Post on 13-Aug-2020
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Loss aversion on the phone1
Christos Genakos2, Costas Roumanias3 and Tommaso Valletti4
First Version: May 2015
This Version: July 2017
Abstract
We use consumer-level panel data to analyze consumer switching between mobile tariff
plans. Consumers receive reminders from a specialist price-comparison website about the
precise amount they could save by switching to alternative plans. We find that being
informed about potential savings has a positive and significant effect on switching.
Controlling for savings, we also find that the effect of incurring overage payments is
significant and seven times larger in magnitude. Paying an amount that exceeds the recurrent
monthly fee weighs more on the switching decision than being informed that one can save
that same amount by switching to a less inclusive plan, implying that avoidance of losses
motivates switching more than the realization of equal-sized gains. We interpret this
asymmetric effect of losses on switching as evidence of loss aversion. We are also able to
weigh how considerations of risk versus loss aversion affect mobile-tariff-plan choices: we
find that consumers’ switching is compatible with loss aversion as implied by prospect
theory, but find scant evidence of risk aversion to support expected utility theory predictions.
Keywords: Loss aversion, consumer switching, tariff plans, risk aversion, mobile telephony
JEL Classification: D03, D12, D81, L96
1 We thank seminar audiences at Bilbao, Bologna, Boston College, Cambridge, Carlo Alberto, Drexler,
ECARES, ESMT, Tel Aviv, Toulouse universities, and CRESSE (2015), CRETE (2016), EARIE (2017), ESEM
(2017), IIOC (2017) conferences for useful comments. We especially thank Stelios Koundouros, founder and
CEO of Billmonitor.com, for sharing the data and his industry experience with us. The opinions expressed in
this paper and all remaining errors are those of the authors alone. 2 Cambridge Judge Business School, AUEB, CEP and CEPR, email: c.genakos@jbs.cam.ac.uk 3 Athens University of Economics and Business, email: roumanias@aueb.gr 4 Imperial College London, University of Rome II, CEPR and CESifo, email: t.valletti@imperial.ac.uk
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1. Introduction
Understanding consumer choice behavior under uncertainty is a central issue across a range
of social sciences. Following Kahneman and Tversky’s (1979) and Tversky and Kahneman’s
(1992) pioneering work, a large literature has shown that individuals evaluate economic
outcomes not only according to an absolute valuation of the outcomes in question, but also
relative to subjective reference points. Loss aversion, one of the pillars of prospect theory,
asserts that losses relative to a reference point are more painful than equal-sized gains are
pleasant. Yet, despite the overwhelming laboratory evidence,5 relatively few field studies
document this phenomenon, and the ones that do involve choices in which risk plays a minor,
even non-existent, role.
In this paper, we present novel evidence that loss aversion plays a pivotal role in explaining
how people select their contracts in the mobile telecommunications industry. We use a new
individual-level panel dataset of approximately 60,000 mobile phone users in the UK
between 2010 and 2012. Consumers in our sample subscribe to monthly plans with a fixed
payment component (the monthly rental) that includes several allowances (for call minutes,
text messages, data usage, etc.). We argue that the monthly rental payment provides a natural
reference point. If a customer exceeds her allowance, she pays extra fees, called overage fees.
Customers who exceed their allowances could save money by switching to a higher, more
inclusive, plan. A customer could also save money by switching to a lower, less inclusive
tariff if her consumption is systematically lower than her allowance. We conjecture that, in
line with loss aversion, paying more than the reference point is a more “painful” experience
and should prompt consumers to switch with higher probability than they would if they could
save the same amount by switching to a lower tariff.6
A unique feature of our data is the way that savings are calculated. In general, people can
make mistakes in predicting their phone usage or have a limited ability to compute the
savings from the many available alternatives, which might generate both biases and inertia. In
our setting, phone users have registered with a specialist mobile-comparison website, and
customers’ potential savings are calculated by an optimizing algorithm devised by a company
5 There is a large body of literature summarizing the main theories of individual decision making in psychology
and economics. Rabin (1998), Camerer et al. (2004), DellaVigna (2009), Barberis (2013), Kőszegi (2014) and
Chetty (2015) provide excellent reviews of the evidence in the field. 6 Kahneman (2003), in his Nobel acceptance speech, similarly remarked: “The familiar observation that out-of-
pocket losses are valued much more than opportunity costs is readily explained, if these outcomes are evaluated
on different limbs of the value function.”
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that is allowed to look into their past bills. Consumers then receive personalized information
on the exact amount they could save by switching to the best contract for them. In other
words, one could argue that, in our sample, consumers know precisely how much they can
save by switching to a lower- or a higher-tariff plan.
Based on this information, we evaluate the within-person changes affecting the likelihood of
switching contracts over time. We show that potential savings are a significant determinant of
switching. More importantly, and in line with our loss-aversion conjecture, we find that,
controlling for savings, switching is seven times more likely if the customer was charged
overage fees. Moreover, we also document that individuals seem to be risk averse in the
domain of gains, and risk seekers in the domain of losses: this differential risk attitude,
resulting in an S-shaped behavior of their value function, is also consistent with prospect
theory.
The case of the mobile phone industry is of particular interest, because mobile phones are
ubiquitous and people spend a considerable amount of money on them.7 Our findings are also
applicable beyond cellular services to many economic settings in which consumers choose
“three-part” tariff contracts that specify fixed fees, allowances, and payments for exceeding
the allowances (e.g., car leases, credit cards, subscription services; see Grubb, 2015). Note
that these environments are, almost by definition, uncertain, because people’s behavior
involves randomness that determines what they ultimately consume and are charged for. This
uncertainty entails an element of risk.
Placing risk aversion vis-à-vis loss aversion is of economic importance, because, in many
real-life environments, the potential of both gain and loss is most likely to co-exist with risk.
In situations of choice under uncertainty, prospect theory first foregrounded the importance
of loss versus gain, whereas expected utility theory typically assumes a uniform attitude
towards risk. Although a large body of literature has focused on assessing the relevant merits
of the two theories (e.g., Rabin, 2000; Fehr and Göette, 2007), to the best of our knowledge,
no one has attempted to account for both with field data. We believe this is important, as we
do not see loss aversion and risk aversion as antagonistic, just as we do not necessarily see
loss aversion and traditional expected utility theory as mutually exclusive. In principle, they
can both help us understand the determinants of choice. Given the appropriate data, testing
7 In the UK, mobile revenues have been stable at over £15bn ($23bn) per year over the past decade. This
corresponds to about £200 ($300) per year per active subscriber (see, Ofcom, 2013) or £230 ($350) per capita
per year.
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whether the predictions from either theory are consistent with the data becomes an empirical
question, as well as the extent to which they can help predict observed behavior. In this study,
we do not assume or impose constraints on our consumers, but rather allow both risk and loss
aversion to affect their choices.
Testing for the influence of both, we find that risk aversion cannot explain consumers’
switching, as traditional expected utility theory would suggest, whereas loss aversion remains
strong and significant under all specifications examined.
1.1 Literature review
Our work is related to a large empirical literature on consumer search and choice behavior.
Five key aspects distinguish our work from earlier studies.
First, the leading mobile-price-comparison site in the UK calculates the savings, and each
consumer receives personalized information via email. Thus, in our environment, customers
should suffer significantly less from “comparison frictions,” as in Kling et al. (2012), who
show that simply making information available does not ensure consumers will use it.8 Most
importantly, consumers’ knowledge of how much they can save in advance means we do not
need to make any assumptions about consumers’ mental representation or calculations of
their contract’s value, whereas Barberis et al. (2016) or Ater and Landsman (2013), for
example, need to infer these ex post. Ater and Landsman (2013), whose paper is closest to
ours, analyze customers’ switching decisions after observing the overcharges on their
previously held plans in a retail bank. They find that customers who incur higher surcharges
have a greater tendency to switch, a finding we also share. However, they calculate potential
savings ex post, and customers themselves conceivably might not have known or could not
have easily calculated the level of savings before their switching decision. Therefore,
customers with overages might react to what they perceive as a savings opportunity, which
customers with usage that falls below their allowance cannot easily detect or calculate. In this
respect, our framework is drastically different. Our customers are explicitly informed about
their potential savings by an expert company with which they have chosen to register and are
therefore fully aware of their potential savings when they make their switching decisions.
8 In addition, since consumers self-register, there is no issue of consumers churning as in Ascarza et al. (2016)
just because they were contacted by their mobile operator and given some advice to switch plans.
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Asymmetries in their reaction cannot be attributed to savings miscalculation or misconstruing
overage as a greater savings opportunity.9
Second, our data allow us to test directly whether consumers exhibit diminishing sensitivity
with respect to savings both in the gains and the losses domain and hence to examine whether
consumers are risk lovers in the loss domain and risk averse in the gains domain, another key
feature of prospect theory. Genesove and Mayer (2001), studying the housing market in
Boston, find that sellers with an expected selling price below the original purchase price set a
higher ask price, on average, than sellers who do not incur losses. Their consumers also seem
to exhibit diminishing sensitivity, but, because of their setup, the authors can test the
curvature in the loss domain only in relation to sellers with profits. Pope and Schweitzer
(2011) show that professional golfers react differently to the same shot when they are under
par compared to when they are over, hence providing evidence of asymmetric reaction to
loss. Moreover, the authors document that athletes are more risk averse below than above par,
which is consistent with prospect theory, but they cannot measure the curvature of athletes’
utility.
Third, we test for loss aversion in an environment in which uncertainty is not fixed. Existing
work typically establishes an asymmetric attitude between gains and losses either when
choices are riskless (the example of the “endowment effect”)10 or in environments in which
uncertainty is excluded as an explanation for observed behavior, because it is held constant
throughout the experiment. For example, Fryer et al. (2012) give evidence of loss aversion by
fixing the mean and variance and exposing subjects to choices between losses and gains in a
field experiment in education. Teachers were shown to have better results when faced with a
compensation program that initially presented them with a bonus that was taken away if
targets were not met (loss) than when facing the same average compensation and same
variance that awarded them a bonus only if targets were met (gain). In Pope and Schweitzer
(2011) there is no readily available measure of the uncertainty of the environment golfers
9 Recently, Engström et al. (2015) show that taxpayers with preliminary deficit balances file for deductions more
than taxpayers with zero or positive preliminary balances, hence also exhibiting an asymmetric behaviour in line
with loss aversion. 10 The “endowment effect” is the observation that experimental subjects, who are randomly endowed with a
commodity, ask for a selling price that substantially exceeds the buying price of subjects who merely have the
possibility to buy the commodity (see, e.g., Kahneman et al., 1990; Knetsch, 1989). List (2003, 2004) questions
the robustness of this effect, demonstrating that experienced dealers are much more willing to exchange an
initial object they are given for another one of similar value. However, Kőszegi and Rabin (2006) argue that
List’s results may be fully consistent with prospect theory, and more recent research tries to explore this
hypothesis further (Ericson and Fuster, 2011; Heffetz and List, 2014).
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over or under par face, so loss aversion cannot be tested alongside risk aversion. Our
environment offers a natural interpretation of loss-gain asymmetry, and, furthermore,
variance can be easily and naturally measured through bill variability to provide an index for
testing risk’s contribution to consumer choice. In other works, authors have taken stances in
favor of one or the other, while arguing that alternative explanations would not be realistic in
the setting they study. For example, Cohen and Einav (2007) estimate risk aversion in
insurance and argue that alternative preference-based explanations are not relevant in their
context, whereas Ater and Landsman (2013) study retail banking and base their approach on
loss aversion, reasoning that risk plays a minor, possibly non-existent, role.
Fourth, we use actual consumer-level information from a large sample of consumers in an
advanced economy,11 and we analyze a context in which switching can ensure rather large
monetary savings.
Fifth, we study telecoms in a mature phase of the industry. We expect customers in our
sample to have considerable experience in searching and selecting among operators’ tariffs,
given that mobile penetration has exceeded 100% of the population since 2004 in the UK,12
and that mobile operators have tried and tested their pricing schemes to optimize profits in a
highly competitive industry.13
In this paper, we concentrate on understanding the determinants of consumer switching.
Although we do examine our consumers’ post-switching behavior, we do not attempt to
evaluate the optimality of consumers’ decisions, and refrain from making welfare claims.14
Therefore, though closely related, our application of behavioral economics to cellular phones
is different from the extant literature on overconfidence and flat-rate bias.15
11 In related work, Jiang (2012) uses survey data from the US, whereas Grubb (2009) and Grubb and Osborne
(2015) use data from a student population only. 12 Hence, we differ, e.g., from Miravete (2002), who considers the early days of the US cellular industry, and
from Jiang (2012), who also uses early data to simulate policies introduced later. 13 Our paper is also related to recent literature that has exploited rich data from cellular companies to analyze a
wide range of issues, such as optimal contracts (Miravete, 2002), consumer inertia (Miravete and Palacios-
Huerta, 2014), as well as competitive dynamics and the impact of regulation (Economides et al., 2008; Seim and
Viard, 2011; Genakos and Valletti, 2011). 14 We have no information on the tariff recommended by the comparison website, and, hence, we cannot
evaluate whether customers followed that advice or chose some other tariff. 15 Using cellular contracts, Lambrecht and Skiera (2006), Lambrecht et al. (2007) and Grubb and Osborne
(2015) discuss how, in the presence of mistakes related primarily to underusage, the consumers’ bias might be
systematic overestimation of demand and could cause a flat-rate bias. Were mistakes due primarily to
overusage, the consumers’ bias might be systematic underestimation of demand, consistent, instead, with naive
quasi-hyperbolic discounting (DellaVigna and Malmendier, 2004).
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The remainder of the paper is organized as follows. Section 2 introduces the UK mobile
communications industry and describes the consumer-switching problem. Section 3
introduces the analytical framework. Data are presented in section 4, as well as the empirical
strategy. Results are discussed in section 5, alongside several robustness checks. Section 6
concludes.
2. The industry and the consumer decision process
2.1 Mobile communications in the UK
Mobile communications in the UK are provided by four licensed operators: Vodafone, O2
(owned by Telefonica), Everything Everywhere,16 and the latest entrant, Three (owned by
Hutchison). They all offer their services nationally. In 2011 (midway through our sample),
there were 82 million mobile subscriptions among a population of 63 million. These
subscribers were split 50:50 between pre-paid (pay-as-you-go) and post-paid (contract)
customers. The latter typically consume and spend more than the former.
A regulator, the Office of Communications (Ofcom) regulates the industry. The regulator
controls licensing (spectrum auctions) and a few technical aspects (e.g., mobile termination
rates and mobile-number portability); otherwise, the industry is deregulated. Operators freely
set prices for consumers. The four operators have entered into private agreements with
Mobile Virtual Network Operators (MVNOs) to allow them use of their infrastructure and re-
branding of services (e.g., Tesco Mobile and Virgin Mobile). These MVNOs typically attract
pre-paid customers and account for less than 10% of the overall subscriber numbers (and less
in terms of revenues).
Post-paid tariff plans are multi-dimensional. They include a monthly rental, a minimum
contract length, voice and data allowances, and various add-ons and may be bundled with a
handset and various services. Pre-paid tariffs have a simpler structure.
As in other industries, there have been concerns about the complexity of the tariffs and the
ability of consumers to make informed choices. Ofcom, however, has never intervened
16 Everything Everywhere was formed after the 2009 merger between Orange and T-Mobile (owned by
Deutsche Telekom).
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directly in any price setting or restricted the types of tariffs that could be offered.17 Instead,
Ofcom has supported the idea that information should let consumers make better choices,
because consumers are more likely to shop around when information is available with which
to calculate savings from switching tariff plans. The regulator has, therefore, awarded
accreditations to websites that allow consumers to compare phone companies to find the
lowest tariffs. In 2009, Billmonitor.com (henceforth BM), the leading mobile phone price-
comparison site in the UK, was the first company to receive such an award for mobile phone
services, and its logo appears on Ofcom’s website.18
Based on Ofcom’s (2013) report, the annual switching between operators (churn rate) varies
between 12% and 14% for the years 2010-2012 that we cover in our sample. No data on
within-operator switching are publicly available, because this information is privately held by
operators. In the BM sample, we observe that some 31% of the customers switch contracts
within-operator at least once annually during the same period. Although the BM sample
consists only of post-paid customers that, on average, consume and spend more, we will
demonstrate that it has a very good geographic spread across the UK and closely matches
mobile operators’ market shares and consumer tariff categories, indicating it is representative
of contract customers rather than pre-paid phone customers. With this caveat in mind,
remember that these customers are consumers who self-register on a price-comparison site
and hence are more price-conscious and likely more prone to switching. Therefore, any
findings concerning behavioral aspects of their choices are likely to be underestimated
compared to the general population.
2.2 The consumer decision process
Upon users’ registration with the website, BM attains access to their online bills. BM
downloads past bills, calculates potential savings for the user, and then informs the consumer
of these potential savings.19 The process is repeated monthly, as shown in Figure 1. In a
17 In the UK, this has instead occurred in the energy and banking sectors. For price controls in the UK energy
sector, see https://www.ofgem.gov.uk/ofgempublications/64003/pricecontrolexplainedmarch13web.pdf. For
price controls in the banking sector, see Booth and Davies (2015). 18 https://www.ofcom.org.uk/phones-telecoms-and-internet/advice-for-consumers/costs-and-billing/price-
comparison. Note that Ofcom emphasizes the independence of these websites. In the BM case, no conflict of
interest exists between the advice they provide and the choice consumers make, because the site neither
sponsors nor accepts advertising from any mobile provider. 19 To calculate savings and suitable contracts, BM builds possible future call, text, and data-usage scenarios for
each customer, based on past usage. Using an advanced billing engine, cost is calculated for different possible
usages for all available market plans. The plan that minimizes the customer’s expected cost is chosen,
controlling for the variance of bills. The cost for the chosen plan is then contrasted with the cost under the
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typical month t, the bill is obtained on day s of the month. BM logs on to the user’s mobile
operator account and updates the user’s bill history. It uses the updated history to calculate
potential savings, which it then emails and texts to the user. Thus, on day s, the consumer
receives her bill, followed by an email and a text from BM with potential savings based on
her usage history and the current market contract availability. BM also recommends a new
plan to the customer. The consumer decides whether to act on the information (switch = 1,
don’t switch = 0), with no obligation to choose the recommended plan. The decision is
reflected in next month’s (t + 1) bill. On day s of month t + 1, the consumer receives her new
bill. Then, the savings for month t + 1 are calculated and communicated to the consumer,
who then decides whether to stay with her current plan, and so on. Thus, the switch decision,
eventually observed at time t + 1, is based upon usage and savings information collected and
sent to the user at t.
[Figure 1]
BM allows registration only to residential customers with monthly contracts, who are
typically the high spenders with more complex tariffs. Two features are immediately relevant
for our purposes. First, despite their complexity, all tariffs are advertised as a monthly
payment, with various allowances. The monthly payment becomes a relevant reference point
for the consumer. We call this anticipated and recurrent monthly payment R, though the
customer may end up paying more than this amount if she exceeds her allowances or uses
add-ons not included in the package. In this case, the actual bill, which we denote by B, is
greater than R. Second, BM calculates the cost of alternative contracts and, given the
expected consumer behavior, picks the cheapest contract for the particular consumer and
informs her about it. If C is the cost of the cheapest contract, as calculated by BM, the
message that BM sends the user should be informative in at least two respects. First, the
customer is directly told the total value of the savings she can make – that is, savings = B –
C. Second, a customer with positive savings will be prompted to see that fees for extras not
included in the monthly bundle have been charged and if she has exceeded the allowances.
Exceeding one’s allowance is called overage in the cellular industry and happens when B >
R.
consumer’s current plan to obtain savings. All savings recommendations are made with respect to the users’
stated preferences at the time they register (e.g., operator, contract length, handset). To protect the intellectual
property of BM, the full details cannot be disclosed.
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In Appendix A, we present snapshots of some key moments of the customer experience with
BM.
3. Conceptual framework
To examine the determinants of switching contracts under a simple model of consumer
choice, consider a customer whose switching cost is given by:
𝑐𝑜𝑠𝑡 (𝑠𝑤𝑖𝑡𝑐ℎ𝑖𝑛𝑔)𝑖 = 𝑋𝑖𝑏 + 𝑐𝑖, (1)
where 𝑋 is a vector of personal characteristics, 𝑏 is a vector capturing the marginal effects of
X on the switching cost of customer i, and 𝑐𝑖 is a randomly distributed disturbance with
cumulative distribution function 𝛷(𝑐𝑖). When a customer is informed she can save an amount
𝑠𝑎𝑣𝑖𝑛𝑔𝑠𝑖, she will switch if and only if:
𝑋𝑖𝑏 + 𝑐𝑖 ≤ 𝑈(𝑠𝑤𝑖𝑡𝑐ℎ𝑖𝑛𝑔 |𝑠𝑎𝑣𝑖𝑛𝑔𝑠𝑖), (2)
where U(∙) denotes the utility of the consumer.20 Hence, the probability that a customer
switches will be:
Prob(𝑐𝑖 ≤ 𝑈(𝑠𝑤𝑖𝑡𝑐ℎ𝑖𝑛𝑔 |𝑠𝑎𝑣𝑖𝑛𝑔𝑠𝑖) − 𝑋𝑖𝑏) = 𝛷[−𝑋𝑖𝑏 + 𝑈(𝑠𝑤𝑖𝑡𝑐ℎ𝑖𝑛𝑔 |𝑠𝑎𝑣𝑖𝑛𝑔𝑠𝑖)].
Under prospect theory, the utility from a given level of savings is asymmetric, depending on
whether the savings are experienced as a gain or as avoidance of a loss. Consumers who
experience overage will see savings as an opportunity to avoid the loss from exceeding their
tariffs. Consumers who do not exceed their allowances, will see savings as an opportunity to
gain the said amount. We begin with the following linear utility model for the two groups:
𝑈(𝑠𝑤𝑖𝑡𝑐ℎ𝑖𝑛𝑔|𝑠𝑎𝑣𝑖𝑛𝑔𝑠) = {𝑎𝑢 + 𝑑 ∙ 𝑠𝑎𝑣𝑖𝑛𝑔𝑠, if overage ≤ 0𝑎𝑜 + 𝑑 ∙ 𝑠𝑎𝑣𝑖𝑛𝑔𝑠, if overage > 0,
(3a)
with 𝑎𝑢 ≤ 𝑎𝑂.
We describe our utility function with the help of Figure 2. Note, first, that because 𝑎𝑢 ≤ 𝑎𝑂,
the same amount of savings seen as gains (under the tariff allowance) yields a lower level of
utility than it yields when seen as loss avoidance (over the tariff allowance, or overage) in
20 For the moment, do not restrict U(∙) to comply to any theoretical specification and allow it to be either
classical von Neumann-Morgenstern utility or a prospect theory utility function. Depending on the form U(∙)
takes, we derive and test different empirical specifications to assess the power of the two theories.
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line with Kahneman and Tversky (1979). In our utility specification, the asymmetric
coefficient for loss aversion enters the utility additively rather than multiplicatively. In
Kahneman and Tversky (1979) and the literature that ensued, the loss-gains asymmetry is
measured by a parameter that typically is seen as a coefficient of gains/losses. Thus, in our
framework, it would enter as a different coefficient for savings between the two groups,
restricting the intercept to be zero (Figure 2a).21 Instead of this multiplicative specification,
we opted to capture loss aversion empirically by the difference between the intercepts (𝑎𝑢 −
𝑎𝑂), as shown in Figure 2b. This approach allows for a clearer identification of loss aversion
through shifts in the intercept and has been used empirically by other authors to capture loss
aversion with field data (e.g., Pope and Schweitzer, 2011).
We also estimate a more general nonlinear model that allows us to test for the consumers’
risk attitude:
𝑈(𝑠𝑤𝑖𝑡𝑐ℎ𝑖𝑛𝑔|𝑠𝑎𝑣𝑖𝑛𝑔𝑠) = {𝑎𝑢 + 𝑓(𝑠𝑎𝑣𝑖𝑛𝑔𝑠), if overage ≤ 0
𝑎𝑜 + 𝑓(𝑠𝑎𝑣𝑖𝑛𝑔𝑠), if overage > 0. (3b)
Using this more general model also allows for diminishing sensitivity both in gains and
losses. Diminishing sensitivity was captured by the convexity/concavity of the utility function
in Kahneman and Tversky’s (1979) utility presented in Figure 2d, which in our case
corresponds to Figure 2e, because loss aversion is again captured by the intercept rather than
the difference between the coefficients of 𝑓(𝑠𝑎𝑣𝑖𝑛𝑔𝑠) between gains and losses. Equation
(3b), which corresponds to Figure 2f, a simple reflection of Figure 2e along the horizontal
axis to express the fact that positive savings can express gains or losses for the two groups,
captures the second-order effects, namely, the risk attitude between groups. If 𝑓(𝑠𝑎𝑣𝑖𝑛𝑔𝑠) is
concave, consumers would exhibit risk aversion in gains and risk-loving attitude in losses,
confirming Kahneman and Tversky’s (1979) prediction of differential risk attitudes between
gains and losses.
It follows from the above that the probability of switching is given by:
21 Note that in the traditional prospect theory framework, utility is written in terms of gains/losses and would be:
𝑈 = {𝑎𝑢 + 𝑑 ∙ 𝑔𝑎𝑖𝑛𝑠−𝑎𝑜 − 𝑑 ∙ 𝑙𝑜𝑠𝑠𝑒𝑠.
This specification would imply that the same level of savings would yield utility 𝑎𝑢 + 𝑑 ∙ 𝑠𝑎𝑣𝑖𝑛𝑔𝑠 when under
the tariff allowance, and 𝑎𝑂 + 𝑑 ∙ 𝑠𝑎𝑣𝑖𝑛𝑔𝑠 when experienced as loss avoidance (overage). The standard
prospect theory utility is depicted in Figure 2b. In our framework, we have positive savings both with and
without overage, which explains why the relevant figure for our case is 2c, a reflection of Figure 2b.
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𝑃𝑟𝑜𝑏(𝑠𝑤𝑖𝑡𝑐ℎ𝑖𝑛𝑔|𝑠𝑎𝑣𝑖𝑛𝑔𝑠) = {𝛷[𝑎𝑢 + 𝑓(𝑠𝑎𝑣𝑖𝑛𝑔𝑠) − 𝑋𝑖𝑏], if overage ≤ 0
𝛷[𝑎𝑜 + 𝑓(𝑠𝑎𝑣𝑖𝑛𝑔𝑠) − 𝑋𝑖𝑏], if overage > 0. (4)
Estimating equation (4) under mild functional assumptions on 𝑓(∙) is straightforward.
[Figure 2]
4. Data and empirical framework
For our analysis, we use information obtained from BM with more than 245,000 observations
that contain monthly information on 59,772 customers from July 2010 until September
2012.22 For each customer-month, we have information on the current tariff plan (voice, text,
data allowance, and consumption, plus the tariff cost), the total bill paid, and the calculated
savings.23
Given that the data come from a price-comparison website on which consumers freely
register, examining the representativeness of our sample is important (see Appendix B for
details). 24 We compare observable characteristics of the BM sample with available
information on UK mobile users. As noted earlier, BM allows only monthly paying
customers to register, so we do not have information on pay-as-you-go mobile customers.
First, looking at the geographic dispersion, the distribution of our customers closely matches
that of the UK population in general (Appendix Figure B1).
Second, the operators’ market shares also match quite accurately. The only exceptions are
Everything Everywhere, which is slightly overrepresented in our sample, and Three (the
latest entrant), where we have a smaller market share in our data compared to data available
from the regulator (Appendix Figure B3).
Third, in terms of average revenue per user (ARPU), we have overall higher revenues, which,
of course, can be explained by the fact that we have only post-paid customers. Otherwise, the
ranking of the operators is roughly equivalent (Appendix Figure B5).
22 The panel is unbalanced. We observe a consumer for 5.4 months, on average, whereas the median consumer’s
life is 4 months. We explore this further in our robustness section. 23 We do not have information on the suggested tariff plan, which is, however, observed by the user. 24 All contracts are single-customer contracts, and we do not observe business contracts, that is, a single entity
owning multiple phone contracts.
13
Fourth, we have a good representation of customers in different tariff plans. We can compare
our sample with the aggregate information available from Ofcom on the percentage of
customers in each segment. The only category that is underrepresented in our sample is the
lowest tariff plan, which is, perhaps, reasonable given that we have reason to believe that
customers who register with BM are those on larger tariff plans, because they can obtain
bigger savings (Appendix Figure B6).
Finally, according to Ofcom information, customers in our data send 50 more text messages25
and talk slightly more26 than the average consumer, which also explains the higher ARPU.
Overall, our sample seems to have a very good geographic coverage of the UK and is in line
with the aggregate market picture of operators and tariffs. The customers in our data seem to
be heavier users, but the overall picture is representative of the post-paid (contract) segment
in the UK.27
4.1 Sample summary statistics
In this section, we highlight some of the most interesting aspects of consumers’ behavior in
our sample, related to savings, overage, and switching.
Savings
A unique aspect of our data is the savings information calculated by BM. A customer can
save money (positive savings) by switching to either a lower or a higher tariff plan,
depending on her consumption. However, a customer might also have negative savings: that
is, the customer would pay more under the best alternative contract than under her current
contract: no better deal is available. Figure 3 plots the distribution of monthly savings. The
majority of customers have positive monthly savings (73%), with the average being £14 and
the median being £11.
[Figure 3]
25 Based on Ofcom (2013), the average number of SMS per month was 201, whereas in the BM dataset,
customers sent 251. 26 Based on Ofcom (2013), the average minutes per month were 207, whereas they were 235 in the BM dataset. 27 We do not have information concerning the age or mobile experience of customers. When we control for the
number of months that we observe each customer in our data, a proxy for contract tenure, the coefficient is not
significant, indicating that, at least within our sample, “experience” does not make any difference for savings.
14
When conditioning savings on some observable characteristics, we find that female
customers have no different savings than men. Likewise, customers throughout the various
UK geographic regions have similar levels of potential savings, reflecting the fact that all
operators are present nationwide (Appendix Figure B2). Additionally, customers across all
operators can save, with some small significant differences among them (Appendix Figure
B4).
An interesting phenomenon is the fact that savings increase significantly as one moves to
higher tariff plans, ranked in different brackets by monthly rentals, following the definition of
Ofcom (Appendix Figure B7).
Overage
Overage is very common: 64% of the customer-months in the BM sample experienced it. If
one looks at the actual difference between the bill (B) and the recurrent tariff cost (R), then
the average amount of overage is £15, with the median being £7. These figures are large
when compared to the average monthly bill, which is £25 in our sample. Overage is common
across genders, different UK regions, and mobile operators. Also interesting is that overage
does not exhibit any particular relationship with different tariff plans, and even customers
with negative savings experience it (55% of observations with negative savings have
overage). Overage is very common, not only because it is caused by consuming over and
above one’s current tariff allowance, but also because mobile operators charge their
customers extra for all sorts of other calls and services, such as helplines, premium numbers,
and so on.
Switching
For data-availability reasons, we examine switching only across different tariff plans offered
by the same operator. Within-operator switching is important for two reasons. First,
switching within operator is relatively easier than switching across operators. Customers can
change tariffs with the same provider without paying penalties if they switch prior to the
expiry of the contract. Thus, we can be less worried about contractual clauses we do not
observe. Second, within-operator switching is an important source of switching in the mobile
industry – as reported earlier, in our data, 31% of customers switch within operator annually.
Hence, this setting is ideal for unraveling frequent consumer choices, though the limitation is
that we cannot say much about industry-wide competitive effects.
15
The average in-sample probability of switching is 0.080 per month, with women switching
more often than men (0.083 vs 0.077, p-value = 0.0002). Switching is evenly distributed
geographically across the UK as well as across months within a year.
Looking at the savings distribution (Figure 4), switchers (before switching) have higher
savings than non-switchers (£9.3 vs £7.3, p-value = 0.000), and their distribution also has a
fatter right tail. So savings seem to be one of the factors triggering the decision to switch.
[Figure 4]
Finally, consumers who had overage on their last bill are also more likely to switch (0.083 vs.
0.075, p-value = 0.000), indicating that overage might also play a role in switching behavior.
Note that conditional on switching, roughly 59% of consumers switch to a lower tariff plan,
whereas the remaining switch to a higher tariff plan. Table 1 reports some key sample
summary statistics.28
[Table 1]
4.2 Empirical framework
To analyze consumer switching behavior, we estimate (4), using the following econometric
framework:
𝑝𝑟 (𝑠𝑤𝑖𝑡𝑐ℎ𝑖𝑛𝑔)𝑖𝑡 = 𝛽0 + 𝛽1 ∙ 1(𝑜𝑣𝑒𝑟𝑎𝑔𝑒)𝑖(𝑡−1) + 𝑓(𝑠𝑎𝑣𝑖𝑛𝑔𝑠𝑖(𝑡−1), 𝛽2 ) + 𝑑𝑖 + 𝑑𝑡 + 𝜀𝑖𝑡. (5)
The switching probability for individual i in month t depends on two critical pieces of
information retrieved at time t – 1 from BM: overage is a binary variable indicating whether
the total bill was higher than the tariff reference cost in a given month (overage = 1(B, R),
where 1(∙) is an indicator function taking the value of 1 if B > R, and zero otherwise); savings
are the monthly savings calculated by BM and communicated to the customer and 𝑓(∙) is a
flexible functional form that we assume to be linear in the vector of parameters 𝛽2. We first
estimate 𝑓(∙) as a linear function of savings in line with model (3a), and then we experiment
with non-linear specifications (quadratic and semi-parametric) along the lines of model (3b)
to capture consumers’ diminishing sensitivity both in gains and losses. Notice that we correct
28 Due to the use of lagged values in our estimation framework, we lose the first observation of each consumer,
as well as a number of consumers who register for only one month.
16
for unobserved heterogeneity by controlling for fixed effects: 𝑑𝑖 captures customer fixed
effects, whereas 𝑑𝑡 represents time (joint month-year) fixed effects. Thus, we control for
unobserved differences across customers and unobserved time trends and shocks. Finally, 𝜀𝑖𝑡
is the error term that captures all unobserved determinants of the switching behavior.
We estimate (5) using mainly a linear probability specification and calculate the standard
errors based on a generalized White-like formula, allowing for individual-level clustered
heteroskedasticity and autocorrelation (Bertrand et al., 2004). We also estimate a simple and
a conditional (fixed effects, FE) logit model. Although such a model is better suited to the
binary dependent variable, it is not ideal for our purposes, because the more appropriate FE
logit model can be estimated only on a subsample of individuals with variation in the
switching variable, that is, those who switch at least once during the period in which we
observe them. This sample is non representative and would overestimate the true marginal
effect of the independent variables. We provide these results to show the qualitative
robustness of our results.
In addition, we also use a proportional hazard model (PHM) for the duration between the
time a consumer registers with BM and the time of tariff switching. We estimate (5) utilizing
a semiparametric estimation procedure that allows for time-varying independent variables
(Cox, 1972). According to the Cox PHM, the hazard function is decomposed into two
multiplicative components: ℎ𝑖(𝑡, 𝑋𝑖) = ℎ0(𝑡)×𝜆𝑖 , where 𝜆𝑖 ≡ exp (𝛽′𝑋𝑖) . The ℎ0(𝑡) is the
baseline hazard function that models the dynamics of the probability of switching (hazard
rate) over time; 𝑋𝑖 is a vector of individual characteristics, and β is a vector of regression
coefficients that includes the intercept; 𝜆𝑖 scales the baseline hazard proportionally to reflect
the effect of the covariates based on the underlying heterogeneity of consumers. The main
advantage of the PHM is that it accounts for censoring29 and is flexible enough to allow for
both time-invariant (e.g., mobile operator) and time-varying control variables (e.g., savings).
5. Results
The main regression results are reported in Tables 2 and 3. Starting with Table 2, when
considered individually, both overage and savings are important in determining a switching
29 Both right censoring since our sample stops at September 2012 and left censoring since consumers join BM at
different points in time.
17
decision (columns 1 and 3, respectively). This result is robust to controlling for time and
individual fixed effects (columns 2 and 4, respectively), and the coefficients increase,
indicating that unobserved individual or common factors are biasing the initial estimates
downward.
Column 5 reports the results of the full specification when both overage and savings are
included in the regression. Although we control for savings, overage still has a large and
statistically significant coefficient. Interestingly, both variables retain their previously
estimated magnitudes, indicating the processes of savings and overage are orthogonal to each
other. More importantly, the economic impact of overage is stronger than that of savings. A
£7.4 monthly savings, which corresponds to the average savings (see Table 1), increases the
expected probability of switching by only 0.17%, whereas if a customer’s monthly bill is
higher than her tariff, the probability of switching increases more than sevenfold, to 1.25%.
Results are qualitatively unchanged when we use a logit model given the binary nature of the
dependent variable. Column 6 reports the estimated coefficients, and column 7 reports the
odds ratios. Both estimated coefficients are positive and significant, but a £1 increase in
savings increases the odds of switching by 0.6%, whereas overage increases the odds by
7.4%.30
Finally, the last two columns present the estimated coefficient of the switching hazard model.
Again, we find that both overage and savings significantly increase the probability of
switching (column 8), where an additional £1 of savings increases the hazard of switching by
0.3%, whereas overage increases the hazard of switching by almost 9% (column 9).
Notice that BM sends customers information about savings, expressed in both monthly (e.g.,
£10) and yearly format (e.g., £120).31 In fact, BM emphasizes the monthly savings, which is
also what we use in our econometric analysis. These monthly savings are directly comparable
to the overage paid the previous month. If the customer paid more attention to the annual
equivalent, our findings on the role of overage are even more striking.32
30 Results using a conditional (individual fixed effects) logit model are even stronger: a £1 increase in savings
increases the odds of switching by 0.8%, whereas overage increases the odds by 16.9%. If we control for
individual fixed effects, the logit approach takes into consideration only the customers who experience
switching, so it restricts the sample in such a way that it is not comparable with the other regressions. For this
reason, Table 2, column 6 reports the results without individual consumer fixed-effects. 31 See Figure A5 in the Appendix. 32 If savings over time are discounted heterogeneously, and the discount factor is unknown but unrelated to other
customer characteristics, we can think about this as measurement error in savings. We address this concern by
18
Hence, results from the different estimation models lead to interesting insights regarding
customer switching among plans. Our findings suggest that if a consumer is reminded that
her plan is suboptimal, that is, if she could save by switching to another tariff, then the higher
the savings, the more likely the customer is to switch.33 This finding is not particularly
controversial and follows from basic economic reasoning. More intriguing, though, is that
whether a customer has experienced overage payments, over and above savings, also matters
considerably. These customers are also more likely to switch to new tariff plans.34
Our results are, therefore, potentially supportive of loss aversion or, more generally, of
mental accounting theories, which occur when individuals group expenditures into mental
accounts and do not treat money as fungible across categories. In our setting, customers treat
fixed monthly payments and overage payments as separate mental accounts, which are
associated with different levels of utility. Customers construct reference points based on such
monthly fees and distinguish between within-budget savings and overage losses. We find that
customers prefer avoiding losses to obtaining gains, which is indeed the central prediction of
the theory of loss aversion.
[Table 2]
Apart from confirming an asymmetric attitude towards gains and losses, the data also allow
us to examine consumers’ risk attitude. In particular, following model (4), we test whether
consumers exhibit diminishing sensitivity with respect to savings both in the gains and the
losses domain, another key feature of prospect theory.
Table 3 reports the results: column 1 estimates a simple OLS regression to test the effect of
savings and its squared term on switching.35 The coefficient of savings continues to be
positive and significant, whereas the coefficient on savings2 is negative and statistically
re-estimating column 5 of Table 2 using log savings (results not reported here, available on request) and in
section 5.1 by calculating moving averages of savings (see also Table A1 in the Appendix). None of our
findings changes in any fundamental way. 33 Consumers switch to both higher and lower tariffs. Of those switching, approximately 55% switch to a lower
tariff plan, whereas 45% switch to a higher tariff plan. 34 In our setup, savings emails and overage act as a trigger for consumer action. In that spirit, our work is also
related to Card and Dahl (2011), who show that unexpected losses of NFL local teams have a significant effect
on incidents of domestic violence, thus providing evidence of both the existence of reference points
(expectations of winning) and the asymmetric effect of losses on triggering cues for violence. Similarly, Backus
et al. (2017) show that bidders in eBay who spend more time in the lead and lose abruptly are 6% more likely to
exit the auction platform altogether, thus demonstrating the impact of reference points on market participation. 35 We restrict the sample to only positive savings, because of the introduction of the savings squared term
(negative savings squared would otherwise contaminate the data), we lose 47,636 customer-month observations.
19
significant, in line with the theoretical prediction regarding consumers’ diminishing
sensitivity. Column 2 repeats the exercise, controlling for consumer and year-month fixed
effects. Both coefficients remain significant and increase in magnitude. Column 3 introduces
also the effect of overage on switching for the same customer-months. The magnitude of the
coefficient on overage obtained previously in Table 2, column 5, remains unchanged.
Having confirmed that consumers overall exhibit a diminishing sensitivity with respect to
savings, in column 4, we include the interaction of both savings variables with overage to see
whether this behavior is true for consumers in the gain as well as the loss domain. For
consumers in the gain domain (when overage = 0), savings exhibit diminishing sensitivity
with both coefficients being statistically significant. The coefficient on savings2 is such that
the maximum of the function36 for these consumers is at £180; hence, the average savings are
well to the left of this point, implying the utility function is on the increasing part. Similarly,
consumers in the loss domain (when overage = 1) also exhibit diminishing returns on savings
(coef. on savings (×103) = 1.947, coef. on savings2(×106) = -3.190), with the maximum for
these consumers being at £305 (so consumers are also in the increasing part of the utility
curve). Hence, consumers in our sample exhibit a risk-loving attitude in the domain of losses
(Figure 2f). On the contrary, customers with no overage are risk averse, because they switch
more often as variance increases. This finding is in line with the familiar S-shaped value
function from prospect theory (Figure 2d), whereby individuals are risk- averse in the domain
of gains and risk-loving in losses.37
[Table 3]
5.1 Alternative interpretations and robustness
In this section, we test the robustness of our results in relation to alternative interpretations of
our findings and to measurement and econometric modeling issues.
Expected utility and risk aversion. Can expected utility theory explain the consumer
switching decision? Expected utility theory would postulate that the opportunity to realize
savings by switching contracts is weighed against the uncertainty a new contract introduces
compared to the current plan in order to reach a decision on switching.
36 The maximum of the function is achieved at the coefficient on savings over twice the absolute value of the
coefficient on savings2 (e.g., 3.755/(2*10.500)*103 ≈ 180) 37 Note that Table 3, column 3 corresponds to Figure 2f, whereas in Table 3, column 4 we relax the common
curvature assumption.
20
Under expected utility theory, we derive the utility of switching as a function of savings as
follows. Consumers facing a random bill 𝐵, are assumed to have a CARA utility function:
𝑈(𝐵) = −𝑒−𝐴(𝑉−𝐵)
𝐴, where 𝑉 is the value of the contract to the consumer and A is her risk
aversion coefficient. BM suggests a consumer currently under an "old" contract with a bill
that has mean 𝜇𝑂 and variance 𝜎𝛰2 to switch to a "new" contract with mean 𝜇𝑁 and variance
𝜎𝑁2. Then, the consumer’s utility from each contract j, in monetary terms, is given by her
certainty equivalent 𝐶𝐸𝑗 = −𝜇𝑗 −𝐴
2𝜎𝑗2, and her expected change in utility from switching
will be:
𝐶𝐸𝑁 − 𝐶𝐸𝑂 = (𝜇𝑂 − 𝜇𝑁)⏟ 𝑠𝑎𝑣𝑖𝑛𝑔𝑠
+𝐴
2(𝜎𝑂
2 − 𝜎𝑁2) = 𝑠𝑎𝑣𝑖𝑛𝑔𝑠 +
𝐴
2Δ𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒.
Hence, the probability of consumer i switching in month t will be 𝛷[−𝑋𝑖𝑡𝑏 +
𝑠𝑎𝑣𝑖𝑛𝑔𝑠𝑖(𝑡−1) +𝐴
2Δ𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒𝑖(𝑡−1)] , and the linear probability model we estimate under
expected utility is:
𝑝𝑟 (𝑠𝑤𝑖𝑡𝑐ℎ𝑖𝑛𝑔)𝑖𝑡 = 𝛽0 + 𝛽1𝑠𝑎𝑣𝑖𝑛𝑔𝑠𝑖(𝑡−1) + 𝛽2 Δ𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒𝑖(𝑡−1) + 𝑑𝑖 + 𝑑𝑡 + 𝑢𝑖𝑡. (6)
To estimate (6), an estimate of the variance of both the old and the new (suggested) contract
is needed. An estimate of the variance of the current contract can be obtained from past bills.
To obtain an estimate of the variance of the suggested contract, we proceed as described in
Appendix C.
Table 4 presents the results: column 1 estimates a simple OLS regression to test the effect of
ΔVariance on switching. The coefficient of ΔVariance is not statistically significant. Column
2 repeats the exercise, controlling for consumer and year-month fixed effects. ΔVariance is
now positively associated with switching, implying consumers exhibit an aversion to variance
(they tend to change contracts with higher variability more often). Column 3 examines the
effect of savings and ΔVariance on switching for the same customer-months following model
(6). The coefficient on savings is positive and significant, but the coefficient of ΔVariance is
no longer statistically significant. Finally, in column 4, we also re-introduce overage. Note
that the effect of overage cannot be accounted for by the expected utility theory, but it is
predicted by prospect theory. Hence, note that in column 4, only overage and savings have
positive and significant coefficients, whereas ΔVariance continues to be insignificant.
[Table 4]
21
Self-selection due to flat-rate bias. Loss aversion coexists with uncertainty in our
environment. Overage payments can be seen as unexpected payments customers try to avoid.
In such an uncertain environment, risk-averse customers may select over-inclusive plans to
avoid fluctuations in their payments, the so-called “flat-rate premium or bias” due to an
insurance motive (Train et al., 1989; Lambrecht and Skiera, 2006; Herweg and Mierendorff,
2013). If the information about overage is related to such fluctuations, these customers then
may also be more likely to switch, all else being equal.
To investigate possible self-selection, we divide the sample into small (0 <savings ≤ 3),
medium (3 < savings ≤ 11), and large savings (11 < savings ≤ 35).38 Customers who fall in
the small-savings bracket are very good at predicting their behavior and do not select large
buffers (otherwise, BM would also find large savings for them). Customers who have large
savings may, instead, choose large buffers because of risk aversion. Yet, as columns 1, 2, and
3 of Table 5 indicate, overage is always significant for all these customers, even though they
may differ in several other ways. Results in column 1 are particularly telling: customers with
very small savings do not react to the information that they have some small potential
savings. Nevertheless, experiencing overage leads them to switch contracts with a higher
probability. 39 Comparing columns 1, 2, and 3, we note that the magnitude of overage
decreases as savings increase. At the same time, the coefficient of savings is not significant
for those who have small potential savings (indicating that these customers are, indeed,
making cost-efficient choices); however, it is positive and very significant for the medium
bracket and positive and significant, but smaller in size, for the large-savings bracket.40
Hence, as savings increase, loss aversion continues to play a significant role, but the
magnitude of its effect is smaller than that of savings.
Sample selection due to truncation. We collected the BM data at the beginning of October of
2012. In general, our data-collection exercise is orthogonal to consumers’ decision to register
and use BM’s services, and, as we discussed earlier, switching decisions over months do not
seem to vary significantly. However, one might question whether the fact that we truncate
38 Cut-off points correspond to the 10th and 90th percentiles of the savings distribution. Results are robust to
alternative cut-off specifications. 39 For customers with small savings, consumption closely matches their chosen plans. Small consumption
shocks (positive or negative) can push them either above or below their allowances, so overage in this case can
be thought of as quasi-randomly allocated across these consumers. Results are very similar if we use a
symmetric savings range of -3 < savings ≤ 3. 40 The coefficient on savings increases in magnitude, compared to the main results in Table 2 for the overall
sample since we now condition on positive savings.
22
consumers’ lives at a particular point in time affects the results in any significant way. To test
this hypothesis, we artificially truncate the data within our sample. Columns 4 and 5 in Table
5 report the results from our baseline specification when we truncate the data in August 2012
and August 2011.41 The results for both overage and savings are statistically significant and
qualitatively unchanged, indicating our timing of sampling had no significant impact on the
results.
Sample selection due to attrition. An alternative sample selection-problem may arise due to
consumers’ endogenous decisions to de-register from BM. For consumers who register,
obtain the necessary information on savings and the best possible tariff, and then de-register,
we cannot verify their subsequent behavior. One may argue that the fact that we do not know
whether or not these consumers switch tariffs, may introduce a sample-selection bias. We
address this concern in two ways. First, we randomly select a given year-month and keep
only consumers (and their observations beforehand) who are alive during that month.
Columns 6 and 7 in Table 5 report the results from our baseline specification when we follow
this procedure and truncate the data at August 2012 and April 2012. 42 Results are
qualitatively unchanged for both overage and savings. Second, in column 8 of Table 5, we re-
estimate our baseline model using information only on the first three months from every
consumer. Three months is the shortest duration that we can impose given our lagged
independent variables and the fixed effects. Note that using only the first three months from
each consumer imposes a very strict hurdle, in that consumers should react immediately when
they receive the necessary information. Column 8 seems to confirm this idea, because the
coefficient on overage is slightly larger than our benchmark estimates in Table 2, column 5,
as is the coefficient on savings. Column 9 repeats the exercise, keeping consumers’ first five
months (which is above the median and slightly below the mean lifetime of consumers in our
data) and provides similar results. Given that BM consumers self-register and hence are
looking for better deals, perhaps the finding that they are ready to act almost immediately is
not surprising.
Controlling for changes in mobile operators’ strategies. Given the dynamic nature of the
telecommunication industry, mobile operators frequently change their tariff specifications
and bundle characteristics. To control for any observed or unobserved (to us) changes in
41 The dates were arbitrarily chosen; results are qualitatively robust to alternative selections of months. 42 These months were randomly chosen within 2012 with the aim to have enough data beforehand for each
customer selected; results are robust to alternative selections of months.
23
mobile operators’ bundles, we re-estimate our baseline model, introducing joint operator ×
time FE. Table 6, column 1, shows that the estimated coefficients are slightly lower (but not
significantly so) and the results remain otherwise unchanged.
Previous lags for overage. Is it just last month’s overage that prompts consumers to switch or
do previous lags also matter in any way? In Table 6, column 2, we re-estimate our baseline
model by replacing (𝑜𝑣𝑒𝑟𝑎𝑔𝑒)𝑖(𝑡−1) with (𝑜𝑣𝑒𝑟𝑎𝑔𝑒)𝑖(𝑡−2) . Its estimated coefficient is
statistically insignificant. The same also holds true in column 3, where we introduce both
lags, whereas the coefficient on last month’s overage retains its value and statistical
significance as in our previous results.
Overage intensity. Next, we look at the magnitude of overage. Specifically, we consider the
actual amount by which a bill is higher than the monthly reference tariff, and we split the
overage observations above and below the median. Table 6, column 4, shows that the higher
the overage, the more likely the consumer is to switch, while still controlling for the
magnitude of savings. This finding seems to indicate that not just overage, but also its
magnitude, play an important role in pushing consumers to switch. The higher the “shock”
associated with overage, the more likely consumers will be to switch to a different tariff.
Contract constraints. Recall that, when consumers register with BM, they are asked to
express their preferences related to the operator they want BM to search, as well as the
features they are interested in (e.g., a special handset). If a consumer does not select anything,
BM looks at the universe of available tariffs. Switching between operators can be more
difficult than switching within an operator, because additional costs may be involved. In
Table 6, column 5, we select consumers who explicitly include their current operator in their
search. As one can see from the number of observations, the vast majority of customers
include their current operator, so savings must be informative. The results clearly do not
change. In column 6, we adopt a more conservative approach and restrict the analysis to those
customers who select only their current operator. In this case, savings must indicate that the
best alternative contract is with their operator and, hence, must be much more informative.
Even with this restriction, the results still hold.
Placebo test: negative savings. As a placebo test, we also examine the behavior of consumers
with negative savings. These customers currently have plans with very good tariffs because
BM cannot find cheaper alternatives. However, even these consumers can experience an
overage (55% of the observations of customers with negative savings have experienced
24
overage), because a total bill is very often the consequence of various extra charges unrelated
to the tariff bundle. But these customers, precisely because their savings are negative, should
not be triggered to take a closer look at their bills, and thus they do not notice overage.
Hence, we would not expect these customers to react either to their savings or to their
overage information. In Table 6, column 7, we find that neither coefficient is statistically
significant.
Differences in reactions. Another possible interpretation of our findings is that consumers
who over-consume behave differently than those who under-consume. In particular, one
could argue that consumers who over-consume and experience overage can respond only by
adjusting their tariff, whereas consumers who under-consume can adjust either their
consumption or their tariff. Hence, probabilistically, consumers with no overage are less
likely to switch. We find this explanation unappealing for two reasons. First, no clear a priori
reason exists why consumers who under-consume can adjust their consumption more easily
than consumers who over-consume. In principle, both can alter their calling behavior when
they receive the relevant information from BM. Second, for those consumers in the small-
savings bracket that we analyzed earlier (Table 5, column 1), the margin to adjust
consumption is minimal, yet overage continues to play a significant role.
Learning. Finally, a variant of the above argument is that consumers learn about their optimal
bundle by starting with a low-tariff plan that they subsequently increase (Miravete and
Palacios-Huerta, 2014; Ater and Landsman, 2017). Thus, the positive coefficient on overage
actually captures the consumer’s learning process and not loss aversion. We also find this
explanation unconvincing in explaining switching. First, we study UK consumers’ behavior
in a mature phase of the telecoms industry. Hence, although we do not have information on
their age, these customers are highly unlikely to be first-time users, unaware of their needs
and consumption patterns. Second, if the learning hypothesis were true, we would expect the
direction of switching to be, on average, upwards, and this increase to be more evident the
lower the tariff category. However, we observe consumers switching more to lower tariffs, on
average (58% vs 42%), and this tendency increases as we move to lower-tariff categories.
[Table 5 and 6]
Next, we consider alternative econometric specifications and also experiment with alternative
measures for some of the key variables. First, one could argue that if measurement error is
25
present in calculating savings, their coefficient would be biased. Similarly, including just last
month’s savings may be a noisier measure of the true potential savings a customer could
achieve. To alleviate these concerns, we recalculate savings for each customer using a
moving average of her last three months, and re-run our baseline results from Table 2. None
of our previous results changes in any fundamental way, whereas the impact of overage
increases slightly (Table A1).
Second, to test the diminishing returns on savings, we also experimented with a semi-
parametric version of our estimation framework. Instead of assuming a concave function for
savings, we split savings into six equidistance brackets (£0-£5, £5-£10, £10-£15, £15-£20,
£20-£25, and above £25) and introduce binary indicators (and their interactions with overage)
into our estimated equation. Table A2 presents the results. Both overall (column 1) and across
the two domains of gains and losses (column 2), the conclusion of diminishing returns
remains qualitatively unchanged.
Third, we also test an alternative measure of ΔVariance by calculating the old and the new
contract’s variance based on a three-month voice-consumption moving average for each
consumer (see Appendix C for details). A consumption moving average will iron out any
spikes in monthly consumption and could also correct measurement errors. Table A3
replicates the analysis in Table 4. Estimated results are very similar to those previously
obtained.
The picture that emerges from this evidence is one in which customers respond, possibly
sequentially, to the information received from BM. If the message says the customer is
already on a plan with a good tariff (negative savings), the customer does not have any
incentives to look deeper into her consumption pattern, and she stops there. If, instead, the
customer receives notice that savings are possible, she is inclined to look much more closely
at her behavior and at the contract. At this point, she learns about overage, on top of savings,
which then initiates the switching patterns we described above. The consumer perceives
overage as a loss, conditional on savings, and, thus, is much more likely to switch contracts.
Our results support prospect theory: we found loss aversion to be significant in determining
consumers’ choice to change plans, but we did not find bill variance to be a determinant of
their choice. Consumers who could reduce losses by a certain amount relative to their salient
point (monthly tariff) changed plans significantly more than consumers who could improve
(gain) by the same amount without having experienced overage. We have established that the
26
asymmetry between losses and gains can explain observed consumer behavior, but that a
uniform attitude towards risk in both losses and gains (an assumption central to expected
utility theory) cannot explain customers’ switching. Consumers’ attitude toward risk was
found to be in line with prospect theory: our consumers exhibit an appetite for risk when they
are in the loss (overage) domain.
5.2 Savings and overage after switching
The main objective of this paper is to understand the causes of switching contracts. Still, we
believe concluding with a preliminary assessment of the effects of switching is important. We
cannot verify whether consumers actually followed BM’s advice and chose the best tariff for
them as calculated by BM. However, we can study the actual tariff choices they made and
how these choices affected their savings and the probability of experiencing overage after
switching. Table 7 reports the results. In columns 1 and 2, we look at the evolution of
savings, whereas in columns 3 and 4, we examine the probability of overage before and after
the switching, separating those who switched to a higher (Post Switch Up) from those who
switched to a lower tariff (Post Switch Down). In columns 1 and 3, we look only at the
sample of consumers who switched, whereas in columns 2 and 4, we also include data for
non-switching consumers that helps improve the efficiency of the estimation.
Results are intriguing. Looking at columns 1 and 3, we can then see that consumers who
switch to a lower tariff reduce their potential savings by about £6.5, which means that, from a
strictly homo economicus perspective, they have chosen a better tariff, without experiencing
any differences in overage. Consumers who switch to a higher tariff, on the other hand,
increase their savings potential by £5.8, but also manage to significantly reduce the
probability of overage, in contrast to consumers who switch down. In other words, consumers
who upgrade seem to trade off43 savings to avoid the psychological pain of experiencing a
loss due to overage, which is yet another way of finding support for loss aversion in our data.
[Table 7]
43 Note that the trade-off between overage and savings is approximately sevenfold, very similar to our main
results in Table 2. Based on Table 7, columns 1 and 3, a consumer who switches up prefers reducing the chance
of overage by 7.5% to saving £5.766 less. This linearly implies she prefers a 64.4% (= mean overage, Table 1)
reduction of overage to £49.51 less savings, which corresponds to about 7 times the average sample savings
(mean savings = 7.44, Table 1).
27
6. Conclusions
We have conducted an assessment of consumer behavior using individual data from UK
mobile operators collected by a price-comparison website. We showed that consumers who
receive reminders about possible savings do respond and switch tariff plans. More
interestingly, we also discussed how consumers employ their monthly fixed payment as a
reference point in their choices. When they spend above this reference point, the resulting
overage payment induces considerable switching. This central finding is very much in line
with the loss aversion model of Kahneman and Tversky (1979) and is robust to several
alternative interpretations and specifications.
We were also able to weigh how both risk- and loss-aversion considerations affect choices in
mobile telephony in a modern economy: this high-stake industry affects the majority of the
population everywhere in the world. We find risk aversion cannot explain consumers’
switching, whereas loss aversion plays an important role.
Our results put the use of price-comparison sites in a new light. Regulators and competition
authorities worldwide oversee price-accreditation schemes for third-party price-comparison
sites covering several industries – in addition to mobile phones – that still exhibit
considerable uncertainty in patterns of consumption over time (e.g., banking, credit cards,
and insurance). The aim of these schemes is to increase consumer confidence about how to
find the best price for the service they wish to purchase, and to increase market transparency
by providing or facilitating expert guidance. Thaler and Sunstein (2008) propose the RECAP
(Record, Evaluate, and Compare Alternative Prices) regulation that would require firms to let
customers share their usage and billing data with third parties, such as BM, which could, in
turn, provide unbiased advice about whether to switch to a competing provider.
The emphasis of these proposals is almost invariably on savings, for example, finding the
most cost-effective tariff given a certain consumer profile. Although this information is
certainly useful for choice, we also show that savings are only a part of the story, and
possibly a minor one. Hence, we introduce a note of caution on expert advisers that is
different from any conflict-of-interest consideration (Inderst and Ottaviani, 2012) or from
cases in which nudging may have adverse market equilibrium effects (Duarte and Hastings,
2012; Handel, 2013). We suggest that regulators hoping to rely on price-comparison engines
to discipline market prices using shared data should first investigate what giving good advice
means in a context with loss aversion. Consumers also switch for behavioral reasons that
28
have little to do with savings, but that still could be consistent with optimal individual
behavior.
In this paper, we have focused our analysis on the positive implications of behavioral
economics, namely, on predicting switching behavior in the presence of loss aversion.
Understanding the effect on social welfare is equally important. In particular, consumer
switching is central to any competitive assessment of an industry. Developing a non-
paternalistic method of welfare analysis in behavioral models is, however, a challenge.
Following Chetty (2015), one possibility is to use revealed preferences in an environment in
which agents are known to maximize their “experienced” utility (their actual well-being as a
function of choices), which may differ from their “decision” utility (the objective to be
maximized when making a choice).44 The approach used in our setting is that the amount of
savings is calculated mechanically by an optimizing algorithm; thus, most cognitive biases
should vanish or at least be kept to a minimum. The fact that we still find a considerable role
of overage implies loss aversion is of the utmost importance directly in the experienced utility
and must be accounted for in any welfare assessment.
44 An alternative approach is to follow structural modeling that specifies and estimates the structural parameters
of a behavioral model. Grubb and Osborne (2015) follow this line to discuss the recent “nudge” adopted by the
FCC (the US telecom regulator) of requiring bill-shock alerts for mobile phones (text messages warning when
allowances of minutes, texts, or data are reached). They show that providing bill-shock alerts to compensate for
consumer inattention can reduce consumer and total welfare because, most likely, firms will adjust their pricing
schedule by reducing overage fees and increasing fixed fees.
29
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33
Appendix A – The consumer experience with Billmonitor.com
In this annex, we present in various screenshots the consumer experience of registering and
using BM’s services. BM was created to provide impartial information and to help monthly
paid mobile phone customers to choose the contract that is best for them. BM was first
accredited by Ofcom in 2009 and still receives accreditation (Figure A1). To safeguard its
impartiality, BM neither receives advertising from any mobile operator nor allows for any
kind of promotions on its website. It simply collects all available contract information from
all UK mobile operators and tries to match each consumer’s consumption pattern with the
best available tariff.
FIGURE A1: BM’s OFCOM RE-ACCREDITATION
When a user visits the BM webpage, she is prompted to register in order to have her bills
analyzed and to determine “exactly the right mobile contract” for her (Figure A2).
FIGURE A2: BM’s HOME PAGE
34
If she chooses to have the BM engine analyze her bills, she is led to a page asking for her
details (mobile operator, phone number, username and password, and email), as shown in
Figure A3.
FIGURE A3: BM’s ANALYSIS PAGE
During the analysis of her bill, she is presented with a screen that informs her that BM
searches through all possible contract combinations to find the “right” contract for her
(Figure A4).
FIGURE A4: BM’s CALCULATION SCREEN
35
Upon analysis of her bill, the user receives an email informing her of potential savings. This
email is repeated monthly, the day after her bill is issued, as described in Figure 1 in the main
text. Figure A5 shows an example of such an email.
FIGURE A5: EMAIL SENT TO USERS INFORMING THEM OF POTENTIAL SAVINGS
36
Appendix B – Representativeness of the sample and summary statistics
In this annex, we discuss the representativeness of our sample and also provide some initial
statistics on savings within our sample.
Figure B1 compares the geographic distribution of the population residing in the UK (ONS,
2011 census) with the customers registered with BM. As the figure shows, BM customers are
well spread across the UK and match the actual population spread closely.
FIGURE B1: POPULATION DISTRIBUTION ACROSS UK REGIONS
Notes: The graph above compares the percentage population distribution across regions in the UK and
in the BM data.
Source: The UK population distribution based on the 2011 census, Office for National Statistics. BM
population distribution based on the data provided by BM.
In all these different regions, consumers can realize savings by switching to different tariffs
(Figure B2). Savings are, on average, positive across all regions, with the highest median
savings in the North East (£7.2) and the lowest in Northern Ireland (£4).
Figure B3 compares mobile operators’ market shares in BM data with aggregate market
information from the Bank of America Merrill Lynch (BoAML) dataset for 2012. Aggregate
market shares are well tracked in the BM data, with the exception of Everything Everywhere
(the merged entity of T-Mobile and Orange), which is slightly overrepresented, and Three
(Hutchison), which is slightly underrepresented. These discrepancies can be attributed to the
fact that aggregate market shares also allocate to the licensed operators market shares of
MVNOs (Mobile Virtual Network Operators) that do not have a spectrum license but rent
12
16
7
13
2
7
16
10
6
109
16
5
13
4
10
17
10
6
11
0
2
4
6
8
10
12
14
16
18 BM
UK
37
airtime from the main licensed operators (they accounted for 8% of the total market in 2010-
2012, mostly in the pre-paid segment; see Ofcom, 2013).
FIGURE B2: SAVINGS DISTRIBUTION ACROSS UK REGIONS
Notes: The graph above compares the savings distribution across different UK regions.
Source: Based on savings data provided by BM.
FIGURE B3: MOBILE OPERATORS’ MARKET SHARES
Notes: The graph above compares the mobile operators’ market shares from BoAML and BM data.
Source: Mobile operators market shares for 2012 based on the BoAML and BM datasets.
-20
02
04
0
sa
vin
gs
EA
ST
MID
LA
ND
S
GR
EA
TE
R L
ON
DO
N
NO
RT
H E
AS
T
NO
RT
H W
ES
T
NO
RT
HE
RN
IR
ELA
ND
SC
OT
LA
ND
SO
UT
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AS
T
SO
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H W
ES
T
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LE
S
WE
ST
MID
LA
ND
S
23
30
43
4
25
30
38
7
0
5
10
15
20
25
30
35
40
45
50
Vodafone O2 EverythingEverywhere
3 (Hutchison)
BM
BoAML
38
Customers across all operators can save, as Figure B4 demonstrates, with small but
significant differences among them (highest median savings for Vodafone, £7.4, and lowest
for Three, £4.1).
FIGURE B4: SAVINGS DISTRIBUTION ACROSS MOBILE OPERATORS
Notes: The graph above compares the savings distribution across mobile operators.
Source: Based on savings data provided by BM.
Figure B5 compares the average revenue per user (ARPU) in the BM sample with aggregate
information obtained from the BoAML dataset for 2012. Given that BM has only post-paid
customers, revenues are higher in the BM compared to the BoAML sample across all
operators.
-40
-20
02
04
0
sa
vin
gs
Vodafone O2 Everything Everywhere 3 (Hutchison)
39
FIGURE B5: AVERAGE REVENUE PER USER ACROSS MOBILE OPERATORS
Notes: The graph above compares the mobile operators’ average revenue per user from the
BoAML and the BM data.
Source: Mobile operators’ average revenue per user based on BoAML and BM data.
More interestingly, Figure B6 compares the distributions of consumers belonging to different
tariff plans from the Ofcom45 and the BM data. The two distributions are very similar, with
the lowest tariff (£0-£14.99) being the only exemption.
FIGURE B6: MARKET SHARES BY TARIFF CATEGORY
Notes: The graph above compares the market shares by tariff category from the Ofcom report and BM data.
Source: Market share by tariff category based on the 2012 Ofcom Communications Market Report and BM
data.
45 Figure 5.75 from the 2012 Communications Market Report (p. 349).
34 3533
29
2022
19
23
0
5
10
15
20
25
30
35
40
Vodafone O2 EverythingEverywhere
3 (Hutchison)
BM
BoAML
12
17 1614 14
17
9
29
17
11 11 10
16
7
0
5
10
15
20
25
30
35
£0-£14.99 £15-£19.99 £20-£24.99 £25-£29.99 £30-£34.99 £35-£39.99 £40+
BM
Ofcom
40
Savings can occur across any tariff category in the BM sample (see Figure B7).
Unsurprisingly, more savings are available to those customers choosing larger and more
expensive plans.
Finally, if we compare the actual consumption, customers in the BM dataset send slightly
more SMS (SMS per month: BM 251, Ofcom 201) and talk slightly more (minutes per
month: BM 235, Ofcom 207) than the Ofcom 2012 report indicates, which also explains the
higher ARPU.
Overall, the BM sample has a very good geographic spread across the UK and matches
mobile operators’ market shares and consumer tariff categories closely. Because it consists
only of post-paid customers, these consumers seem to consume and spend more, on average,
compared to the aggregate statistics, but without any particular mobile operator or geographic
bias.
FIGURE B7: SAVING DISTRIBUTION ACROSS TARIFF CATEGORY
Notes: The graph above compares the savings distribution across tariffs.
Source: Based on savings data provided by BM.
-20
02
04
06
0
sa
vin
gs
£0-£14.99
£15-£19.99
£20-£24.99
£25-£29.99
£30-£34.99
£35-£39.99
£40+
41
Appendix C – Obtaining estimates for the variance of existing and suggested contracts
Under the assumption that customer i experiences identically distributed disturbances across
periods, the variance of the old contract, 𝜎𝑂2, is measured as the variance of the last three
bills of a given customer.46
The variance of the new contract, 𝜎𝑁2, cannot be calculated by the consumer and is not
available by BM. All the information a consumer has is the means of her old and new
contracts and the variance of her old contract, 𝜎𝑂2 . She also knows if her current usage
exceeds her current allowance, 𝑡𝑂 , so that she can save by upgrading, which we will call
CASE 1, or if it is below her tariff, in which case she can save by downgrading, CASE 2.
In CASE 1, her future variance might be correlated with her current variance but should in
principle decrease. In CASE 2, on the other hand, current variance might be an indicator of
future variation: however, she will expect her variance to increase after the downgrade. So we
should expect her future variance to be a function of her current variance, 𝜎𝑁2 = 𝑔(𝜎𝑂
2). To
obtain an estimate of the consumer’s estimation of the variance for the suggested contract, we
assume that it is a linear function of the variance of the old contract:
𝜎𝑁2 = (1 + 𝑎)𝜎𝑂
2,
where 𝑎 ≡ max (𝑡𝑂−𝑡𝑁
𝑡𝑂, −1) : when she upgrades (𝑡𝑁 > 𝑡𝑂) , the variance of her contract
should increase. The opposite is expected when she downgrades. We restrict 𝑎 to be greater
than −1 to account for non-negativity of 𝜎𝑁2. Finally, note that whereas 𝑡𝑂 is observed, 𝑡𝑁 is
not. So in order to obtain an estimate of 𝑎, and noting that typically when her consumption
exceeds (resp., falls below) her allowance, she will be suggested a higher (resp., lower)
allowance, we proxy the proposed allowance by her current consumption; that is, 𝑎 ≡
max (𝑡𝑂−𝑐𝑂
𝑡𝑂, −1). When her current consumption 𝑐𝑂 exceeds her tariff 𝑐𝑂 > 𝑡𝑂, she needs to
upgrade and she will expect her variance to drop with a new contract. The opposite is true in
case of a downgrade. We allow different functional forms for the variance of her new
contract, 𝜎𝑁2, in the robustness section.
46 Denote the monthly bill as 𝐵𝑖𝑡 . Then, we calculate the average of the last three months, 𝑀𝐴 =(𝐵𝑖𝑡−3 + 𝐵𝑖𝑡−2 + 𝐵𝑖𝑡−1) 3⁄ , and, hence, the Bill Variance is equal to 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒𝑖𝑡 =[(𝐵𝑖𝑡−3 −𝑀𝐴)
2 + (𝐵𝑖𝑡−2 −𝑀𝐴)2 + (𝐵𝑖𝑡−1 −𝑀𝐴)
2] 3⁄ .
FIGURE 1: CONSUMER'S DECISION PROCESS
FIGURE 2: LOSS AVERSION IN BM's CONTEXT
Jan
1st
t=January
Bil
l tS
avin
gst
Switch decision (SDt )
Bil
l t+1
:SD
t ob
serv
ed
Sav
ings
t+1
Switch decision (SDt+1 )Feb
1st
t+1=February ....
Jan s Feb s
42
FIGURE 3: MONTHLY SAVINGS DISTRIBUTION
Notes: The figure presents information on the monthly savings distribution overlaid with a normal density curve.
Source: Authors’ calculations based on data from Billmonitor.com.
05000
1.0
e+04
1.5
e+04
2.0
e+04
Fre
quency
-50 0 50Monthly savings (in GBP)
43
FIGURE 4: SAVINGS DISTRIBUTION FOR SWITCHERS AND NON-SWITCHERS
0.00
0.01
0.02
0.03S
avi
ngs
dis
trib
utio
n
-50 0 50Monthly savings (in GBP)
SwitchersNon-switchers
Notes: The figure presents information on the monthly savings distribution of consumers who do not switch (non-switchers)and those who switch within operators (switchers) but before switching.Source: Authors’ calculations based on data from Billmonitor.com.
44
VariableMean
Standard
Deviation10
th percentile 50
th percentile 90
th percentile Observations
Pr(switching)it 0.080 0.271 0 0 0 181,886
Overagei (t –1) 0.644 0.479 0 1 1 181,886
Savingsi (t– 1) 7.440 31.939 -7.405 6.547 25.053 181,886
TABLE 1 - SUMMARY STATISTICS
Notes: The table above provides summary statistics on the key variables used in our analysis.
Source: Authors’ calculations based on the Billmonitor.com data.
45
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Estimation method OLS FE OLS FE FE Logit (MLE) Odds ratioProportional
Hazard (MLE)Hazard ratio
Dependent variable pr(switching)it pr(switching)it pr(switching)it pr(switching)it pr(switching)it pr(switching)it pr(switching)it
Overagei (t– 1) 0.008*** 0.013*** 0.013*** 0.071*** 1.074*** 0.083*** 1.087***
(0.001) (0.002) (0.002) (0.019) (0.021) (0.017) (0.019)
Savingsi (t –1) (x 103) 0.185*** 0.240*** 0.235*** 6.239*** 1.006*** 3.408*** 1.003***
(0.039) (0.051) (0.050) (0.711) (0.001) (0.476) (0.000)
Observations 181,886 181,886 181,886 181,886 181,886 181,886 181,886
Clusters 33,242 33,242 33,242 33,242 33,242 33,242 33,242
Year-Month FE no yes no yes yes yes yes
Consumer FE no yes no yes yes no no
TABLE 2 - SWITCHING AND LOSS AVERSION
Notes: The dependent variable is the probability of switching to a different tariff plan within operator for consumer i in month t. Standard errors clustered at the consumer level are reported in parenthesis
below coefficients: *significant at 10%; **significant at 5%; ***significant at 1%.
Source: Authors’ calculations based on the Billmonitor.com data.
46
(1) (2) (3) (4)Estimation method OLS FE FE FE
Dependent variable pr(switching)it pr(switching)it pr(switching)it pr(switching)it
Overagei (t –1) 0.014*** 0.034***
(0.003) (0.004)
Savingsi (t –1) (x 103) 1.261*** 2.296*** 2.267*** 3.763***
(0.092) (0.172) (0.171) (0.274)
Savings2i (t –1) (x 106) -2.050*** -4.160*** -4.110*** -10.500***
(0.644) (1.020) (1.010) (1.380)
Overagei (t –1) × Savingsi (t –1) (x 103) -1.799***
(0.280)
Overagei (t –1) × Savings2i (t –1) (x 106) 7.240***
(1.550)Observations 134,237 134,237 134,237 134,237Clusters 29,438 29,438 29,438 29,438Year-Month FE no yes yes yesConsumer FE no yes yes yes
TABLE 3 - SWITCHING AND RISK ATTITUDE
Notes: The dependent variable is the probability of switching to a different plan within operator for consumer i in month t. Standard errors clustered at the consumer level are reported in parenthesis below coefficients: *significant at 10%; **significant at 5%; ***significant at 1%.Source: Authors’ calculations based on the Billmonitor.com data.
47
(1) (2) (3) (4)Estimation method OLS FE FE FE
Dependent variable pr(switching)it pr(switching)it pr(switching)it pr(switching)it
Overagei (t –1) 0.014***
(0.002)
Savingsi (t –1) (x 103) 0.166*** 0.160***
(0.048) (0.046)
ΔVariancei (t –1) (x 106) 0.006 0.053** -0.051 -0.051
(0.034) (0.020) (0.035) (0.034)Observations 109,692 109,692 109,692 109,692Clusters 21,253 21,253 21,253 21,253Year-Month FE no yes yes yesConsumer FE no yes yes yes
TABLE 4 - SWITCHING AND EXPECTED UTILITY THEORY
Notes: The dependent variable is the probability of switching to a different plan within operator for consumer i in month t. Standard errors clustered at the consumer level are reported in parenthesis below coefficients: *significant at 10%; **significant at 5%; ***significant at 1%.Source: Authors’ calculations based on the Billmonitor.com data.
48
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Estimation method FE FE FE FE FE FE FE FE FE
Dependent variable pr(switching)it pr(switching)it pr(switching)it pr(switching)it pr(switching)it pr(switching)it pr(switching)it pr(switching)it pr(switching)it
Description 0<savings<3 3<savings<11 11<savings<35Truncated in
August 2012
Truncated in
August 2011
Attrition
corrected
August 2012
Attrition
corrected
April 2012
First three
months only
First five
months only
Overagei (t –1) 0.016*** 0.013*** 0.011** 0.013*** 0.011** 0.016*** 0.009*** 0.028*** 0.020***
(0.006) (0.004) (0.004) (0.002) (0.005) (0.003) (0.003) (0.006) (0.004)
Savingsi (t –1) (x 103) 0.401 4.818*** 2.115*** 0.224*** 0.255*** 0.189*** 0.188*** 0.291** 0.268***
(2.855) (0.816) (0.292) (0.048) (0.085) (0.053) (0.045) (0.133) (0.070)
Observations 19,003 49,911 63,961 173,794 41,879 106,073 77,645 57,804 95,887
Within R2
0.007 0.007 0.007 0.012 0.014 0.012 0.014 0.013 0.014
Clusters 8,978 16,449 19,255 32,576 9,826 18,050 13,034 33,120 33,241
Year-Month FE yes yes yes yes yes yes yes yes yes
Consumer FE yes yes yes yes yes yes yes yes yes
TABLE 5 - SWITCHING AND LOSS AVERSION - SAMPLE SELECTION
Notes: The dependent variable is the probability of switching to a different plan within operator for consumer i in month t. Standard errors clustered at the consumer level are reported in parenthesis below coefficients: *significant at 10%; **significant at 5%; ***significant at 1%.
Source: Authors’ calculations based on the Billmonitor.com data.
49
(1) (2) (3) (4) (5) (6) (7)
Estimation method FE FE FE FE FE FE FE
Dependent variable pr(switching)it pr(switching)it pr(switching)it pr(switching)it pr(switching)it pr(switching)it pr(switching)it
DescriptionOperator × Time FE
Previous
overage lag
Previous
overage lag
Small and high
overage
Include current
operator in
savings
Only current
operator in
savings
Consumers with
negative savings
Overagei (t –1) 0.012*** 0.014*** 0.013*** 0.008*** 0.001
(0.002) (0.002) (0.002) (0.003) (0.004)
Savingsi (t –1) (x 103) 0.226*** 0.242*** 0.196*** 0.229*** 0.229*** 0.146*** 0.017
(0.049) (0.052) (0.048) (0.049) (0.049) (0.044) (0.027)
Overagei (t –2) -0.003 -0.003
(0.002) (0.002)
Overagei (t –1) 0.007***
below the median (0.002)
Overagei (t –1) 0.022***
above the median (0.003)
Observations 181,886 141,622 141,622 181,886 179,084 68,191 47,539
Within R2
0.018 0.006 0.006 0.011 0.011 0.012 0.007
Clusters 33,242 26,591 26,591 33,242 32,735 11,291 14,005
Year-Month FE yes yes yes yes yes yes yes
Consumer FE yes yes yes yes yes yes yes
TABLE 6 - SWITCHING AND LOSS AVERSION - ROBUSTNESS
Notes: The dependent variable is the probability of switching to a different plan within operator for consumer i in month t. Standard errors clustered at the consumer level are
reported in parenthesis below coefficients: *significant at 10%; **significant at 5%; ***significant at 1%.
Source: Authors’ calculations based on the Billmonitor.com data.
50
(1) (2) (3) (4)Estimation method FE FE FE FE
Dependent variable savingsit savingsit pr(overage)it pr(overage)it
Post Switch Downit -6.520*** -6.731*** 0.007 0.010
dummy=1 after switching to a lower tariff (0.352) (0.360) (0.008) (0.008)Post Switch Upit 5.766*** 5.427*** -0.075*** -0.070***
dummy=1 after switching to a higher tariff (0.675) (0.686) (0.009) (0.009)Observations 69,808 167,366 69,808 167,366Clusters 10,857 33,242 10,857 33,242Year-Month FE yes yes yes yesConsumer FE yes yes yes yes
TABLE 7 - SAVINGS AND OVERAGE AFTER SWITCHING
Notes: The dependent variable in columns 1 and 2 are the savings for consumer i in month t, whereas in columns 3 and 4 is the probability of experiencing overage. Standard errors clustered at the consumer level are reported in parenthesis below coefficients: *significant at 10%; **significant at 5%; ***significant at 1%.Source: Authors’ calculations based on the Billmonitor.com data.
51
(1) (2) (3) (4) (5) (6) (7)
Estimation method OLS FE FE Logit (MLE) Odds ratioProportional
Hazard (MLE)Hazard ratio
Dependent variable pr(switching)it pr(switching)it pr(switching)it pr(switching)it pr(switching)it
Overagei (t –1) 0.014*** 0.150*** 1.162*** 0.163*** 1.178***
(0.002) (0.029) (0.034) (0.028) (0.033)
Savingsi (t –1) (x 103) 0.207*** 0.231*** 0.227*** 7.677*** 1.008*** 5.270*** 1.005***
three month lagged moving average (0.053) (0.058) (0.057) (1.240) (0.001) (1.085) (0.001)
Observations 110,256 110,256 110,256 110,256 110,256
Clusters 21,311 21,311 21,311 21,311 21,311
Year-Month FE no yes yes yes yes
Consumer FE no yes yes no no
TABLE A1 - ROBUSTNESS - ALTERNATIVE MEASURE OF SAVINGS
Notes: The dependent variable is the probability of switching to a different plan within operator for consumer i in month t. Standard errors clustered at the consumer level are
reported in parenthesis below coefficients: *significant at 10%; **significant at 5%; ***significant at 1%.
Source: Authors’ calculations based on the the Billmonitor.com data.
52
(1) (2)
Estimation method FE FE
Dependent variable pr(switching)it pr(switching)it
Overagei (t –1) 0.013*** 0.028***
(0.003) (0.004)
D2_Savingsi (t –1) 0.029*** 0.033***
Dummy =1 if lagged savings between £5-£10 (0.003) (0.005)
D3_Savingsi (t –1) 0.048*** 0.065***
Dummy =1 if lagged savings between £10-£15 (0.004) (0.006)
D4_Savingsi (t –1) 0.066*** 0.086***
Dummy =1 if lagged savings between £15-£20 (0.004) (0.007)
D5_Savingsi (t –1) 0.086*** 0.111***
Dummy =1 if lagged savings between £20-£25 (0.005) (0.008)
D6_Savingsi (t –1) 0.099*** 0.113***
Dummy =1 if lagged savings greater than £25 (0.005) (0.009)
Overagei (t –1) × D2_Savingsi (t –1) -0.008
(0.005)
Overagei (t –1) × D3_Savingsi (t –1) -0.027***
(0.006)
Overagei (t –1) × D4_Savingsi (t –1) -0.029***
(0.007)
Overagei (t –1) × D5_Savingsi (t –1) -0.035***
(0.009)
Overagei (t –1) × D6_Savingsi (t –1) -0.021**
(0.009)
Observations 134,237 134,237
Clusters 29,438 29,438
Year-Month FE yes yes
Consumer FE yes yes
TABLE A2 - SWITCHING AND RISK ATTITUDE - ROBUSTNESS
Notes: The dependent variable is the probability of switching to a different plan within operator for
consumer i in month t. Standard errors clustered at the consumer level are reported in parenthesis below
coefficients: *significant at 10%; **significant at 5%; ***significant at 1%.
Source: Authors’ calculations based on the the Billmonitor.com data.
53
(1) (2) (3) (4)Estimation method OLS FE FE FEDependent variable pr(switching)it pr(switching)it pr(switching)it pr(switching)it
Overagei (t –1) 0.014***(0.002)
Savingsi (t –1) (x 103) 0.167*** 0.161***(0.048) (0.046)
ΔVariancei (t –1) (x 106) -0.030 0.054 -0.093 -0.094*Alternative calculation (0.075) (0.038) (0.058) (0.057)Observations 109,411 109,411 109,411 109,411Clusters 21,234 21,234 21,234 21,234Year-Month FE no yes yes yesConsumer FE no yes yes yes
TABLE A3 - SWITCHING AND EXPECTED UTILITY THEORY - ROBUSTNESS
Notes: The dependent variable is the probability of switching to a different plan within operator for consumer i in month t. Standard errors clustered at the consumer level are reported in parenthesis below coefficients: *significant at 10%; **significant at 5%;***significant at 1%.Source: Authors’ calculations based on the the Billmonitor.com data.
54