1

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.

12

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

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43

4

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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