Switching Costs and Competition in Retirement Investment∗
Fernando Luco
Department of Economics
Texas A&M University
November 1, 2016
Abstract
This paper studies how different switching costs affect retirement-investment choices and
competition in a private-pension system. The different switching costs are identified exploiting
variation in employment status that exposes enrollees to costs of different nature. I estimate
demand for pension funds and show that the cost of evaluating financial information is 27%
higher than the cost faced when switching funds. I then show that eliminating the cost faced
when switching funds intensifies competition and decreases equilibrium fees more than eliminating the cost of evaluating financial information, though eliminating all switching costs decreases
equilibrium fees the most.
JEL: D12, D22, L8. Keywords: Demand for Pension Funds, Inertia, Switching Costs, Dynamic
Competition, Defined-Contribution Pension System.
∗ This
paper is a revised version of the first two chapters of my Ph.D. thesis at Northwestern University and
it subsumes a previously circulated working paper titled “Identifying Sources of Inertia in a Defined-Contribution
Pension System”. I am especially grateful to Igal Hendel for his guidance and generosity. I am also grateful to Robert
Porter and Aviv Nevo for their help and support. I thank Iván Canay, Ben Handel, Manuel Hermosilla, Christopher
Lau, Guillermo Marshall, Álvaro Parra, Esteban Petruzzello, Tiago Pires, and Steve Puller for helpful comments
and suggestions, and seminar participants at Analysis Group, the Board of Governors of the Federal Reserve System,
IIOC 2014, Mannheim, NERA, Northeastern, Northwestern, the STATA Texas Applied Micro Conference 2014, Texas
A&M, and UCLA Anderson for their feedback. Part of this project was done using resources provided by the Open
Science Grid (OSG), which is supported by the National Science Foundation and the U.S. Department of Energy’s
Office of Science. I thank Balamurugan Desinghu and the OSG support team for their help while I was a user of the
OSG. All errors are mine. E-mail: [email protected].
1
1
Introduction
In many markets, such as retirement investment and health care, consumers stick to their decisions
even when their economic environment changes. Economists refer to this behavior as “inertia” and
often explain it as a consequence of switching costs. Though switching costs have been of interest
to economists for decades (see Farrell and Klemperer, 2007 and the references therein), a number
features of switching costs have often been overlooked. For example, we know little about the
nature of switching costs in actual settings as they may involve psychological costs, time costs, and
penalty fees, among others. In addition, consumers may face several of these costs simultaneously
and the individual contribution of each of these costs to inertia and how they affect competition is
unknown. For this reason, identifying the different switching costs that affect consumer behavior
and competition may inform the design of policies targeted at helping consumers to make better
decisions in these complex environments and to intensify competition among firms.
In this paper, I study inertia in retirement-investment choices in the Chilean defined-contribution
pension system. The Chilean system, which is described in detail in Section 2, was reformed in 1981
and went from being a pay-as-you-go system to being a defined-contribution one. This reform made
the Chilean system ideal for the kind of analysis proposed in this paper, for three reasons. First,
following the reform of 1981, the Chilean system has been a model for many retirement-investment
reforms around world, making the Chilean experience valuable for similar settings.1 Second, this
paper studies how switching costs of different nature affect consumer and firm behavior in a market
in which participation is mandatory. Thus, the Chilean setting is also informative for other markets
with mandatory participation. Third, and the focus of the paper, the Chilean setting allows for
separately identifying two sources of switching costs: the cost associated with analyzing financial
information and choosing a pension fund (“decision cost”), and a hassle cost in the form of a
time-consuming bureaucratic process that enrollees have to follow when switching pension funds
(“enrollment cost”).
This paper makes three main contributions to the literature. First, it provides evidence of both
the sources of inertia and its costs. I show that over a period of fourteen years (1988–2001), 56% of
the people in my sample did not switch pension funds despite significant changes in fees and market
structure. Furthermore, while the data show that accumulated balances do not vary significantly
1 Many
countries have adopted retirement-investment systems based on the Chilean model. Among these, we find
Argentina, Bolivia, Colombia, Costa Rica, Dominican Republic, Ecuador, Mexico, Peru, and Uruguay, among others.
Also, countries such as Hungary, Poland, and Kazakhstan reformed their retirement-investment systems following
some of the ideas on which the Chilean system is based. In addition, the Chilean model has been part of debates
about retirement-investment reforms in many other countries.
2
with the number of times that people switch pension funds, a consequence of regulation that limits
both enrollees’ exposure to risk and the financial assets that pension funds can include in their
portfolios (more on this in Section 2), the fees that enrollees pay do. Indeed, while few enrollees
choose funds to minimize the fees they pay, enrollees that switch more often choose cheaper funds
and pay significantly less than more inactive enrollees.
Second, I estimate demand for pension funds to quantify the magnitude of the different switching
costs. The results show that, on average, decision costs are equivalent to $37, while enrollment costs
are equivalent to $30. There is, however, significant heterogeneity across the population (see Section
4). These findings add to the existing literature that shows that people may avoid making decisions
that involve analyzing complex information (see Madrian and Shea, 2001; Thaler and Sunstein,
2008; Choi et al., 2009; Beshears et al., 2013; Grubb, 2015, and the references therein). However,
this paper goes beyond this literature by quantifying the magnitude of the underlying switching
costs.
Third, I use two counterfactual exercises to study how switching costs affect enrollees’ and firms’
choices. I first show that, conditional on observed fees, policies that eliminate switching costs may
result in enrollees switching too often motivated by non-fee attributes of the pension funds. This
exercise, however, does not take into account that pension funds may react to the reduction in
switching costs. To take this into account, I embed the demand model into an infinite-horizon
pricing-game to show that, when firms are allowed to re-optimize following the implementation of
policies that either reduce or eliminate switching costs, fees decreases significantly. Specifically, while
eliminating switching costs decreases equilibrium fees the most (a 58% reduction relative the case
with all switching costs), eliminating either decision or enrollment costs decreases fees significantly
too (38% and 41% respectively). This suggests that identifying the nature of switching costs is
important as policies that eliminate specific sources of switching costs may have significant impact
on competition.
The main challenge faced by this paper, that is a feature of the empirical literature on switching
costs, is to separately identify unobserved preferences from switching costs, as their impact on
choice behavior is observationally equivalent. In addition, in this paper I need to identify the nature
of switching costs. To accomplish this, I extend the identification strategy used in Handel (2013)
exploiting that in the Chilean pension system enrollees belong to one of three groups, and decisions of
enrollees in each group are affected by different switching costs. The first group, “existing enrollees,”
consists of people who have contributed to their accounts every month for a period of time. Existing
enrollees face both decision and enrollment costs when they switch pension-fund administrators
(“PFA”), which means that either cost may be large enough to induce them to remain enrolled
3
with their current PFA. The second group, “returning enrollees,” consists of people who return to
the system after a period in which they did not contribute to their accounts. This group faces
enrollment costs regardless of whether they want to switch PFAs because their change in status has
to be registered even if they decide to remain enrolled with their current PFA. As a consequence,
enrollment costs cannot affect their decisions as these are independent of the alternatives on the
market. However, decision costs may induce them to remain enrolled with their current PFAs.
Therefore, comparing choices by existing and returning enrollees identifies enrollment costs and
also provides a way to test the validity of the underlying identification assumption. Indeed, this
assumption implies that returning enrollees should be more likely to switch than existing enrollees.
Section 3 shows that, indeed, the probability that a returning enrollees switches is 10.9%, which
drops to 2.5% in the case of existing enrollees (Duarte and Hastings, 2012, report similar patterns
using Mexican data).
To identify decision costs, I exploit the existence of a third group, “new enrollees”. New enrollees
are people who are entering the system for the first time and do not have a default option.2 For
new enrollees, both costs are unavoidable as they have to choose and enroll with a PFA. This means
that neither cost can affect their choices as they are incurred regardless of the alternative chosen.
Therefore, comparing the decisions of new and returning enrollees identifies decision costs, as these
rationalize the difference in choice probabilities between these groups.
For the identification strategy to be valid, it is necessary that new, returning, and existing
enrollees have the same preferences, so that differences in choice behavior may only be explained
by differences in the nature of the switching costs they face. To test this assumption, in Section
3 I present reduced-form evidence that compares choice behavior among observationally equivalent
enrollees who left the market at the same time and returned in consecutive periods facing different
fees. I show that those who returned when fees have changed, have a significantly higher probability
of switching PFAs in that period than those who returned in the previous one, consistent with
switching costs, rather than preferences, inducing inertia.
This paper contributes to four strands in the literature. The first one studies implications of
switching costs for consumer behavior. Within this area of study, few papers have tried to distinguish
between sources of inertial behavior and, to the best of my knowledge, this is the first paper to
identify the nature of coexisting switching costs. Miravete and Palacios-Huerta (2014) distinguish
between inattention, state dependence, and learning in the context of telephone contracts. Hortaçsu
et al. (2015) distinguish between incumbency advantage and consumer inattention in the context of
residential electricity markets. Goettler and Clay (2011) study tariff choice in the case of an online
2 This
changed in 2009.
4
retailer, allowing for consumer learning and switching costs. Handel (2013) studies the role of inertia
in choosing health insurance. Sudhir and Yang (2015) exploit the choice-consumption mismatch to
separately identify state dependence and unobserved heterogeneity. Polyakova (2016) studies how
switching costs interact with regulation and adverse selection in Medicare Part D. Shcherbakov
(2016) studies the impact of switching costs in the paid television services and Nosal (2012) studies
the impact of switching costs in the Medicare Advantage market. Finally, there are also studies that
investigate the impact of inertia without quantifying its value (e.g., Marzilli Ericson, 2014 in health
insurance, and Crawford et al., 2011 in telephone contracts).
The second strand of the literature studies pricing implications of switching costs. The theoretical
literature on switching cost and prices has shown that in the presence of switching costs prices can
either increase (Klemperer, 1987a,b; Beggs and Klemperer, 1992) or decrease (Arie and Grieco, 2014;
Cabral, 2016). Finally, to the best of my knowledge, there is only one paper that has empirically
studied the pricing implications of switching costs in a setting of dynamic price competition with
“small” switching costs. Dubé et al. (2009) study the impact of switching costs on steady-state
prices of two consumption goods, orange juice and margarine. They conclude that switching costs
resulted in lower equilibrium prices than they would be if these costs did not exist.
The third strand of the literature studies investment choices in the context of the Chilean and
Mexican defined-contribution pension systems. Though this literature has grown significantly in
the last years, most of it is focused on studying how information and the way in which prices are
expressed affects choices. Duarte and Hastings (2012) study the case of Mexico, where government
intervention shifted consumers’ and firms’ attention from multiple fees to a single fee index. Hastings
(2010) who shows evidence of heterogeneity in the weights people put on past performance and fees.
Hastings and Tejeda-Ashton (2008) and Hastings et al. (2010) show that the way in which fees are
presented has significant impact on choices.
There is, also, a second line of research that has taken a different approach. Hastings et al.
(2013) studies investor choices and pricing in the Mexican privatized Social Security System, focusing
on how the interaction between enrollees and pension-fund sales-force is associated with enrollees
shifting attention from fees to non-fee fund attributes. Krasnokutskaya et al. (2016) studies how
regulation that was meant to limit Chilean enrollees’ exposure to risk may have resulted in pensionfund managers choosing riskier portfolios. Illanes (2016) also studies how switching costs affected
enrollees’ and firms’ behavior, but does so in a later period, when, from a practical perspective, only
one of the switching costs studied in this paper remains. I further discuss the relationship between
this paper and Krasnokutskaya et al. (2016) and Illanes (2016) in Section 4.3
3 There
is a broad body of literature that estimates demand functions for PFAs in reduced form using Chilean
5
Finally, this paper is also related to the literature that studies investment choices in the context
of 401(k) plans in the United States. This literature studies how plan design affects participation
rates, asset allocation, and contribution rates. This literature has also documented the existence of
inertia, but it neither quantifies it nor identifies its nature. Madrian and Shea (2001) and Carroll et
al. (2009) show that automatic enrollment increases participation as well as the fraction of people
who choose default options. In a similar setting, Chetty et al. (2014) show that policies that require
active decisions by enrollees, such as systems based on tax subsidies, are less effective in increasing
total savings than those that do not, such as automatic employer contributions. Finally, Beshears
et al. (2015) and Choi et al. (2011) show that providing information to enrollees has little impact
on their choices, suggesting that in the context of this paper delegated management may be more
effective in reducing decision costs than personalized information.
2
The Chilean System
2.1
Institutions, Enrollees, and Pension Funds
The Chilean pension system was reformed in 1981, when it transitioned from a traditional pay-asyou-go system to a defined-contribution system. Prior to this change, the Chilean system consisted
of multiple providers that collected resources from contributors and paid retirees. During this period,
the contribution rate was high and the level of pensions depended on the provider with which an
investor was enrolled. In addition, there was significant uncertainty about whether the system would
be able to meet its payments.4
Between 1981 and 1983, people who entered the labor force could choose whether to enroll in
the old system or the new one. Fees in the new system were half of those charged in the old system,
thus giving incentives to enroll in it. Starting in 1983, it was mandatory for those employed in the
formal sector to participate in the new system by contributing to their own private pension account
and choosing a PFA to manage it.5 At the same time, entry, exit, and mergers of PFAs, as well
as the type of financial assets in which they could invest, have always been regulated, and PFAs
operate across the country as the market is defined at the national level.
In terms of market structure, the number of PFAs has varied significantly over time (providing
variation in the choice set faced by enrollees). Figure 1a shows that while in 1988 there were twelve
data (Bernstein and Micco, 2002; Bernstein and Ruiz, 2004; Marinovic and Valdés, 2005; Bernstein and Cabrita, 2006;
Cerda, 2005). The approach in these papers is quite different from the one in the present paper and the literature
described above.
4 See Ferreiro, ed (2003) for a comprehensive description of the Chilean pay-as-you-go system.
5 Since the implementation of the new system, the contribution rate has been 10% of monthly salary.
6
PFAs, this number had increased to twenty-two by 1994 and then it decreased between 1995 and
2001, mostly through mergers.
PFAs may freely choose the level of fees they charge, though price discrimination is not allowed.
In addition, since 1988, fees may only be charged over contribution flows, not over the balance.
Since then, PFAs have either charged a percentage fee over monthly salary (that is also the base
for computing contributions) or a percentage fee plus a fixed fee. Figure 1b shows the evolution
of the mean fixed fee in the left axis and the mean percentage fee in the right axis. The fixed fee
is reported in U.S. dollars of December 2001. Finally, Figure 2 shows the evolution of quartiles of
fees over time and show that, because of the frequent changes in relative fees, inertia may result in
enrollees paying high fees even if they chose to minimize fees when they enrolled.
Between 1981 and 2001, each PFA offered only one investment product and invested all new
contributions and existing balances in different financial instruments.6 Because regulation allows
for investing in a limited set of financial assets, this results in little portfolio differentiation across
pension funds, reducing the (relative) risk that enrollees face.7 Furthermore, Chilean regulation also
explicitly limits enrollees’ exposure to risk. In particular, regulation requires PFAs with returns of
2% or more below the industry mean to cover the losses with their own capital. In addition, until
2008, if returns were 2% or more above the industry mean, the excess returns were saved to cover
losses in case the lower bound was reached.8 This has resulted in PFAs having strong incentives to
mimic each other and, as a consequence, there is little variation in returns (Figure 3).
Finally, it is important to describe the process that enrollees had to follow when switching PFAs.
After an enrollee had chosen a new PFA, she had to either visit an office of that PFA or contact a
sales person. The enrollee would then provide proof of current enrollment to the newly chosen PFA.
This is important because, while today the switching process can be done online, this was certainly
not the case during the period analyzed in this paper, when a Certificate of Affiliation could be
obtained from either the regulator or the PFA in which the enrollee was currently registered. Then,
and different to what happened in other countries during the same period (Duarte and Hastings,
2012), the process of switching an enrollee from one PFA to another was done by the newly chosen
6 Starting
in 2002, PFAs could offer up to five investment alternatives, and enrollees could divide their balance into
up to two of these alternatives, always within the same PFA. In addition, PFAs are not allowed to charge differently
for the different investment alternatives. Because my dataset does not allow me to observe in which investment
alternative enrollees have invested their funds, I limit the analysis to the period between 1988 and 2001.
7 Though investment limits have changed over time, there has always been a limit on fractions of portfolios allocated
to risky assets by type and by origin. See Ferreiro, ed (2003), pages 138 and 139, for the evolution of investment
limits over time.
8 This bandwidth is defined for the 36-months annualized real returns and it is enforced for every month. See
Ferreiro, ed (2003), page 82.
7
PFA and not the PFA with whom the enrollee was originally enrolled. Hence, PFAs do not have
incentives to delay transfers of funds or the switching itself.9 Finally, when switching jobs, the
enrollee had to provide evidence of prior enrollment to the new employer. If the enrollee wanted
to switch PFAs at the same time as she switched jobs, she would need to contact the sales force of
the chosen PFA, provide them with proof of enrollment, sign the required paperwork, and the sales
person would continue the process with the new employer. Hence, when switching jobs or returning
to the system, the enrollment process was unavoidable.
As described in this section, the Chilean system shares some similarities with private definedcontribution systems in the United States, though there are a number of important differences.
First, in the Chilean system participation is mandatory for people employed in the formal sector.10
Second, the Chilean market covers the whole country and everybody faces the same choice set and
fee schedule, though paid fees vary with salary. Finally, until 2002, enrollees could only choose a
PFA, but not asset allocation. For these reasons, from the perspective of its enrollees, the Chilean
system could be perceived as simpler than other private-pension systems in which enrollees must
chooses asset allocation as well. This has the benefit of allowing for cleaner identification of sources
of switching costs. On the other hand, this makes estimates of switching costs in this system a
lower bound for those that could be obtained in more-complex systems. Furthermore, because i)
investment by PFAs is heavily regulated, ii) there is little dispersion in realized returns, iii) there is
essentially no persistence in the ranking of profitability, and iv) enrollees only choose one PFA to
manage their accounts; it is natural to model enrollees’ decisions following a discrete choice approach.
2.2
Data
This paper uses an administrative dataset provided by the regulator of the Chilean retirementinvestment market, Superintendencia de Pensiones (SP). The dataset is a panel of individual histories that starts in 1981 and contains information from the moment an individual enrolled for the
first time until either 2009 or the time of their last contribution. The dataset consists of a random
sample of Chileans and was generated in 2002 by the SP. The individual histories of contributions
were recreated by the supervisor using administrative records of the PFAs.
I use a sample of individuals chosen according to the following criteria. First, because the
dataset only records fees paid, I use fees to match individuals with PFAs. Therefore, I dropped
all individuals whom I was unable to unambiguously match to a PFA. Second, I dropped those
individuals who participated in the old pension system because the (voluntary) decision to move
9 This
10 Since
is true today as well, as the online process is done through the website of the newly chosen PFA.
2015 it is also mandatory for independent and self-employed workers.
8
from the old system to the new one made them different from those who entered the system later.
Third, I dropped all individuals who entered before 1988 because the fee schedule used between 1981
and 1987 (which allowed charging fees over balances) generated a significant number of false matches
between individuals and PFAs. Fourth, I dropped the few cases in which the first contribution of
an enrollee happened after turning 65 or before turning 15. Finally, I dropped all individuals who
had not contributed to their accounts for more than sixty consecutive months. The final sample
consists of 350,660 observations of 8,888 people who enrolled between 1988 and 2001 and includes
their initial choice and every contribution to their accounts between 1988 and 2001. In the sample,
635 people on average entered the system each year (Figure 4a).
For each person, the dataset includes information on salaries and fees paid at the time of each
contribution and characteristics such as gender, birth, enrollment date, and whether the enrollee
opened a voluntary savings account to save additional resources for retirement.11 In addition, I
observe the choice set of every individual, the fees charged by all PFAs, all mergers that occurred
during this period, and daily returns of the portfolios managed by each PFA, though not their
composition. I focus on monthly returns because this matches the data that enrollees have, and
in the analysis I use average annual real returns computed over 36 months as a measure of past
performance.
Table 1 reports summary statistics for the samples generated by the different criteria explained
above. The first column reports statistics for people that I was unambiguously able to match to
PFAs. The second column restricts this sample by dropping people who enrolled before 1988 and
also people who, when enrolling, were either younger than 15 or older than 65 years old, both of
which are rare cases. Finally, the estimation sample is obtained after dropping individuals that
did not contribute for sixty or more consecutive periods. The table shows that the main impact of
restricting the sample is that in the estimation sample there are more women than in the original
one (50% vs. 44%), the mean enrollment age is lower (25 vs. 28), and the fraction of enrollees with
voluntary savings account is lower (16% vs. 21%). The average monthly salary in the estimation
sample is 222,552.4 Chilean pesos of 2001 (332.6 U.S. dollars of December 2001). Finally, of the
350,660 observations, 12,196 correspond to people switching PFAs (3.5% of all observations, which
is similar across samples), while 43,648 correspond to active decisions by people who return to the
system after periods without contributions (12.4% of all observations). Table 1 and Figure 4b also
show something that is widely known about the Chilean system: people can go a long time without
11 The
voluntary account is managed by the same PFA as the mandatory account and invested in the same instru-
ments. The data only identifies if the enrollee opened a voluntary account but not the moment at which the account
was opened.
9
contributing to their accounts, even though the mean number of months between the first and last
recorded contribution is high and participation is mandatory for formal employees. This phenomenon
could be caused either by long unemployment spells, frequent transitions between employment and
unemployment, transitions between formal and informal employment, long periods of informal employment, or transitions between formal employment and self-employment. The data available do
not allow to distinguish between these cases. However, because during the period considered in this
paper only formal employees were required to participate in the system, and participation rates of
those in other categories were low, the assumption that all observed contributions correspond to
formally employed individuals is not strong.12
3
Evidence
I begin the analysis of inertia in the Chilean retirement-investment market, providing evidence along
three dimensions. First, I show that there is a cost associated with inertia and that this cost takes
the form of higher fees paid, as returns do not vary with the number of times enrollees switch.
Second, having shown that inertia has a cost, I turn to study when people switch and who are more
likely to be switchers. The results show that returning enrollees are significantly more likely to
switch than existing enrollees, even after controlling for a rich set of demographics. Finally, I turn
to study, in reduced form, the validity of the assumption that allows me to separately identify each
switching costs. I show that similar enrollees, who left the market at the same time, and returned
in consecutive periods facing different fees, behave significantly different. In particular, those who
returned when the fee schedule had changed are significantly more likely to switch than those who
returned in the previous period. This suggests that inertia is generated by switching costs rather
than unobserved heterogeneity.
3.1
The Cost of Inertia
Before turning to the evidence, it is important to know whether Chileans switch pension funds at
all and if there is any cost associated with inertia. Figure 5a reports the switching rate, the ratio
between the number of times an individual switched pension funds and the number of times this
individual made a contribution, for the whole sample. The figure shows that switching is rare,
though as figure 5b shows, it is more common among those that have been enrolled longer.
Given that people do not switch often, is there any cost associated with inertia? If not, then
12 Independent
workers between 1988 and 2002 accounted for 2.9% of total enrollees. See the series “Afiliados por
tipo y sexo” (Enrollees by type and gender) in www.spensiones.cl for more details.
10
inertia may not be caused by switching costs, but rather because enrollees may not benefit from
switching. To study whether there are benefits from switching PFAs, I focus on how returns and
fees vary with the number of times people switch. Figure 6a reports a local polynomial regression of
realized returns in the three years following the moment an enrollee switches PFAs and shows that
returns do not vary with the number of times enrollees switch. This, a consequence of regulation,
suggests that enrollees should minimize the fees they pay. Figure 6b shows that though this is not
the case, enrollees that switch more tend to choose cheaper options.13 Indeed, the figure reports
fees paid in excess of the cheapest fund and shows a negative relationship between fees paid and
the number of times people switch.14 This means that, while those who switched five or more times
paid 9% more than with the cheapest fund, those who never switched paid, on average, 18% more
than with the cheapest fund. At the mean level of income and fees, this is equivalent to two months
of fees per year, or 0.5% of income.
Having established that people who switch less pay more than more active enrollees, I now turn
to studying how fees paid are related to the time elapsed since the last active decision (i.e., the last
time the enrollment cost was sunk). Figure 7a plots a local polynomial smoothing regression of the
probability of facing lower fees, as a function of the time elapsed since the last active decision. The
figure shows that the probability of facing a lower fee decreases significantly in the months after an
active decision and then remains stable. Overall, the evidence suggests that inertia has a cost in
terms of fees and that part of this cost decreases when enrollees return to being active contributors.
The next subsection studies when people switch and who those people are.
3.2
When Do People Switch? Who Are Those Who Switch?
The identification assumption that allows us to identify the nature of switching costs is that people
with different contribution statuses behave differently because they face switching costs of different
nature. This means that if decisions of existing enrollees are affected by more sources of switching
costs than returning enrollees, then switching PFAs should be more common among those who return
to the system than among those who have contributed continuously. Table 2 shows that this is the
cases. First, 40% of changes of PFAs correspond to people returning to the system, who account
for 12.5% of the total number of observations in the sample. Hence, changing PFAs is significantly
more common among returning enrollees than among existing enrollees. This translates to 10.9% of
observations from returning enrollees involving changes, while only 2.5% of observations of existing
13 Enrollees
may also choose funds because of non-fee fund attributes. This is considered Section 4. This section,
however, focuses on returns perceived and fees paid only.
14 Because participation is mandatory, I measure the cost of inertia relative to the cost of choosing the cheapest
fund available.
11
enrollees fall into the same category. Second, when restricting the sample to people who in addition
to the mandatory savings account also have a voluntary savings account, both probabilities increase
significantly. In the case of returning enrollees, the probability of switching PFAs increases to 15%,
while in the case of existing enrollees it increases to 3.3%.
Though the findings of the previous paragraph are appealing, there could be other factors that
are unaccounted for that also affect switching. If this is the case, the effect of returning to the system
will be overestimated by not taking the other factors into account. An example of such factors is
a change in salary that happens at the same time an enrollee returns to the system. Indeed, if
an enrollee is both returning to the system and receiving a higher salary than at her previous job,
then not controlling for the effect of the increase in salary will result in overestimating the effect
of returning to the system. To take this into account, I estimate several probit regressions with
different sets of regressors and fixed effects. The results are reported in Table 3.
The first specification includes only the indicator that is equal to one if the enrollee was a
returning enrollee in that month. The effect of returning is both positive and highly significant.
The estimated coefficient implies a 10.93% higher probability of switching than in the case of an
existing enrollee.15 The second column replaces the indicator for returning with an indicator that
is equal to one if the enrollee had an increase in salary of 10% or more relative to her average
income over the last five months during which she was an existing enrollee. The result, positive and
significant, disappears once we add the indicator for a returning enrollee (column three). Column
four adds year fixed effects and shows that the previous results are robust to changes in specification.
Column five adds demographic information. It shows that older people switch less frequently, that
gender does not affect the probability of switching, and that people with a voluntary savings account
switch more often than those without. The marginal effect decreases slightly with respect to the
first specification, reaching 10.59%. Finally, column six adds PFA fixed effects and shows that the
results are robust to controlling for PFA-specific unobservable characteristics. Here, the marginal
effect of returning increases to 10.7%. These regressions suggest that the probability of switching
PFAs is mostly affected by returning to the system rather than by other individual characteristics.
What the results do not show is how the probability of switching changes with the number of months
elapsed since an enrollee returned to the system. In other words, one may ask whether the impact of
returning to the system is limited to the first month after returning or if it lasts longer. To address
this question, I replicate the probit regression of specification 6 in Table 3, replacing the indicator for
returning with a variable that measures the number of months since an individual returned and, in
Figure 7b, I plot the predicted probability of switching (and its 95% confidence interval) associated
15 In
what follows, all marginal effects are significant at the 1% level.
12
with the marginal effects of the number of months elapsed since returning for twelve months after the
enrollee returned to the system. The figure shows that the most significant impact on the probability
of switching happens when enrollees return to the system and the impact vanishes after the second
month. Overall, the evidence shows that the higher probability of switching is associated with the
first month after returning, which is consistent with returning enrollees having lower switching costs.
To take advantage of the richness of the data, Table 4 adds other regressors to the probit regressions of Table 3. The first column adds an indicator variable that takes the value of one for years
1998 to 2001. This follows because at the end of 1997 the regulator reformed the system and made
it more difficult to switch in response to salespeople offering gifts to induce switching. As expected,
such reforms had a negative effect on the probability of switching. The second column also controls
for time elapsed before returning to the system and salary level. The results show that the longer
a person was not participating before returning, the higher the probability of switching, though in
this case the impact of changes in salary turns out to be negative and significant, while salary level
is positively associated with the probability of switching. The third column replicates column two,
dropping salary level and replacing it with account balance. It is shown that the probability of
switching increases with account balance. Finally, column four controls for all these variables jointly
and shows that, not surprisingly, it is salary–that determines fees paid–rather than account balance
what affects the probability of switching.
The relationship between demographics and the probability of switching is also shown in Figure
8, which plot the outcome of local polynomial regressions of switching on the number of months a
person was away from the system before returning, age, and income levels. The figure shows that the
number of months without contributing before returning to the system is positively correlated with
the probability of switching, as is also the case when considering income level. Finally, as suggested
by the different probit specifications reported above, the probability of switching decreases almost
monotonically with age.
3.3
Testing Identification
Though all the results presented above suggest the presence of switching costs, there is an implicit
assumption that has not been discussed: returning and existing enrollees are similar and they do not
select into each group. This assumption is valid as long as people switch groups randomly and not
because they would face fewer sources of switching costs when returning. Though it is not possible
to have random assignment, as people transition deterministically from one group to the next as
they transition through different employment stages, as long as people do not transition between
employment and unemployment (or self-employment or informal employment) motivated by a desire
13
to switch PFAs, selection is not a concern. However, though this argument is appealing, it does not
rule out that preferences may differ across groups. In other words, though there may not be selection
into the different groups, people in each group may be different, or their preferences may change
when switching groups. To rule this out, I provide four arguments that suggest that what drives the
differences in behavior across groups is switching costs rather than unobserved heterogeneity.
First, almost everybody in my sample was a returning enrollee at least once. Indeed, the mean
number of times that an enrollee is classified as returning is 5 and the median 4. 82% of the sample
was a returning enrollee at least once, and among those who were never classified as returning
enrollees, more than half entered the system in the last two years covered by my data (Figure 9).
Hence, it is unlikely that returning and existing enrollees consistently differ on their preferences as
enrollees happen to transition not only from being returning to being existing enrollees but also in
the opposite direction.
Second, Table 5 shows that in terms of age and income, both groups are remarkably similar.
However, they do differ significantly on gender composition and whether they have a voluntary
savings account. Indeed, though 50% of the sample is female, males are overrepresented in the
returning group. This means that, after leaving the market, males are more likely to return to it
than females, a fact that for years has worried the Chilean authorities because it results in low
pensions for women. This, however, is associated to specifics of the labor market rather than to
selection in the pension-funds market. Furthermore, even if people were to return to the formal
labor market because of a desire to participate in the retirement-investment system, this type of
selection is not a concern from the perspective of identification of switching costs. Indeed, it would be
necessary for people to transition between returning and existing because of relative preferences for
a PFA, and not for the system, for selection to be a concern. Finally, that existing enrollees are more
likely to have a voluntary savings account suggests that there might be further differences across
individuals that have to be taken into account. I do so in estimation, as I control for observable
individual characteristics, such as age, income, gender, and whether an enrollee has a voluntary
savings account, and I also incorporate time-invariant individual-specific unobserved heterogeneity
on a number of dimensions. This is explained in the next section.
Finally, though the analysis above is sound in terms of comparing the different groups, I now
study whether unobserved factors explain the higher switching rate among returning enrollees, rather
than the lower switching costs that they face. First, I look at whether the length of time since the
last change in fees is able to explain differences in the switching probability between returning
and existing enrollees. Figure 10, that reports a local polynomial smoothing of the probability of
switching on the time since fees changed for the last time, shows that this is not the case. Indeed, the
14
length of time since fees last changed seems not to be correlated with the probability of switching.
The figure shows that returning enrollees always have a higher probability of switching than existing
enrollees, regardless of when fees changed for the last time. In other words, the time elapsed since
fees last changed does not explain the differences in switching probabilities.
Second, to take this idea one step further, I estimate probit regressions that are similar to those
reported in tables 3 and 4, with the main difference being that the object of interest here is to study
how switching probabilities differ across similar individuals who return in periods t − 1 and t, when
the fee schedule changes in t relative to that of t − 1. The idea behind this test is that if someone
returned to the system in t − 1 and fees changed in t, if switching is caused by changes in preferences
rather than lower switching costs, then this enrollee should be equally likely to switch PFA in t as
an identical enrollee that returns to the system in t. On the other hand, if switching is facilitated by
lower switching costs when returning, we should observe that those returning in t are significantly
more likely to switch than those who returned in t − 1.
While ideally one would do this analysis constraining the sample to enrollees that when returning
in t − 1 faced the same fees as when they left the system, and so, in t those who returned in t − 1
and those who returned in t would face the same change in relative fees, this is not possible in our
setting because of data limitations. Indeed, imposing this restriction leaves few cases in which all
restrictions are satisfied. For this reason, I relax the constraint that fees in t − 1 have to be the same
as when the enrollee left the system, but I restrict the sample to individuals that did not switch
PFAs in t − 1, so after the change in fees that takes place in t, those who returned in t − 1 face the
same change in relative fees as those returning in t.
The results are reported in Table 6. In the first column, the sample corresponds to individuals
who returned to the market either in period t−1 or t, when fixed fees changed in t relative to t−1. The
results show that someone who returns in period t, when the fixed fee changed, is significantly more
likely to switch PFAs than someone who returned in the previous month, conditional on observable
characteristics. In column 2, I repeat the regression but considering changes in percentage fees.
Column 3 and column 4 repeat the exercise but including fixed effects for the time when an enrollee
left the system. I do this to take into account that people who left the market at different times
did so under different economic conditions that may affect future labor-market outcomes. In all
cases, including these fixed effects is associated with a larger marginal effect of returning, and the
magnitude is in line with that reported above. What is important from these results is that they
show that similar enrollees, that left the market at the same time (columns 3 and 4), but returned
in consecutive periods, behave significantly different when facing the same change in relative fees.
This suggest that inertia is not determined by differences in preferences, but rather by the different
15
switching costs that each group faces. The demand model that is proposed and estimated in the
next section makes use of this, as well as other information to model consumer heterogeneity in both
inertia and preferences for product characteristics such as fees and past performance.
4
Structural Analysis
The evidence discussed in the previous section suggests that enrollees’ decisions are affected by different sources of switching costs depending on their contribution status. Because of this, comparing
the behavior of people with different contribution statuses allows us to quantify the magnitude of
each of these costs as well as the extent of heterogeneity across the population. In this section, I
propose and estimate a demand model that allows to do this and to study how inertia varies across
the population.
4.1
Model and Identification
In the model, I assume that consumers make decisions every period. In doing so, they must decide
whether to remain enrolled with their current manager or switch. If they switch, depending on their
contribution status, they not only face the decision cost associated with choosing a new manager,
but also the administrative cost of enrollment. The model also assumes consumers to be myopic,
an assumption that I discuss below. However, in order to capture the trade-off between returns,
which only affect future utility through the pension level, and current fees, I model utility using a
traditional discrete choice approach in which consumers have heterogeneous valuation for product
attributes. In particular, I consider fees and returns to be product characteristics, and I assume that
these characteristics are perceived by consumers through the information that is publicly available.16
Let fjt and pjt denote the fixed and percentage fee charged by pension fund j in period t, Xjt
be observable fund characteristics, ηit be the cost of switching if in t − 1 j was not chosen, ξj be
unobserved (to the econometrician) fund characteristics, and εijt be an idiosyncratic taste shock to
16 I
do not include any measure of risk as an observable characteristic of the funds for three reasons. First,
as explained earlier, because of the regulatory framework there is little dispersion and no persistence in returns,
essentially eliminating any persistent risk associated to a specific PFA. Second, and more importantly, enrollees do
not have easy access to information that may allow them to infer any measure of risk. Indeed, enrollees receive
information about the annualized returns for different time periods and the fees that each PFA charges. To compute
measures of volatility, an enrollee would need to request the time series of returns from the regulator and compute
volatility herself (or collect all of the statements she has received over a time period and extract the information on
returns and compute, for example, the variance). Finally, Hastings et al. (2010) show evidence that suggests that
financial illiteracy is common among enrollees in the Chilean system, making it unlikely they they would know how
to compute measures of risks.
16
consumer i, assumed to be identically and independently distributed Extreme Value Type I (this
assumption will be discussed further later in this section). Under these assumptions, the indirect
utility of consumer i when choosing alternative j in period t is given by
′
uijt = αit (yit − 0.1yit − fjt − pjt min{yit , ȳt }) + Xjt
βit − ηit 1[dit−1 6= j] + ξj + εijt ,
(1)
where αit is the marginal utility of income and βit is a taste coefficient for product characteristics
included in Xjt . Below I assume a specific parametric form for these coefficients.17 In this setting,
consumer i chooses fund j if uijt ≥ uikt for all k 6= j.
Though the proposed model is simple and allows for estimating the distributions of preferences
and switching costs, some assumptions need to be discussed. First, though there is a growing body
of literature that models enrollees’ decisions in private pension systems as a discrete choice problem
(e.g., Duarte and Hastings, 2012; Hastings et al., 2013; Krasnokutskaya et al., 2016; Illanes, 2016),
this is not standard in other literature on savings and investment. What makes this possible in this
context is that contribution rates are set by law and consumers are not allowed to choose portfolios,
just a pension fund. Hence, the problem is in fact a discrete-choice one.
Second, I assume enrollees to be myopic. This has two main implications. First, it implies that
the utility function is defined in reduced form because enrollees derive flow utility from returns of
their pension accounts, even though these payoffs will only be realized upon retiring. This, however,
is based on that the best prediction that enrollees can make regarding future fees and returns is
precisely the one that they currently observe. Second, I do not consider that enrollees may anticipate
either changes in fees or just the direction of these changes. If this is the case, switching costs would
be overestimated relative to flow utility as while enrollees may wait for uncertainty to be realized, the
model would rationalize this as inertia caused by switching costs. However, though switching costs
may be overestimated relative to flow utility, there is no reason to believe that the relative magnitude
of the different switching costs would be affected. Furthermore, the differences in observed switching
behavior between returning and existing enrollees, that face the same uncertainty, suggests that it
is switching costs, rather than uncertainty what drives the decision to switch.
Though without doubt these are limitations of a static setting, it is important to note that I
have chosen this framework because I believe it represents the Chilean retirement-investment system
in a better way than a dynamic one. This is so because of two reasons. First, market structure
and fees changed significantly and often during the period of analysis. Indeed, the number of PFAs
went from 12 in 1988 to 22 in 1994 to 7 in 2001, making it hard for consumers to form expectations
17 In
the computation of fees, income is bounded above by a value that changes monthly. This reference income
is defined as 60 U.F., where U.F. is a monetary unit of constant value (adjusted by inflation). Though this limit is
introduced in the computation of fees, it is not used when specifying taste coefficients.
17
of how the industry, and the fee schedule, would look like in the future. Second, regulation concerning the investment limits that PFAs had to follow when constructing their portfolios and the
instruments they could use also changed significantly and often during this period. These changes
introduced complexities that make unlikely that consumers would follow a dynamic approach when
choosing PFAs. It is important to note, though, that this is a different setting from that studied
by Illanes (2016), as he focuses on a later period in which market structure and financial regulation
were significantly more stable, making a dynamic framework better suited than for earlier periods.
Nonetheless, to take changes in preferences over the life cycle into account (i.e., preferences over fees
and returns), the random coefficients vary with demographics such as age and income.18
Third, the model assumes that existing enrollees face the decision and enrollment costs at the
same time. In practice, these costs could be faced sequentially. If this is the case, modeling the
problem as simultaneous will overestimate decision costs as some enrollees may decide to incur these
costs but choose not to switch. However, from a computational perspective, taking this approach
reduces the extent to which heterogeneity can be included in the model. For this reason, I have
estimated a simpler sequential specification of the model, and the results show that there are no
qualitative differences in how switching costs are distributed across the population, though the level
of costs changes as expected.19 Note, however, that the relative magnitude of switching costs changes
little. Because there are no other important differences between the two models, I use the model
proposed above in the remainder of the paper.
Fourth, I model both switching costs as being equivalent to a tangible switching cost, though
in practice it is likely that only enrollment costs fall in this category (as a transaction cost), while
decision costs are implicit. This assumption should not have a significant impact on the rest of the
parameters to be estimated, because, as I explain below, parameters associated with preferences are
identified from initial choices. Indeed, though not reported here, estimating the model with only
initial choices results in qualitatively similar estimates of αit and βit to those obtained with all the
data and considering both sources of switching costs.
Fifth, I have assumed that εijt is an i.i.d. shock, as it is common in the demand-estimation
literature. In this setting, however, it could happen that εijt is correlated over time. If this is the
case, the model will attribute the induced inertia to switching costs rather than preferences, thus
overestimating switching costs. To take this into account, one of the specifications estimated in the
next section drops the i.i.d assumption and introduces autocorrelation in ε. The results show that
allowing for autocorrelation does not significantly affect the estimated distributions of switching
18 Another
(practical) benefit of the static model is that it allows me to study dynamic price competition in the
presence of switching costs in a richer way than what a dynamic framework would do.
19 These results are available upon request.
18
costs and preferences, which suggests that what causes inertia in this setting is the existence of
switching costs rather than persistence in ε.
Sixth, I have assumed that unobservable fund characteristics are constant over time. This assumption, though strong, is necessary for two reasons. First, it is unfeasible to allow for time-varying
fund unobservables using period-fund fixed effects because of the resulting number of fixed effects
to estimate. Second, an alternative procedure would be to use the “BLP inversion” (see Berry et
al., 1995). However, this requires all PFA to have positive market shares in all periods, which is not
the case in my data, in particular in the first months after a new PFA has entered the market. For
this reason, instead of dropping these observations from the data, I estimate ξj as fixed over time,
but I interact it with individual demographics (that do change over time), to capture heterogeneity
in brand preferences.
Finally, identification of taste coefficients follows standard arguments. In particular, taste coefficients are identified using initial choices and exploiting variation in choice sets, prices, and characteristics. The remaining choices identify switching costs as explained at length in previous sections.
This, however, does not solve the potential problem of price endogeneity that is common the in the
demand-estimation literature, as prices might be correlated with the unobserved component ξ (this
does not change when ξ is interacted with demographics). To address this concern, I follow Train
(2009) and use a control function approach using PFA age, the number of PFAs in the market, and
PFA returns as instruments, in addition to unobserved manager characteristics not varying over
time.
4.2
Specification and Estimation
In estimation, I specify taste coefficients to be a function of observable characteristics such as age,
gender, accumulated balance, and income, among others, and individual-specific time-invariant unobservables. As the dataset covers fourteen years, I allow for variables such as age, income, and
balance to change over time, meaning that switching costs (ηit ) and taste coefficients (αit and βit )
change over time as well. Specifically, I assume
α
αit = α0 + Dit
α + σα µα
i
β
βit = β0 + Dit
β + σβ µβi
k
η
k
ηit
= η0 + Dit
η + ση µηi k k = {D, E}
µli ∼ N (0, 1), l = {α, β, η D , η M },
β
η
α
where Dit
, Dit
, and Dit
are vectors of observed demographics. I use Halton draws to simulate all
µli ’s.
19
In this context and under the assumption that taste shocks are i.i.d Extreme Value Type I, the
probability that enrollee i chooses alternative j in period t is given by
Pijt =
Z
′
exp(−αit (fjt + pjt min{yit , ȳt }) + Xjt
βit − ηit 1[dit−1 6= j] + ξj )
P
dFµ ,
′
exp(−α
(f
+
p
min{y
,
ȳ
})
+
X
it kt
kt
it t
k
kt βit − ηit 1[dit−1 6= k] + ξk )
(2)
where Fµ represents the joint distribution of µi ’s. In estimation, I further assume that µi ’s are
independent and I numerically integrate over them.
Finally, because there is no outside option, a normalization is required. I assume that ξk is
equal to zero for one of the PFAs that was always present in the market. With this, the Simulated
ˆ σ̂} is given by
Maximum Likelihood estimator θ̂ = {η̂, α̂, β̂, ξ,
θ̂ = arg max
θ∈Θ
XXX
i
k
log(Pikt )1[dit = k].
t
Note, however, that when ε is allowed to be autocorrelated, the previous approach cannot be
followed. For this scenario, I simulate draws of ε and compute the associated utility levels for each
option in the choice set. Then, I use frequencies to compute the choice probabilities, rather than
the analytic form presented above. In this case, standard errors are computed using the Bootstrap
with 25 bootstrap replications drawn with replacement from the original dataset.
4.3
Estimated Parameters and Implications
In this subsection, I report the estimated parameters and discuss their implications. Table 7 reports
the estimated coefficients of the distributions of switching costs for different specifications that differ
on the demographics included in the taste coefficients and on whether I allow for random coefficients.
In each specification, returns are measured using the absolute ranking of returns, following Cerda
(2005).20 The first four columns do not include unobserved heterogeneity while the last three do
include it. The first column is used as a baseline. Column 2 adds the accumulated balance in the
specification of switching costs and taste coefficients. Column 3 includes time unenrolled before
returning in the specification of decision costs. Column 4 allows the error to be autocorrelated. Column 5 replicates the baseline specification including unobserved heterogeneity. Column 6 replicates
column 5 adding the interaction between brand fixed effects and individual demographics. Finally,
column 7 includes a control function. Because the results do not seem to change when including the
control function, I discuss the results based on specification 6.
20 In
a previous version of this paper, I reported estimated coefficients for specifications that differed on how returns
were measured. As the results did not differ, in this version I have introduced different specifications of the utility
function rather than different ways to measure returns.
20
As the table shows, the results are similar across specifications. In the case of both decision
and enrollment costs, the constant defines the level of switching costs (the mean of the distribution)
and the demographics rationalize heterogeneity around the mean. Regarding the constants, decision
costs appear to be 35% larger than enrollment costs, though once all heterogeneity is taken into
account, decision costs are, on average, 27% larger than enrollment costs. In addition, both switching
costs increase with age, are not affected by gender, and decrease with income. This is consistent
with high income people being more financially literate. In addition, people with voluntary savings
accounts have lower decision costs but higher enrollment costs, which is somehow surprising. One
explanation for this finding is that, when comparing two returning enrollees, one with a voluntary
savings account and the other without it, the one with the voluntary savings account would benefit
from a lower decision cost. However, once in the system, part of this lower cost disappears.21 Also,
regulation passed in 1997 that made switching more difficult, is associated with a higher enrollment
and decision costs. Finally, the estimated values of σ are significant for both switching costs and,
in the case of enrollment costs, it is an order of magnitude larger than that of decision costs. This
means that demographics are not able to explain as much heterogeneity in enrollment costs as they
do for decision costs. Note, also, that the introduction of unobserved heterogeneity has little impact
on the estimates of decision costs. This is not, however, the case with enrollment costs. Indeed, the
constant of enrollment costs more than doubles relative to the specifications that do not consider
unobserved heterogeneity.
Columns 2 and 3, in Table 7, also show that decision costs are lower for those individuals with
higher accumulated balances, while enrollment costs increase with balance. In addition, decision
costs are lower for those who had been unenrolled for longer time periods before returning, which
is consistent with the evidence presented in Section 3. Finally, allowing for autocorrelated shocks
is associated with a slight decrease in decision costs but also a slight increase in enrollment costs.
However, as shown in column 4 of Table 9, the autocorrelation coefficient is not significant.
Figure 11 plots the distribution of switching costs by component for the specification in column
6.22 The figure shows that decision costs are, on average, larger than enrollment costs, but it also
shows that there is significantly more heterogeneity in enrollment costs than in decision costs. This
is, of course, consistent with the estimates presented in Table 7 and it can be interpreted as capturing
the heterogeneity in the cost of the time involved in the administrative process that enrollees have
to follow when switching funds. This results in a significant fraction of enrollees having higher
21 This
is consistent with the “Voluntary savings account” indicator being a proxy for a third variable that is not
observed. As the result suggest that this variable should induce lower decision costs, then the voluntary savings
account may be proxying for, for example, higher financial literacy.
22 Figure 11b omits 5e-6% of the simulated switching costs that have values below -10.
21
enrollment than decision costs. Indeed, though not reported here, decision costs are higher than
enrollment costs for most enrollees, but the opposite is true for 40% of the population.
Table 8 reports different statistics of the distribution of switching costs in U.S. dollars of 2001,
and compares them to utility also in monetary terms. To compute switching costs in dollars, it
is necessary to divide the estimated switching costs (measured in utils) by the estimated marginal
utility of income, α̂it . The table shows that, on average, decision costs are $37.5, while enrollment
costs are $30, both higher than the average fee payed. This situation, a consequence of the low
switching rate and relatively inelastic demand (low α̂), is not uncommon. Indeed, Handel (2013)
reports switching costs of the order of $2,500 for a single enrollee, while Goettler and Clay (2011)
report switching costs of $208.
The estimated tastes coefficients α̂ and β̂ are reported in Table 9 and the distributions are
presented in Figure 12.23 The table shows that older people and males have a lower marginal utility
of income than young people and females. At the same time, older enrollees derive a higher marginal
utility from past performance than younger enrollees. This is consistent with older enrollees, that are
closer to retirement, being more interested in maintaining higher balances rather than on minimizing
fees. Indeed, new contributions represent a small fraction of the accumulated balance when closer
to retirement. Hence, older enrollees may try to keep their balances unaffected by returns in the
short run, even if that is associated with paying a higher fee. Finally, as was the case with switching
costs, gender is not significant.
In terms of model fit, Table 10 reports actual and predicted average choice probabilities (market
shares) for the PFAs with average market shares greater than 1%, for three different samples. The
first three columns report choice probabilities according to the estimated parameters using the whole
sample. The table shows that fit is quite good for the largest PFAs, while it is less good smaller
PFAs (though these represent less than 7% of the market). The second set of three columns uses
the same set of estimates but reports choice probabilities for initial choices only. These columns
show that, though fit is still good, it is not as good as the fit obtained when the whole sample is
considered. This is a consequence of some PFAs having zero market share among initial choices,
while the model predicts strictly positive probabilities for all of them. Finally, the last set of three
23 It
is important to point out that different sets of demographics enter each specification, as income does not enter
the specification of α. Indeed, if income were to be included in the parametrization of α, it could happen that when
both income and fees change at the same time, disposable income (income after paying fees) may not change, but α
would change mechanically. On the other hand, one could specify α as a function of disposable income rather than
income before paying fees. However, that would result in α varying across options in the choice set, meaning that
the marginal utility of income would depend on the PFA that an enrollee chooses, and would change as an enrollee
switches PFAs, even if nothing else changes. For these reasons, I do not include income in the specification of α.
22
columns reports choice probabilities among switchers. In this case, the model does worse than in
the previous cases (though still quite well), a consequence of the large estimated switching costs,
that results in the model predicting a switch with relatively low probability, as switches are rare in
the data.
In summary, the estimated parameters of the demand model proposed here give the same results as those discussed in previous sections. In particular, people who return to the system have
significantly lower switching costs than those who have continuously contributed to their accounts.
Furthermore, there is significant heterogeneity in switching costs as the distributions of these costs
show. In this sense, the results in this paper suggest that simplifying both the administrative and
the decision process may help to improve consumer choices.
5
Switching Costs, Choices, and Dynamic Price Competition
The previous sections have shown that in the Chilean retirement-investment system switching costs
are significant, that people who return to the system switch significantly more often than those
who have continuously contributed to their accounts, and that those who switch more often tend to
pay less than those who switch less often—though they still fail to minimize fees, probably because
they value other non-fee fund characteristics such as returns. Furthermore, there is little dispersion
in realized returns (because of the incentives introduced by regulation) and little persistence in the
ranking of realized returns. In this context, it is not obvious how or if a planner should intervene. On
the one hand, it is clear that the main cost of inertia is the fees that enrollees pay, as returns do not
seem to vary with the number of times people switch PFA. Then, eliminating switching costs may
intensify price competition among PFAs and reduce equilibrium fees. On the other hand, policies
that eliminate switching costs may result in enrollees switching funds often while chasing non-fee
attributes of the pension funds, which could have a negative impact on their accumulated balances.
Finally, it is important to note that because participation is mandatory, eliminating switching costs
would not affect total welfare but for the mechanic increase in utility. This is so because with
mandatory participation, switching costs do not generate a “quantity distortion” as they do in other
markets with an outside option. Hence, with mandatory participation, switching costs only affect
fees, which are a transfer between enrollees and PFAs. The exception is, of course, the case where
switching costs, because of the high equilibrium fees they induce, may result in someone either
abandoning the formal labor market or remaining informally employer. Such an option is left for
future research. In any case, the complexities introduced by switching costs, in particular the tradeoff between lower fees and active enrollees that may seek non-fee attributes of the funds, makes it
23
difficult for a policy maker to determine when and how to intervene. For this reason, I now turn
to study how the identification of the nature of the different switching costs may better inform the
design of policy.
For the reasons described above, this section studies how both consumers and firms are affected
by policies that decrease or eliminate switching costs. I start by looking at how enrollees’ choices,
fees paid, and accumulated balances change as switching costs decrease. Then, I turn my attention
to dynamic competition and study how fees change when switching change. Because the latter
requires the introduction of additional assumptions, the two sets of exercises are presented in different
subsections.
5.1
Consumer Behavior and Switching Costs
The counterfactual exercises presented here use the estimated parameters in the sixth column of
tables 7 and 9, the preferred specification with random coefficients and interaction between brand
fixed effects and demographics. With these estimates, I simulate draws of ε’s, compute the utility
associated with the initial choice of each individual, and then compute the sequence of the resulting
choices. Because the process is computationally demanding, as each counterfactual requires computing the sequence of choices for each individual over a large number of ε simulations and random
draws for the taste coefficient (100 draws of ε for each individual and alternative, plus 50 Halton
draws for each taste coefficient and switching cost), I run the counterfactuals on a random sample
of enrollees who represent 30% of the whole sample. The results do not change significantly when
using different random samples or increasing the sample size (though increasing sample size requires
reducing the number of simulated draws because of memory constraints).
The results of these exercises are presented in Table 11. I start simulating a base case that
corresponds to individuals behaving according to the estimates of the demand model. The results
show that, in this case, enrollees pay, on average, 5.89% more than if they were to choose the cheapest
fund.24 This suggests that individuals in the simulation tend to choose cheaper PFAs in their initial
choice than what is recorded in the data, as they rarely switch PFAs when fees change (this is true
both in the simulation and in the data).
In the second counterfactual, I study how the elimination of enrollment costs affects overpayment
and accumulated balances. The results show that the elimination of enrollment costs is associated
with a 5.60% overpayment rate relative to the cheapest fund, which represents a reduction of 0.29
percentage points relative to the base case (a 5% reduction), and accumulated balances remain
essentially unchanged. At the same time, though not reported here, most enrollees make the same
24 Because
there is no outside option, I describe all fees relative to those charged by the cheapest fund.
24
choices as when they faced all switching costs. This highlights that eliminating enrollment costs
may not be enough to affect behavior if decision costs are too high.
In the third counterfactual, I study how the elimination of decision costs, which affects decisions
of all but new enrollees, changes individual behavior. In this case, the results show that the mean
overpayment rate is 5.77%, 0.12 percentage points lower than that of the base case, but 0.17 percentage points higher than the one associated with the elimination of enrollment costs. What explains
this result? Recall that once enrollees enter the system, they will always be affected by decision
costs. In addition, decision costs are, on average, 27% larger than enrollment costs. This means
that when decision costs are eliminated, more enrollees become “more active” than when enrollment
costs are eliminated. If enrollees only cared about fees, this would result in these enrollees choosing
a cheaper fund. However, the demand model shows that enrollees also value other observable and
unobservable characteristics of the pension funds, which means that “more active” behavior may
reflect in a larger overpayment rate if enrollees switch funds because of factors other than fees.
In the fourth counterfactual, to highlight the relevance of distinguishing between switching costs,
I study how eliminating all switching costs affects behavior. Not surprisingly, enrollees switch more
than when decision costs are eliminated, sometimes looking for lower fees and other times looking
for, for example, higher returns. In the end, the second effect dominates and overpayment increases
0.12 percentage points relative to the base case, to 6.01%. Hence, this exercise shows exactly why
eliminating all switching costs may not be desirable in some environments and why carefully studying
the nature of switching costs is important. Indeed, the results show that allowing for some switching
costs (i.e., switching costs of a magnitude similar to that of decision costs) may result in enrollees
paying less than when all switching costs are eliminated. Nonetheless, it is important to note that
this result may depend on whether firms are allowed to re-optimize following the policy intervention.
If they are not, then the result just presented suggest that some switching costs may result in lower
payments than completely eliminating switching costs. The next section studies what happens when
firms are allowed to re-optimize following the policy intervention.
5.2
Switching Costs and Dynamic Competition
I now turn to study how price competition changes when policy either reduces or eliminates switching
costs. In this context, it is necessary to introduce a dynamic-competition model in which PFAs
choose their fees to compete for enrollees that face different levels of switching costs. An important
assumption of the model is that, instead of requiring PFAs to keep track of the status of each
enrollee, we will assume PFAs make their decisions based on their shares of enrollees of each status.
To compute these aggregate shares, it is necessary to integrate over the distribution of consumer
25
preferences. This is,
skt =
Z
sikt (pt , Xt , dit−1 , ξ; αit , βit , ηit )dF (α, β, η),
where k ∈ {new, returning, existing}, pt is the vector of fees charged in period t, X is the vector of
observable fund characteristics, dit−1 represents individual i’s choice in the previous period, ξ is a
vector containing all ξj , and η the inertia components that determine current market shares.
In this setting, if there are Mkt enrollees in status k at the beginning of period t, static profits
of firm j are given by
Πjt (st , pt , Xt ) =
X
(pjt − cjt )Mkt skt (st−1 , pt , Xt ),
k
where st−1 corresponds to the share vector at the end of the previous period, that contains information about each firm’s share among consumers of each type.
In the setting studied here, however, marginal costs are likely to be negligible as the cost of the
sale force or of the investment department do not depend directly on the marginal consumer. For
this reason, I assume cjt to be equal to zero for all PFAs.
Because switching costs introduce dynamics in the firm’s problem, this can be represented as
Vj (st−1 , Xt ) = max Πjt (st , pt , Xt ) + βEt [Vj (st , Xt+1 )].
pjt
The first-order condition associated with equation (3) is then
#′ "
#
"
∂Πjt
∂Vj (st , Xt )
∂st
= 0,
+β
Et
∂pjt
∂pjt
∂st
where
h
∂st
∂pjt
i′
and Et
h
∂Vj (st ,Xt )
∂st
i
(3)
(4)
are the two elements that follow from applying the chain rule to
the derivative of the expectation of the value function with respect to the fee chosen by firm j.
In the setting studied in this paper, equation (4) is one of many first order conditions that have to
be satisfied simultaneously (two per firm). In addition, the dimensions of the state make the problem
intractable as well. For these reasons, I introduce four assumptions that allow me to numerically
solve the dynamic problem. The first assumption reduces the firms’ problem by assuming that
instead of firms having to choose a fixed and a percentage fee, they choose the percentage fee only.
This simplification is somehow natural as most PFAs revenues were generated by the percentage
fee.25
25 In
practice, the fixed fee represents, on average, 8.8% of total revenues, with the median being 6.5%. Furthermore,
the financial records of the PFAs show that the relevance of the fixed fee decreased over time. For example, in January
of 2000, for seven of the eight PFAs in the market, the percentage fee corresponded to between 93 and 100% of revenues
generated by mandatory contributions. The exception was PFA Planvital in which case the percentage fee generated
81% revenues. Finally, the fixed fee was eliminated in 2008.
26
The rest of the assumptions are needed to reduce the dimensions of the state space. Specifically,
I assume that i) excess returns are always zero, meaning that all funds generate the same returns to
their enrollees; ii) the share vector only consists on shares among returning and existing enrollees;
and iii) I follow an approach inspired in Ifrach and Weintraub (2016) and Benkard et al. (2015) and
assume that three of the PFAs in the data behave as strategic players, and keep track of each other,
while the rest are aggregated as a secondary option and assumed to be nonstrategic. Though each
of these assumptions is rather strong, they are justified as follows. First, regarding excess returns,
this is somehow a natural simplification as, while simplifying computation significantly, the setting
studied here is one in which returns vary little and show little dispersion. This means that, in period
t, enrollees’ have no reason to expect one PFA to generate higher returns than another one in period
t + 1. Second, eliminating new enrollees appears to be a stronger assumption than what it actually
is, as though new enrollees do induce some competition, they are a small fraction of the total number
of enrollees each month (and a decreasing one during the first decade of the system). Furthermore,
even with a small number of firms, the problem is intractable with consumers that belong to one of
three different statuses. For this reason, I assume firms make their decisions based on the number
of returning and existing enrollees. As said above, this assumption is less strong as more years have
passed since the market was created, as new enrollees represent a small fraction of the enrollees
making decisions each month.26 Finally, the third assumption is probably the strongest one, as it
reduces the number of firms that are perceived as strategic. However, in my data, three of the firms
jointly had around 90% of the overall market share during the period of analysis, which suggests
that the assumption is less strong than what it first appears. Overall, these assumptions allow me
to numerically solve for equilibrium fees for each element of the state space. Appendix A describes
the algorithm used to compute these prices as well as the resources employed. I use the setting
just described to compute equilibrium prices for four cases that replicate the ones in the previous
subsection. The results are presented in Table 12.
The first scenario that I study corresponds to a base case that aims at replicating the data under
the additional assumptions just described. For this reason, one should not expect this scenario
to match the data, but to be informative about the effectiveness of policies that either reduce or
eliminate switching costs in this simpler environment that follows from the additional assumptions
just introduced. The results in this base case show that the mean expected fee (computed using
the implied market shares given the equilibrium prices that each firm charges) is 6.2%. This should
26 Specifically,
the number of elements of the state is given by |P |(|N|×|S|) , where |P | corresponds to the number of
points in which the state is discretized, |N | is the number of PFAs, and |S| is the number of shares that a firm takes
into account when choosing prices. Hence, even with a small number of firms, the number of elements in the state
becomes too large when enrollees belong to one of three types.
27
serve as our baseline to evaluate the impact of the different policies that I now introduce.
I now turn to study how eliminating each switching costs individually or jointly affects competition among firms. The results show that when enrollment costs are eliminated, equilibrium fees
decreases by 2.53 percentage points, a 41% reduction from the base case. On the other hand, when
decision costs are eliminated, equilibrium fees decrease by 3.36 percentage-points (a 38% reduction).
This suggests that, conditional on having to choose a single switching cost to eliminate, enrollees are
better off when enrollment costs are eliminated, even though decision costs are larger. However, the
results also show that eliminating all switching costs reduces equilibrium fees to 2.61%, the lowest
among all options.27
Regarding the two sets of counterfactuals presented here, it is possible to see that in both cases
consumers are better off when enrollment rather than decision costs are eliminated. However, the
elimination of all switching costs reduces equilibrium fees the most, a result that was impossible to
capture when firms were not allowed to re-optimize. This shows that, as enrollees must participate
in the market, switching costs results in significant transfers between enrollees and PFAs. Hence,
policies that reduce or eliminate switching costs may allow enrollees to use the newly available
resources in other alternatives. Nonetheless, a note of caution: all the results presented here assume
that PFAs do not change their behavior in other areas under their control. For example, if the
lower equilibrium fees induce funds to hire low-quality managers, then enrollees may be affected
through lower balances. Hence, policy makers that may be interested in designing policies to reduce
or eliminate switching costs should be concerned about indirect effects that those policies may have,
that have not been explored here.
6
Conclusions
Though the existence of switching costs has been extensively documented in economics, little is
known about what causes them. Furthermore, in situations with coexisting switching costs, researchers have been unable to distinguish between them and to quantify their impact on choice
behavior separately. In this paper, I study and quantify the impact of two sources of inertia among
enrollees in a defined-contribution pension system: the cost associated with analyzing financial information and choosing a pension fund, and a hassle cost in the form of a time-consuming bureaucratic
process that enrollees must follow when switching pension funds.
By exploiting variation derived from changes in employment status, I show that enrollees who
27 In
is important to note that in this last case the game is static as the only source of dynamics is the existence of
switching costs.
28
return to the system after periods during which they did not save for retirement are four times more
likely to switch pension funds than enrollees who have contributed continuously, which is consistent
with these returning enrollees having lower switching costs. Furthermore, I show that switching
behavior does not seem to be explained by differences in preferences across groups of consumers,
but rather by the nature of the switching costs they face.
To quantify the impact of switching costs on consumer behavior, I estimate demand for pension
funds. The results show that switching costs are mostly determined by the cost of analyzing financial
information and choosing a pension fund, while the rest is explained by the hassle cost associated
with switching.
I then turn to study how enrollee’s and firm’s decision are affected by switching costs. I first
study how enrollee’s behavior changes when the different switching costs are eliminated and firms
are not allowed to re-optimize. Then, I study how switching costs affect dynamic price competition
among pension funds. The results show that, when funds are not allowed to re-optimize, enrollees
become more active as switching costs decrease, and switch pension funds more often. However,
when decision costs are eliminated, some consumers seek non-fee attributes (such as returns) and
pay higher fees than when they face all switching costs. However, when funds are allowed to reoptimize, eliminating all switching costs intensifies competition the most, resulting in the lowest
equilibrium fees (though eliminating either source of switching costs alone has a significant impact
on equilibrium fees as well). This suggests that policies that eliminate switching costs may result in
significant savings for enrollees.
Regarding policy implications outside the environment studied here, this paper has shown that
identifying sources of switching is important for designing policy, as in many cases eliminating all
switching may not be possible, while eliminating some sources of switching costs may be a realistic
alternative.
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A
Dynamic Price Competition
This appendix describes the procedure followed when analyzing how switching costs affect equilibrium pricing. The starting point is Equation 4 that is reproduced below
#′ "
#
"
∂Πjt
∂Vj (st , Xt )
∂st
= 0.
+β
Et
∂pjt
∂pjt
∂st
(⋆)
Equation (⋆) represents the set of first-order conditions that have to be solved, simultaneously, by the
equilibrium fees. To solve the system of equation, it is necessary to compute the whole second term,
h
i
∂Vj (st ,Xt )
and, in particular, Et
. This is, the expectation of the derivative of the value function
∂st
with respect to the share vector. To compute this derivative, I follow a two-step procedure. First, I
estimate a policy function p = p(st , ξ). With the policy function, I use the sequential representation
of the value function and simulate N paths of length T . This is,
V (st , Xt ) =
N T
1 XX t
β Π(st , pt , Xt ).
N i=1 t=0
This approximation of the value function allows me to compute the continuation value for any given
initial st . Then, to compute the derivative of the value function, I use
∂V (st+1 , Xt )
V (st + ǫl, Xt ) − V (st − ǫl, Xt )
=
,
∂sjt
2ǫ
33
(5)
where ǫ is a small constant and l is a vector (of the same length as st ) with a one in position l and
zeros everywhere else. This is, the derivative of the value function with respect to share is computed
by definition.
The approximation just described allows to solve for equilibrium fees for any given starting vector
of shares st . Furthermore, once the space of shares has been discretized, the equation can be solved
independently for all points in the grid. Finally, though the share grid may be coarse, this does not
affect the computation of the derivative by using forward simulation as the sequential representation
of the value function results in shares, period to period, that need not be in the grid of points
originally defined.
As described above, once the state has been discretized, the problem can be solved independently
for every point in the grid. However, the problem is still difficult from a computational perspective
as the derivative of the value function has to be recomputed, by forward simulation, in all iterations
during the search for optimal fees. For this reason, I make use of the Open Science Grid (Pordes et
al., 2007; Sfiligoi et al., 2009) to compute equilibrium fees for each point in the grid of initial states
(each initial point in the grid defines a different job submitted to the OSG). Then, I interpolate
the resulting grid of equilibrium fees, to compute fees for a finer grid of states. Finally, to compute
steady-state fees, I draw 10, 000 random initial states from the finer grid (the interpolated one)
and for each randomly drawn state I search for the associated optimal fees within the array just
described. With these fees, I recompute the implied shares and iterate until fees (and shares) do
not change between two iterations. The fees reported in Section 5 correspond to the mean expected
fee computed across the 10,000 simulations using the implied shares to compute the expected fee for
each simulation.
34
B
Tables
Table 1: Summary statistics by sample
Sample 1
Sample 2
Estimation Sample
Number of people
15,458
9,257
8,888
Gender (Female)
0.44
0.5
0.49
Age when enrolling
27.98
24.65
24.66
(10.26)
(8.89)
(8.92)
36.35
30.74
30.58
(12.02)
(9.7)
(9.71)
0.21
0.16
0.16
(0.4)
(0.37)
(0.37)
89.57
66.12
63.94
(58.11)
(48.68)
(48.17)
247,073.9
221,901.1
222,552.4
(490,296.8)
(238,748.1)
(239,173.8)
15.77
14.61
11.85
(21.01)
(19.49)
(13.82)
105,356
45,188
43,648
(as % of total decisions)
11.9%
12.6%
12.4%
Number of changes
30,091
12,560
12,196
(as % of total decisions)
3.4%
3.5%
3.5%
Number of observations
886,087
358,800
350,660
Age in 2001
Voluntary savings
Number of months observed
Income in pesos of December 2001
Time inactive
Active decisions
Note: The table reports means and standard deviations (in parenthesis) for selected
demographics across the different samples that result from applying the selection criteria described in Section 2. Sample 1 corresponds to people who are unambiguously
matched to a PFA. Sample 2 drops people who enrolled before 1988 and people who
when enrolling were younger than 15 or older than 65 years old. The estimation sample drops people who did not contribute to their accounts for more than 60 months in
an attempt to avoid selection into informality.
35
Table 2: Fraction of observations involving switching behavior by contribution status
Contribution
Number of
Number of
observations
changes
All data
With savings account
Returning enrollees
43,648
4,772
10.9%
15%
Existing enrollees
298,124
7,424
2.5%
3.3%
status
Changes as % of observations
Note: The table presents the number of observations, number of changes of PFA, and
the number of changes as percentages of observations for existing and returning enrollees. The table was constructed using all observations except initial choices.
36
Table 3: Effect of changes in monthly salary and demographics on the probability of switching
(1)
(3)
(4)
(5)
(6)
0.732
0.729
0.736
0.744
0.784
(0.01)
(0.01)
(0.011)
(0.011)
(0.011)
0.123
0.013
-0.006
-0.015
-0.008
(0.009)
(0.009)
(0.01)
(0.01)
(0.01)
-0.007
-0.009
(0.001)
(0.001)
0.003
0.015
(0.014)
(0.013)
Has a voluntary
0.172
0.151
savings account
(0.015)
(0.014)
Returning
Increase in salary > 10%
(2)
Age
Male
Marginal effect
10.93%
10.9%
10.52%
10.59%
10.7%
Year fixed effects
No
No
No
Yes
Yes
Yes
PFA fixed effects
No
No
No
No
No
Yes
341,772
341,772
341,772
341,772
341,772
341,769
0.054
0.002
0.054
0.0963
0.102
0.149
-49,809.5
-52,530.4
-49,808.5
-47,557.7
-47,283.3
-44,755.2
5,339.9
194.8
5,454.1
6,578.3
6,774.3
11,776.5
N
Pseudo R
2
Log Likelihood
χ
2
Note: Standard errors, clustered at the individual level, in parentheses. An observation is an
individual–month combination. The dependent variable is equal to one if the individual switched
and zero otherwise. Estimation method is by maximum likelihood. The specified model is a probit
model. All marginal effects are significant at the 1% level.
37
Table 4: More on the effect of demographics on the probability of switching
(1)
(2)
(3)
(4)
0.783
0.687
0.703
0.688
(0.0110)
(0.0125)
(0.0123)
(0.0125)
-0.004
-0.0421
0.00194
-0.0407
(0.009)
(0.0104)
(0.00981)
(0.0105)
-0.009
-0.00989
-0.0100
-0.0100
(0.001)
(0.000843)
(0.000849)
(0.000852)
0.013
-0.00280
0.00452
-0.00333
(0.013)
(0.0132)
(0.0133)
(0.0132)
Has a voluntary
0.150
0.137
0.137
0.136
savings account
(0.014)
(0.0138)
(0.0141)
(0.0139)
Year≥ 1998
-0.443
0.0177
0.0173
0.0178
(0.000947)
(0.000940)
(0.000948)
Returning
Increase in salary > 10%
Age
Male
(0.013)
Time elapsed
before returning
Salary (tens of
thousands of Chilean pesos)
0.00440
0.00429
(0.000319)
(0.000334)
Account balance (tens of
thousands of Chilean pesos)
Marginal effect of returning
0.000441
0.0000406
(0.0000696)
(0.0000733)
10.83%
9.32%
9.55%
9.33%
Year fixed effects
No
Yes
Yes
Yes
PFA fixed effects
Yes
Yes
Yes
Yes
341769
341769
341769
341769
0.140
0.156
0.153
0.156
-45272.9
-44410.6
-44545.1
-44410.3
11554.0
12866.8
18755.7
12892.9
N
Pseudo R2
Log likelihood
χ
2
Note: Standard errors, clustered at the individual level, in parentheses. The dependent variable is an indicator that is equal to one if the enrollee switches managers
in that period and zero otherwise. A unit of observation is an enrollee in a month.
Estimation corresponds to a probit regression. All marginal effects are significant at
38
the 1% level.
Table 5: Demographics among returning and existing enrollees
Year of initial enrollment
1988
1994
2000
Returning
Existing
Returning
Existing
Returning
Existing
30
31.1
27.6
28.3
24.8
25.7
(8.1)
(8.0)
(9.6)
(8.9)
(9.0)
(8.7)
159947.7
167897.4
210069.2
192524.5
194350.9
203370.7
(247714.5)
(190575.9)
(304510.3)
(177790.8)
(209558.2)
(198063.1)
Male
0.62
0.58
0.57
0.50
0.49
0.46
Voluntary savings account
0.31
0.36
0.22
0.26
0.07
0.08
Age
Income
Note: This table reports means and standard deviations for each variable depending on the year of enrollment. For each year, the average are taken across all observations that correspond to people either returning
to the system or people classified as existing enrollees.
39
Table 6: Effect of returning on the probability that returning enrollees switch when fees change
Fee changing in month t relative to t − 1
Fixed
Percentage
Fixed
Percentage
(1)
(2)
(3)
(4)
0.672
0.514
0.887
0.648
(0.144)
(0.0854)
(0.335)
(0.166)
-0.0112
-0.00415
-0.0146
-0.00581
(0.00612)
(0.00483)
(0.00839)
(0.00517)
-0.0271
-0.00375
-0.157
-0.0277
(0.117)
(0.0773)
(0.138)
(0.0876)
0.164
0.123
0.113
0.0691
(0.136)
(0.0882)
(0.163)
(0.0998)
0.00464
0.00392
0.00516
0.00459
(tens of thousands)
(0.00164)
(0.00108)
(0.00186)
(0.00118)
Account balance
0.0000674
-0.0000682
0.000449
0.000392
(tens of thousands)
(0.000424)
(0.000232)
(0.000405)
(0.000211)
8.67%
7.52%
12.20%
9.32%
1363
3309
1003
2720
Pseudo R2
0.0765
0.0469
0.2231
0.1955
Log likelihood
-283.71
-660.82
-207.12
-522.39
45.29
58.57
127.34
258.51
Returning in t
Age
Male
Has a savings account
Salary
Marginal effect
N
χ2
Note: Standard errors, clustered at the individual level, in parentheses. The
dependent variable is an indicator that is equal to one if the enrollee switches
managers in that period and zero otherwise. A unit of observation is an enrollee in a month. Estimation corresponds to a probit regression. The sample
corresponds to individuals who returned in consecutive periods (t − 1 and t),
when fees change in t relative to t − 1. In all cases, the sample is restricted to
individuals who, if returning in t − 1, did not switch PFAs at that time, and
compares their behavior in t with that of enrollees who returned in period t.
Columns 3 and 4 repeat regressions presented in columns 1 and 2 adding fixed
effects for the time when the enrollee left the market before she returned. All
marginal effects are significant at the 1%
40 level.
Table 7: Estimated parameters of the structural model: Switching costs
Includes
Decision cost
Constant
Age
Male
Income
Voluntary savings
Regulation
Autocorrelated ε
Random Coefficients
Baseline
Balance
Time unenrolled
ρεijt−1 + εijt
Baseline
(5) +PFA FE & demographics
(1)
(2)
(3)
(4)
(5)
(6)
(6) + Control function
(7)
3.503
3.488
3.621
2.913
3.477
3.432
3.430
(0.068)
(0.069)
(0.069)
(0.449)
(0.070)
(0.070)
(0.070)
0.015
0.015
0.014
0.055
0.015
0.016
0.016
(0.002)
(0.002)
(0.002)
(0.012)
(0.002)
(0.002)
(0.002)
-0.020
-0.019
-0.021
0.026
-0.025
-0.021
-0.019
(0.034)
(0.034)
(0.034)
(0.007)
(0.034)
(0.034)
(0.034)
-0.004
-0.004
-0.004
0.042
-0.004
-0.004
-0.004
(0.001)
(0.001)
(0.001)
(0.017)
(4E-4)
(5E-4)
(5E-4)
-0.393
-0.383
-0.421
-0.312
-0.396
-0.392
-0.393
(0.036)
(0.036)
(0.036)
(0.050)
(0.036)
(0.036)
(0.036)
0.520
0.535
0.539
0.633
0.539
0.531
0.532
(0.037)
(0.038)
(0.037)
(0.031)
(0.038)
(0.038)
(0.038)
Balance
-1E-4
(2E-4)
Time unenrolled
-0.019
(0.002)
Sigma
Enrollment cost
Constant
Age
Male
Income
Voluntary savings
Regulation
0.043
0.043
0.043
(0.011)
(0.011)
(0.011)
1.175
1.312
1.057
1.116
2.551
2.538
2.523
(0.084)
(0.089)
(0.085)
(0.090)
(0.279)
(0.253)
(0.268)
0.013
0.009
0.014
0.051
0.018
0.018
0.017
(0.003)
(0.003)
(0.003)
(0.010)
(0.003)
(0.003)
(0.003)
0.003
-0.009
0.003
0.058
0.026
0.023
0.021
(0.041)
(0.041)
(0.041)
(0.009)
(0.045)
(0.045)
(0.045)
-0.005
-0.009
-0.004
0.026
-0.010
-0.010
-0.010
(0.001)
(0.001)
(0.001)
(0.005)
(0.001)
(0.001)
(0.001)
0.164
0.115
0.191
0.206
0.113
0.112
0.113
(0.043)
(0.044)
(0.043)
(0.022)
(0.048)
(0.048)
(0.048)
0.423
0.345
0.403
0.397
0.709
0.710
0.702
(0.047)
(0.048)
(0.047)
(0.039)
(0.075)
(0.071)
(0.074)
Balance
0.001
(2E-4)
Sigma
McFadden’s Pseudo R2
− N1 L
1.988
1.962
1.943
(0.211)
(0.194)
(0.209)
0.890
0.890
0.890
0.484
0.890
0.891
0.891
0.267
0.267
0.267
1.295
0.266
0.266
0.266
Number of observations
350,660
Note: Standard errors in parentheses. PFA fixed effects included in all specifications. The dependent variable is an indicator that is equal to one for the chosen PFA and zero
for the rest. Estimation is via Maximum Likelihood in columns 1 to 3 and Simulated Maximum Likelihood in columns 4 to 6. In column 4, standard errors correspond to those
obtained using 25 bootstrap samples. In columns 5 and 6, estimation uses 50 Halton draws per individual. Column 7 includes a control function term.
41
Table 8: Switching costs and utility in monetary units
Decision cost
Enrollment cost
Utility
Mean
$37.5
$30.2
$266.8
Median
$34.2
$27.1
$168.0
Standard deviation
$16.2
$22.9
$294.4
Note: All numbers correspond to the ratio between the variable of
interest and α̂it . Computation excludes the upper and lower 1%
of the distributions to avoid issues with extreme values affecting
computation of the mean and standard deviation.
Table 9: Estimated parameters of the structural model: Preferences
Includes
Marginal utility of income
Constant
Age
Male
Autocorrelated ε
Random Coefficients
Baseline
Balance
Time unenrolled
ρεijt−1 + εijt
(1)
(2)
(3)
(4)
(5)
(6)
(7)
4.1362
3.9879
4.1265
4.1827
4.7118
3.1856
3.1632
(0.3295)
(0.3308)
(0.3297)
(0.1078)
(0.3725)
(0.45705)
(0.46287)
-0.0979
-0.0668
-0.0978
-0.0992
-0.10124
-0.023692
-0.022957
(0.0097)
(0.0102)
(0.0097)
(0.0131)
(0.010179)
(0.013526)
(0.01373)
-0.7342
-0.58
-0.7367
-0.7356
-0.82899
-0.90085
-0.93544
(0.1602)
(0.1615)
(0.1604)
(0.1583)
(0.17276)
(0.20117)
(0.2013)
Balance
PFA FE & demographics
(6) + Control function
-0.0047
(0.0003)
Sigma
Marginal utility of returns
Constant
Age
Male
Income
0.16107
0.17609
0.16607
(0.067523)
(0.067235)
(0.067984)
-0.045
-0.036
-0.045
-0.0464
-0.047802
-0.031791
-0.027829
(0.0059)
(0.0060)
(0.0059)
(0.0044)
(0.0062535)
(0.0065931)
(0.0068169)
0.0013
0.0009
0.0013
0.0018
0.0013794
0.00096116
0.00089198
(0.0002)
(0.0002)
(0.0002)
(0.0003)
(0.00020687)
(0.00020866)
(0.00021236)
-0.0042
-0.0064
-0.0041
-0.0037
-0.0048057
-0.004732
-0.0047347
(0.0030)
(0.0031)
(0.0030)
(0.0035)
(0.0032833)
(0.0033422)
(0.0033546)
0.0005
0.0003
0.0005
0.001
0.00056803
0.0005015
0.00049486
(4.56E-005)
(4.84E-005)
(4.55E-005)
(8.82E-005)
(0.000048595)
(0.000047673)
(0.000047842)
Balance
0.0002
(1.27E-005)
Sigma
|ρ| or Control Function
McFadden’s Pseudo R2
− N1 L
0.0036656
0.0044024
0.0044737
(0.0067551)
(0.007038)
(0.0070553)
0.0039
-0.000037456
(0.0884)
(0.0000098405)
0.890
0.890
0.890
0.484
0.890
0.891
0.891
0.267
0.267
0.267
1.295
0.266
0.266
0.266
Number of observations
350,660
Note: Standard errors in parentheses. PFA fixed effects included in all specifications. The dependent variable is an indicator that is equal to one for the chosen PFA and zero for the
rest. Estimation is via Maximum Likelihood in columns 1 to 3 and Simulated Maximum Likelihood in columns 4 to 6. In column 4, standard errors correspond to those obtained
using 25 bootstrap samples. In columns 5 and 6, estimation uses 50 Halton draws per individual. Column 7 includes a control function term.
42
Table 10: Model fit: Choice probabilities (percent)
Market Share over All Choices
Market Share over Initial Choices
Market Share among Switchers
PFA
Data
Predicted
PFA
Data
Predicted
PFA
Data
Predicted
20
36.6
33.3
20
37.1
27.3
20
24.6
23.9
12
24.5
24.0
22
22.5
16.7
12
21.4
20.9
22
18.1
20.3
12
20.5
18.9
22
10.9
15.7
23
7.1
6.9
23
4.7
8.0
7
9.4
7.7
7
5.9
4.6
19
3.4
7.0
23
8.9
7.8
19
2.1
4.8
6
3.1
3.8
19
5.7
6.5
13
1.5
1.2
24
1.9
7.5
6
3.6
8.8
24
1.3
3.0
7
1.7
6.2
1
3.3
5.2
Note: The table reports mean predicted choice probabilities for different samples. The predicted probabilities are computed using specification 6 of tables 7 and 9.
Table 11: Counterfactuals: Overpayment and savings under different policies
Overpayment rate
Mean final balance
Policy
Mean
Median
relative to base case
Base simulation
5.89%
4.66%
-
No enrollment cost
5.60%
4.33%
+0.02%
No decision cost
5.77%
4.52%
-0.02%
No switching costs
6.01%
4.81%
+0.03%
Note: The table reports the mean and median overpayment rate
and the mean balance relative to the base case, for each of the
policies under study. None of the mean differences reported in the
last column is statistically different from zero. Also, differences in
median savings relative to the base case are always zero.
43
Table 12: Counterfactuals: Equilibrium fees and Confidence Intervals
Case
Mean and 95% CI
Base simulation
6.195%
[6.181%,6.210%]
No enrollment cost
3.666%
[3.660%,3.671%]
No decision cost
3.837%
[3.833%,3.842%]
No switching costs
2.607%
Note: The table reports the mean expected
fees and 95% confidence intervals for the
different scenarios under study.
Means
and confidence intervals computed over
the equilibrium fees obtained from starting
from 10, 000 random initial states.
44
C
Figures
.04
.035
.03
1.5
.025
1
.5
.02
Number of pension funds
10
15
20
Mean fixed fee
in US dollars of December 2001
2
Mean percentage fee
25
Figure 1: Number of PFAs and fees over time
0
5
1988m1 1990m1 1992m1 1994m1 1996m1 1998m1 2000m1 2002m1
1988m1
1990m1
1992m1
1994m1
1996m1
1998m1
2000m1
Year
2002m1
Mean fixed fee
Date
(a) Number of pension funds
Mean percentage fee
(b) Mean fees
Figure 2: Distribution of fees over time
.04
2
.035
Percentage fee
1.5
1
.03
.025
.5
Note: Excludes outside values
01
00
20
99
20
98
19
97
19
96
19
95
19
94
19
93
19
92
19
91
19
90
19
89
19
88
19
01
00
20
99
20
98
19
97
19
96
19
95
19
94
19
93
19
92
19
91
19
90
19
19
19
19
89
.02
88
0
19
Fixed fee
in US dollars of December 2001
2.5
Note: Excludes outside values
(a) Fixed fee
(b) Percentage fee
The figures show the median (horizontal line), 25th and 75th percentile (upper and lower extreme of the boxes), and
the maximum and minimum adjacent values.
45
Figure 3: Distribution of 36-months annualized realized returns and difference to industry mean
.6
Density
.4
15
10
.2
36−month real returns, %
20
5
0
0
−6
−4
−2
0
2
Difference in real returns relative to the industry mean (%)
19881989199019911992199319941995199619971998199920002001
Note: Excludes outside values
(a) Distribution of returns
(b) Returns relative to the industry mean
The figure on the left shows the box-plot of realized returns over time, reporting the median, 25th and 75th percentile,
and the maximum and minimum adjacent values. The figure on the right reports the distribution of returns relative
to the industry mean.
0
0
100
Number of months
50
Number of people enrolled
200 300 400 500 600
700
100
800
Figure 4: Statistics about contributions by enrollment year
1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Year of enrollment
(a) Enrollment by year
1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Year of enrollment
Mean number of months between first and last recorded contribution
Mean number of contributions
(b) Number of months observed and contributions
The figure on the left shows the number of people in the sample by year of initial enrollment. The figure on the
right reports the mean number of months between the first and last reported contribution and the mean number of
contributions.
46
40
30
20
Density
0
10
20
0
10
Density
30
40
Figure 5: Total number of changes and switching rate
0
.2
.4
.6
Switching rate
Total number of changes/Total number of contributions
.8
(a) Whole sample
0
.2
.4
Switching rate
Total number of changes/Total number of contributions
.6
(b) Enrollees who entered on or before 1995
The figures report the switching rate for two samples. The figure on the left reports the switching rate for the whole
sample and the figure on the right for those that enrolled for the first time on or before 1995.
8
.08
.1
Excess payment over
cheapest alternative
.12
.14
.16
.18
Mean Real Annual Return (%)
8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10
Figure 6: Overpayment and returns by number of changes of PFAs
0
2
4
6
Number of changes
95% Confidence Interval
8
10
Mean Real Annual Return
0
2
4
6
Number of changes
95 Confidence Interval
(a) Excess returns
8
10
Excess Payment
(b) Excess payment
The figures report local polynomial smoothing of payments in excess of the cheapest option and realized returns for
the three years following a change of PFA.
47
.08
Probability of paying a lower total fee
.2
.25
.3
.35
.4
.45
.02
Probability of Switching PFA
.04
.06
95% CI
0
20
40
60
Time elapsed since last active decision
80
1
2
3
4
5
6
7
8
Months since returning
kernel = epanechnikov, degree = 0, bandwidth = 1.42, pwidth = 2.13
(a) Predicted probability of paying lower fees
9
10
11
12
(b) Predicted probability of paying lower fees
The left figure reports a local polynomial smoothing the probability of paying lower fees on the time elapsed since the
last active decision (i.e., the last time enrollment costs were sunk). The figure on the right reports the probability of
switching PFA (and the 95% confidence interval) as a function of the number of months since an enrollee returned
to the system. The baseline specification is that in column 6 of Table 3, replacing the indicator of returning by a
variable that measures the number of months since an individual returned.
Probability of Switching PFA
.1
.15
.2
.25
.025
95% Confidence interval
.01
65
80
10
20
30
40
50
60
Age
.05
95% Confidence interval
Probability of switching PFA
.03
.035
.04
.045
Probability of switching PFA
.02
.03
.04
.05
.3
Figure 8: Probability of switching and demographics
95 125 155 185 215 245 275 310 340 370 >385
110 140 170 200 230 260 290 325 355 385
Income
Tens of thousands of Pesos
95% Confidence interval
0
5
10
15
20
25
30
35
40
45
Months elapsed before returning
50
55
60
(c) Prob. of switching and number
(b) Prob. of switching by income of months away from the system
(a) Prob. of switching by age
The figures report local polynomial regressions of the probability of switching as a function of age, income level, and
the time away from the system before returning.
0
10
20
Number of times returning
(a) 1988
30
40
0
0
0
10
2
5
20
%
%
%
4
30
6
40
10
8
Figure 9: Distribution of the number of times enrollees return to the system by year of enrollment
0
5
10
15
Number of times returning
(b) 1994
48
20
25
0
2
4
6
Number of times returning
(c) 2000
8
10
Probability of Switching PFA
.05
.1
.15
Figure 10: Probability of Switching by status and months after a fee changed
0
95% Confidence interval
Existing Enrollees
0
Returning Enrollees
5
10
Months elapsed since a fee changed
15
The figure reports local polynomial smoothing regressions (and 95% confidence intervals) of the probability of switching, by status, as a function of the time elapsed since fees last changed.
Figure 11: Distributions of estimated switching costs
0.3
0.2
Decision cost
Enrollment cost
0.18
Decision cost
Enrollment cost
0.25
0.16
0.14
Probability
Probability
0.2
0.15
0.1
0.12
0.1
0.08
0.06
0.04
0.05
0.02
0
-10
-5
0
5
10
15
η̂itk k ∈ {M, E}
M and η̂ E
(a) Distribution of η̂it
it
0
-50
0
50
100
U.S. dollars of December 2001
(b) Distribution of
M
η̂it
α̂it
and
E
η̂it
α̂it
The left figure reports the estimated distribution of both switching costs. The right figure reports the distribution of
switching costs in US dollars.
49
Figure 12: Distributions of estimated taste coefficients
0.18
0.18
Males
Females
0.14
0.14
0.12
0.12
0.1
0.08
0.06
0.1
0.08
0.06
0.04
0.04
0.02
0.02
0
-10
-8
-6
Males
Females
0.16
Probability
Probability
0.16
-4
-2
0
2
4
0
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
β̂it
α̂it
(a) Distribution of α̂it
(b) Distribution of β̂it
The left figure reports the distribution of the marginal utility of income (α̂) by gender and the right figure reports
the distribution of preferences over the ranking of returns (β) also by gender.
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