Measuring the Impact of Entry:

The Case of Mobile Telephony∗

Pedro Pereira†

AdC and IST

Tiago Ribeiro‡

Indera

September 2008

Abstract

We develop a framework to simulate and assess the impact of entry in oligopolistic

markets with product differentiation. For this purpose, we develop a model of the

mobile telephony industry that includes both a demand and a supply side. The model

is estimated for a rich panel of Portuguese firm level data, and used to perform three

policy exercises. First, we simulate the impact on prices and social welfare of the

merger that would reduce the number of firms from three to two. Second, we simulate

the entry of a third firm after the merger. Third, we simulate the entry of a fourth

firm, without the merger.

Key Words: Entry, Merger, Prices, Mobile Telephony.

JEL Classification: L13, L43, L93

∗We thank D. Brito for useful comments. The opinions expressed in this article reflect only the authors’

views, and in no way bind the institutions to which they are affiliated.†Autoridade da Concorrencia, Rua Laura Alves, no 4, 6o, 1050-188 Lisboa, Portugal, e-mail:

jpe.pereira@netcabo.pt.‡Indera - Estudos Economicos, Lda, Edifıcio Penınsula, Praca Bom Sucesso, 127/131, Sala 202, 4150-146

Porto, Portugal, e-mail: tiago.ribeiro@indera.pt.

1

1 Introduction

Merger simulation is one of the success stories of the application of structural econo-

metric methods to industrial organization. Competition authorities and sectoral regulators

routinely conduct merger simulations. The methods used to simulate mergers can be ex-

tended to simulate entry. The simulation of entry is important in many circumstances.

Competition authorities might be interested in knowing the impact of entry following a

merger. Telecommunications sectoral regulators might be interested in knowing the impact

of awarding an additional license. Firms might be interested in knowing the profitability of

entering into a market.

We develop a framework to simulate and assess the impact of entry in oligopolistic

markets with product differentiation. The methodology is illustrated with an application to

the Portuguese mobile telephony industry.

The Portuguese mobile telephony industry provides a suitable application of our frame-

work. In Portugal there are three mobile telephony firms, Tmn, Vodafone, and Optimus,

which in 2005 had revenue market shares of 50%, 37%, and 13%, respectively. In 2006,

the merger of Tmn and Optimus was proposed. The merger was cleared by the Portuguese

Competition Authority, but did not go through. On November 2007, the sectoral regulator

launched a public consultation about the assignment of a fourth licence.

We develop a structural model of the mobile telephony industry, that includes both the

demand and the supply side. The demand data generating process has two components: (i)

the sampling process, and (ii) the consumer structural decision model. For the sampling

process, we assume that entry into the market by consumers follows an S-shaped diffusion

process.1 For the consumer structural decision model, we assume a discrete choice model.

For the cost model, we assume a log quadratic cost function.

We take advantage of the richness of our data set in the specification of the demand and

cost models. The demand model includes both mobile and fixed telephony products. For

mobile telephony, we will consider two products: a pre-paid card product, and a contract

product. In addition, we include the prices of SMS as a characteristic of the of mobile

telephony products. For fixed telephony, we consider also two products: the product of the

telecommunications incumbent, and an aggregate product for the entrants in fixed telephony.

The cost function includes the prices of four production factors: labor, capital, materials,

and interconnection.

1Alternatively, one could assume that the evolution of the characteristics of mobile telephony with respect

to fixed telephony explains fully the evolution of the market shares, and take to the data a simple discrete

choice model. Although in the present case both alternatives would yield very similar results, they are,

nevertheless, conceptually very different.

2

The demand model on which we base our analysis is a nested logit model. We use the

demand model to estimate the price elasticities of demand. Consumers have elastic demands

for mobile telephony. We use the cost model to estimate the marginal costs.

The comparison of observed and estimated price-cost margins suggests that the assump-

tion of Nash behavior is plausible.

We use the model to perform three policy exercises. In the first policy exercise, we

simulate the impact over prices and welfare of the merger of Tmn and Optimus. The

purpose of this exercise is to establish a benchmark for the two other policy exercises. In

the second policy exercise, we simulate the impact on prices and welfare of the entry of a

firm in the mobile telephony market after the merger of Tmn and Optimus. The purpose

of this exercise is to evaluate if entry after the merger would mitigate the anti-competitive

effects of the merger. In the third policy exercise, we simulate the impact on prices and

welfare of the entry of a firm in the mobile telephony market without the merger. The

purpose of this exercise is to evaluate the desirability of the entry of a fourth firm.

Our methodological approach draws on the discrete choice literature, represented among

others by Domencich and McFadden (1975), Mcfadden (1974), McFadden (1978), and Mc-

Fadden (1981). In the industrial organization literature, Berry (1994), Berry, Levinsohn,

and Pakes (1995), and Nevo (2001) applied discrete choice models to the analysis of market

structure. Dube (2005), Ivaldi (2005), Ivaldi and Verboven (2005), Nevo (2000), and Pinkse

and Slade (2004) analyzed the impact of a merger in a framework similar to ours.2 These

studies used aggregate data, with the exception of Dube (2005), which used household level

data.

Regarding the empirical literature on mobile telephony, Parker and Roeller (1997) use US

data from 1984 to 1988 to estimate a structural model of the mobile telephony industry. They

report an own-price elasticity of demand of −2.5, and increasing marginal costs. Using the

same data, Miravete and Roeller (2004) estimate an equilibrium model of horizontal product

differentiation where firms compete in nonlinear tariffs. They report constant marginal

costs. Madden and Dalzell (2004) use annual panel data for 56 countries from 1995− 2000.

They estimate an own-price elasticity of −0.55 and an income elasticity of 4.76. They also

estimate network effects. Hausman (1997) reports an own-price elasticity of subscription of

−0.51 for cellular subscription in the 30 largest US markets over the period 1988 − 1993.

Hausman (2000) using more recent data reports an own-price elasticity of subscription of

−0.71. Gagnepain and Pereira (2007) studied the effect of entry of Optimus in 1997 on

costs and competition in the Portuguese mobile telephony industry. The results suggested

that the entry of a third operator in 1998 lead to significant cost reductions and fostered

2See also Baker and Bresnahan (1985) and J. Hausman and Zona (1994).

3

competition. The authors construct and estimate a model that includes demand, network,

and cost equations. The latter accounts for inefficiency and cost reducing effort. Grzybowski

and Pereira (2007) analyzed the merger of Tmn and Optimus. They used only mobile

telephony demand data and a simple aggregate nested logit model effects with market shares

in terms of subscribers. Their results indicate that the merger would lead to price increases of

7− 10%. Okada and Hatta (1999) using annual Japanese data from 1992 to 1996, totaling

235 observations, estimated an almost ideal demand system. They report an own-price

elasticity of demand for mobile telephony of −3.963 and −1.405, respectively, a cross-price

elasticity of the demand of mobile telephony with respect to the price of fixed telephony

of 0.866, and a cross-price elasticity of the demand for fixed telephony with respect to the

price of mobile telephony of 0.276. Rodini and Woroch (2003) use a US household annual

survey for the period 2000 to 2001, with 327.920 observations to estimate own and cross

price elasticities of mobile and fixed telephony. Estimated cross-price elasticities show that a

second line and mobile services are substitutes of one another. They estimate an own-price

elasticity of mobile access demand of −0.43, an own-price elasticity of mobile access and

usage of −0.60 and a cross-price elasticity of mobile demand with respect to fixed access of

0.13.

The rest of the article is organized as follows. Section 2 gives an overview of the Por-

tuguese mobile telephony industry. Section 3 presents the model. Section 4 describes the

data and the econometric implementation, and presents the basic estimation results. Section

5 conducts analysis. Section 6 concludes.

2 Overview of the Portuguese Industry

In Portugal, the firm associated with the telecommunications incumbent, Tmn, started

its activity in 1989 with the analogue technology C-450. In 1991, the sectorial regulator,

ICP-ANACOM, assigned two licenses to operate the digital technology GSM 900. One of

the licenses was assigned to Tmn. The other license was assigned to the entrant Vodafone.

Tmn introduced pre-paid cards in 1995 for the first time worldwide. In 1997, the regulator

assigned three licenses to operate the digital technology GSM 1800. Two licenses were

assigned to Tmn and Vodafone. A third license was assigned to the entrant Optimus,

which was also granted a license to operate GSM 900. In 2001, ICP-ANACOM assigned

licences to operate the 3G technology IMT2000/UMTS. Three licenses were assigned to

Tmn, Vodafone, and Optimus. A fourth license was assigned to the entrant Oniway, which

4

was not granted a license to operate GSM, and never operated. Service began in 2003.3

[Figure 1]

After its inception in 1989, the Portuguese mobile telephony industry had a fast diffusion,

analyzed in Gagnepain and Pereira (2007) and Pereira and Pernias (2006). In 2005 the

penetration rate of mobile telephony in Portugal was 110%. After entering the market in

1992, Vodafone gained revenue market share rapidly. During the duopoly period, i.e., from

1992 to 1997, Tmn and Vodafone essentially shared the market. The entry of Optimus

led to an asymmetric split of the market, which suggests that this event had a significant

impact in the industry, illustrated in Figure 1. A similar perspective can be gleaned from

the analysis of the time series of average prices of Tmn and Vodafone, presented in Figure

1. The average prices of Tmn and Vodafone move in parallel, and have a downward break

in 1997. This suggests that the entry of Optimus in 1998 caused the rivals to reduce prices.4

On February 2006, the holding company Sonaecom, which owns Optimus, made a hostile

take-over bid for the holding company Portugal Telecom, the telecommunications incumbent,

which owns Tmn. The transaction required the approval of the Portuguese Competition Au-

thority. Sonaecom justified the merger of Tmn and Optimus on the basis of: (i) substantial

putative efficiency gains, and (ii) the inability of the firms increasing prices under the cur-

rent market conditions. The Portuguese Competition Authority approved the transaction

with six remedies in mobile telephony. First, the merged firm would return to ANACOM

the licenses to use the GSM and the UMTS spectrum of either Tmn or Optimus. Second,

the merged firm would develop a wholesale reference offer for mobile virtual network opera-

tors. Third, there would be a financial compensation scheme, intended to overcome the price

mediated network externalities faced by an entrant mobile network operator. Fourth, the

merged firm would limit the differences between the on-net and off-net prices with respect to

any entrant, mobile network operator or mobile virtual network operator. Fifth, the merged

firm would take steps to reduce the customer switching costs in mobile telecommunications.

Sixth, the merged firm would be subject to a price-cap. However, the transaction did not

go through because the shareholders of PT voted against changing a clause of the statutes

of the firm limiting the voting rights of the shareholders, a prerequisite for the operation.5

3All of the licenses for GSM 900 and for GSM 1800 were assigned through public tenders, following EU

Directives 91/287 and 96/2, respectively. The first Directive instructed Member States to adopt the GSM

standard, and the second to grant at least two GSM 900 licenses and to allow additional firms to use GSM

1800. System GSM 900 operates on the 900 MHz frequency. System GSM 1800 operates on the 1800 MHz

frequency. The licenses for 3G were assigned through public tenders, following EU Decision 128/1999/EC.4There is no simple relation between the number of firms in an industry and prices levels. Garcia et al.

(2006), Rosenthal (1980), and Seade (1980) develop models where prices increase with the number of firms

in the market.5The statutes of PT imposed that no shareholder could have more than 10% of the voting rights,

5

On November 2007, ICP-ANACOM launched a public consultation about the assignment

of a fourth licence for the 450− 470 MHz frequency range.

3 Econometric Model

In this Section we present the econometric model. First, we present the demand model,

and afterwards we present the supply model.

3.1 Demand

3.1.1 Utility of Telephony Services

We index products with subscript i = 1, ..., I. A consumer chooses among a set of

alternative products for mobile and fixed telephony. The products differ in: (i) the price,

(ii) the type of subscription of mobile telephony, i.e., pre-paid card or contract, (iii) the size

of the network of the firm, and (iv) the price of SMS of the firm. We assume that the size

of the network and price of SMS are not relevant for fixed telephony, and set these values

to zero in fixed telephony products.

Denote by ri, the price of alternative i, by xi a J dimensional vector the characteristics

of alternative i other than price, by θ a vector of parameters to be estimated, and finally,

by εi a random disturbance.

A consumer derives from alternative i utility:

Ui(pi, xi, θ) = Vi(pi, xi, θ) + εi. (1)

We assume additionally that:

Vi(pi, xi, θ) := riα + g(xi, β),

where

g(xi, β) :=∑J

j=1xijβj,

and where α is the price coefficient, i.e., the negative of the marginal utility of income.

Expression g(·) is a linear combination that summarizes the utility component associated

with all product characteristics other than price. The components of vector β translate the

consumer valuation of the different product characteristics. Thus, θ := (α, β).

We assume that εi is independent across products, and identically distributed. This

formulation encompasses all the models analyzed in this paper. If εi has an extreme value

Type I distribution, one obtains the standard multinomial logit model. If εi has a joint

irrespective of the number of shares owned.

6

distribution of the generalized extreme value family, with the required generating function,

one obtains the nested logit model.

3.1.2 Choice Probabilities

Denote by F (·), the joint distribution function of (ε1, . . . , εI), and let Fi(·) := ∂F (·)∂εi

. The

probability that a consumer chooses product i if Ui > Uj, for all j 6= i, is:

Pi := Pr [Vi − Vj + εi > εj, for all j 6= i, j = 1, . . . , I] =∫Fi(Vi − V1 + u, . . . , u, . . . , Vi − VI + u)du.

If F (·) is an extreme value type I distribution, with the generating function H (z1, . . . , zI)

=∑I

i=1 zi, one obtains the standard multinomial logit expression for the choice probabilities:

Pi =eVi

∑j eVj

.

If F (·) is a generalized extreme value joint distribution, with the generating function

H (z1, . . . , zI) =∑G

g=1

(∑i∈Bg

z1

λg

i

)λg

, one obtains the nested logit model:

Pi =e

Viλg

∑j∈Bg

eVjλg

(∑j∈Bg

eVjλg

)λg

∑l

(∑j∈Bl

eVjλl

)λl, i on nest g;

where Bg is the the set of products in nest g = 1, ..., G, and λg is a parameter associated

with nest g, sometimes referred to as the inclusive value of nest g.

Let product i belong to nest g, and product 1 belong to nest 1. The probability that a

consumer chooses product i, given that the chooses products from nest g is:

Pi|g :=e

Viλg

∑j∈Bg

eVjλg

.

3.1.3 Aggregate Market Shares

With aggregate data, it is common to express market shares as a linear function of the

indirect utilities. For the multinomial logit and nested logit models, we have, respectively:

log

(Pi

P1

)= Vi − V1, (2)

log

(Pi

P1

)= Vi − V1 + (1− λk) log(Pi|g)− (1− λ1) log(P1|1). (3)

The so-called inversion of market shares is given by expressions (2) and (3) for the multino-

mial logit and nested logit models, respectively.

7

3.1.4 Observed Market Shares

Mobile telephony is not adopted immediately by all consumers as soon as it becomes

available. Rather, consumers adopt mobile telephony progressively, over time. This occurs,

possibly, for several reasons: first, due to network effects, second, due to consumer inertia,

third, due to the information about the benefits of the new service spreading through word-

of-mouth-communication, etc. We do not observe the consumers’ choices directly. The

observed market shares are a result of the choices of the consumers that in the past decided

to buy mobile telephony services, and the choices of the consumers that have not yet decided

to buy mobile telephony services. As these last consumers enter the market, the diffusion

of mobile telephony unfolds.

According to this view, we model the observed demand as having two components:

(i) a diffusion process describing the evolution of the market from the inception of mobile

telephony, up to the equilibrium between mobile and fixed services, and (ii) a discrete choice

model for the equilibrium market shares.

[Figure 2]

[Figure 3]

To motivate our approach, we present the plot the market shares and prices in Figures 2

and 3. The normalized market shares in Figure 3 present a clear trend which is not matched

by any of the variables defining the product characteristics.

Denote by P0 and P1, the vectors of consumer equilibrium market shares before and

after the introduction of mobile telephony, respectively. Vectors P0 and P1 are determined

by the choice model of Section 3.1.1. Denote by N(t), the number of subscribers of mobile

telephony in period t, by κ, the saturation level, i.e., κ := limt N(t), and by D(t) := N(t)κ

, the

normalized diffusion curve. The expression D(t) is a reduced form of the adoption process

of mobile telephony. Denote by P(t), the vector of observed market shares in period t, with

generic element Pi(t). The expression P(t) results form a fraction D(t) of the population

having chosen according to P1, and a fraction 1 −D(t) not having made any decision yet.

Therefore:6

P(t) ' (1−D(t))P0 + D(t)P1. (4)

The expression of P(·) is an approximation because P1 depends on variables that change

over time, most notably the size of the network. This simplification is meant to express

6We assume that the diffusion is the same across all products and depends on the total number of

subscribers. In Figure 3, with the exception of OTHfix, in the initial period the lines are almost parallel.

Thus, for our sample period this assumption is justifiable.

8

the assumption that most of the time the evolution of the market shares is driven by the

diffusion of mobile telephony.

Define product 1 as the fixed line product of the telecommunications incumbent. Then,

P0 = (1, 0, ..., 0). Using equation (4), we obtain the ratio of observed market shares:

Pi(t)

P1(t)=

P 1i D(t)

1−D(t) + P 11 D(t)

=P 1

i

P 11

1

1 + D(t)1−D(t)

1P 1

1

.

If P 11 does not change much over time, i.e., if xi is more or less stable over time, then the

denominator is just a function of t. If we take D(t) to be the normalized logistic diffusion

curve, i.e.,

D(t) =1

1 + exp(γ1 + γ2t),

then we have:D(t)

1−D(t)

1

P 11

= exp(γ1 + γ2t− log(P 11 )).

Let h(t) := − log(1+exp(γ1+γ2t)). The ratio of observed market shares can then be written

as:

ln

(Pi(t)

P1(t)

)= ln

(P 1

i

P 11

)+ h(t). (5)

The first term in the left-hand side of equation (5) was derived in Section 3.1.1, and h(·) is

an almost linear function in t. Expression h(·) is not an utility component. It is a correction

term to account for the diffusion process.

3.1.5 Price Elasticities of Demand

Denote by εij, the elasticity of demand of product i with respect to the price of product

j:

εij :=∂Pi

∂rj

rj

Pi

.

In the multinomial logit model, the partial derivative is:

∂Pi

∂rj

=

αPi(1− Pi) if i = j

−αPiPj otherwise;

implying the following elasticities:

εij =

αri(1− Pi) if i = j

−αrjPj otherwise.

In the nested logit model the partial derivatives are:

∂Pi

∂rj

=

αPi

[(1− 1

λg)Pi|g − Pi + 1

λg

]if i = j; i on nest g

αPi

[(1− 1

λg)Pj|g − Pj

]if i 6= j; i, j on nest g

−αPiPj if i 6= j; i, j in different nests;

9

implying the following elasticities:

εij =

αri

[(1− 1

λg)Pi|g − Pi + 1

λg

]if i = j; i on nest g

αrj

[(1− 1

λg)Pj|g − Pj

]if i 6= j; i, j on nest g

−αrjPj if i 6= j; i, j in different nests.

3.1.6 Consumer Welfare Valuation

Let superscript b and a denote the levels of variables before and after a policy change,

respectively. Denote by Vb

i and Va

i , the utility levels before and after a policy change,

respectively. A policy change may imply three types of changes. First, prices may change,

which requires computing the market equilibrium after the policy change. Second, the

characteristics of the products may change, i.e., xi may change. Third, the number of

products offered may change.

The generalized extreme value model, of which the multinomial and the nested logit

models are particular cases, provides a convenient computational formula for the exact

consumer surplus, up to a constant, associated with a policy that changes the attributes of

the products in the market. This expression, known as the “log sum” formula, is:7

∆CSn =1

α

[ln H

(eV

a

1 , . . . , eV aI

)− ln H

(eV

b

1 , . . . , eVb

I

)].

This formula is valid only when the indirect utility function is linear in income, i.e., when

price changes have no income effects, which is the case assumed here.

3.2 Supply

3.2.1 Costs of Mobile Telephony

We index firms with subscript f = 1, ...F , and index labor, capital, materials, and

interconnection with subscript s = l, k,m, a, respectively. Denote by Cf , the total cost of

firm f , by yi, the total output of product i, by ωsf , the price of production factor s for firm

f , and by If , the set of products owned by firm f . The cost of firm f is:8

ln(Cf ) = α0 +∑i∈If

αyiln(yi) +

∑i∈If

∑j∈If

αyiyjln(yi) ln(yj) +

∑

s=l,k,m,a

αs ln(ωsf ) + εf . (6)

This expression is a simplified version of a translog cost function, where, with the exception

of ln(yi) ln(yj), all cross terms were set to zero. From equation (6), we compute the marginal

7This expression was developed by Domencich and McFadden (1975), and Mcfadden (1974) for the

multinomial logit model, and by McFadden (1978) and McFadden (1981) for the nested logit model. Small

and Rosen (1981) elaborate on the connection between the above measures of welfare and standard measures

of consumer surplus.8In the empirical implementation we allow α0 to vary across firms and time.

10

cost of product i on If :

MgCit :=Cf

yi

αyi

+ 2∑j∈If

αyiyjln(yj)

.

3.2.2 Price Equilibrium

Let r := (r1, ..., rI)′ and y := (y1, ..., yI)

′. Whenever relevant, we allow the output levels

to depend on the price vector: yi(r). Denote by yf (r), the vector of outputs of the products

controlled by firm f , and by Cf (yf (r)), the cost function of firm f . The profit function of

firm f is:

Πf =∑i∈If

riyi(r)− Cf (yf (r)).

We assume that firms choose prices and play a static non-cooperative game, i.e., a

Bertrand game. Let ci(r) = ci(yf (r)) :=∂Cf (yf (r))

∂yi, and γij = 1 if products i and j are sold

by the same firm, and γij = 0 otherwise. The Nash equilibrium of the game is characterized

by the following set of first order conditions for i on If :9

∂Πf

∂ri

= yi(r) +I∑

j=1

γij∂yj(r)

∂ri

(rj − cj(r)) = 0.

Let matrices Γ and Φ(r) consist of the elements Γij := γij and Φij(r) :=∂yj(r)

∂ri, respec-

tively. Matrix Γ represents the market structure, and matrix Φ consists of the demand

estimates. Denote by A ◦ B the element by element product of matrices A and B, i.e., the

Hadamard product. Let c(r) := (c1(r), ..., cI(r))′. The system that defines the equilibrium

can be written as:

y(r) + (Γ ◦ Φ(r))(r− c(r)) = 0. (7)

3.2.3 Profit Variation

Taking a first-order approximation of the cost function of firm f around the the output

level y0f , the profit level of firm f is:

Πf =∑i∈If

[riyi(r)− ci(y

0f )(yi(r)− y0

i )]− Cf (y

0f )

Define the profit variation induced by the policy change for product i on If as:

∆πi := (rai − ci(y

0f ))y

ai − (rb

i − ci(y0f ))y

bi ,

and let y0f = yb

f :

∆πi = (rai − ci(y

bf ))y

ai − (rb

i − ci(ybf ))y

bi .

9We assume that a Nash equilibrium exists for strictly positive prices. Caplin and Nalebuff (1991) proved

existence in a general discrete choice model, with single product firms. Anderson and de Palma (1992) proved

existence for the nested logit model with symmetric multiproduct firms.

11

3.2.4 Welfare Variation

The welfare variation induced by a policy change is then:

∆CSn +F∑

f=1

∆Πf .

In the case of entry, one should subtract the entry costs from the expression above.

4 Econometric Implementation

In this Section, we describe the data and the econometric implementation, and present

the basic estimation results.

4.1 Data

The data consists of quarterly observations for the period 1992:1 − 2005:4. For the

demand models, we use a panel for the period 2000:1−2005:4. For the models with products

of the fixed telephony entrants the panel is unbalanced. For the cost models, we use data

for the period 1996:1− 2005:4 for Tmn, for the period 1999:1− 2005:4 for Vodafone, and for

the period 2000:1− 2005:4 for Optimus.

The variables were constructed as follows. The total costs of firm f , Cf , are the total

costs in thousands of euros. The production level of product i, yi, is the originated voice

traffic in thousands of minutes. The wage, ωlf , are the total labor costs over number of

employees, the price of materials, ωmf , is the cost of supplies over originated voice traffic,

the access price, ωaf , is the termination costs over originated voice traffic, and the price

of capital, ωkf , is interest rate of ten-year treasury bonds. The observed market share of

product i in period t, Pi(t), is the originated traffic for product i over total voice traffic in

period t. The price of product i, ri, is the total revenues over traffic originated. Finally, the

size of the network of firm f , Nf , is the number of subscribers of firm f .

[Figure 4]

[Figure 5]

The raw data exhibits significant quarterly variation, which may reflect mostly account-

ing practices, and not the underlying evolution of the market. This is the case of the behavior

of the average prices, which should evolve smoothly, and not exhibit quarterly variation of

the magnitude present in the original data. In accordance with this interpretation, we re-

moved the higher frequencies from our time series by means of kernel smoothing algorithms.

In the series where it was appropriate, the data was first isotonized and afterwards smoothed.

12

The series for originated minutes and subscribers where set to be in clear expansion. The

comparison between raw and smoothed data is presented in Figures 4 and 5.

[Figure 6]

We classified the mobile telephony options into six products. For each of the three

mobile telephony firms we consider: (i) a pre-paid card product, and (ii) a contract prod-

uct.10 Consumers with pre-paid card and contracts have different consumption patterns, as

presented in Figure 6.

For fixed telephony we consider two products: (i) the product of the incumbent, PTC,

and (ii) an aggregate product for the entrants in fixed telephony, as their individual relevance

is small.

4.2 Demand Estimates

We estimated two models of the demand function, both by OLS and IV, to account for

the possible endogeneity of prices. We used the following instruments: total costs, labor

costs, materials costs, and interconnection costs. Table 1 presents estimates of models 1 and

2.

[Table 1]

Model 1 is a multinomial logit model expressed in equation (2), with the modification

described in equation (5).

Model 2 is a nested logit model, expressed in equation (3), with the modification de-

scribed in equation (5), with two nests: (i) mobile telephony, and (ii) fixed telephony. We

restricted the coefficients associated with each nest to be equal. This restriction was not

rejected statistically. The values of the nest coefficients are statistically significant, and

consistent with random utility maximization. Therefore, we reject the multinomial logit

model, and its implied substitution patterns. The IV estimates differ substantially from

the OLS estimates.11 The most relevant case is that of the price coefficient, which with

the IV estimator assumes a value consistent with economic theory. We therefore base our

calculations on the IV nested logit model.12 In this model the coefficients of the variables

network size and price of SMS are statistically significant and assume the expected sign.

10With the exception of Miravete and Roeller (2004), the literature considers only one product per firm.11The test statistic of a Hausman test is 9.49 with a p-value of 0.002, which implies the rejection of the

null hypothesis that the OLS estimates are consistent.12We estimated four additional models. The first two differ from models 1 and 2 only in that the former

split recent fixed telephony into several products, each corresponding to a firm: Cabovisao, Novis, Oni, and

Tele 2. These models generated slight larger estimates of the price elasticities of demand than models 1

and 2. The third model includes only mobile telephony firms. In addition, the market in each period is

the increase in minutes from the previous period. This is intended as an approximation of the minutes

13

4.3 Price Elasticities of Demand

We computed the price elasticities of demand for the IV nested logit model. Table 2

presents the estimates.

[Table 2]

Consumers have elastic demands for mobile telephony services. The demands of the

fixed telephony entrants are smaller, but still elastic. The demand of PTC has an own-price

elasticity slightly higher than 1, and in some models lower than 1.

4.4 Cost Function Estimates

We estimated four cost functions. The results are presented in Table 3.

[Table 3]

Models 1 and 2 contain only one aggregate output measure per firm, defined as the sum

of minutes of the contract and pre-paid card products. Models 3 and 4 disaggregate these

two output measures per firm: (i) minutes of the contract product, and (ii) minutes of the

pre-paid card products. Models 2 and 4 allow for different time trends between firms, i.e.,

different technological progress across firms.

There is a high degree of collinearity in the data, and the trending variables tend to

capture most of the variation in the dependent variable. The large number of explanatory

variables used in the present context are likely to result in overfitting, as is suggested by

the erratic behavior of some coefficients under alternative OLS specifications. Some form of

dimensionality reduction of the projection space is required to avoid overfitting. Instead of

eliminating some explanatory variables, at the expense of the economic interpretability of

some of the models, we opted for a ridge regression procedure, where the shrinkage parameter

was determined by cross-validation. In the case of models 3 and 4 this problem is even more

severe. The output series are highly correlated. Hence, the empirical identification of the

effects of both products on costs is difficult to achieve. For these models, we augmented the

OLS objective function with a term that penalizes square differences between the estimated

marginal costs of the contract and pre-paid card products. The extent to which this term

is allowed to affect the OLS objective function is determined by cross-validation.13

of the new consumers in the market, i.e., the consumers that are really choosing for the first time to use

mobile telephony. This model generated slightly smaller price elasticities of demand than models 2. The

fourth model had with random coefficients associated with price, i.e., is a mixed logit model. This model

produced results very similar to those of the multinomial logit. Since mobile telephony products are relatively

homogeneous, the assumption of independence of irrelevant alternatives is not like to matter much.13In summary, in the estimation of models 3 and 4 the objective function to minimize is: (Y −Xα)′(Y −

14

For each model, and for each firm, we computed the marginal costs.14

Across all models, Tmn has the lowest marginal costs, and benefits from higher economies

of scale. Optimus and Vodafone have similar marginal costs. Optimus had a more substan-

tial technological progress than the other two firms.

We base our analysis on model 4 , because it has disaggregated output measures con-

sistent with demand estimates, and because it allows different technological progress across

firms, which is statistically significant.

Figure 7 plots the average costs of the three firms, considering only one aggregate output

measure per firm.

[Figure 7]

The average cost curve of Tmn is always below the average cost curves of the other two

firms. This implies that Tmn is the most efficient of the three firms. In addition, the average

cost curve of Tmn appears to have flatten out. This suggests that economies of scale have

been exhausted by this firm. Vodafone and Optimus seem to have similar average costs.

Overall, the efficiency gains associated to the merger are likely to be small. Most of

these gains would accrue to the products of Optimus, which would be produced at a lower

marginal cost, benefiting from the higher efficiency of Tmn.15

5 Policy Analysis

In this Section, first we examine the plausibility of the Nash equilibrium assumption,

and afterwards we perform three policy exercises. In the first policy exercise, we simulate

the effect of a merger between Tmn and Optimus. In the second policy exercise, we simulate

the effect of the entry of two types of firms, after the merger of Tmn and Optimus : (i) a

firm with a product with the characteristics of Optimus ’s pre-paid card product, and (ii)

Xα) + λα′Z ′Zα, where Y is the vector of log costs, X are the explanatory variables and Z = Z1 − Z2

such that Ziα is the marginal cost of product i=subscription, pre-paid. the parameter λ is determined by

cross-validation.14 McKenzie and Small (1997), using quarterly data from 5 US mobile telephony firms from 1993-1995,

totaling 28 observations, estimated a composite cost function with subscribers as the output. They found

mild decreasing returns do scale. Foreman and Beauvais (1999) using monthly data from a large panel of

GTE wireless mobile market areas from 1996-1998, totaling 3.333 observations, estimated a translog cost

function with subscribers and minutes of conversation as the outputs. They found mild increasing returns

do scale. Parker and Roeller (1997) found increasing marginal costs, wheras Miravete and Roeller (2004)

report constant marginal costs. Gagnepain and Pereira (2007) found constant returns to scale.15We considered the case where the merger could generate efficiency gains. However, if the firms in the

industry face moral hazard problems, such as those analyzed by Gagnepain and Pereira (2007), the decrease

in competitive pressure caused by the merger could lead firms to lower their cost reducing efforts, and

thereby lead to higher marginal costs. See also Brito and Pereira (2007).

15

a firm with two products identical to Optimus ’s pre-paid card and contract products. The

first type of firm represents a mobile virtual network operator, and the second type off firm

represents a mobile network operator. In the third policy exercise, we simulate the effect of

the entry of the previous two types of firms, without the merger of Tmn and Optimus.

Merger Simulation Merger simulation consists on the following five steps. First, assume

an equilibrium condition. We assume a Nash equilibrium, given by equation (7). Second,

given the observed rb and yb, and possibly other information, estimate Φ(·). Third, con-

struct Γb and Γa such that they reflect the ownership structure before and after the merger,

respectively. Fourth, given(yb, Γb, Φ(·), rb

), solve equation (7) numerically with respect to

c, to obtain an estimate of marginal costs, cb. Fifth, given(yb, Γa, Φ(·), cb

), solve equation

(7) numerically with respect to r, to obtain an estimate of the equilibrium prices after the

merger, ra.16 ¥

Entry Simulation Entry simulation consists on the following six steps. First, assume

an equilibrium condition, say a Nash equilibrium given by equation (7). Second, given the

observed rb and yb, and possibly other information, estimate Φ(·). Third, construct Γb such

that it reflects the ownership structure before the merger. Fourth, given(yb, Γb, Φ(·), rb

),

solve equation (7) numerically with respect to c, to obtain an estimate of marginal costs,

cb. Fifth, augment(yb, Γb, Φ(·), cb

)to reflect the existence of new products and firms in

the market, generating (ya, Φa(·), Γa, ca). The demand for the products of the new firm is

computed by specifying all the characteristics of these products, i.e., by specifying the vector

xi defined in equation (1), as well as the prices. One possibility, which we follow in this

article, is to give to the entering products the characteristics of the last products introduced

in the industry. Sixth, given (ya, Φa(·), Γa, ca), solve equation (7) numerically with respect

to r, to obtain an estimate of the equilibrium prices after entry, ra. ¥

Calibration We also test the sensitivity of the results to different scenarios regarding an

hypothetical outside option. This is done by introducing and outside option, defined as a

product whose characteristics are all set to zero with the exception of the product dummy.

All product dummies are then calibrated such that the outside option has a market share of

10% and 20% in the alternative scenarios. Briefly the procedure used is as follows. Partition

the vector of coefficients, θ, into (θ1, θ2), where θ1 represents the coefficients associated with

product dummy variables, and θ2 represents all the remaining coefficients. Let si represent

the market share for product i, and θ2 the estimated value of θ2. The calibrated value of θ1,

16It is not necessary to assume the same equilibrium condition before and after the merger.

16

denoted by θ1, is defined by:17

θ1 := arg minθ1

I∑i=1

(si − Pi(θ1, θ2)

)2

¥

5.1 Plausibility of the Nash ex-ante Assumption

Next, we examine the plausibility of several equilibrium assumptions regarding the firms’

behavior. We compare the observed price-cost margins, obtained from the observed prices

and the marginal cost estimates of model 4 reported in Table 3, with the estimated price-

cost margins, assuming various equilibrium conditions and using the IV nested logit model

reported in Table 1.

In Figure 9, we plot the observed price-cost margins and the estimated price-cost margins,

assuming firms play a Nash equilibrium.

[Figure 9]

For Tmn, both for the contract and pre-paid card products, the estimated Nash margin

is not significantly different from the observed margin.18 For Vodafone and Optimus, and

for the contract product, initially the estimated Nash margin is higher than the observed

margin. However, by the end of the period the two margins are not significantly different.

Also for these two firms, and for the pre-paid card product, the estimated Nash margin is

always higher than the observed margin.

In Figure 10, we plot the observed price-cost margins and the estimated price-cost mar-

gins, assuming that PTC and Tmn collude, i.e., assuming that the fixed and mobile tele-

phony firms of the telecommunications incumbent collude.

[Figure 10]

For all firms and products, except perhaps for the end of the period, the estimated Nash

margin is higher than the observed margin.

In Figures 11 and 12, we plot the observed price-cost margins and the estimated price-

cost margins, assuming first that Tmn, Vodafone, and Optimus collude, and second that

Tmn and Vodafone collude.

[Figure 11]

17There are several alternative techniques to correct the bias of some of the coefficients of the model.

See, e.g., Manski and McFadden (1981), in particular chapters 1 and 2. The first method that appeared in

the econometrics literature addressing this issue was the WESML estimator of Manski and Lerman (1977)

dealing with choice based samples.18This is not al test of hypothesis, since we did not account for the variance in the estimated margins.

17

[Figure 12]

In both cases, for all firms and products, the estimated Nash margin is higher than the

observed margin.

To sum up, for Tmn the observed behavior fits well with the Nash equilibrium assump-

tion. For Vodafone and Optimus, the observed behavior is no less competitive than that

predicted by the Nash equilibrium assumption; by the end of the period the observed be-

havior fits well with the Nash equilibrium assumption. We interpret these results as lack

of evidence against the assumption that firms play a Nash equilibrium. Furthermore, we

discard the possibility of collusive behavior.19

5.2 Merger of Tmn and Optimus

Next we simulate the impact over prices and welfare of the merger of Tmn and Optimus.

The purpose of this exercise is to establish a benchmark for the two other policy exercises.

Initially there are three mobile telephony firms: Tmn, Vodafone, and Optimus. Each

firm controls two products: a pre-paid card product, and a contract product.

The merger of Tmn and Optimus would result in a market with two mobile telephony

firms: (i) a firm controlling the products of Tmn and Optimus, and (ii) Vodafone, which

would maintain its products.

Given the procedure described at the beginning of Section 5, first we estimated the

marginal costs, and afterwards we simulated the equilibrium prices after the merger. Table

4 presents the results.20

[Table 4]

Table 5 reports the impact of the merger on market shares and welfare.

[Table 5]

Recall that before the merger, Tmn, Vodafone, and Optimus have market shares of 45%,

40%, and 15%, respectively. After the merger, the merged firm and Vodafone would market

shares of 55% and 45%, respectively.

19Assuming that Vodafone and Optimus play a Nash equilibrium when they play more competitively

equilibrium leads to overestimating the price increase caused by a merger, and to underestimating the

price decrease caused by entry. Both of these ”conservative” biases are acceptable, if not desirable, for a

Competition Authority or a Sectoral Regulator.20This procedure identifies changes in the price-cost margins, irrespective of the marginal costs estimates.

We estimate implicit marginal costs in a first step, and then maintain them fixed in a second step, because

we assume that marginal costs do not decrease with the merger. This is justifiable given the marginal

cost estimates reported in Table 3. Nevertheless, the impact of a reduction in marginal costs is reflected

one-to-one on the new equilibrium prices, and is, therefore, readily computable from the reported results.

18

After the merger, on average, the prices of mobile telephony increase 0.011 euros per

minute, i.e., increase 5.4% of their pre-merger levels. The largest increases occurs for Opti-

mus, for which prices increase by as much as 0.034 euros per minute, i.e., increase 20% of

their pre-merger levels.21

After the merger, on average: the consumer surplus decreases by 5.692× 10−3 euros per

minute, profits increase by 5.909 × 10−3 euros per minute, and social welfare increases by

0.217× 10−3 euros per minute.

This last result clashes with what is usually expected to be the impact of a merger on

welfare.A merger increases prices. In an oligopoly with differentiated products a price in-

crease has several effects. First, it has the usual negative direct effect of a single product

monopoly, or a homogeneous product oligopoly, of increasing the dead-weight loss. However,

the increase in the price of a given product also expands the demand of its substitute prod-

ucts. This indirect effect, in turn, can be decomposed in three parts. First, the consumer

surplus of the substitute products increases. Second, the profit of the substitute products

increases. Third, the equilibrium prices of the substitute products increases, thereby in-

creasing the deadweight loss of those products. However, this last negative impact is more

than compensated by the first two positive impacts. Thus, in an oligopoly with differenti-

ated products a price increase has a direct negative impact, and an indirect positive impact.

As a consequence, the net impact of a merger on welfare is potentially ambiguous.

Next we conduct a sensitivity analysis of our results to different assumptions about the

total size of the market, using the calibration procedure described in the beginning of Section

5. The outside option is taken as a product with all its characteristics set at zero, including

price, and it is placed in a separate nest.

Tables 6 and 7 report the impact on prices of the merger, assuming that the outside

option has an initial market share of 10% and 20%, respectively.

[Table 6 ]

[Table 7 ]

With an outside option, the price elasticities of demand decrease in absolute value. As a

consequence, the price increases caused by the merger assuming that there is outside option

are smaller than those assuming that there is no outside option. However, the former price

increases do not differ substantially from the latter. After the merger, without an outside

option the prices of mobile telephony are 5.4% higher than their pre-merger levels, whereas

with an outside option with an initial market share of 20% they are 5.0 higher.

21Given the estimated elasticities, the new equilibrium is characterized by the merged firm setting prices

close to the pre-merger prices of Tmn.

19

Tables 8 and 9 report the impact of the merger on market shares and welfare, assuming

that the outside option has an initial market share of 10% and 20%, respectively.

[Table 8]

[Table 9]

If the outside option has an initial market share of 20%, after the merger, on average: the

consumer surplus decreases by 4.236×10−3 euros per minute, profits increase by 4.011×10−3

euros per minute, and social welfare decreases by 0.225× 10−3 euros per minute.

5.3 Entry After the Merger

Next we simulate the impact on prices and welfare of the entry of a firm in the mobile

telephony market after the merger of Tmn and Optimus. The purpose of this exercise is to

evaluate if entry after the merger would mitigate the anti-competitive effects of the merger.

Tables 4 and 10 report the impact on prices of the entry after the merger of a firm with

a product with the characteristics of the pre-paid card product of Optimus, and of a firm

with two products identical to Optimus ’s pre-paid card and contract products, respectively,

assuming no outside option. Tables 5 and 11 report the impact on market shares and welfare

for the entry of these two types of firms, respectively, assuming no outside option.

[Table 10 ]

[Table 11]

An entrant with a product identical to the pre-paid card product of Optimus obtains

a market share of 9%, mostly at the expense of Vodafone and the pre-merger products of

Tmn, whose market shares decrease 4% each. The price of the entrant is 2% lower than

the pre-merger price of the similar product of Optimus. On average, the prices of mobile

telephony are 3% higher than their pre-merger levels.

After the entry of a firm with a product identical to the pre-paid card product of Optimus,

on average: the consumer surplus decreases by 1.256×10−3 euros per minute, profits increase

by 2.296 × 10−3 euros per minute, and social welfare increases by 1.040 × 10−3 euros per

minute.

An entrant with two products identical to the pre-paid card and contract products of

Optimus obtains a market share of 14%, mostly at the expense of Vodafone an Tmn, whose

market shares decrease 7% and 6%, respectively. The prices of the entrant are 0.2% and

0.3% lower than the pre-merger prices of the similar products of Optimus. On average, the

prices of mobile telephony are 1% higher than their pre-merger levels.

20

After the entry of a firm with two products identical to the pre-paid card and contract

products of Optimus, on average: the consumer surplus increases by 1.615× 10−3 euros per

minute, profits increase by 0.409 × 10−3 euros per minute, and social welfare increases by

2.024× 10−3 euros per minute.

To sum up, unless the entrant offers products valued highly by the consumers, and

thereby obtains a market share of about 16%, entry after the merger mitigates, but does

not remedy, the anti-competitive effects of the merger. The prices of mobile telephony

after a merger followed by entry are higher than before the merger. As a consequence,

consumer surplus decreases. Interestingly, profits increase enough to more than compensate

the consumer surplus decrease, and welfare increases. It is doubtful that in a saturated

market with the inertia characteristics of mobile telephony, an entrant could obtain a market

share of the order of 16% within two years.22

As before, we conduct a sensitivity analysis of our results to different assumptions of the

total size of market. For the case where the entrant has a product identical to the pre-paid

card product of Optimus, Tables 6 and 7 report the impact on prices, and Tables 8 and 9

report the impact on market shares and welfare. The results for the cases where there is an

outside option with an initial market share of 10% and 20% are qualitatively similar, and

hardly change quantitatively, compared to the case where there is no outside option. The

results for the case where the entrant has two products identical to the pre-paid card and

contract products of Optimus are identical, and are therefore omitted.23

5.4 Entry without the Merger

Next we simulate the impact on prices and welfare of the entry of a firm in the mobile

telephony market without the merger of Tmn and Optimus. The purpose of this exercise is

to evaluate the desirability of the entry of a fourth firm.

Table 4 and Table 10 report the impact on prices of the entry of a firm with a product

with the characteristics of the pre-paid card product of Optimus, and a firm with two

products identical to Optimus ’s pre-paid card and contract products, respectively, assuming

no outside option. Tables 5 and 11 report the impact of entry on market shares and welfare.

An entrant with a product identical to the pre-paid card product of Optimus obtains

a market share of 7%, mostly at the expense of Vodafone and Tmn, whose market shares

decrease 3% each. The price of the entrant is 2% lower than the pre-entry price of the

similar product of Optimus ’s. On average, the prices of mobile telephony are 1.2% lower

than their pre-entry levels.

22This is usually the time horizon considered by Competition Authorities for merger evaluation.23These results are available upon request.

21

After the entry of a firm with a product identical to the pre-paid card product of Optimus,

on average: the consumer surplus increases by 2.951×10−3 euros per minute, profits decrease

by 1.973 × 10−3 euros per minute, and social welfare increases by 0.978 × 10−3 euros per

minute.

An entrant with two products identical to the pre-paid card and contract products of

Optimus obtains a market share of 12%, mostly at the expense of Vodafone and Tmn, whose

market shares decrease 5% each. The prices of the entrant are 0.7% and 0.6% lower than

the pre-entry prices of the pre-paid card and contract products of Optimus. On average, the

prices of mobile telephony are 1.8% lower than their pre-entry levels.

After the entry of a firm with two products identical to the pre-paid card and contract

products of Optimus, on average: the consumer surplus increases by 5.081× 10−3 euros per

minute, profits decrease by 3.096 × 10−3 euros per minute, and social welfare increases by

1.985× 10−3 euros per minute.

To sum up, entry of a fourth firm in the mobile telephony market would lead to lower

prices and a higher welfare level. The impact, however, would be small.

As before, we conducted a sensitivity analysis of our results to different assumptions

about the size of the market. The results for the cases where there is an outside option

with an initial market share of 10% and 20% are qualitatively similar, and hardly change

quantitatively, compared with the previous results. We therefore omit them.24

We conclude this Section by computing the net present value of the entry investment of

a firm with two products identical to Optimus ’s pre-paid card and contract products.

Net Present Value of the Investment Consider a firm with two products identical

to Optimus ’s pre-paid card and contract products. In addition, assume that: (i) the time

horizon of the investment is ten years, (ii) the entrant has no sales on the first quarter,

and (iii) thereafter the entrant grows at a 30% quarterly rate to attaining 100% of its

equilibrium market share at the end of the 8th quarter. Using the estimates of the marginal

costs of Table 4, the simulated post-entry equilibrium prices of Table (10), and the simulated

post-entry equilibrium market shares of Table 11 we computed the quarterly profits of the

entrant. Assuming an annual discount rate of 5%, 10%, and 15%, the net present value of

the profit flow of the entrant is e490.095.897, e385.397.363, and e310.435.454, respectively.

These numbers, which were computed simply to illustrate the methodology, should be taken

as a rough approximation, since they do not include: the fixed set-up costs, the quarterly

fixed costs, or the revenues and costs of mobile broadband access to the internet. However,

as a reference, Optimus has 366.246.868 shares, whose average price in the last months was

e2.25, which gives a total of e824.055.453. ¥24These results are available upon request.

22

6 Concluding Remarks

We developed a framework to simulate and assess the impact of entry in oligopolistic

markets with product differentiation. The methodology was illustrated with an application

to the Portuguese mobile telephony industry. We developed a structural model, that includes

both the demand and the supply side, and estimated it using a rich panel of firm level data.

The model was used to perform three policy exercises. First, we simulated the impact on

prices and social welfare of the merger that would reduce the number of firms from three to

two. Second, we simulated the entry of a third firm after the merger. Third, we simulate

the entry of a fourth firm.

23

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26

Table 1: Demand estimatesMultinomial Logit Nested Logit

No IVs with IVs No IVs with IVsvar coef tstat coef tstat coef tstat coef tstat

price -2.703 -1.719 -43.109 -5.783 0.806 2.826 -5.919 -3.884

network -0.220 -3.607 -0.229 -4.085 0.098 8.316 0.091 7.803

price sms -1.840 -0.527 11.217 2.913 -3.471 -5.555 -1.895 -2.499

time 0.093 17.844 0.050 5.579 0.047 41.627 0.042 24.473

TMNcon -4.754 -12.728 2.323 1.752 -3.255 -46.513 -2.136 -8.186

TMNpre -4.311 -12.294 1.942 1.651 -3.120 -48.109 -2.128 -9.171

VODcon -4.992 -13.214 1.663 1.325 -3.087 -42.504 -2.042 -8.333

VODpre -5.490 -16.248 -0.383 -0.392 -3.150 -45.819 -2.371 -12.607

OPTcon -5.979 -10.141 -0.981 -0.925 -2.879 -25.255 -2.090 -10.319

OPTpre -6.005 -10.436 -1.828 -1.969 -2.856 -25.513 -2.202 -12.464

OTHfix -6.554 -26.908 -4.057 -8.125 -2.694 -38.742 -2.418 -24.644

Nest coef 0.761 71.160 0.740 66.695

R2 0.850 0.872 0.995 0.995F 886.293 1073.440 32313.574 33631.493N 168 168 168 168

Table 2: Elasticities - Nested Logit∂Yi

∂rj

rj

YiPTfix OTHfix TMNcon TMNpre VODcon VODpre OPTcon OPTpre

PTfix -0.919 0.673 0.112 0.168 0.147 0.081 0.042 0.039OTHfix 0.870 -1.087 0.112 0.168 0.147 0.081 0.042 0.039TMNcon 0.129 0.100 -4.270 1.113 0.976 0.536 0.279 0.256TMNpre 0.129 0.100 0.746 -3.437 0.976 0.536 0.279 0.256VODcon 0.129 0.100 0.746 1.113 -3.738 0.536 0.279 0.256VODpre 0.129 0.100 0.746 1.113 0.976 -3.305 0.279 0.256OPTcon 0.129 0.100 0.746 1.113 0.976 0.536 -4.024 0.256OPTpre 0.129 0.100 0.746 1.113 0.976 0.536 0.279 -3.583

7 Tables

27

Table 3: Cost functionsVariable Model 1 Model 2 Model 3 Model 4ctmn 9.349 5.978 1.236 -2.570

3.732 17.617 0.795 -1.991

cvod 9.773 6.285 1.289 -2.6413.849 18.522 0.818 -2.013

copt 9.709 6.345 1.143 -2.5943.800 18.464 0.719 -1.974

y -0.318 0.339-0.771 14.053

y2 0.041 0.0122.525 13.028

y1 0.543 0.8224.667 8.331

y2 0.706 1.2374.273 9.284

y21 0.055 0.053

17.655 18.909

y22 0.049 0.036

16.036 17.084

y1y2 -0.129 -0.151-9.134 -12.571

ωl 0.184 0.077 0.228 0.0512.350 1.065 2.747 0.676

ωk 0.118 0.051 0.245 0.1511.300 0.746 2.504 2.060

ωm 0.100 0.152 0.115 0.2182.585 6.173 2.885 6.934

ωa 0.077 0.069 0.078 0.0862.608 2.369 2.424 2.800

time -0.007 0.005 -0.000 0.015-2.460 1.430 -0.058 3.568

time*(vod==1) -0.004 -0.004-1.418 -1.176

time*(opt==1) -0.019 -0.025-4.999 -5.924

N 92.000 92.000 92.000 92.000R2 0.969 0.976 0.965 0.975

MgCtmn−sub 0.136 0.118 0.117 0.100MgCtmn−pre 0.136 0.118 0.132 0.081MgCvod−sub 0.242 0.198 0.172 0.122MgCvod−pre 0.242 0.198 0.174 0.121MgCopt−sub 0.249 0.195 0.203 0.145MgCopt−pre 0.249 0.195 0.222 0.152

28

Table 4: Post-entry prices

Product p0 mc p0−mcp0

pa1 pb

1 pc1 ∆pa

1% ∆pb1% ∆pc

1% mktsh

PTfix 0,078 -0,007 1,088 0,079 0,079 0,078 0,4 0,1 -0,2 0,28OTHfix 0,077 0,006 0,920 0,077 0,077 0,077 0,3 0,1 -0,2 0,22TMNcon 0,220 0,148 0,329 0,231 0,226 0,217 5,0 2,6 -1,3 0,09TMNpre 0,200 0,127 0,362 0,211 0,205 0,197 5,5 2,9 -1,4 0,14VODcon 0,207 0,140 0,325 0,212 0,208 0,204 2,6 0,5 -1,1 0,12VODpre 0,169 0,101 0,399 0,174 0,170 0,166 3,1 0,6 -1,4 0,08OPTcon 0,189 0,138 0,268 0,222 0,216 0,188 17,4 14,6 -0,3 0,04OPTpre 0,168 0,118 0,300 0,202 0,196 0,168 19,6 16,4 -0,4 0,04NEW 0,168 0,166 0,165 -1,8 -2,1Avg mob 0,197 0,130 0,342 0,208 0,200 0,192 5,4 2,6 -1,2 0,10

pa1 - prices with merger and without entry; pb

1 - prices with merger and with entry; pc1 - prices

without merger and with entry;

Table 5: Merger and new product effects on shares and CSProduct Today After New product

Merger I II

AllPTfix 0.277 0.286 0.279 0.273OTHfix 0.218 0.225 0.219 0.214TMNcon 0.086 0.084 0.079 0.082TMNpre 0.142 0.138 0.131 0.135VODcon 0.12 0.133 0.123 0.113VODpre 0.081 0.09 0.083 0.076OPTcon 0.038 0.022 0.021 0.034OPTpre 0.039 0.023 0.022 0.035NEW 0 0 0.043 0.037

MobileTMNcon 0.171 0.171 0.158 0.160TMNpre 0.281 0.282 0.26 0.263VODcon 0.237 0.271 0.245 0.220VODpre 0.16 0.183 0.165 0.149OPTcon 0.074 0.045 0.042 0.066OPTpre 0.077 0.046 0.043 0.069NEW 0 0 0.087 0.073

∆CS† 0 -5.692 -1.256 2.951∆π† 0 5.909 2.296 -1.973∆π† - Mobile 0 4.492 1.987 -1.255

I - New Nash eq. w/ merger; II - New Nash eq. w/omerger; † - 10−3 euros per minute; Total minutes perquarter: 5.5863× 109

29

Table 6: Post-entry prices - Outside option at 10%Product p0 pa

1 pb1 pc

1 ∆pa1% ∆pb

1% ∆pc1%

PTfix 0.072 0.072 0.072 0.072 0.3 0.1 -0.2OTHfix 0.065 0.065 0.065 0.065 0.3 0.1 -0.1TMNcon 0.221 0.231 0.227 0.218 4.8 2.6 -1.2TMNpre 0.200 0.211 0.206 0.198 5.3 2.8 -1.3VODcon 0.208 0.213 0.209 0.205 2.4 0.5 -1.1VODpre 0.169 0.174 0.170 0.167 2.9 0.6 -1.4OPTcon 0.200 0.232 0.227 0.199 16.0 13.4 -0.4OPTpre 0.179 0.212 0.207 0.179 17.9 15.1 -0.4NEW 0.179 0.177 0.176 -1.6 -1.9Avg mob 0.199 0.209 0.202 0.195 5.1 2.4 -1.2

pa1 - prices with merger and without entry; pb

1 - prices with mergerand with entry; pc

1 - prices without merger and with entry;

Table 7: Post-entry prices - Outside option at 20%Product p0 pa

1 pb1 pc

1 ∆pa1% ∆pb

1% ∆pc1%

PTfix 0.072 0.072 0.072 0.072 0.3 0.1 -0.1OTHfix 0.065 0.065 0.065 0.065 0.2 0.0 -0.1TMNcon 0.221 0.231 0.226 0.218 4.7 2.5 -1.2TMNpre 0.200 0.211 0.206 0.198 5.2 2.8 -1.3VODcon 0.208 0.212 0.209 0.205 2.3 0.5 -1.1VODpre 0.169 0.174 0.170 0.167 2.8 0.6 -1.3OPTcon 0.200 0.231 0.226 0.199 15.5 13.2 -0.5OPTpre 0.179 0.211 0.206 0.179 17.4 14.8 -0.4NEW 0.179 0.177 0.176 -1.6 -1.9Avg mob 0.199 0.209 0.202 0.195 5.0 2.4 -1.2

pa1 - prices with merger and without entry; pb

1 - prices with mergerand with entry; pc

1 - prices without merger and with entry;

30

Table 8: Merger and new product effects on shares and CS - Outside option at 10%Product Today After New product

Merger I II

AllPTfix 0.249 0.256 0.251 0.246OTHfix 0.196 0.202 0.197 0.193TMNcon 0.078 0.075 0.071 0.074TMNpre 0.128 0.124 0.117 0.122VODcon 0.108 0.119 0.110 0.102VODpre 0.073 0.08 0.074 0.069OPTcon 0.034 0.02 0.019 0.031OPTpre 0.035 0.021 0.020 0.032NEW 0 0 0.039 0.034OUT 0.1 0.103 0.101 0.098

MobileTMNcon 0.171 0.171 0.158 0.160TMNpre 0.281 0.282 0.26 0.263VODcon 0.237 0.271 0.245 0.220VODpre 0.16 0.183 0.165 0.149OPTcon 0.074 0.046 0.043 0.067OPTpre 0.077 0.047 0.044 0.069NEW 0 0 0.086 0.073

∆CS† 0 -4.94 -1.065 2.598∆π† 0 4.9 1.964 -1.598∆π† - Mobile 0 3.816 1.733 -1.043

I - New Nash eq. w/ merger; II - New Nash eq. w/omerger; † - 10−3 euros per minute; Total minutes perquarter: 5.5863× 109

31

Table 9: Merger and new product effects on shares and CS - Outside option at 20%Product Today After New product

Merger I II

AllPTfix 0.222 0.227 0.223 0.219OTHfix 0.174 0.179 0.175 0.172TMNcon 0.069 0.067 0.063 0.066TMNpre 0.113 0.11 0.104 0.108VODcon 0.096 0.105 0.098 0.091VODpre 0.065 0.071 0.066 0.061OPTcon 0.03 0.018 0.017 0.028OPTpre 0.031 0.019 0.018 0.028NEW 0 0 0.034 0.030OUT 0.2 0.205 0.201 0.197

MobileTMNcon 0.171 0.171 0.158 0.160TMNpre 0.281 0.282 0.26 0.263VODcon 0.237 0.27 0.244 0.220VODpre 0.16 0.182 0.165 0.148OPTcon 0.074 0.047 0.043 0.067OPTpre 0.077 0.048 0.044 0.069NEW 0 0 0.086 0.073

∆CS† 0 -4.236 -0.904 2.292∆π† 0 4.011 1.677 -1.299∆π† - Mobile 0 3.199 1.505 -0.869

I - New Nash eq. w/ merger; II - New Nash eq. w/omerger; † - 10−3 euros per minute; Total minutes perquarter: 5.5863× 109

Table 10: Post-entry prices - 2 productsProduct p0 pa

1 pb1 pc

1 ∆pa1% ∆pb

1% ∆pc1%

PTfix 0.078 0.079 0.078 0.078 0.4 -0.1 -0.3OTHfix 0.077 0.077 0.077 0.077 0.3 -0.1 -0.3TMNcon 0.220 0.231 0.223 0.215 5.0 1.2 -2.1TMNpre 0.200 0.211 0.202 0.195 5.5 1.4 -2.3VODcon 0.207 0.212 0.206 0.203 2.6 -0.6 -1.9VODpre 0.169 0.174 0.167 0.165 3.1 -0.8 -2.4OPTcon 0.189 0.222 0.213 0.188 17.4 13.0 -0.6OPTpre 0.168 0.202 0.193 0.167 19.6 14.6 -0.7NEWcon 0.189 0.188 0.188 -0.3 -0.6NEWpre 0.168 0.168 0.167 -0.2 -0.7Avg mob 0.197 0.208 0.197 0.191 5.4 1.3 -1.8

pa1 - prices with merger and without entry; pb

1 - prices with mergerand with entry; pc

1 - prices without merger and with entry;

32

Table 11: Merger and new product effects on shares and CS - 2 productsProduct Today After New product

Merger I II

AllPTfix 0.277 0.286 0.275 0.269OTHfix 0.218 0.225 0.216 0.211TMNcon 0.086 0.084 0.076 0.079TMNpre 0.142 0.138 0.125 0.130VODcon 0.12 0.133 0.116 0.108VODpre 0.081 0.09 0.078 0.073OPTcon 0.038 0.022 0.020 0.032OPTpre 0.039 0.023 0.021 0.033NEWcon 0 0 0.036 0.032NEWpre 0 0 0.037 0.033

MobileTMNcon 0.171 0.171 0.149 0.152TMNpre 0.281 0.282 0.246 0.250VODcon 0.237 0.271 0.228 0.209VODpre 0.16 0.183 0.154 0.141OPTcon 0.074 0.045 0.040 0.061OPTpre 0.077 0.046 0.041 0.063NEWcon 0 0 0.070 0.061NEWpre 0 0 0.072 0.063

∆CS† 0 -5.692 1.615 5.081∆π† 0 5.909 0.409 -3.096∆π† - Mobile 0 4.492 0.801 -1.878

I - New Nash eq. w/ merger; II - New Nash eq. w/omerger; † - 10−3 euros per minute; Total minutes perquarter: 5.5863× 109

33

8 Figures

34

1994 1996 1998 2000 2002 20040

0.1

0.2

0.3

0.4

0.5

0.6

% o

f tot

al m

obile

rev

enue

Revenues

TMNVodafoneOptimus

1994 1996 1998 2000 2002 20040

0.2

0.4

0.6

0.8

1

Pric

e (e

uros

)

Prices

Figure 1: Mobile shares and prices

35

2000 2001 2002 2003 2004 2005

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Shares − Minutes

TMNsub

TMNpre

VODsub

VODpre

OPTsub

OPTpre

OTHfix

PTfix

2000 2001 2002 2003 2004 2005

0.1

0.15

0.2

0.25

prices − Minutes

Figure 2: Shares and prices

2000 2001 2002 2003 2004 2005

−5

−4.5

−4

−3.5

−3

−2.5

−2

−1.5

−1

log(si/s

0) − Minutes

TMNsub

TMNpre

VODsub

VODpre

OPTsub

OPTpre

OTHfix

2000 2001 2002 2003 2004 2005

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

pi−p

0 − Minutes

Figure 3: Transformed data

36

1995 1997 2000 2002 20050

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TMNsub

Minutes

Min

utes

(10

9 )

1995 1997 2000 2002 20050

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

TMNpre

Minutes

Min

utes

(10

9 )

1995 1997 2000 2002 20050

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

VODsub

Minutes

Min

utes

(10

9 )

1995 1997 2000 2002 20050

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

VODpre

Minutes

Min

utes

(10

9 )

1995 1997 2000 2002 20050

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

OPTsub

Minutes

Min

utes

(10

9 )

1995 1997 2000 2002 20050

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

OPTpre

Minutes

Min

utes

(10

9 )

1995 1997 2000 2002 20050

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

OTHfix

Minutes

Min

utes

(10

9 )

1995 1997 2000 2002 20050

1

2

3

4

5

6

7

PTfix

Minutes

Min

utes

(10

9 )

1995 1997 2000 2002 20050

1

2

3

4

5

6

7Total Minutes

Min

utes

(10

9 )

Figure 4: Observed and smoothed minutes

37

1995 1997 2000 2002 20050

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

TMNsub

Revenues

Rev

enue

s (1

09 )

1995 1997 2000 2002 20050

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

TMNpre

Revenues

Rev

enue

s (1

09 )

1995 1997 2000 2002 20050

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

VODsub

Revenues

Rev

enue

s (1

09 )

1995 1997 2000 2002 20050

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

VODpre

Revenues

Rev

enue

s (1

09 )

1995 1997 2000 2002 20050

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

OPTsub

Revenues

Rev

enue

s (1

09 )

1995 1997 2000 2002 20050

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

OPTpre

Revenues

Rev

enue

s (1

09 )

1995 1997 2000 2002 20050

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

OTHfix

Revenues

Rev

enue

s (1

09 )

1995 1997 2000 2002 20050

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PTfix

Revenues

Rev

enue

s (1

09 )

1995 1997 2000 2002 20050

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Total Revenues

Rev

enue

s (1

09 )

Figure 5: Observed and smoothed revenues

38

2000 2001 2002 2003 2004 2005

4.8

5

5.2

5.4

5.6

5.8

6

6.2

6.4

x 106 Total Minutes

2000 2001 2002 2003 2004 2005

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Min

utes

Minutes per subscriber

TMNsub

TMNpre

VODsub

VODpre

OPTsub

OPTpre

Fixed

Figure 6: Minutes per subscriber

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

1.2

1.4Cost per Minute

Minutes

Eur

os

TMNVODOPT

Figure 7: Average costs

39

1994 1996 1998 2000 2002 2004

0.5

1

1.5

Min

utes

(10

9 )

Total minutes

TMNVODOPT

1994 1996 1998 2000 2002 20040

0.1

0.2

0.3

0.4

0.5

0.6

Sha

re

Total minutes

1994 1996 1998 2000 2002 2004

0.02

0.04

0.06

0.08

Min

utes

(10

9 )

Change in minutes

1994 1996 1998 2000 2002 2004

0.1

0.2

0.3

0.4

0.5

0.6

Sha

re

Change in minutes

Figure 8: Change in minutes

40

Figure 9: Price cost margins implicit under Nash and estimated price cost margins

00 01 02 03 04 05

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

TMN − subNash

PCM − estPCM − eq

00 01 02 03 04 05

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

TMN − preNash

00 01 02 03 04 05

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

VOD − subNash

00 01 02 03 04 05

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

VOD − preNash

00 01 02 03 04 05

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

OPT − subNash

00 01 02 03 04 05

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

OPT − preNash

Note: Dotted lines indicate 95% confidence interval for estimated price-cost margins.

41

Figure 10: Price cost margins implicit under Nash + coordination by PT on mobile andfixed and estimated price cost margins

00 01 02 03 04 05

−0.1

0

0.1

0.2

0.3

0.4

TMN − subNash + PT coord

PCM − estPCM − eq

00 01 02 03 04 05

−0.1

0

0.1

0.2

0.3

0.4

TMN − preNash + PT coord

00 01 02 03 04 05

−0.1

0

0.1

0.2

0.3

0.4

VOD − subNash + PT coord

00 01 02 03 04 05

−0.1

0

0.1

0.2

0.3

0.4

VOD − preNash + PT coord

00 01 02 03 04 05

−0.1

0

0.1

0.2

0.3

0.4

OPT − subNash + PT coord

00 01 02 03 04 05

−0.1

0

0.1

0.2

0.3

0.4

OPT − preNash + PT coord

Note: Dotted lines indicate 95% confidence interval for estimated price-cost margins.

42

Figure 11: Price cost margins implicit under mobile collusion and estimated price costmargins

00 01 02 03 04 05

−0.1

0

0.1

0.2

0.3

0.4

0.5

TMN − subMobile Collusion

PCM − estPCM − eq

00 01 02 03 04 05

−0.1

0

0.1

0.2

0.3

0.4

0.5

TMN − preMobile Collusion

00 01 02 03 04 05

−0.1

0

0.1

0.2

0.3

0.4

0.5

VOD − subMobile Collusion

00 01 02 03 04 05

−0.1

0

0.1

0.2

0.3

0.4

0.5

VOD − preMobile Collusion

00 01 02 03 04 05

−0.1

0

0.1

0.2

0.3

0.4

0.5

OPT − subMobile Collusion

00 01 02 03 04 05

−0.1

0

0.1

0.2

0.3

0.4

0.5

OPT − preMobile Collusion

Note: Dotted lines indicate 95% confidence interval for estimated price-cost margins.

43

Figure 12: Price cost margins implicit under TMN+VD collusion and estimated price costmargins

00 01 02 03 04 05

−0.1

0

0.1

0.2

TMN − subTMN+VD Collusion

PCM − estPCM − eq

00 01 02 03 04 05

−0.1

0

0.1

0.2

TMN − preTMN+VD Collusion

00 01 02 03 04 05

−0.1

0

0.1

0.2

VOD − subTMN+VD Collusion

00 01 02 03 04 05

−0.1

0

0.1

0.2

VOD − preTMN+VD Collusion

00 01 02 03 04 05

−0.1

0

0.1

0.2

OPT − subTMN+VD Collusion

00 01 02 03 04 05

−0.1

0

0.1

0.2

OPT − preTMN+VD Collusion

Note: Dotted lines indicate 95% confidence interval for estimated price-cost margins.

44