Network competition: Empirical evidence on
mobile termination charges and profitability∗
Version as of 15.12.07
By:
Kjetil Andersson∗* and Bjørn Hansen∗**
Abstract
We model competition between N mobile networks. The model allow for asymmetric
termination rates, differences in marginal costs and vertical differentiation. We
show that the operators’ equilibrium profit is unaffected by an identical change in
all termination rates in the market - we call this property the profit neutrality
hypothesis. When demand is specified as an address model and the disutility from
not consuming the most preferred variety is linear in distance, the specification of
the profit function is well suited for econometric implementation. We test the profit
neutrality hypothesis on a panel data set on European mobile operators and find
that we cannot reject this hypothesis at 5% level of significance. Thus, we cannot
reject that the profit of mobile operators is unaffected by an identical change in all
termination rates in the market.
∗
We are grateful to Øystein Foros, and seminar participants at the Departments of Economics at the
Norwegian School of Management and the Department for Economics at the Norwegian University of
Science and Technology for very helpful comments..
∗*
Affiliation: Telenor R&I, email: [email protected]
∗**
Corresponding author, affiliation: The Norwegian School of Management and Telenor R&I,
email: [email protected]
1
1.
Introduction
Since the deregulation of the telecommunications sector, most countries have granted
licences to several competing mobile operators. For instance, in the EU all member
states have three or more facility-based mobile operators with nationwide coverage.
Together with the impressive growth in the number of mobile subscribers this highlights
the economic importance of mobile-to-mobile interconnection.
When one mobile subscriber calls a subscriber belonging to another mobile operator,
the originating operator pays a termination charge to the terminating operator. These
termination charges are frequently regulated. The national regulatory authorities in the
EU member states consider mobile operators as de-facto monopolist on the wholesale
voice termination market. The operators are therefore subject to ex ante regulation in
this market irrespective of the competitive pressure in the retail market. The EU
Commission considers that mobile termination rates should be based on ‘the costs of an
efficient operator’ and hence normally symmetric1. Nevertheless, more often than not,
mobile termination rates are asymmetric within a particular member state and average
levels vary substantially between states. The Commission has recognised that
asymmetries may be justified, exceptionally and temporarily, by “objective cost
differences which are outside the control of the operators concerned”.2 In this case
asymmetric termination rates in favour of entrants are seen as a means to promote
competition. Recently however the commission has signalled that the mobile
termination rates should be reduced and harmonised within the EU member states. This
is expected to benefit consumers3.
The seminal papers by Armstrong (1998), Laffont, Rey and Tirole (1998a) and Laffont,
Rey and Tirole (1998b) provide a general framework to assess the outcomes of
competition between interconnected networks. In this literature competition is modelled
as a two-stage game. At the first stage the termination charge of each network is
determined, and at the second stage the networks compete in attracting customers. A
1
EUROPA Press Releases. Reference: IP/07/1203 Date: 02/08/2007
Ibid
3
EUROPA Press Releases. Reference: IP/07/1333 Date: 14/09/2007
2
2
principal question is whether the networks, in an unregulated economy, can use the
termination charges as a collusive device to soften competition at the second stage. In
particular, the case studied is that of a symmetric duopoly where the two firms agree on
reciprocal (symmetric) termination charges. A major insight is that that the effect of
changes in the symmetric termination charge on the networks’ profits depends on the
type of tariffs offered to consumers. With the above move order, this effect is of course
unaffected by whether the symmetric charge is negotiated by the firms, or set by
regulatory authorities. Armstrong (2002) provides an excellent review of the literature
following the above cited papers. The main results of the effects of changes in a
reciprocal termination charge on profits in symmetric equilibrium can be summarized as
follows:
•
Armstrong (1998) and Laffont, Rey and Tirole (1998a) study the case with
linear pricing and no discrimination based on whether the call terminates on-net
or off-net. They find that an increase in a symmetric termination charge
increases profits. In this case the networks can use a high termination charge as
an instrument to soften competition at the second stage by raising each others
marginal cost. Laffont, Rey and Tirole (1998a) demonstrate that this effect
disappear when the networks compete in two-part tariffs with no network based
discrimination at the second stage. Profits are in this case independent of the
termination rate. The increase in profits from incoming off net traffic following
an increase in the termination charge is exactly matched by the profit loss
following the induced decrease in the fixed fee. Dessein (2003) and Hahn (2004)
extend the basic model to allow for customer heterogeneity. They find that the
profit neutrality result still holds when the network competes in menus of nonlinear tariffs without network based discrimination.
•
Laffont, Rey and Tirole (1998b) and Gans and King (2001) consider the case of
network based discrimination. Gans and King (2001) show that when the
networks compete in two-part tariffs with network based discrimination an
increase in the termination charge decreases profits. The intuition is that the
3
competing networks will wish to negotiate a termination charge below marginal
costs. This softens the competition for market shares at the second stage.4 The
effects of an increase in the termination charge when the networks compete in
linear prices with network based discrimination is ambiguous. Laffont, Rey and
Tirole (1998b) find that profits increase when the networks are not too close
substitutes, while the effect is ambiguous otherwise.
It is not easy to draw on these results to predict the effects on profits (or welfare) of a
reduction in mobile termination charges as put forward by The Commission. Firstly, the
results are derived in symmetric duopoly.5 All European states have more than two
operators and they are frequently highly asymmetric in terms of market shares and
termination charges. It is a reasonable conjecture that the theoretical results above could
be generalised to symmetric oligopoly, but not to asymmetric market structures.
Secondly, the price lists of an accidental European mobile operator reveals that a typical
operator at any point in time offers a menu of call plans that include most of the tariffs
discussed above. Consequently, it is hard to assess which kind of tariffs, if any,
dominate the competitive situation.
This paper presents the first, to our knowledge, empirical evidence on the effect of
mobile termination charges on operator profits. Building on Armstrong (2002) we
develop a theoretical model of competition between N potentially asymmetric,
interconnected networks. The key modelling assumption is that usage is inelastic. This
simplifying assumption enables us to derive a simple closed form solution for
equilibrium profits. We show that an identical change in all termination charges does
not affect profits. Thus, like the models where the networks compete in two-part tariffs
with no network based discrimination reviewed above, the current model exhibit a form
of profit neutrality. Unlike the former models, this profit neutrality result holds also in
an asymmetric equilibrium with an arbitrary number of firms.
4
In line with this the authors argue that bill-and-keep may be a form of tacit collusion.
Asymmetric duopoly has been investigated by Carter and Wright (2003) and de Bijl and Peitz (2002)
and Peitz (2005). Carter and Wright demonstrate that the profit neutrality result may brake down. In some
cases a small network can benefit from increased symmetric termination rates. This result rests on the
assumed tariff structure.
5
4
We estimate the model on a panel dataset on firm specific mobile termination rates and
profits comprising 26 mobile operators in 9 European countries during the period 20032006. The data does not reject the model. The econometric model performs in general
very well, and parameters are significant and of expected signs. The main result is that
we cannot reject that equilibrium profits are unaffected by an identical change in all
mobile termination charges.
The rest of the paper is organised as follows. In section 2 we develop the theoretical
model of competition between asymmetric networks. In section 3 we describe the data
and present the econometric specification. In section 4 we discuss the estimation results
and the results of testing the profit neutrality hypothesis. Finally, we offer some
concluding remarks in section 5.
2.
Modelling competition between N asymmetric
networks
The final objective in this section is to derive a closed form equilibrium profit function,
i.e. profit as a function of termination charges, suitable for econometric implementation
on firm data from European mobile markets. This involves the following major
challenges: Firstly, most markets include more than two firms. The firms vary in size
and possibly marginal costs, and are frequently subject to different termination charges6.
Secondly, most mobile firms offer a menu of call plans that includes all the tariffs
reviewed in the previous section7.
There are no models that can simultaneously cope with these issues in a tractable way.
Clearly, some powerful simplifying assumptions are necessary. The approach taken here
6
Calzeda and Valletti (2005) and Jeon (2005) consider models with more than two firms. However, these
papers focus on symmetric firms and symmetric termination charges. Carter and Wright (2003) and de
Bijl and Peitz (2002) and Peitz (2005) consider asymmetric duopoly.
7
There is limited public information on the distribution of customers and profits on different call plans. In
their quarterly reports, most operators split the figures on the number of customers, traffic revenues and
minutes in the categories 1) Prepaid and 2) Subscription. The former category resembles linear tariffs,
while the second category comprises various forms of non-linear tariffs including the two-part tariffs
discussed in the literature. However both the linear and non-linear tariffs frequently include call plans
with and without network based discrimination. Hence, it is hard to put the special cases discussed in the
literature to an empirical test.
5
is to generalize the model of asymmetric duopoly in Armstrong (2002) to N firms8. It
turns out that this generalisation has a simple closed form solution for equilibrium
profits.
The model
The crucial modelling assumption is that subscribers’ demand for calls is inelastic, i.e.
independent of the calling price. In addition, we assume that the calling pattern is
balanced, i.e. that all customer, irrespective of which network they belong to, are
equally likely to receive a call. As a normalisation, we assume that each subscriber
makes exactly one call in the time period under consideration (this normalisation is
relaxed in the empirical implementation). Finally, we assume that the market is fully
covered i.e.,
∑
N
i =1
xi = X , where xi is the number of customer of firm i, X is the total
number of potential customers, and the market share of firm i, s i = xi / X .
These assumptions are basically the same as in the asymmetric duopoly model in
Armstrong (2002).
Given the unit demand, the mobile networks compete for customers in a single price pi .
An interpretation is that the networks compete in ‘total charges’ for making the
exogenous number of calls9.
There are N ≥ 2 interconnected mobile firms in the economy (the national market).
Without loss of generality, we assume zero fixed costs per subscriber and that the
marginal cost of originating a call is equal to the marginal cost of terminating a call.
These marginal costs can vary between firms, such that, for network i, an on-net call
consists of origination and termination costs, 2ci . Let ai denote the termination charge
network i receives per incoming call. A call from network i to network j thus has
8
Section 4.2.4 in Armstrong (2002)
The present model also closely resembles section 6.3 in de Bijl and Peitz (2002) where the networks
compete in ‘flat-rate’ tariffs, i.e. a subscription fee and a zero charge for calls. Such tariffs exist in some
markets, but are not widespread. A related, very frequently offered tariff is that of ‘included minutes’ – a
tariff with a subscription fee, an included number of minutes at a zero charge, followed by a positive
marginal charge. This kind of three-part tariff has however, to our knowledge, not been analysed in the
context of interconnected networks, see Grubb (2007) for a general analysis without interconnection.
9
6
perceived marginal costs ci + a j , and the net (wholesale) profits on an incoming call is
ai − ci .
Profit for firm i is then given by
(
)
π i = si X pi − si 2ci − ∑ j ≠i s j (ci + a j ) + si X ∑ j ≠i s j (ai − ci ) .
144444
42444444
3
Net profits retail
14442444
3
Net profits wholesale
Using the full market cover assumption this profit expression can be simplified to
(
)
π i = si X pi − 2ci + ∑ j ≠i s j (ai − a j ) .
1)
The market shares entering the profit expression are functions of the vector of prices,
p = {p1 , p 2 ,..., p N } , and a vector of, in the present case, exogenous or predetermined
firm specific characteristics, u = {u1 , u 2 ,..., u N } ,
s i = s (p, u),
∂si
< 0.
∂pi
2)
Normally we would consider situations where all products are substitutes, but
Proposition 1 below holds also in the case where ∂si ∂p j < 0 for some pairs of i and j.
The vector of firm specific characteristics, u , is a parameterization that allows
asymmetric market shares even if all prices are equal.
The game proceeds in the usual fashion: At stage 1 the firms’ termination charges,
a1 , a 2 ,..., a N are determined, for instance set by the regulatory authority; at stage 2 the
firms compete one-shot in prices.
If we differentiate 1) with respect to price and rearrange, we can write the first-order
condition for firm i, i = 1, 2,..., N , as
⎛ ∂s
pi = 2ci − ∑ j ≠i s j (ai − a j ) − s i ⎜⎜ i
⎝ ∂pi
⎞
⎟⎟
⎠
−1
∂s
⎞
⎛
⎜⎜1 + ∑ j ≠i j (ai − a j )⎟⎟ .
∂pi
⎠
⎝
3)
7
The solution of the N first-order conditions gives a candidate equilibrium. In general, an
interior equilibrium will exist if the combination of the exogenous parameters,
a = {a1 , a 2 ,..., a N } , c = {c1 , c 2 ,..., c N } and u = {u1 , u 2 ,..., u N } are not ‘too asymmetric’,
and if the firms products are not ‘too close substitutes’10. The interior equilibrium is a
price vector p ∗ = { p1∗ , p 2∗ ,..., p ∗N } that satisfies the first-order conditions such
that ∑ s i∗ = 1, si∗ ∈ 0,1 and π i∗ ≥ 0 ∀i . The equilibrium market share of firm i is given
by
(
)
s i∗ = si p1∗ (a, c, u ), p 2∗ (a, c, u )... p N∗ (a, c, u ), u = s i∗ (a, c, u ) ,
4)
and equilibrium profit of firm i, π i∗ , is obtained by inserting p ∗ and s ∗ in 1). In the
following discussion we will assume that an interior equilibrium exists.
The duopoly model in Armstrong (2002) is a special case of the current model. As
shown there, the market shares are totally independent of the termination charges, a1
and a 2 . This result does, however, not carry over to the situation where the number of
firms is larger than two. In this case market shares will in general depend on the
structure of the termination rates such that ∂si∗ ∂a i > 0 and ∂si∗ ∂a j < 0 . The
following invariance property holds in the general case:
Proposition 1. If an interior equilibrium exists, equilibrium prices, market shares and
a = {a1 + d , a 2 + d ,...., a N + d } for any
profits are identical under a = {a1 , a 2 ,..., a N } and ~
d.
Proof. In the first order conditions, 3), the termination charges enter as differences,
ai − a j , ∀j ≠ i. Hence, equilibrium prices, and consequently market shares and profits
of all firms i = 1, 2,..., N , are unaffected by an identical change in all termination rates.
Q.E.D.
10
We have verified this in simulations with “Hotelling style” market share functions, see the next section.
The exact conditions for existence in the general N-firm case are complex.
8
Hence, an equal change in the termination charges does not affect market outcomes.
This result may be compared with the profit-neutrality results obtained when the
networks compete in two-part tariffs with no network based discrimination [Laffont,
Rey and Tirole (1998a), Dessein (2003) and Hahn (2004)]. In general, these authors,
and others, are very careful not to overestimate the robustness of the profit neutrality
result. In particular the dependence on symmetry is stressed11. In contrast, the present
result is very robust to asymmetric conditions: The result holds even if the firms are
subject to different termination charges, different marginal costs and vertical
differentiation. However, we stress that the result is obtained assuming i) inelastic
demand for calls, ii) uniform calling pattern and iii) full participation.
Equilibrium profits
In line with most of the theoretical literature on competition between interconnected
networks we take as our point of departure a Hotelling style product differentiation. We
assume that the market share functions satisfy:12
∂s j
∂pi
= σ , all j ≠ i, σ > 0
∂si
= −( N − 1)σ .
∂pi
(A.1)
(A.2)
This is consistent with a generalisation of the Hotelling framework to a market with
more than two competing firms within an address framework (see Anderson, de Palma
and Thisse, 1992). Both firms (services) and consumers have an address in the attribute
space. The service offered by a firm is a composite of the attributes it embodies, and the
11
”This analysis of two-part tariffs and nonlinear pricing seems to suggest that the choice of termination
charge cannot affect profits at all…. However, it is important to stress that this convenient result is nonrobust in a number of dimensions. For instance the assumed cost and demand symmetry across networks
plays an important role in the argument”. Armstrong (2002), p.370. “I do not make any claim of
robustness of the above profit-neutrality result. In particular, as is clear from the proof of Proposition 3,
what is needed is (i) symmetry in demand, ..” Dessein (2003) , p. 602. “Note that the profit-neutrality
result has been reached under several simplifying assumptions. In particular, we needed the following:
Uniformity (symmetry) in demand21 ..”, Hahn (2004) , p. 622. Furthermore, the footnote 21 in the
previous citation stress that “Symmetry in marginal cost seems also crucial”.
12
In a recent paper, Armstrong and Wright (2007), deploy identical assumptions with respect to the
system of market share functions.
9
consumers derive utility from the attributes, not the service itself. In the present
framework such attributes could be for instance brand loyalty, hand set subsidy,
network coverage, or other services bundled with the particular subscription. The
service’ address is its position in this attribute space.
The address of each consumer is given by the combination of attributes that is most
preferred. Since there is a limited number of services available and the addresses of
consumers are assumed to be continuously distributed in the attribute space, consumes
have to choose a service that differs from the most preferred variety. The disutility from
not consuming the most preferred variety is an increasing function of the distance
between the most preferred and the consumed variety.
The assumptions A.1 and A.2 are consistent with every service being a neighbour to all
the other services in the attribute space i.e. that all cross price effects are strictly larger
than zero.13 Furthermore the disutility from not consuming the most preferred variety is
linear in distance. Finally the consumer preferences are uniformly distributed along line
segments connecting all the product varieties and that all consumers buy one and only
one variety.
The parameter σ measures the disutility associated with distance in the attribute space.
This parameter will typically differ between markets (countries) due to differences in
the number of competing firms. A.1 and A.2 are fulfilled in the Hotelling duopoly case
considered above, as well as in a Salop type circular city [Salop (1979)] with three firms
and linear transportation costs. An example of market shares satisfying (A.1) and (A.2)
is the ‘Hotelling style’ market share function
si =
(
)
1
+ σ ( N − 1)u i − ∑ j ≠i u j − (( N − 1) pi − ∑ j ≠i p j ) ,
N
5)
where the u ’s are the vertical differentiation parameters introduced earlier (and should
not be confused with the attributes discussed above).
13
Anderson, de Palma and Thisse (1992) characterizes this property as “strong gross substitutes”. A
necessary condition for this property to hold is that M ≥ N – 1, where M is dimensions of the attribute
space and N is the number of competing varieties, see Theorem 4.3 p 115.
10
Proposition 2. If an interior equilibrium exists and the markets shares obey (A.1) and
(A.2) equilibrium profit is given by
∑ j ≠i a j
1
+ ai −
⎜ ( N − 1)σ
N −1
⎝
⎛
π i∗ = X si∗ (a, c, u) 2 ⎜
⎞
⎟
⎟
⎠
6)
Proof. By inserting the rule for optimal pricing 3) using (A.1) and (A.2) into the profit
definition 1) we obtain:
⎛⎛
π i = si X ⎜⎜ ⎜⎜ 2ci − ∑ j ≠i s j (ai − a j ) +
⎝⎝
(
)
⎞
⎞
si
1 + ∑ j ≠i σ (ai − a j ) ⎟⎟ − 2ci + si ∑ j ≠ i s j (ai − a j )⎟⎟
σ ( N − 1)
⎠
⎠
Rearranging this expression, using that in equilibrium are actual market shares equal to
equilibrium market shares, s i = si∗ , gives 6).
Q.E.D.
Hence profit is the product of market size, X , squared equilibrium market share, ( si∗ ) 2 ,
and the term 1 /( N − 1)σ + ai − a −i , where a −i = ( N − 1) −1 ∑ j ≠i a j . That profit is a
function of squared market shares is a consequence of the Hotelling style market share
functions, or assumptions (A.1) and (A.2). In the classic Hotelling duopoly model,
equilibrium profit is given by
( pi∗ − ci ) = si∗ / σ such that
π i∗ = si∗ ( pi∗ − ci ) . It is easily shown that
π i∗ = ( si∗ ) 2 / σ (and the familiar 1 / 4σ in symmetric
equilibrium).
When the market share functions are given by 5) the second order condition is
− 2(1 /( N − 1)σ + ai − a −i ) < 0 . Hence, from the last term in 6) profits must be strictly
positive in an interior equilibrium. As seen, the second order condition (or equivalently,
the requirement of strictly positive profits) restricts the maximum degree of
differentiation in the mobile termination charges. In particular we have that
ai − a −i > −1 /( N − 1)σ for each i. Thus, all else equal, the higher the number of
operators, and the higher the cross-price elasticity, the less the lowest termination
charge may deviate from the average of the other termination charges.
11
A key feature of 6) is that it is separable in equilibrium market shares. As will be shown
in the next section, this is a very convenient feature for the current econometric purpose.
The separability is a consequence of the, admittedly, very restrictive assumptions A1)
and A2).14
3.
Data and econometric specification
The primary goal of the paper is to test the profit neutrality hypothesis, Proposition 1, in
the previous section. To guide the specification of the econometric model, we will use
the profit function in 6).
Definitions and descriptive statistics
The data are from Ovum and Wireless Intelligence, and comprises 26 mobile operators
in 9 countries located in north-western Europe15. The countries are similar in the sense
that they are all high-income countries with a very high mobile penetration. Thus they
come close to satisfy the assumptions of full participation underlying the theoretical
model. The data contains quarterly information on key operator indicators, market
statistics and termination rates in the period Q1 2003 to Q3 2006, see Table 1 below for
further details. The data set is complete in the sense that each country includes all the
mobile operators present in each time period.
Let subscript t denote period, i firm, and k the national market of firm i. We ignore
international and fixed line traffic. In relation to the current model this implies that the
mean of the termination rates on outbound traffic of firm i is taken over all other mobile
14
Alternatively, if the market shares are of the logit type such that:
∂s j ∂pi = si s j μ and ∂si ∂pi = − si (1 − si ) μ ,
it is easily shown that equilibrium profits are given by
π i∗ =
( si∗ ) 2 X
1 − si∗
⎛μ
⎞
⎜ ∗ + 1 − si∗ a i − ∑ s ∗j a j ⎟
⎜s
j ≠i
⎟
⎝ i
⎠
(
)
While it is possible to estimate this function, it is not separable in market shares. We will not pursue this
specification here.
15
The countries are Belgium, Denmark, Finland, France, Germany, The Netherlands, Norway, Sweden
and the United Kingdom.
12
operators in firm i’s national market, i.e. a−it = 1 /( N k − 1)∑ j ≠i a jt . We shall discuss
some possible implication of this simplification in the next section. To avoid
cumbersome notation it is implicitly assumed that the summation is taken only on
operators within each national market k ∈ [1,2,..K ] . The number of firms in each
national market is not time indexed because there is no operator entry or exit in the
markets in the sample period.
Let mtrit denote the termination rate per minute of firm i in period t. The theoretical
model in the previous section assumed unit demand, i.e. that each customer made
exactly one call per period. If we assume that this call has a duration of one minute we
have that ait = mtrit for each firm i. It is now easily verified that if we instead assumed
that each customer made, say 3 calls of one minute per period, the profit function would
be
like
in
6)
with
ait = mtrit 3 .
Following
this
reasoning
we
let
ait = mtrit M kt , ∀ i ∈ k ∈ K , where M kt is the average number of originated mobile
minutes per customer in country k in period t. Consequently, we assume that the
customers in market k have an inelastic demand equal to M kt each period, and that
evolution in M kt is due to exogenous shocks.
As a measure of operator profit we use ebitda (earnings before interests, taxes,
depreciations and amortisations). Since there is no investment in the theoretical model,
this is the economic performance indicator that comes closest to the profit measure, π it ,
in equation 6).
13
Table 1. Descriptive statistics
Variables
Definitions
ebitdait
mtrit
sit
M kt
Explanation
Mean
Std.dev
Min
Max
Quarterly earnings before interest, taxes,
depreciation and amortisation of firm i (in
million Euros).
Mobile termination rate per minute
of firm i in Euros.
Firm i’s market share (of customers)
280.81
266.82
-11.05
1007.83
0.12
0.04
0.06
0.21
0.30
0.14
0.08
0.58
141.08
41.57
74.00
253.00
33.87
28.28
3.47
83.12
3.58
0.82
2
5
ebitdait / X kt sit2 .
121.88
66.68
-249.00
523.02
mtrit M kt .
50.64
20.77
23.83
136.18
50.19
17.74
25.38
114.62
Average, quarterly number of mobile
minutes in national market k
Number of mobile customers, in
millions, in market k
Number of mobile network operators
in market k. Time invariant in sample.
X kt
Nk
Dependent
yit
Explanatory
ait
a−it
1 /( N k − 1)∑ j ≠i mtr jt M kt .
Sources: The mobile termination rates are from Ovum. All other variables are from Wireless
Intelligence. The data are from Q1 2003-Q3 2006. The number of observations is 258. This
comprises 26 operators in Belgium, Denmark, Finland, France, Germany, The Netherlands,
Norway, Sweden and the United Kingdom.
Table 1 reveals that the sample comprises firms and markets of considerable
heterogeneity. The smallest market in the sample comprise about 3.5 million customers
(Norway in 2003) while the largest, Germany, is well above 80 million in 2006. The
smallest firm in the sample (relative to market size) has 8 % of the market, while the
largest (again relative to market size) has 58%.
Figure 1 shows the evolution in the termination charges per minute, in Eurocents, of the
firms having the highest and the lowest mtr in each respective market. As may be seen,
Denmark is the only country that has maintained symmetric termination charges the
whole period, while Finland and Sweden have periods with symmetric termination
charges. Moreover, in general there have been quite frequent changes in the termination
rates, and except for Denmark and perhaps the Netherlands, the correlations within each
market of these changes does not seem to be prohibitively high. The data should hence
be informative on the impact of termination charges on profits.
14
In a regression of ebitdait on the average level of termination charges each period,
∑
i∈k
mtrit / N k , including firm specific fixed effects and time dummies, we obtain a
coefficient of 49.5 with a standard error off 198. Hence, the level of the termination
charges has no impact on ebitda. Even if this is an interesting observation itself, it
leaves unexplained how the structure of termination rates affect profits, and is not
necessarily an implication of the theoretical model in the previous section. Proposition 1
says that an equal change in all termination rate should not affect profit but this not
necessarily imply that profit should be independent of the termination charge level.
Denmark
Finland
France
Germany
Netherlands
Norway
Sweden
UK
5 10 15 20
5 10 15 20
5 10 15 20
Belgium
0
5
10
15
0
5
10
15
0
5
10
15
time_period
max_mtr
min_mtr
Graphs by country
Figure 1. Termination charges per minute in the period 2003 - 2006
15
The econometric model
Having clarified the empirical representation of the variables, we can now present the
econometric model. We assume that the mobile operators within each national market
compete one shot in ‘total charges’ each period. If we divide both sides of the profit
2
function 6) in the previous section by X it sit , we obtain
π it
X it sit
2
=
1
+ ait − a−it , ,
σ k ( N k − 1)
which is a model that can be estimated by linear regression. An econometric
specification suitable to the available data that nests the profit function is given by
y it = γ i + β1 ait + β 2 a −it + vit , ∀i, t
E (vit , vit ) = δ it2 , E (vit , v jt ) = ρ k ,
(i, j ) ∈ k ,
E (vit , v jt ) = 0 (i ∈ k ∨ j ∈ l ≠ k )
7)
where yit = π it / X it sit , γ i is a firm specific constant and vit is an error term. As is
2
evident from 7) we allow the errors to be heteroskedastic and correlated within clusters
defined by each national market. The former account for the large heterogeneity in the
sample, and the latter for the fact that the firms may be subject to country-specific,
unobservable shocks.16
Furthermore, there are several reasons why vit is likely to be correlated with the
regressors. Firstly, our approach to capture the inelastic, identical demand assumption in
the theoretical model by defining ait = mtrit M kt ∀ i ∈ k , induce measurement errors
almost by construction. Even if demand is in fact inelastic, the specification will
generate measurement errors if M it ≠ M jt (i, j ) ∈ k . Secondly, although the termination
rates are set by the national regulators (and not the firms) the equation may be subject to
endogeneity. A common conjecture in the industry is that regulators allow “weak”
and/or small operators a relatively higher termination rate on inbound traffic. This may
16
Correlated error within cross sections in the same country may also be generated by shocks to exchange
rates since we measure all monetary variables in Euros and some of the countries in the sample have their
own currency.
16
arise from a desire of the regulators to promote competition possibly combined with
successful lobbying activities by the smaller firms.17. Note that this may introduce
endogeneity also in a−it if the regulators prefers to strengthen weak/small operators
through imposing a low termination rates on the stronger firms.
Table 2. Correlation: Termination charge and firm performance
Ebitda2)
S1)
-0.5
-0.13
mtr
1) p < 0.01, 2) p <0.05
ebitda/customer1)
-0.35
Table 2 shows the correlation between termination charge and some firm performance
indicators. As seen there is a clear tendency that small and/or low-profit operators have
a higher termination rate on inbound traffic. This is supports the notion that the model
7) may be subject to simultaneity.
The measure of profits (ebitda) will in general contain revenue components that are not
incorporated in the theoretical model, for instance roaming and various kinds of data
traffic, as well as cost components that are not direct marginal costs. Thus, we allow for
a firm specific constant in 7) although the model outlined in the previous only requires a
nation specific constant.
In general, the structure of the profit functions makes the econometric specification very
robust to unobservable firm specific effects. The unobservable firm specific effects, i.e.
the differentiation parameters, affect profits through market shares only. Since the profit
function is separable in equilibrium market shares the specification is robust even to
time varying, firm specific differentiation parameters.
4.
Results
From the discussion in the previous section it is clear that we need a robust panel
estimator that can take account of correlation between cross-sections within clusters
(countries) as well as endogeneity. Table 3 below presents the results from GMM
17
Some argue that newcomers to the mobile industry should be granted an additional margin on mobile
termination, see e.g. ERG 2006 and Peitz (2005).
17
instrumental variable estimation of the econometric model 7)18. The fixed effects are
removed by the within transformation.19 The table displays two sets of estimates:
Models (1)-(3) and models (1a)-(3a). Model 1 is identical to model 1a and so forth
except that the latter does not include time dummies. We display both sets of results
because, in order to implement the cluster option, the time dummies had to be
“partialled out” from the other variables, including excluded instruments, in order to get
the covariance matrix of orthogonality conditions of full rank, see Baum, Schaffer and
Stillman (2006). This implies that the coefficients of the time dummies cannot be
displayed and we cannot perform conventional tests on their impact. We therefore
present the effect of including them by displaying both sets of results. Appendix A
shows the results of estimating the model without the cluster option.
To identify the parameters in the model we need a set of instrumental variables - that is
variables that are a) uncorrelated with the error term and b) correlated with the
explanatory
variables.
The
candidate
instruments
are
z = ait −1 , a −it −1 , sit −1 , (ebitda / cust ) it −1 . Let’s start with b) correlation with the explanatory
variables: The first to variables in z will be correlated with the explanatory variables
whenever there is some inertia in the termination rates. Current termination rates may be
correlated with the last two variables if the regulators use firm indicators to determine
future termination rates, recall Table 2 and the discussion in the previous section.
Indeed, as shown by the first stage regression in Appendix A, there is probably no need
to worry about weak instruments. The Shea R2 from the first stage regressions is in the
range of 0.44-0.48.
Why should z be valid? Regarding ait −1 and a −it the intuitive argument is that the first
lag of the right hand side variables are valid instrumental candidates in the static
regression because it is the current termination rates that affect profits – lagged
termination rates does not affect contemporary profits except possibly indirectly via
18
The results presented in this section are based on a sample where the operators in Denmark have been
removed. This is because the Danish operators have been subject to symmetric regulation in every quarter
which causes the regressors to be perfectly correlated for these cross-sections.
19
The estimation is performed in the module xtivreg2 for Stata using the gmm, robust, cluster option.
Prior to estimating the models in Table 3 we ran some regressions with explicit firm dummies and tested
for heteroskedasticity. All tests revealed a strong presence of heteroskedasticity.
18
inertia in the pricing decision. The same argument holds for sit −1 and (ebitda / cust ) it −1 ,
past performance should not affect profit in a static model.
The latter two proposed instruments highlights that the arguments for the orthogonality
of z depends critically on the assumption that the estimated model is in fact static. If the
true model is dynamic z will be correlated with the omitted lagged endogenous variable
and hence invalid. There is however nothing that indicates that this is the case. In
models (2) and (2a) z is used as excluded instruments. As is evident from Table 3 the
Hansen J test does not reject null of valid instruments. The same holds for regressions
using further lags of the variables in z .20
It is tempting to infer that if the model is in fact static, then y it −1 itself should be a valid
instrument. The models (3) and (3a) use z and y it −1 as excluded instruments and tests
whether y it −1 is suspect. Neither the Hansen J nor the C statistics is able to reject the null
of validity21. Appendix C shows the results from estimating a dynamic first differenced
model with the Arellano Bond estimator, Arellano Bond (1991). As can be seen, we
cannot reject that the coefficient of the lagged endogenous variable is zero at any
conventional level of significance.
20
Results available upon request.
However, as shown by Nickell (1981) the coefficient of the lagged endogenous variable is seriously
biased downwards in a fixed effects regression - y it −1 is correlated with the contemporary error term by
21
construction. Thus, the failure to reject
y it −1 as a suspect instrument in models (3) and (3a) questions the
strength of the Hansen J and C-statistics in the present context.
19
Table 3. Termination rates and profit: GMM cluster fixed effects1
Model: y it = γ i + β1 ait + β 2 a −it + vit
ait
a −it
Time dummies
(1)2
(2)3
(3)4
(1a)2
(2a)3
(3a)4
1.17**
1.18**
1.16**
1.16**
1.27***
1.26***
(0.56)
(0.53)
(0.52)
(0.50)
(0.44)
(0.44)
-0.57
-0.70**
-0.68**
-0.62*
-0.78***
-0.74***
(0.35)
(0.32)
(0.32)
(0.37)
(0.29)
(0.28)
Yes
Yes
Yes
No
No
No
0.05
0.05
0.05
0.05
0.05
0.05
R2
Obs
236
231
231
236
231
231
Firms
22
21
21
22
21
21
6
Diagnostics
Hansen J
0.56
0.70
0.62
0.76
C Statistic
0.60
0.64
Endogeneity
0.11
0.09
0.06
0.26
0.18
0.19
Notes:
1) The variables are defined in table 1. Standard errors in parentheses. ***, ** and *
indicate significance at the 0.01%, 0.05% and 0.1% level respectively. All models use
the within transformation (fixed effects) to handle the firm specific constants. The
estimation method is two-step GMM with standard errors robust to arbitrary
heteroskedasticity and arbitrary correlation within countries using the xtivreg2 package
for Stata. In the estimation of (1)-(4) the time dummies are “partialled out”, to get the
covariance matrix of orthogonality conditions of full rank.
2) The excluded instruments are the first lag of a and a
3) The excluded instruments are the first lag of a , a , s and ebitda/customer
4) The excluded instruments are the first lag of a , a , s , ebitda/customer and y
5) All diagnostics report robust p-values. Hansen J is the Sargan-Hansen test of overIdentifying restrictions. The C statistics is the “difference-in-Sargan test of a subset of
orthogonality conditions. The instrument tested is the lagged endogeneous variable, y .
Endogeneity is a test of the null hypothesis that a and a are exogeneous.
The last column in Table 3 reports the test statistics for the nil hypothesis that ait and
a −it is in fact exogenous variables. We see that exogeneity is rejected at the 10% level
for models (2) and (3), but not for the other models. Given strong apriori suppositions of
endogeneity, and a reluctance to rely on the models with no time dummies, we proceed
with the current estimates. Model (2) is the preferred.
Turning to the estimated coefficients we see that, except for the exactly identified
models (1) and (1a), the coefficients are significant the 5% level for the models with
20
time dummies, and 1% level for the models without time dummies. The estimates are
slightly higher in absolute value, in the model without time dummies. In all models the
coefficients has the expected sign - an increase in the own termination rate will increase
profit, and an increase in the competitors termination rate will decrease profit.
Furthermore the coefficients are close to 1 and -1 as predicted by the theoretical model.
4.1.
The profit neutrality hypothesis
What do the results tell us about the profit neutrality hypothesis; I.e. that an equal
change in all termination rates in a market k does not affect profit? Recall from
Proposition 2 that an equal change in termination rates does not affect pricing and hence
market shares. Conditioned on this proposition, it follows directly that profit neutrality
implies that β1 + β 2 = 0 in model 2. Furthermore, the model implies the stronger
restriction that the absolute value of the coefficients is equal to unity, i.e. β1 = − β 2 = 1 .
Table 4 below shows the results of testing these hypotheses.
Table 4. Tests of profit neutrality
Ho:
Ho:
β1 = − β 2
β1 = − β 2 = 1
1
2
3
1a
2a
3a
0.09
0.13
0.14
0.07
0.09
0.07
0.06
0.10
0.09
0.10
0.15
0.08
P-value reported. Test statistics are obtained from the corresponding
models in Table 3.
As may be seen from Table 4. neither model rejects the null of profit neutrality at the
5% level, and neither model reject that the β1 = − β 2 = 1 at the 5% level. Nevertheless,
the pattern with a coefficient slightly above 1 for the own termination rate and slightly
below |1| for the competitor’s termination rate seems quite consistent across different
specification.
21
5.
Conclusions
We have modelled competition between N mobile networks with inelastic demand. The
model allow for asymmetric termination rates, marginal costs and vertical
differentiation. We show that the operators equilibrium profit is unaffected by an
identical change in all termination rates in the market - we call this property the profit
neutrality hypothesis. If demand is specified as an address model and the disutility from
not consuming the most preferred variety is linear in distance, the specification of the
profit function is well suited for econometric implementation. We test the profit
neutrality hypothesis on a panel data set comprising 21 European mobile operators and
finds that we cannot reject the profit neutrality hypothesis at 5% level of significance.
Thus, we cannot reject that the profit of mobile operators is unaffected by an identical
change in all termination rates in the market.
22
References
Anderson, S.P., A de Palma and J.-F. Thisse, 1992, Discrete Choice Theory of Product
Differentiation, The MIT Press, Cambridge, Mass
Arellano, M. and S. Bond, 1991. Some Tests of specification for Panel Data: Monte
Carlo Evidence and an Application to Employment Equations, Review of
Economic Studies, 58, 277-297.
Armstrong, M. 1998, Network Interconnection in Telecommunications, The Economic
Journal, 108, pp 545 - 564
Armstrong, M, 2002, The theory of access pricing and interconnection, in Cave et. al.
(eds) Handbook of Telecommunication economics, Vol 1, pp 295-384 (Elsevier
science, Amsterdam)
Armstrong, M. and J. Wright, 2007, Mobile Call Termination, mimeo available at;
http://else.econ.ucl.ac.uk/papers/uploaded/255.pdf
Baum, C.F., M.E. Schaffer, S. Stillman, 2006. ivreg2: Stata module to Extended
instrumental variables/2SLS, GMM and AC/HAC, LIML and k-class regression.
Calzada, J. and T. Valletti, 2005, Network Competition and Entry Deterrence, CEPR
Discussion Paper No. 5381 (November 2005). Available at SSRN:
http://ssrn.com/abstract=886366
Carter, M., and J. Wright, 1999, Interconnection in Network Industries, Review of
Industrial Organization, 14, 1–25.
Carter, M. and J. Wright, 2003, Asymmetric Network Interconnection, Review of
Industrial Organization, 22, 27 – 46
De Bijl and Peitz 2002, Regulation and Entry into Telecommunications Markets.
Cambridge University Press, Cambridge.
Dessein, W. 2003, Network Competition in Nonlinear pricing, RAND Journal of
Economics, vol 34, no 4, pp 539 - 611
ERG, 2006, Revised ERG Common Position on the approach to Appropriate remedies
in the ECNS regulatory framework, Final Version May 2006, ERG (06) 33,
23
available at:
http://erg.eu.int/doc/meeting/erg_06_33_remedies_common_position_june_06.p
df
Gans, JS and SP. King, 2001, Using “Bill and Keep” to interconnect arrangements to
soften network competition, Economic Letters, 71, 413 – 420.
Grubb, MD, 2007, Selling to Overconfident Consumers, May 4, 2007, mimeo available
at http://www.stanford.edu/~mgrubb/SellingToOverconfidentConsumers.pdf
Hahn J-H., 2004, Network competition and interconnection with heterogeneous
subscribers, International Journal of Industrial Organization, 22, pp 611 - 631
Jeon, DS, JJ Laffont and J. Tirole 2004, On the “receiver pays” principle, Rand Journal
of economics, vol 35, no 1, pp 85-110 ?????
Laffont, JJ., P. Rey, J. Tirole, 1998a, Network Competition: I. Overview and nondiscriminatory pricing, RAND Journal of Economics, 29, (1) 1 – 37
Laffont, JJ., P. Rey, J. Tirole, 1998b, Network Competition: II. Price discrimination,
RAND Journal of Economics, 29, (1) 38 – 58
Nickell, S. 1981. Biases in dynamic models with fixed effects. Econometrica 49: 14171426
Peitz, M. 2005, Asymmetric access price regulation in telecommunications markets,
European Economic Review, 49, 341 – 358.
Salop, S. C, 1979, Monopolistic Competition with Outside Goods, The Bell journal of
Economics, 10, pp 141 - 156
24
Appendix A
Table A1. Termination rates and profit. GMM fixed effects, no clusters
Model: y it = γ i + β1 ait + β 2 a −it + vit
ait
a −it
(1)
(2)
(3)
(1a)
(2a)
(3a)
1.17
1.20
1.18
1.16
1.26
1.23
(0.46)
(0.45)
(0.44)
(0.50)
(0.49)
(0.49)
-0.57
-0.66
-0.61
-0.62
-0.74
-0.69
(0.45)
(0.44)
(0.43)
(0.48)
(0.48)
(0.47)
Time dummies
Yes
Yes
Yes
No
No
No
R2
N
N_g
0.17
236
22
0.16
231
21
0.16
231
21
0.05
236
22
0.05
231
21
0.05
231
21
0.08
0.48
0.59
0.06
0.65
0.67
0.06
0.15
0.58
0.64
0.10
0.74
0.71
0.11
Hansen J
C Statistics
Endogeneity
Notes, see Table 3.
Appendix B
Table B1. First stage regressions. Models (1), (2) and (3) (t-values in parentheses)
1
2
3
ait
a −it
ait
a −it
ait
a −it
ait −1
0.78
(11.24)
0.14
(2.70)
0.83
(18.09)
0.15
(3.12)
0.82
(17.56)
0.15
(3.47)
a −it
-0.08
(-1.28)
0.55
(7.29)
-0.12
(-3.24)
0.55
(7.83)
-0.12
(-4.78)
0.55
(8.59)
sit −1
-6.59
(-0.43)
8.65
(0.45)
-4.72
(-0.35)
8.35
(0.38)
(ebitda / cust ) t −1
-0.05
(-1.45)
-0.06
(-3.39)
-0.07
(-0.75)
-0.06
(-0.97)
0.01
(0.18)
0.00
(-0.05)
0.48
231
21
0.45
231
21
y it −1
Shea R2
N
N_g
0.45
236
22
0.44
236
22
0.47
231
21
0.45
231
21
25
Appendix C. Dynamic models
Table C1. Termination rates and profits: Arellano-Bond dynamic panel1
Model: y it = γ i + β 0 y it −1 + β1 ait + β 2 a −it + vit
Variable
(1)2
y it −1
0.02
0.07
(0.09)
(0.10)
1.10
1.45*
(0.73)
(0.83)
-0.61
-1.15
ait
a −it
(2)2
(0.90)
(0.89)
Time dummies
yes
no
Obs
Firms
228
21
228
21
Diagnostics3
AR(1)
AR(2)
Sargan
-1.78*
-0.04
1.94
-1.71*
-0.27
18.29
Notes:
1) The variables are defined in Table 1. Robust standard errors in parentheses. *
denotes significance at the 10% level. The model use first differences to handle the firm
specific effects. The estimation method is Arellano-Bond dynamic panel data using the
xtabond package for Stata, see Arellano and Bond (1991). The reported estimates are
first step, except Sargan which is two-step.
2) ait and a −it are treated as endogeneous with the second lags of s and ebitda/cust as
additional instruments. All valid orthogonality conditions up to 5 lags is used.
3) AR(1) is the Arellano-Bond test that average autocovariance in residuals of order 1 is
0, AR(2) is the corresponding test average autocovariance of order 2. Sargan is the
Sargan-Hansen test of over-identifying restrictions. The p-value of both Sargan statistics
is 1, note however that the Sargan-Hansen statistics in this model is well known to have
little power.
26