Download Quantifying network effects in dynamic consumer decisions

Quantifying network effects in dynamic
consumer decisions
An analysis of the US cellphone industry using group-level data
Stefan Weiergräber∗
February 16, 2014
- Work in progress -
Abstract
In many industries, network effects and switching costs interact leading to important
implications for market outcomes and economic policy. Almost all empirical studies consider
these two effects separately. In this paper, I develop an empirical framework that allows to
estimate dynamic demand models in which consumer decisions are simulataneously driven
by both network effects and switching costs. I outline how collinearity problems in the style
of Manski (1993)’s reflection problem can be transformed into a well-studied endogeneity
problem and show which kind of network effects can be separately identified from statedependence when only group-level data is available. I apply my framework to the US wireless
industry using large-scale survey data. Results from a myopic model reveal that estimates of
switching costs are very hetereogeneous across consumers ranging from US-$ 146 to US-$
395. Moreover, consumers value a large network. The willingness to pay for a 20%-point
increase in an operator’s market share within a consumer’s reference group is on average 10
US-$ per month.
∗
Center for Doctoral Studies in Economics, University of Mannheim; E-mail: stefan.weiergraeber[at]gess.
uni-mannheim[dot]de. I would like to thank my advisors Philipp Schmidt-Dengler and Yuya Takahashi for
continuous support and guidance. I thank Isis Durrmeyer, Christian Michel, Martin Peitz, Alex Shcherbakov,
Jordi Teixidó, Tommaso Valletti, Naoki Wakamori as well as participants of the PhD-IO Seminar at the
University of Mannheim for valuable comments.
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1 Introduction
In many "high-tech" consumer goods and service industries, such as telecommunications, computer
operating systems or online platforms, consumer purchase decisions are characterized by the
presence of both switching costs and network effects: Consumers not just take into account their
own previous choice but also consider what other people in their peer group do. While there
have been several recent papers that quantify consumer switching costs (Nosal 2011; Shcherbakov
2009), the presence of network or social effects has mostly been ignored in dynamic demand
models. Empirical studies on social interactions often run into identification problems in the style
of Manski’s reflection problem - in particular when only aggregate data are available. Moreover,
similarly to the issue of identifying switching costs, it is typically hard to disentangle network
effects from the effects of quality differences and consumer heterogeneity in tastes (Farrell and
Klemperer 2007).
In this paper, I develop an empirical framework that allows to separately identify switching costs
and network effects in a model of dynamic consumer decisions. I show under what assumptions
the reflection problem can be transformed into a well-known endogeneity problem and how
switching costs and certain kinds of social effects - in particular those that are very similar to a
local spillover - can be separately identified from preference heterogeneity. Non-identification
problems of the network effect as in Manski (1993) occur when for example market shares
are regressed on a deterministic function of the same market shares. This problem can be
circumvented as long as there is at least one observational characteristic, e.g. the local market,
that does not affect consumer preferences, but only shifts a consumer’s network environment
or reference group. Intuitively, this characteristic allows to observe individuals with identical
preferences in different network environments making econometric identification of localized
network effects possible.
Throughout the paper, the term "network effect" denotes what is usually referred to as an
anonymous firm-specific network effect. Put differently, network effects in my model measure the
effect of a product’s aggregate market share within a consumer’s reference group on individual
choice probabilities. I do not explicitly model the particular channels through which network
effects might operate so that the model might be applied to a range of different industries.
For the cellphone industry, Grajek (2010) argues that there are several channels that lead to
anonymous network effects. The most prominent driver is the presence of discounts for on-net
calls (tariff-mediated network effects). In addition, consumers may be uninformed about an
operator’s network quality and so interpret the installed base as a signal for service quality.
Finally, the psychological desire to conform with the crowd may cause consumers to consider the
established network size in their choice.
These network effects might operate on several levels (national, regional level, or even within
a narrowly defined demographic group). Aggregate network effect on the national level have
been analyzed extensively (Grajek 2010; Kim and Kwon 2003) - mostly in reduced-form models.
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However, one may question that individuals really care about the market share distribution in all
regions of the country, including those where they may have no established contacts and where
they may never be traveling. Instead, for most people, their social network is likely to be very
much localized within their home region. Consequently, consumers may consider local market
shares instead of global ones. Refining consumers’ reference groups further to a narrowly-defined
demographic group may be interesting but can lead to two problems. First, from an empirical
perspective it is hard to construct reliable estimates of narrow demographic-group specific market
shares even with an enormous amount of observations. Second, one may question that an
individual’s reference group consists only of types that are of exactly the same type. For example,
family members might be in a different age group, friends may have a different ethnicity or fall
into a different income group.
My economic model is relatively general in this point. In the empirical application however,
I focus on geographically localized network effects and take the model to the data analyzing
demand for wireless services in the US which has not been empirically investigated so far. For
the estimation, I use a panel of group-specific market shares constructed from a large-scale
survey. The detailed data set allows me to identify consumers’ preference heterogeneity from
group-specific market shares. Information on the switching behavior, i.e. aggregate churn rates,
identifies a vector of switching cost parameters. Throughout the paper, my definition of switching
costs follows the existing literature. It comprises all hassle costs associated with buying a different
product today than the one an individual has chosen in the past. Switching costs can include
explicit early-termination fees, transaction costs of canceling current contracts as well learning
costs associated with new products. Variation across distinct local markets identifies the network
effect. As long as consumers’ preference heterogeneity does not systematically differ across local
markets, the reflection problem will not be an issue in my model. As shown in section 4, the
network effect can then be estimated using standard IV techniques.
This paper is related to several strands of literature. Methodologically, I build on the literature
estimating dynamic demand models initiated by (Gowrisankaran and Rysman 2009) who extend
the methodology originally developed by Berry et al. (1995). The identification of network effects
shares some features with the sorting problems dealt with in the housing market literature (Bayer
and Timmins 2007; Bayer et al. 2011). Studies that combine the estimation of a dynamic model
with indirect network effects comprise Gowrisankaran et al. (2010) or Lee (2010). My paper
is one of the very few that develop an empirical model that allows for both switching costs
and direct network effects. In contrast to the switching costs studies on the cellphone industry
(Cullen and Shcherbakov 2010), I introduce network effects in a model of wireless carrier choice.
In contrast to Kim and Kwon (2003) and Kim et al. (2004), I account for the dynamic nature of
subscription decisions. The paper most closely related to mine is Yang (2011). His is to the best
of my knowledge the only study that considers network effects and switching costs in the same
model. However, his model is very restrictive in several respects, analyzes only global network
effects and cannot provide identification arguments. Due to my definition of network effects,
I neglect two kind of network effects that received attention in the literature, but are difficult
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to investigate with the data set used in this paper: Industry-wide network effects and network
effects through direct social links. Studies using direct social links and calling clubs have shown
that consumers tend to make calls to a small number of contacts very frequently and that these
calling clubs often join the same network (Hoernig et al. 2011; Maicas et al. 2009; Birke and
Swann 2006). Analyzing these personal links is not possible with just the random survey data I
have available. An analysis of these kind of social effects requires at best social network data
or at least extensive information on individuals calling patterns. Industry-wide network effects
are mostly relevant in newly emerging industries. For example, Goolsbee and Klenow (2002)
analyze the role of network effects in the adoption of home computers. In the early stages of the
wireless industry, a consumer’s decision of whether to adopt a cellphone at all was affected by the
overall adoption rate because this determined the possibilities for using a cellphone for mobile
communication. In my empirical application, I look at a period in which the overall penetration
rate was already very high (75%-90%). Therefore, I expect industry-wide network effects not to
play a significant role anymore.
The results from a myopic model give several new insights and contrast to the literature
estimating only one of the two effects. In general, estimates of switching costs vary across
consumer types from US-$ 146 to US-$ 400. These numbers are consistent with the results of
studies that do not account for network effects and consumer heterogeneity. However, they reveal
that there is large heterogeneity in switching costs. Moreover, consumers indeed value a large
network. When reference groups are defined in a geographical dimension, the willingness to pay
for a 20%-point increase in an operator’s market share within a consumer’s reference group is
around 10 US-$ per month, but also varies significantly across consumer types.
The remainder of this paper is structured as follows: The next section describes important
characteristics of the US cellphone industry and illustrates why it is important to identify
switching costs and network effects separately. Section 3 presents the economic model, section 4
develops the identification arguments and outlines the estimation strategy. The following sections
describe the data used for the estimation in more detail and the estimation results. Section 8
concludes.
2 Industry characteristics and policy relevance
The US wireless industry does not only fit the characteristics of my model very well, but is also
an interesting industry with respect to economic policy. A merger wave between 2004 and 2010
led to an oligopolistic market structure with 4 dominant players. The biggest two operators
(AT&T and Verizon) together have a market share of almost 70 %, while each of the two smaller
operators (Sprint and T-Mobile) controls 10-15 % of the market. The remaining market is
shared among a larger number of smaller operators often with limited regional coverage mostly
in rural areas. While the smaller operators usually sell more specialized products, the four major
carriers offer only slightly differentiated service bundles with respect to contract types, payment
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schemes, tariff structure, handsets subsidized and customer service. However, carriers can differ
significantly in local coverage quality.
Service subscription decisions in the US wireless industry exhibit state-dependence. Survey
data indicates that the vast majority of cellphone users has not switched their provider for more
than 3 years. The FCC has been concerned about this consumer inertia so that measures have
been undertaken to reduce switching costs. However, customer mobility across operators remains
low with average quarterly churn rates of around 1-2 %. Furthermore, a look at the raw data
reveals that larger operators in general have lower churn rates than smaller ones. The two big
players (AT&T and Verizon) enjoy substantial profit margins, while the smaller operators (Sprint
and T-Mobile) are struggling to survive. These observations yield empirical evidence for both
the presence of switching costs and network effects in the US wireless industry.
Postpaid contracts in the US typically take the form of 24-months contracts specifying a
monthly fee plus some included number of minutes (e.g. a 400-minute package for 40 US-$ per
month). During my sample period, most of these contracts included unlimited free calls to an
operator’s own network. Admittedly, tariff-mediated network effects in the form of on-net call
discounts have been on the decline very recently while wireless carriers shifted their business
models from selling phone services to data plans. Still it is interesting to quantify these effects for
several reasons. First, on-net discounts have definitely been in place during my sample period and
a precise quantification of the magnitude of network effects may help in explaining the current
market structure. Second, on-net discounts are still in place in many other countries, particularly
in Europe. Finally, re-investigating the cellphone industry in this period is worthwhile in order
to check that earlier research quantifying switching costs without taking network effects into
account did not mismeasure switching costs.
In general, both switching costs and network effects can substantially harm consumer welfare:
They create barriers to entry and cause incumbent firms with a large network to exploit
considerable market power. Similarly, both effects may prohibit the establishment of new and
better products because improvements in operator quality need to outweigh a large incumbents’
advantage of the installed base. Therefore, large operators may have only little incentive to
improve products, once they accumulated sufficiently high market share or charge higher prices
for products of the same quality. In the cellphone industry, there may be an amplification effect
between switching costs and network effects. The interaction with switching costs make network
effects longer-lasting. Especially in such a fast-changing industry where people may not be
able to forecast the technology evolution perfectly over a longer horizon, this can have severe
welfare consequences when switching costs prohibit consumers form re-optimizing quickly. So an
interaction of switching costs and network effects can give large operators not only extensive but
also very persistent market power.
There is a longstanding debate in the literature whether switching costs increase or decrease
consumer prices. In a recent paper, Chen (2011) suggests that the answer may critically depend
on the magnitude of network effects present in the industry. In his model of price competition,
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the size of the network effect determines whether firms tend to behave as a "fat cat" or a "top
dog".1
This suggests that reliably evaluating how the industry reacts to regulation of switching costs
or network effects requires to identify both effects separately. In order to credibly assess the
effectiveness of regulators’ policies it is important to get a precise idea on where operators’ market
power comes from. Policy implications might well be different depending on whether consumer
inertia is due to preference heterogeneity, switching costs or network effects. In particular,
policies reducing switching costs may not have a big effect on customer mobility if inertia is in
fact due to network effects. Empirical models that consider only one of the effects might result
in confounded estimates and yield misleading conclusions for economic policy. Especially in
light of the on-going debate about further industry consolidation and mergers involving Sprint
and T-Mobile, quantifying the importance of switching and network effects and their effect on
industry structure and conduct, deserves careful analysis.
3 Model
In this section, I present a dynamic demand model of the US cellphone industry.
3.1 Demand model with myopic consumers
I start by outlining the static components of the consumer optimization problem which may also
be interpreted as a demand model of myopic consumers. In the next subsection, I present the
dynamic components that lead to a model of forward-looking consumers. [A model of the supply
side will be developed in section 3.3.]
Each period, consumers can choose a wireless network to subscribe to. There are 4 major
operators and a fringe of smaller operators. Throughout the model, not subscribing to a postpaid
plan of any of the major four operators is treated as choosing the outside option. The utility of
the outside option is normalized to zero. This results in a total of 5 different products and implies
that I do not model the technology adoption decision that e.g. Grajek and Kretschmer (2009)
analyze. Given that the wireless penetration rate was already quite high (75%-90%) during my
sample period, I treat the set of consumers in the market as constant. In contrast to the study by
Cullen and Shcherbakov (2010), I abstract from consumers’ specific handset choice. In addition,
I do not model the decision of which specific plan to choose. Each consumer is assigned to a
local market based on his residency. I classify geographic markets on the DMA-level. A DMA
(designated market area) is defined as a collection of counties where consumer receive the same
satellite signal and so have the same media coverage. The time period of observation is a quarter.
1
Similarly, Suleymanova and Wey (2011) show in a stylized Bertrand model that the ratio of switching costs to
network effects is a key determinant of whether the market evolves to a market sharing or market tipping
equilibrium.
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Consumers care about operators’ observable quality characteristics (Xgt ). Xgt includes operator
fixed effects, proxies for local coverage quality, quality of the handset portfolio subsidized and
subscription prices. Moreover, consumers care about the dynamic implications of their decision
today: A consumer incurs a switching cost when choosing a different provider today than in the
previous period. In the myopic model, consumers’ optimal choices are state-dependent but they
are myopic in the sense that consumers do not form explicit beliefs about the future evolution
of network characteristics or network sizes. As in Berry et al. (1995), the utility uijgt in such a
model should be interpreted as the expected lifetime utility of choosing operator j in period t.
Finally, for reasons outlined above, individuals prefer to be on a network with a larger installed
base.
Consumers have heterogeneous preferences as a function of individual demographic characteristics d. This results in a discrete number of consumer types which may e.g. be defined by age
group and income. The utility of consumer i belonging to demographic group d in geographic
market g choosing operator j in quarter t is given by a linear-quadratic function in observed
quality attributes (X 1 , X 2 , p), unobserved shocks and usage quantity q:
1
uigjt = Xdjt
β
|
Xd1
i
2
+ (Xjgt
β
Xd2
i
1 2
− βdpi pjt + ξdjgt + αsjri t )qigjt − γqijgt
+ ψdi 1{ait−1 6=ait } +igjt
2
{z
}
δ̃ijgt
where X 1 denotes a set of nation-wide brand-fixed effects independent of the quantity an
individual consumes, X 2 contains proxies for local call quality and p denotes the (average) price
per quantity consumed.
In principle, the model allows each consumer to consume different quantities qijgt of phone
service. This structure can be derived from an underlying utility function is quasi-linear in
phone service and an outside good whose price is normalized to one. The price coefficient βdpi
may eventually vary as a function of individual income. Ignoring non-negativity constraints and
assuming all interior solutions, a standard static maximization problem yields a closed-form
solution for the optimal quantity consumed conditional on having chosen operator j in period t:
∗
qijgt
=
1 2 X
(X β − βdpi pjt + ξjgt + αsjri t )
γ jgt di
The indirect utility as a function of consumers information set Ωit may similarly be written as:
s.t.
wijgt (Ωit ) = max uijgt
qijgt
qigjt ≥ 0
An underlying assumption is that all consumers face the same average price pjt , i.e. the total
price paid by consumer i is Rij = qij · pj . So implicitly, I abstract from the two-part tariff
pricing schemes often observed in the telecommunications industry. Moreover, in the simple
model with consumers that are homogeneous within a group d, all consumers within d have the
same usage quantity. One can easily relax this assumption by allowing for individual unobserved
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heterogeneity ν as in Schiraldi et al. (2011):
1
uigjt = Xdjt
β
|
Xd1
i
2
+ (Xjgt
β
Xd2
i
1 2
+ ψdi 1{ait−1 6=ait } +igjt
− βdpi pjt + ξdjgt + αsjri t + νijgt )qigjt − γqijgt
2
{z
}
δ̃ijgt
Across local markets, wireless carriers can differ substantially in their quality coverage pattern.
Such quality differences are often unobserved by the econometrician. In the model, they are
captured by ξjgt which is a real-valued unobserved vertical characteristic. I assume that ξ evolves
according to an AR(1)-process:
ξdjgt = ιξdjgt−1 + νdjgt
νdjgt = ξdjgt − ιξdjgt−1
where ι are parameters to be estimated. This is justified by noting that typical components
of ξ, like brand-reputation effects and unobserved components of carriers’ infrastructure are
relatively persistent across quarters. ijt is an iid error shock drawn from a Type-1 extreme
value distribution.
ψdi represents a consumer’s switching costs, i.e. a cost that has to be paid once the consumer
decides to be on a different network in the current period than in the previous period. In line
with the existing literature, ψdi comprises all hassle costs associated with the switching process,
i.e. transaction costs for canceling a subscription, explicit early termination and start-up fees,
costs of buying new equipment and potential learning costs. If applicable, "poaching payments",
i.e. one-time payments made by an operator to whom a consumer switches reduce the switching
costs. So ψdi is a net switching costs. ψdi may be heterogeneous across consumer types and
products. However, it is crucial for my identification strategy that it is constant across local
markets.
The coefficient α measures consumers willingness to pay for additional subscribers being on
the same network. The specification of the reference group is crucial for the model outcome.
In principle, the reference group r (not necessarily equal to d) can be defined by an arbitrary
interaction of demographic characteristics and geographic location. For most parts of the
estimation, I assume that a consumer’s reference group consists of all consumers in her home
region. In the current specification, network effects enter linearly. As a robustness check, one
can use various functions (concave, convex, s-shaped,...) of network size. Moreover, the network
effect is specified such that its intensity may depend on the individual usage quantity. This may
for example allow consumers with high usage intensity to pay more attention to the network size.
In general, social or network effects introduce the reflection problem into my model. This
kind of problem was first described by Manski (1993): The fact that operator market shares are
both dependent variables and regressors within an estimating equation can lead to econometric
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non-identification. In section 4, I describe the problem in more detail and show that with
group-level data, (in some dimension) localized network effects can be identified.
The timing of consumer decisions within a period is as follows:
1. Consumers observe the industry structure Ωt = (Xjgt , ξjgt , st−1 ) and ijgt . They do not
observe the -realizations of other consumers.
2. Given (1), consumers form expectations on the choices of other consumers. The vector of expected network size is a J-component vector with the jth component given
R
by: Ei [sjri t |X, ξ, sjri t−1 ] = i0 ∈r P r(ai0 t = j)dG(di0 ). In my model, this is equivalent to
consumers having rational expectations.
3. Each demographic group d consists of a continuum of atomistic consumers so that consumers
take the equilibrium as given and do not act strategically. Together with (2) this implies
that rational expectations consumers do not face any uncertainty in the aggregate.
4. Based on their expectations from (2) consumers simultaneously choose their utility maximizing alternative. Market shares st and churn rates ct are realized. This implies that
the observed market shares are the outcome of a "self-consistent equilibrium" (Brock and
Durlauf 2003) and one of possibly several fixed points of the following mapping:
st = Ψ(Ωt , E[st ])
This is essentially the definition of perfect Bayesian equilibria: Each consumer chooses her
utility maximizing product given her beliefs and these beliefs are consistent with actual consumer
behavior. However, because of the assumption of a continuum of consumers there is no uncertainty
in the aggregate which provides a justification for using observed market shares as measures
for consumers’ expectations on network size. This specification abstracts from problems of
limited information as in Goeree (2008). In my model, people are perfectly informed about
product characteristics and prices, but not necessarily about the modalities of the switching
process. This information structure can be justified by noting that wireless carriers heavily
engage in advertising and marketing so that consumers can get an accurate picture of the market
environment easily.
In principle, there are many alternative ways to model consumer expectations. One alternative
is to assume perfect foresight where consumers predict network sizes perfectly right away. This is
an restrictive assumption that is conceptually hard to justify. Yang (2011) constructs expectation
in a bounded rationality framework: Consumers’ prediction of market shares is a linear function
of various factors, such as product characteristics, prices, switching costs and previous market
shares. Coefficients are estimated such that individuals are correct on average. This model is very
easy to implement but quite arbitrary and lacks a theoretical foundation. An advantage is that it
circumvents the problem of multiple equilibria. Grajek (2010) does not model expectations at all.
He assumes naive consumers that do not project the market environment in the current period,
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but simply consider the previous period’s market share when making a decision today. This is
another simple specification that avoids the issue of multiple equilibria. However, it is not clear,
why consumers should ignore current period’s information when making a potentially long-term
decision, in particular if the decision period is larger. When measuring indirect network effects,
previous periods’ network size may be reasonable to look at as they may serve as an indicator
for complementary goods being developed in the future. With direct network effects, it is more
convincing to assume that consumers pay more attention to the current and future period than
to the past.
3.2 Model of forward-looking consumers
In a dynamic model, consumers not only consider instantaneous payoff, but maximize their
discounted lifetime utility. The dynamic version of the model developed in the previous section is
based on a recent series of papers on dynamic demand models, like Gowrisankaran and Rysman
(2009), Shcherbakov (2009), Nosal (2011) and Conlon (2011). Consumer i’s infinite-horizon
decision problem can be described by a value function:
V i (j̃, it , Ωt ) = max{uij̃t + βE[V i (j̃, Ωt+1 )|Ωt )],
max{−ψ i + uijt + βE[V i (j, Ωt+1 )|Ωt ]}}
j6=j̃
with β denoting the discount factor and j̃ the product owned at the beginning of the period. A
consumer can be subscribed to exactly one cellphone operator, i.e. if she subscribes to a new
operator, the old contract is canceled at a cost included in the switching cost ψ i . Ω denotes the
industry state, i.e. it contains all payoff-relevant information. So the relevant state space of a
consumer is characterized by (j̃, it , Ωt ). As characteristics such as coverage quality call rates
and network size may change every period, uij̃t may change as well and is not fixed to be the
same as in the initial purchase period (in contrast to the models by Gowrisankaran and Rysman
(2009) or Conlon (2011)). The industry characteristics Ω evolve according to some exogenous
Markov process g(Ωt+1 |Ωt ). The logit structure implies that the ex-ante value function can be
written as:
E(V i (j̃, Ωt )) = v i (j̃, Ω) = log[exp(uij̃ ) + E[V i (uij̃ , Ω0 )|Ω] + exp(∆i (j̃, Ω))]
with v i (·) denoting the ex-ante value function. It is obtained by integrating over the iid shock
. The last term captures the present discounted value of choosing the best alternative today
except for the one currently owned:
∆i (j̃, Ω) = log(
X
exp(uij − ψ i + βE[V i (j, Ω0 )|Ω]))
j6=j̃
A dynamic model where consumers keep track of each state variable individually is compu-
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tationally infeasible. Therefore, the literature has adopted assumptions to reduce the state
space. I follow Gowrisankaran and Rysman (2009) in imposing a logit inclusive value sufficiency
assumption:
∆i (Ω) = ∆i (Ω̂)
⇒ g∆ (∆(Ω0 )|Ω) = g∆ (∆(Ω̂0 |Ω̂))
Similarly, for the evolution of the mean utility of the good currently owned, this assumption
implies:
wji (Ω) = wji (Ω̂)
⇒ gw (wi (j, Ω0 )|Ω) = gw (w(j, Ω̂0 |Ω̂))
This assumption ensures that consumers need to keep track only of uij̃ , the mean utility of the
good currently owned and the logit inclusive value ∆i (Ω) as a sufficient statistic for the industry
evolution.
In order to construct the expectations of the continuation value, I need to specify how consumers
form beliefs about the evolution of the relevant state variables. Two commonly used assumptions
are perfect foresight and bounded rationality. For the moment, I stick to the bounded rationality
assumption which may not be consistent with an economic model of belief formation or a supply
side model. However, it may be interpreted as consumers being able only to track some summary
statistic of the overall market as well as their own product (Gowrisankaran and Rysman 2009).
This is plausible as it is unrealistic that consumers track each and every aspect of the market
environment but rather keep an eye on the market as a whole with more detailed information
about the product they currently own. More specifically, I model the evolution of the market
statistics as:
∆t+1 = γ1 + γ2 ∆t + ν∆t+1
ujt+1 = τ0 + τ1 ujt + νut+1
ν∆ , νu ∼ N (0, σν )
For the dynamic model, redefine
wijt = uijt + βE(V i (j, Ωt+1 )|Ωt )
and let i’s previous choice be j̃. This implies that the conditional choice probabilities can be
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written as:
P r(j̃|j̃) =
P r(j|j̃) =
exp(wij̃t )
exp(wij̃t ) + exp(∆i (j̃, Ω))
exp(wijt − ψ)
exp(wijt − ψ) + exp(∆i (j, Ω))
Market share predictions are then given by:
sijt =
X
P i (j|j 0 )sij 0 t−1
j0
These market share and (analogously churn rate) predictions can be taken to the data to from
moment conditions or likelihood functions.
3.3 Supply side model [to be added]
At the moment, I assume that consumers’ decision-relevant perception of the supply side is
fully captured by the exogenous AR(1)-process specifying consumer beliefs about the industry
evolution. In order to compute more meaningful counterfactuals, I will present an explicit model
of platform competition on the supply side in the spirit of Cabral (2011).
[to be added]
4 Identification and Estimation
In this section, I show under what assumption the parameters of the demand model are identified.
In particular, I show that switching costs and localized network effects can be disentangled and
that the reflection problem does not occur in this model. The following identification arguments
require more than aggregate market share data. However, they do not rely on detailed panel data.
A panel of group-specific market shares which can be constructed from a repeated cross-section
of individual-level observations is sufficient.
4.1 Myopic logit model with localized network effects
I focus on identification arguments for the myopic logit model. By replacing the mean utilities
with ex-ante value functions most of the main results carry through. Consumer heterogeneity
in the sense of coefficients that are demographic-group-specific is identified by differences in
group-specific market shares. Identification arguments to a random coefficient logit model should
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be straightforward and, similarly to Berry et al. (1995), be based on variation in the choice set
across local markets and time periods. The key variables to identify the switching cost parameters
ψ are churn rates. High switching costs make quitting a service (and subscribing to a new one)
more expensive and thereby reduce churn rates compared to a setting where switching costs are
low. Localized network effects, very similar to a local spillover, are identified by comparing the
dynamics of different local markets over time. The key assumption for avoiding the reflection
problem is that there preference heterogeneity and reference group definition are orthogonal to
each other in at least dimension. Intuitively, this requires two things. First, a characteristic that
allows to observe the same individual (in terms of preferences) in different network environments.
The prime example for such a characteristic is the local market. Second, that there is some
heterogeneity across the consumers within a reference group. This heterogeneity can be used to
construct the encessary exclusion restrictions. The identification strategy will make use of the
following assumptions:
Identifying assumptions
Assumption 4.1. Consumers are characterized by a discrete type as a function of their demographic characteristics d. Within this group, consumers have homogeneous preferences with
respect to observables. [The extensions to consumer heterogeneity in the style of Berry et al.
(1995) with random coefficients should be straightforward]
Assumption 4.2. Each consumer has a reference group r the average behavior of which she
takes into account. r is not a function of d and d is not a function of r.
In particular, Assumption 4.2 includes the case where consumers do not only care about the
individuals who are exactly of the same type as themselves. For example, d may be defined by
(age group and income) whereas r may be defined as (location, income).
Assumption 4.3. Local markets g differ with respect to local coverage quality, initial market
shares and aggregate demographics Dgt , e.g. the income or age distribution. Dgt affects an
individual consumer’s utility only through its effect on the market share distribution within her
reference group.
Assumption 4.4. Switching costs are constant across local markets and enter the utility function
in an additively separable way. All switching costs are paid when a consumer quits a service.
Data requirements The identification strategy proposed in the remainder of this section requires
that the following data is observed or can be estimated non-parametrically from the observed
data:
• sdjgt ∀d, j, g, t: market shares for each demographic group d, each operator j, local market
g and time period t.
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• srd jgt ∀d, j, t: the reference-group market shares for each d, j, g, t. The reference group is
characterized by r ∈ Rs .
• Xgjt : operator-quality characteristics that differ across geographic regions g and each t, j.
• Zdgjt : instruments for endogenous product characteristics, such as price, and endogenous
network size.
• cdgjt : A vector of average churn rates, i.e. the share of people discontinuing an operator
service subscription in period t.
In the following, I illustrate the identification arguments and the estimation strategy for the
myopic model in more detail. Again, by replacing the static mean utilities with ex-ante value
function terms, the main results can be extended to the fully dynamic model.
Step 1a: Back out type-specific mean utilities Define the (static) mean utilities δdjgt = wdjgt .
The group-specific market shares in a model with switching costs can be written as:
sdgjt = P r(i, j|di , g, Xt , ait−1 = j) · sdgjt−1 +
X
= P r(i, j|δdi jgt , g, ait−1 = j) · sdgjt−1 +
X
P r(i, j|di , Xt , g, ait−1 = j 0 ) · sdgj 0 t−1
j 0 6=j
P r(i, j|δdi jgt , g, ait−1 = j 0 ) · sdgj 0 t−1
j 0 6=j
The conditional choice probabilities are a function only of the static mean utilities δd and the
switching cost parameter ψ d . Note that the mean utilities of other groups δ−d affect group d
only through the network effect:
exp(δdjgt )
∀i, j, t
exp(δ
dj 0 gt − ψ) + exp(δdjgt )
j 0 6=j
P r(i, j|di , δdgt , ait−1=j ) = P
exp(δdjgt − ψ)
∀i, j, g, t
j 0 6=j̄ exp(δdgj 0 t − ψ) + exp(δdg j̄t0 )
P r(i, j|di , δdt , g, ait−1=j̄ ) = P
Conditional on knowing the parameters including the switching cost parameter ψ, this logic
yields a system of I × J × G × T in I × J × G × T unknowns, i.e. the vector of static mean
utilities δ where I denotes the number of consumer types. The backed out δdjgt will be a function
only of the current and lagged within-group market shares of all products sdgt and the switching
cost parameters ψ:
δdjgt = f (sd·gt , sd·gt−1 , ψ)
A straightforward extension of the contraction mapping proof in Berry et al. (1995) establishes
the existence of a unique fixed point of the mapping: f (st , st−1 , θ)[δjdt ] = δjdt + log[sjdt ] −
log[Sdjt (sdjt−1 , θ, δdt )] where sjdt denotes observed market shares and S denotes the model’s
predicted market shares. In a dynamic model with forward-looking consumers not all products
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(across firms and time) are substitutes. Therefore, it may not be possible to extend the classical
BLP-proof of a unique fixed point, cf. Gowrisankaran and Rysman (2009).
Step 1b: Back out switching cost parameter and mean utilities simultaneously If the
switching cost parameters are not known, but have to be estimated, one needs additional
information. As shown by Yang (2010) churn rates can be used to identify switching costs. The
operator-group-local market specific churn rate is given by:
cdjgt =
X
P r(i, j 0 |ψ, δdgt , ait−1 = j)
j 0 6=j
cdjgt = 1 − P r(i, j|ψ, δdgt , ait−1 = j)
By straightforward differentiation, one can show that the churn rate predictions are monotone in
the switching cost parameters ψ resulting in a one-to-one mapping between switching costs and
churn rates which can be inverted to back out the ψ-parameters. These churn rate predictions
can be aggregated in several ways depending on how many and what kind of switching cost
parameters, one wants to estimate. For example, the operator-group specific churn rate can be
written as:
cdjt =
X X
cdjt =
X
P r(i, j 0 |ψ, δdt , ait−1 = j) · Mjgdt−1
j 0 6=j
g
1 − P r(i, j|ψ, δdt , ait−1 = j) · Mjgdt−1
g
Mjgdt denotes the mass of consumers with characteristics d among the subscribers to operator
j in local market g in period t − 1 which can be calculated from the survey data directly.
Substituting the structural expressions for the conditional choice probabilities, we can rewrite
churn rates:
cdjt =
X
1−
g
exp(δjdgt )
P
· Mjgdt−1
exp(δjdgt ) + j 0 6=j exp(δj 0 dgt − ψ)
The industry-wide average churn rate in period t can then be expressed as:
ct =
XX
j
cdjt · Mjgdt−1 · sjt−1
d,g
The churn rates can directly be observed from the data. The churn rate equations do not add
any additional unknowns to the system and so allow us to back out the additional parameters of
the ψ-vector. In practice, I use the classical BLP contraction mapping to back out the mean
utilities conditional on (θ, ψ):
(1)
f (st , st−1 , ψ, θ) [δt ] = δt + log (st ) − log (St (st−1 , θ, δt , ψ))
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Conditional on this δ-vector, I can directly calculate the new guess for the ψ-vectors using churn
rate data, e.g. by solving the following system of equations:
(2)
cdjgt − Cdjgt (st−1 , θ, δt , ψ) = ζdjgt
In principle, there are several ways to proceed. In the current specification, I directly form
moment conditions based on ζ and include them into the criterion function. Mathematically it is
much more involved to show that the joint mapping of (1) and (2) has a unique fixed point than
showing this separately for mean utilities and switching cost parameters. It should be possible
to extend the contraction mapping proof in Berry et al. (1995) to establish the existence of a
fixed point. However, uniqueness cannot be proven using their argument.
Step 2: Back out ξ and avoiding the reflection problem Given market shares sdjgt ∀d, j, g, t
and a vector of churn rates, the mean utility vector δ and the unobservable quality characteristics
ξjdgt can be backed out exactly. The model specifies mean utilities to be decomposed as follows:
(3)
δdgjt = Xjt βdi + αsjtrd + ξjdgt
(4)
→ ξjdgt = δdjgt − Xjgt βdi − αsrd jt
(5)
→ νjdgt = ξdjgt − ιξdjgt−1
To see in what form the reflection problem occurs in this model, reconsider the market share
equation and its specific arguments:
sdjgt = f (δdgt , srd jgt , sdgt−1 ) = f (δdgt , sdgt−1 , srd jgt )
with −d = {d0 |d0 ∈ r, d0 6= d}, srd jgt is a function of
srd jgt = f˜(δdgt , δ−dgt , sdjgt−1 , s−djgt−1 , Dgt )
where Dgt denotes aggregate demographic characteristics in local market g, such as age or income
distribution. Identification of the network effect comes from different dynamics across different
local markets. Intuitively, one can think of this identification strategy as observing the same
consumer type d in different local market environments. These local markets differ with respect
to several factors:
1. local coverage quality patterns
2. initial conditions and previous period’s market share distribution
3. distribution of demographic characteristics Dgt
The reflection problem arises in equation 3 , if δdgjt is a function of exactly the same variables as
srd jgt . In this case, the network effect α will only be identified by the specific functional form of
δ. However, if srd jgt depends on factors, that do not directly affect δdgjt , these factors can serve
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as exogenous shifters (exclusion restrictions) that move srd jgt independently of δdjgt . This will
identify α independently of the functional form of δ.
Consider for example, s−djgt−1 = f (Xgt−1 , ξ−dgt−1 , s−djgt−2 , sr−d jgt−1 ) which is not a function
of the same variables as sdjgt . In addition, Dgt is clearly exogenous and varies across local markets
and time. Different Dgt will lead to different weightings of the distinct types within a reference
group. This introduces an additional non-linearity that shifts srd jgt exogenously across local
markets. Therefore, interactions between s−djgt−1 and Dgt can serve as appropriate exclusion
restrictions in the sense that they shift sdjgt across local markets only through the network effect.
Specific components of Dgt could be the share of young/old people or poor/rich people in a local
market [alternatively: any other function of the age or income distribution]. For a construction
of valid moment conditions see the subparagraph in Step 3.
Step 3: Construct GMM criterion function to back out structural parameters By Assumption, there exists a set of valid instruments Z such that the structural parameters can be backed
out using a set of moment conditions which I specify as follows:
1
E[ξjdgt · Zdjgt
|θ0 ] = 0
2
E[νjdgt · Zdjgt
|θ0 ] = 0
3
E[ζjdgt · Zdjgt
|θ0 ] = 0
In my model, Z 1 will contain observable exogenous product characteristics such as proxies for
local network coverage quality and brand-fixed effects on various levels. There may be instruments
(Z 2 ) that are correlated with ξ but not with the innovation in ξ, i.e. ν. Using moment conditions
based on both the levels and innovation terms in ξ will exploit the dynamic structure of the
model and the panel data, cf. Lee (2010), Schiraldi (2011). ζ is the vector of error terms from the
churn rate predictions and may either be interacted simply with type dummies or some market
characteristics Z 3 .
Discussion of instruments In order to back-out the the price coefficients, endogenous prices
pjt could be instrumented using cost side information; e.g. Yang (2010) backs out short-run
variable costs using data on revenue and EBITDA margins. A drawback of cost side data is that
it is only available on the national level, and does not exhibit a lot of variation. Consequently, a
potential concern of using cost side instruments is that they may be valid but weak.
For identifying the network effect, the logic of the proposed exclusion restrictions suggests
to use an interaction of the previous period’s market shares within other demographic groups
and the demographic characteristics of a local market as instruments for the expectation of the
current period market share within group d. For example, specifying D−dgt to be a (normalized)
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vector indicating the mass of types other than group d, one could instrument srd jgt with
ŝrd jgt = s−djgt−1 · D−dgt =
X
sd0 jgt−1 · Dd0 gt
d0 6=d
This variable is clearly correlated with the endogenous network size variable srd jgt . It is
uncorrelated with ξdgjt if the ξ-terms are either uncorrelated across demographic groups or time
periods. However, it is likely that the unobserved quality characteristics are correlated in both
dimensions. So moment conditions like E[ŝrd jgt · ξdjgt ]|θ0 ] = 0 may not be valid. Instead of basing
moment conditions on the levels of ξ one can exploit the dynamic structure of the model and
the panel data by interacting the instruments with the innovation terms in the ξ-process, i.e. ν.
The values of ŝrd jgt are fully determined in t − 1. So by definition they are uncorrelated with
νt . Moment conditions in the form of E[ŝrd jgt · νdjgt ]|θ0 ] = 0, should therefore be valid. These
estimating equations make use of the exogenous variation in demographic distributions, as well
as differences in previous period’s market shares, in particular those of other demographic groups.
The details of the selection of instruments and moment conditions are similar to Lee (2010) and
Schiraldi (2011).
Multiplicity of equilibria A well-known problem with models of social interactions is that
there are may be multiple equilibria. Issues of equilibrium multiplicity are more prevalent when
network effects are large. Under the assumption that there is a continuum of consumer for
each type, Bayer and Timmins (2007) show that the parameters of a sorting model can be
backed out without knowing the equilibrium selection parameters, i.e. without knowing all the
equilibria. In this case, the equilibrium is only a function of the primitives of the model and not
of the endogenous individual choices. The problem of multiple equilibria confounding parameter
estimates is obvious when two-step methods (PML, NPL, ALS, BBL) are used to estimate
dynamic games. Often, separate markets in which different equilibria may be played are pooled
for the first-stage estimation of conditional choice probabilities. The estimated CCPs will yield
only a convex combination of the true CCPs of different equilibria which leads to inconsistent
estimates in the second stage.
To see whether and how equilibrium multiplicity may confound the parameter estimates in my
model, consider the estimation and identification step-by-step: In the first step, I back out a
vector of mean utilities by inverting the market share equation market-by-market, i.e. I do not
pool market shares (which are the CCPs in my demand model) in the inversion step:
sdjgt = f (δdjgt , sdjgt−1 , Θ, σ)
which may depend on σ, the equilibrium selection probability. If the social interaction effect
leads to multiple equilibria, f (·) may be a correspondence with multiple predictions for sjdgt .
E.g. if there are three equilibria, a given industry structure may result in three different market
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share predictions:
sdjgt = f (δdjgt , sdjgt−1 , Θ, σ1 )
0
s0djgt = f (δdjgt
, sdjgt−1 , Θ, σ2 )
00
s00djgt = f (δdjgt
, sdjgt−1 , Θ, σ3 )
So depending on the chosen equilibrium, the δ-vector will differ as well, i.e. each equilibrium is
associated with a unique δ. Consequently, there is a one-to-one mapping between the equilibrium
selection indicator the δ-vector. So if indeed multiple equilibria may exist, I back out only one of
them in the first stage of my estimation routine. I pool the δ-vectors of all markets only in the
second step when I decompose the mean utility vectors in the effect of the different structural
factors such as quality, price or network effects conditional on a particular equilibrium being
played. In this step, multiplicity of equilibria may actually help in identifying the network effect
because it introduces an additional source of variation into the model.
However, for doing counterfactual analysis, the issue persists. A computational intensive, but
feasible solution is to simply compute all equilibria of the demand-game and so get bounds on
measures such as welfare gains or simulated market share distributions.
4.2 Estimation of the myopic model
For estimating the myopic model described above I choose the following specification: d =
(age group, income), both measured in a binary way. Consequently, I allow for four different
consumer types: (younger than 45, below median income), (younger than 45, above median
income), (older than 45, below median income), (older than 45, above median income). A
consumer’s reference group consists of all individuals in her home region, i.e. r = (location).
Other examples on how one could define d and r are displayed in Table 1.
Table 1: Possible specifications for d and r
1
2
3
4
5
6
d
r
(age,income)
(age,ethnicity)
(income, ethnicity)
(age, usage intensity)
(education, usage intensity)
...
local market
local market
local market
local market
(education, local market)
...
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4.3 Estimation routines for a model with forward-looking consumers
4.3.1 Nested fixed point (NFXP) algorithm
Estimating the dynamic model using the nested fixed-point algorithm follows the typical 3-level
estimation routine as developed by Gowrisankaran and Rysman (2009).2
Inner loop The inner loop takes a guess for the parameters θ and a level of mean utilities δ
as given and uses these to solve the dynamic programming problem which results in updated
guesses for the predicted market shares and churn rates. Technically, this step involves finding a
joint fixed point of the following sets of equations:
1. Value functions / Bellman equations (for each consumer type i)
2. Logit inclusive values: ∆
3. AR(1)-regressions for belief evolution of ∆ and w
For solving the value functions, one needs to discretize the state space for (wj , ∆) and take
meaningful starting guesses for the value functions, ∆ and AR(1)-regression coefficients. The
inner loop outputs predictions for market shares and churn rates to the middle loop.
Middle loop The middle loop executes the inversion step as in BLP: It is based on parameter
guesses passed in from the outer loop and model predictions passed in from the inner loop. In
the myopic model this is a contraction mapping which is not guaranteed for the dynamic model.
The middle loop takes market share and churn rate predictions and finds the fixed point of the
inversion equation by updating the mean utilities δ. The updated mean utilities are sent back to
the inner loop. Convergence of the middle loop consequently implies joint convergence of the
inner loop (individual dynamic programming problems) and middle loop (BLP-style inversion
step). After convergence the middle loop outputs values for ξ(θ) and ζ(θ) to the outer loop.
Outer loop The outer loop takes the error terms ξ(θ) and ζ(θ) as functions of the structural
parameters and interacts them with instruments to form moment conditions which are stacked
in the criterion function which is finally minimized over θ.
2
The NFXP algorithm is computationally very demanding. Su and Judd (2012) propose a reformulation of the
estimation problem of structural models as a mathematical programming problem with equality constraints
(MPEC). Conlon (2011) has applied this estimation strategy in a related dynamic demand model. Instead of
solving for the model equilibrium for each parameter guess, the MPEC method just assures that all constraints
imposed by the model are satisfied at the optimal solution. This estimation strategy works particularly well
when the Hessian of the objective function is relatively sparse. As I estimate group-specific coefficients, this
may be the case in my model so that the MPEC reformulation may be much more efficient than the NFXP
routine.
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5 Data Description
For the estimation, I use group-level data from a large-scale survey and operator-level statistics
from the Global Wireless Matrix, an industry report by Merrill Lynch Research. The sample
period is from January 2006 to December 2010.
Survey data The survey is conducted quarterly by comscore, a US market research firm.
It surveys about 30,000 cellphone users throughout the US and is stratified in order to be
representative for the whole US population. It contains detailed information on the operator and
handset choice of individual consumers as well as their demographic characteristics (in categorical
variables). Information on the specific contracts chosen by individuals is limited to the type
of contract (individual post-paid, family plan, prepaid) and the monthly expenditure for the
cellphone bill (in 20-US-$ ranges).
A problem for the estimation is that I do not observe neither price nor usage but just
expenditure data in the survey. Previous papers on the cellphone industry have mostly assumed
individuals to consume identical quantities and taken the average revenue per user as price to be
paid. To mitigate this restrictive assumption, I construct a price index for an average service
bundle, e.g. a 100-minute package on a particular network in quarter t and take this as the
price pjt that enters consumers’ utility function. More specifically, using firm-level data (see
below), I divide the "Average Revenue per User" by the "Average Minutes-of-Use" for each
quarter-operator observation to get the price index pjt . Data on switching behavior comprises
only the duration of a consumer’s current operator subscription and the time elapsed since she
bought her current handset.
Finally, the survey asks for consumers satisfaction with the quality of the provided wireless
service rated on a scale from 1 to 10. In most specifications, operator-year fixed effects control for
differences in the national mean of quality characteristics such as the exclusive availability of the
iPhone on the AT&T network in some years. To control for variation in local coverage quality, I
use the average satisfaction level of all customers of a particular type of an operator within a
local market as proxy for this operator’s network quality in this region. This variable does not
necessarily capture physical signal quality but more likely an aggregate index of perceived service
quality. Kim et al. (2004) have shown that in the Korean market customer satisfaction and call
quality are highly correlated. In using these variables, I cannot rule out biased reporting due to
consumer selection, e.g. in the sense that the more demanding consumers may choose higher
quality operators. To solve this problem, I do not use the absolute level of satisfaction. Instead,
I take the normalized deviation of the average rating within a region by a specific group d from
the national average rating of this group-operator combination. As the fixed-effects capture the
mean quality level anyway, the satisfaction deviation measure should appropriately control for
regional variation in coverage quality.
Unfortunately, the survey is not a panel, but a repeated cross-section. So it will not be possible
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Table 2: Overview of consumer types
d
Age
1
2
3
4
>45
>45
<45
<45
Income
below
above
below
above
median
median
median
median
income
income
income
income
to use the individual-level data directly to analyze dynamic consumer behavior. Therefore, I
construct a panel of demographic group-specific market shares. For data availability reasons,
I focus on four consumer types (see Table 2) and the biggest local markets (see Table 1). In
my estimation, this effectively results in having 18 geographically separated markets consisting
mostly of the urban areas around the largest US cities. As the survey is extremely large and
representative for the US population, I construct group-specific and local market shares as a
simple average over the choices of individuals within a particular demographic group and/or
local market.
Table 3:
dma
ATLANTA
BOSTON
CHICAGO
DALLAS-FT. WORTH
DETROIT
HARTFORD-NEW HAV
HOUSTON
LOS ANGELES
MIAMI-FT. LAUDER
MINNEAPOLIS-ST.
NEW YORK
PHOENIX
SACRAMENTO-STOCK
SALT LAKE CITY
SAN FRANCISCO-OA
SEATTLE-TACOMA
TAMPA-ST. PETERS
WASHINGTON DC
Total
N
19450
22218
31259
25703
17702
8815
16301
41793
12858
16488
63626
17753
11308
8203
20769
17154
20510
14376
386286
Source: /Users/stefan/workspace/cellphone/bld/out/data//survey_full_recoded.dta
The geographical size and distribution of the local markets is illustrated in Figure 1.
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Network effects & dynamic consumer decisions
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Figure 1: Overview of local markets used in the estimation
Global Wireless Matrix The Global Wireless Matrix contains quarterly data on various operational and accounting figures for the major 4 carriers as well as averages for the most important
regional operators. These are not broken down by regional market, but only available on the
national level. Most importantly, I use these data to construct the price indices for each operator
and quarter from "Average Minutes of Use" and "Average Revenue per User" statistics. In
addition, I consider information on the cost side, e.g. EBITDA margins and revenue data as
potential instruments for prices charged by operators.
6 Results
6.1 Myopic logit model
The results for a simple version of the model with myopic consumers are displayed in Table 4.
The estimated model is quite parsimonious and stylized in several dimensions:
• Consumers within a demographic group d are perfectly homogeneous with respect to
observables. Consumers belong to one of the four types in Table 2.
• Quantity (minutes of use) choice is not endogenous, i.e. I estimate a pure discrete-choice
model. Consumers with the same type in the same local market consume the same
quantities.
• The GMM-routine uses the identity matrix as weighting matrix for the different moments.
In spite of these limitation the results are plausible and some estimates contrast to the existing
literature in a striking way. Not surprisingly, price coefficients are all negative. Young people
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Network effects & dynamic consumer decisions
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Table 4: Results for myopic logit model
Quarterly subscription price,
Quarterly subscription price,
Quarterly subscription price,
Quarterly subscription price,
Local coverage quality,
Local coverage quality,
Local coverage quality,
Local coverage quality,
Quality handset portfolio,
Quality handset portfolio,
Quality handset portfolio,
Quality handset portfolio,
Network effect,
Network effect,
Network effect,
Network effect,
Switching cost,
Switching cost,
Switching cost,
Switching cost,
Point Estimates (naive GMM)
Magnitude in US-Dollar
-0.8839
-1.1792
-1.4743
-1.2976
0.5021
0.4604
0.0406
0.3090
-0.0120
0.2169
0.2473
0.3318
1.9443
2.0621
1.6096
0.7369
3.4985
2.6163
2.3613
1.9049
-100.0000
-100.0000
-100.0000
-100.0000
56.8049
39.0418
2.7534
23.8170
-1.3568
18.3907
16.7759
25.5697
219.9650
174.8685
109.1828
56.7901
395.7994
221.8670
160.1673
146.8051
d=1
d=2
d=3
d=4
d=1
d=2
d=3
d=4
d=1
d=2
d=3
d=4
d=1
d=2
d=3
d=4
d=1
d=2
d=3
d=4
are significantly more price-sensitive than older consumers with young consumers below medianincome (d = 3) being most price-sensitive. One reason for this may be that young consumers can
substitute easier to other modern forms of communication such as e-mail or instant messaging via
the Internet. Local coverage quality enters with a positive coefficient for all types. The perceived
quality of an operator’s handset portfolio has a positive coefficient for almost all demographic
groups being the largest for the group (d = 4: young, above median income). For (d = 1:
old, below median income) the handset quality coefficient is basically zero which may not be
surprising given that old and poor consumers may be looking for simple and cheap handsets
whereas young and rich consumers may pay more attention to technically advanced handsets.
Network effects are positive and significant for all consumer types. The estimated coefficients
imply reasonable magnitudes in terms of willingness-to-pay: For an increase in an operator’s
local market share by 20%-points, which is the typical difference in market shares between one
of the two big operators and the smaller ones, most consumers would be willing to pay between
US-$4 and US-$15 per month with older consumers paying more attention to network size than
the young consumers.
Finally, the estimates suggest that switching costs are very heterogeneous across consumer
types. Earlier papers found switching costs estimates between US-$ 150 and US-$ 250 using
models with homogeneous consumers. My switching cost estimates are consistent with this earlier
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Network effects & dynamic consumer decisions
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literature, but reveal a vast amount of heterogeneity. For (d = 1: old,below median income) the
number is substantially larger (US-$ 395). For younger consumers, switching costs are much
lower: They amount only to US-$ 146 for (d = 4: young, above median income) US-$ 160 for
(d = 3: young, below median income).
6.2 Dynamic model with forward-looking consumers
[Estimation results to be added]
6.3 Dynamic model with unobserved heterogeneity
[Estimation results to be added]
6.4 Dynamic model with endogenous quantity choice
[Estimation results to be added]
7 Counterfactual Analysis
[to be added] The estimates for the structural parameters can be used for a series of counterfactual
policy simulations. For example, one could investigate how market shares and industry concentration would evolve if network effects would be eliminated due to perfect network compatibility
enforcements. In addition, together with a model of the supply side, these demand estimates
may be used for performing merger simulations, e.g. on a merger between Sprint and T-Mobile
which has recently been debated.
8 Conclusion
In this paper, I developed a dynamic demand model that allows consumer decisions to be driven
by both state-dependence through switching costs and (direct) network effects. The use of detailed
group-level panel data allows me to identify switching costs and network effects separately from
consumer heterogeneity and unobserved quality attributes. While the identification of consumer
heterogeneity follows from standard arguments based on Berry et al. (1995), switching costs
are identified by matching churn rate predictions to observed churn rates. Identification of the
network effect comes from observing the dynamics of several distinct local markets. Even though
the empirical application was tailored towards the US cellphone industry, my model may be
applied to other industries where reference groups are localized in some dimension and where
there is at least one consumer characteristic that does not affect the consumer’s preferences
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but just her reference group and vice versa. The prime example of such a setting is looking at
geographically separated markets that consist of somewhat heterogeneous consumers.
Results from the estimation of a model with myopic consumers reveal several new insights on
the magnitude of switching costs and network effects in the US cellphone industry. During the
sample period (2006 - 2010) the industry was characterized by the presence of both significant
network effects as well as switching costs. I find that switching costs are very heterogeneous
and generally smaller when network effects and consumer heterogeneity are taken into account.
While earlier papers estimated switching costs to be around US-$ 250, in this paper I find that
switching costs vary from US-$ 140 to US-$ 395. The coefficients on localized network size imply
that on average consumer are willing to pay around US-$ 10 per month to be on one of the larger
networks (with around 30%-35% market share) compared to one of the smaller networks (with
usually around 10-15% market share).
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