could even change sign.
To investigate this, we collected additional information on traffic patterns in the telephony industry to see how these changed over time. First, we collected annual information on the ratio of mobile to total outgoing voice traffic 14 from the Body of European Regulators for Electronic Communications (BEREC) and the reports published by the EU Electronic Communications Market indicators. Using this information, Figure 1 looks at mobile traffic as a percentage of the total outgoing traffic and reports the change in this percentage between 2005 and 2010 for almost all the countries in our sample. 15 The UK example is by no means an outlier: the average increase of the mobile traffic percentage was 63% across all countries, indicating the strong trend from fixed to mobile usage. In addition, we also collected similar A u s t r a l i a A u s t r i a B e l g i u m C a n a d a D e n m a r k F i n l a n d S w i t z e r l a n d U K T u r k e y S w e d e n S p a i n S l o v e n i a S l o v a k i a P o r t u g a l P o l a n d N o r w a y N e t h e r l a n d s M e x i c o K o r e a J a p a n I t a l y I r e l a n d H u n g a r y G r e e c e G e r m a n y F r a n c e E s t o n i a C z e c h R e p . information on the ratio of mobile (M2F + M2M) to total (F2M + M2M + M2F) outgoing voice traffic 16 on a quarterly basis from the market research company Analysys Mason. We also looked at other measures (e.g. the percentage of mobile subscribers of the whole telephony industry) and at other periods. They are not reported here for the sake of brevity but they all show an unmistakable pattern: fixed telephony has been declining over time in its importance compared to mobile telephony as far as voice and text communications are concerned. 17 As a consequence, the waterbed effect should have been overtaken by competitive effects within the mobile industry.
Using these new data sets, we calculated the ratio of mobile to total traffic at the time of the introduction of MTR regulation across all countries. We then split the sample into those countries with above and below median mobile to total traffic ratio and compare the evolution of prices in those countries using as a control the countries that Notes. The dependent variable is the logarithm of the PPP adjusted total bill paid by consumers with different usage at every quarter. Columns (1) and (2) utilise information on mobile to total traffic from the Body of European Regulators for Electronic Communications (BEREC), whereas the last two columns use similar information from the market research company Analysys Mason (see, subsection 4.1 in the main text for more details). The instrumental variable MaxCountryMTR is an index that takes larger values the more regulated a mobile operator is compared to the MTR prior to regulation in that country. p-values for diagnostic tests are in brackets. Standard errors clustered at the country-operator-usage level are reported in parenthesis below coefficients: *significant at 10%; **significant at 5%; ***significant at 1%. Source. Authors' calculations based on the Teligen data corresponding to the best deals available at every quarter.
were always regulated. Table 5 reports the results. Using the BEREC/EU information, we find a positive and significant waterbed effect in column (1) for those countries that introduced the MTR regulation when they had a below median mobile to total traffic ratio but no waterbed effect in column (2) for those countries that introduce the same regulation when they had an above median similar ratio. Columns (3) and (4) repeat the same exercise using the Analysys Mason information. Again, countries with below median ratio seem to experience a positive and significant waterbed effect, which disappears for those with a high mobile total traffic ratio. Notice that in all columns the first stage effect of a cut in MTRs on prices is always negative and significant.

Impact on Profits
We finally looked at the impact of regulation of termination rates on mobile operators' profits. Operators often challenge, and vehemently so, regulatory cuts in court. They argue that regulatory cuts will reduce their profitability and, more importantly, will diminish their incentives to invest in the industry, for example, via technology improvements and upgrades. The operators' behaviour is, however, mixed in this respect, as these views are not shared by all, especially as some operators have argued that, on the contrary, reduced termination rates will be pro-competitive since they will reduce asymmetric treatments between on-net and off-net calls. We do not find any statistically relevant result. 18 MTR regulation did not seem to affect profits either way over the entire period. We also tested if there was any differential impact of regulation of termination rates on the profits of 'large' versus 'small' operators (we defined as 'small' any other than the two biggest operators in each country). On the one hand, smaller operators typically have more outgoing than incoming off-net traffic, so they might benefit from cuts that will reduce their net outgoing payments. On the other hand, smaller operators have been allowed for some time higher (asymmetric) termination rates, thus a cut in termination rates might be tougher for them. Again, we find no differential impact of regulation of termination rates on the profits of small and large operators. The effects are not significantly different from zero.
On balance, we do not find evidence that profits of mobile operators have been affected by regulatory cuts in termination rates. Data, however, are considerably noisier than the price basket data and results should therefore be taken with caution. It is in fact possible that regulation did have a negative effect on profits but our data do not capture the fact that mobile operators have also been effective at reducing their cost base at the same time. For instance, policies such as cell site sharing, or exploiting economies of scope between voice and data (migration from 2G to 3G services) occurred over the same period as MTR regulation became tighter. To the extent that these cost reductions applied differentially between markets over time, then our time dummies would not properly account for them. This issue requires further investigation, which largely depends on having access to better data on the operators' accounts. 18 Results are reported in Table B2 (see online Appendix B).

Conclusions
We have conducted an assessment of regulation of MTRs over the last decade , using a large sample of mobile operators which have been subject to various degrees of regulation over time. Our new results qualify in an important way our earlier findings (Genakos and Valletti, 2011) which were obtained using a similar approach, but employing a data set valid only until 2006.
We have found that the waterbed effect has essentially unwound over time. While, in the earlier periods, regulatory cuts in termination rates also produced an increase in mobile customers' bills, this does not hold on average using the more recent data. We demonstrate that this is due to the diminishing importance of F2M calls relative to M2M calls. This is in line both with theoretical predictions and with actual industry trends.
The implications of our results are strong. Earlier regulation of termination rates had to find the right balance between the benefits that would accrue to fixed users calling mobile phones and the negative impact on mobile phone users. This was quite a difficult exercise. We show that this trade-off only emerges if the F2M calls traffic is significantly larger than the M2M traffic. Since the trend in all countries is towards an increase in M2M traffic, the case for intervention is now more compelling as unintended consequences of regulation, such as the waterbed effect, are less likely to arise.
Clearly, regulatory cuts cannot continue forever since rates are reaching the natural limit of the incremental costs. 19 Regulation in the EU is therefore close to an end, in that it cannot get any tighter than it currently is, though it cannot be removed as otherwise operators could respond by increasing termination rates again. However, the regulatory battleground is still very much open elsewherein particular in African and Latin American countries, where termination rates are typically much higher than in the EU. As also in these countries, the mobile industry has surpassed fixed telephony in terms of subscribers and call volumes, our results suggest that competitive effects within the mobile industry should now prevail over the waterbed effect.
The impact of regulation has also to account for the impact it has on firms' profits and their incentives to invest. Possible short-run benefits from wholesale regulation must always be confronted with their long-run consequences. We found scant evidence that profits have been reduced by regulation. We also pointed out as a caveat that available price data are typically richer than information about operators' profits. It would be very interesting to find more granular data at the firm level in order to investigate if this type of regulation actually induced firms to take actions that affected their network costs or the quality of their offerings. simple assumptions. To do so, we propose a model that builds directly on Armstrong and Wright (2009) and Hurkens and Lopez (2014).
Imagine a setting with one fixed network and two competing mobile networks, denoted as firms 1 and 2. There is a total mass of n F users on the fixed network. The two mobile firms compete for a continuum of mobile consumers of mass n M . Each firm i = 1, 2 charges consumers a fixed fee f i and can discriminate between calls made on-net (i.e. made to customers belonging to the same network i) and off-net (i.e. made to customers belonging to the rival network j). Firm i's marginal on-net price is denoted as p ii and the off-net price is denoted as p ij . Mobile consumers' utility from making calls of length q is given by a concave, increasing and bounded utility function u(q). Call demand q(p) is defined by u 0 [q(p)] = p. The indirect utility derived from making calls at price p is v(p) = u[q(p)] À pq(p), where v 0 (p) = Àq(p).
Each mobile firm is assumed to incur a marginal cost c o of originating a call and a marginal cost c T of terminating a call, so the actual marginal cost of a M2M call is given by c o + c T . In addition, there is a fixed cost f of serving each mobile subscriber, which includes, for example, the subscriber's handset and the billing costs. If calls are made off-net, the sending firm does not incur the termination cost c T , but pays its rival a termination charge, denoted by a. Instead, termination costs c T are borne by the receiving firm, which gets a from the sending firm.
As for F2M calls, there are also the same costs c o for origination and c T for termination of calls. The fixed network, again, has to pay the termination charge a instead of the termination costs, which are borne by the receiving network. We assume that there are q(P) minutes of F2M calls to each subscriber on network i (mobile customers only receive calls from the fixed network), where P denotes the F2M per-minute price. We also assume that P is given by P = c o + a. As discussed by Armstrong and Wright (2009), such pricing could arise as a result of the regulation of the fixed network or competition between fixed networks. 20 If x i denotes mobile firm i's market share, its total profits are given by The expression is made of several terms in the curly bracket. The first terms, grouped in the square bracket, correspond to profits from own customers who subscribe and make both a fraction x i of on-net M2M calls and a fraction 1 À x i of off-net M2M calls. The other two terms correspond to profits from termination respectively from M2M off-net calls and from F2M calls. To close the model, we follow Hurkens and Lopez (2014) and assume that mobile networks are differentiated a la Hotelling. Consumers are uniformly distributed on the segment [0, 1], while the two networks are located at the two ends of this segment (x 1 = 0 and x 2 = 1). We assume full participation so that each consumer subscribes to the network that yields the highest net utility. A consumer located at x and joining network i obtains a net utility given by where t is the customary 'transportation cost' which measures the degree of horizontal differentiation between the two networks, and w i is the value to a consumer subscribing to network i. In particular, given that consumers call each other with the same probability, the surplus from subscribing to network i (gross of transportation costs) equals w i ¼ n M ½x e i vðp ii Þ þ x e j vðp ij Þ À f i ; where x e i is the expected market share of firm i. Market share of network i is thus given by We solve for the equilibrium where firm i (and similarly, j) maximise its profits (A.1) with respect to the multi-part tariff {p ii , p ij , f i }, subject to (A.2), and where consumers' expectations are selffulfilled at equilibrium, that is, x e i ¼ x i The symmetric equilibrium is actually quite simple to characterise (for further details about existence, see Hurkens and Lopez, 2014). Because of the multi-part nature of the tariff, call prices are set at the 'perceived' marginal costs, i.e. p ii = c o + c T and p ij = c o + a. The fixed fee is equal to f i = f + t À (a À c T )q(a + c T )q(a + c T n F ). The total bill of a mobile consumer is then This expression shares the features of (1) in the main text. The bill reflects fixed costs to supply the service ( f ) and the intensity of competition as described by the transportation cost (t). There are then two terms which directly depend on the termination charge a. One term represents the waterbed effect coming from F2M calls: if termination regulation cuts a and thus reduces the rents from F2M calls, the bill will go up. This effect is bigger the larger the fixed network, as captured by n F . Finally, the last term produces an opposite effect: the lower a, the cheaper will be off-net M2M calls, thus reducing the customer's bill. This effect prevails as the mobile network gets larger, as captured by n M . Let us define F(a) (a À c T )q(a + c T ) and M ðaÞ ½ðc o þ c T Þqðc o þ c T Þ þðc o þ aÞqðc o þ aÞ=2. It is for sure F 0 (a) > 0 and M 0 (a) > 0, as long as a is set close to cost. Then (A.3) becomes which forms the basis for our empirical specification. The total impact of regulation on the bill is @Bill @a ¼ ÀF 0 ðaÞn F þ M 0 ðaÞn M : (A.5) The sign varies as follows: @Bill=@a ¼ 0 $ n F =n M \M 0 =F 0 : The overall waterbed effect in this model thus depends on the ratio n F /n M . If this ratio is large, the waterbed effect is predicted and bills will go up as a consequence of a regulation which cuts termination charges. If this ratio is small, the waterbed effect will vanish and can even change sign.