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 Iv´ an Canay, Ben Handel, Manuel Hermosilla, Christopher ´ Lau, Guillermo Marshall, Alvaro 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. Horta¸csu 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. Dub´e 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 Vald´ es, 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 , y¯t }) + 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 , y¯t }) + Xjt βit − ηit 1[dit−1 6= j] + ξj ) P dFµ , ′ exp(−α (f + p min{y , y ¯ }) + 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 ξ, ˆσ Maximum Likelihood estimator θˆ = {ˆ η, α ˆ , β, ˆ } is given by θˆ = 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, α ˆ it . 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 α ˆ ), 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 α ˆ and βˆ 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.

References Arie, Guy and Paul LE Grieco, “Who pays for switching costs?,” Quantitative Marketing and Economics, 2014, 12 (4), 379–419. Beggs, Alan and Paul Klemperer, “Multi-Period Competition with Switching Costs,” Econometrica: Journal of the Econometric Society, 1992. Benkard, C. Lanier, Przemyslaw Jeziorski, and Gabriel Y. Weintraub, “Oblivious equilibrium for concentrated industries,” The RAND Journal of Economics, 2015, 46 (4), 671–708.

29

Bernstein, Solange and Alejandro Micco, “Turnover and Regulation: The Chilean Pension Fund Industry,” Documento de Trabajo 180, Banco Central de Chile 2002. and Carolina Cabrita, “Los Determinantes de la Elecci´on de AFP en Chile: Nueva Evidencia a Partir de Datos Individuales,” Documento de Trabajo 19, Superintendencia de AFP December 2006. and Jos´ e Luis Ruiz, “Sensibilidad de la Demanda con Consumidores Desinformados: El caso de las AFP en Chile,” Documento de Trabajo 4, Superintendencia de AFP 2004. Berry, Steven, James Levinsohn, and Ariel Pakes, “Automobile Prices in Market Equilibrium,” Econometrica, 1995, 63 (4), pp. 841–890. Beshears, John, James J. Choi, David Laibson, and Brigitte C. Madrian, “Simplification and saving,” Journal of Economic Behavior & Organization, 2013, 95 (0), 130–145. , James J Choi, David Laibson, Brigitte C Madrian, and Katherine L Milkman, “The effect of providing peer information on retirement savings decisions,” The Journal of Finance, 2015, 70 (3), 1161–1201. Cabral, Luis, “Dynamic pricing in customer markets with switching costs,” Review of Economic Dynamics, 2016, 20, 43–62. Carroll, Gabriel D., James J. Choi, David Laibson, Brigitte C. Madrian, and Andrew Metrick, “Optimal Defaults and Active Decisions,” The Quarterly Journal of Economics, 2009, 124 (4), 1639–1674. Cerda, Rodrigo, “Movilidad en la Cartera de Cotizantes por AFP: La Importancia de ser Primero en Rentabilidad,” Documento de Trabajo 309, Pontificia Universidad Cat´olica de Chile 2005. Chetty, Raj, John N. Friedman, Soren Leth-Petersen, Torben Nielsen, and Tore Olsen, “Active vs. Passive Decisions and Crowd-out in Retirement Savings Accounts: Evidence from Denmark,” The Quarterly Journal of Economics, 2014, 129 (3), 1141–1219. Choi, James J., David Laibson, and Brigitte C. Madrian, “Reducing the Complexity Costs of 401(k) Participation Through Quick Enrollment,” in David A. Wise, ed., Developments in the Economics of Aging, NBER Book Series - The Economics of Aging, University of Chicago Press, March 2009, pp. 57–82. ,

, and

, “100 Bills on the Sidewalk: Suboptimal Investment in 401(k) Plans,” The Review

of Economic Studies, August 2011, 93 (3), 748–763. 30

Crawford, George S., Nicola Tosini, and Keith Waehrer, “The Impact of ‘Rollover’ Contracts on Switching Costs in the UK Voice Market: Evidence from Disaggregate Customer Billing Data,” Working Papers Series DP8693, SSRN December 2011. Duarte, Fabian and Justine Hastings, “Fettered Consumers and Sophisticated Firms: Evidence from Mexico’s Privatized Social Security Market,” Technical Report 18582, National Bureau of Economic Research December 2012. Dub´ e, Jean-Pierre, G¨ unter J. Hitsch, and Peter E. Rossi, “Do Switching Costs Make Markets Less Competitive?,” Journal of Marketing Research, 2009, 46 (4), pp. 435–445. Farrell, Joseph and Paul Klemperer, “Coordination and Lock-in: Competition with Switching Costs and Network Effects,” Handbook of Industrial Organization, 2007, 3, 1967–2072. Ferreiro, Alejandro, ed., The Chilean Pension System, fourth ed., Superintendencia de Administradoras de Fondos de Pensiones, May 2003. Goettler, Ronald L and Karen Clay, “Tariff Choice with Consumer Learning and Switching Costs,” Journal of Marketing Research, August 2011, 48 (4), 633–652. Grubb, MichaelD., “Failing to Choose the Best Price: Theory, Evidence, and Policy,” Review of Industrial Organization, 2015, 47 (3), 303–340. Handel, Benjamin, “Adverse Selection and Inertia in Health Insurance Markets : When Nudging Hurts,” The American Economic Review, 2013, 103 (7), 2643–2682. Hastings, Justine, “Investor Decisions and the Financial Crisis in Mexico’s Privatized Social Security Market,” September 2010. Hastings, Justine S., Ali Horta¸ csu, and Chad Syverson, “Advertising and Competition in Privatized Social Security: The Case of Mexico,” Working Paper 18881, National Bureau of Economic Research March 2013. and Lydia Tejeda-Ashton, “Financial Literacy, Information, and Demand Elasticity: Survey and Experimental Evidence from Mexico,” Working Paper 14538, National Bureau of Economic Research December 2008. Hastings, Justine S, Olivia S Mitchell, and Eric T Chyn, “Fees, framing, and financial literacy in the choice of pension manager,” Pension Research Council WP2010-09, 2010.

31

Horta¸ csu, Ali, Seyed Ali Madanizadeh, and Steven L. Puller, “Power to Choose: An Analysis of Consumer Inertia in the Residential Electricity Market,” Technical Report February 2015. Working Paper. Ifrach, Bar and Gabriel Y Weintraub, “A Framework for Dynamic Oligopoly in Concentrated Industries,” 2016. Illanes, Gast´ on, “Switching Costs in Pension Plan Choice.” PhD dissertation, Massachusetts Institute of Technology 2016. Klemperer, Paul, “Markets with Consumer Switching Costs,” The Quarterly Journal of Economics, 1987, 102 (2), 375–394. , “The Competitiveness of Markets with Switching Costs,” The RAND Journal of Economics, 1987, 18 (1), pp. 138–150. Krasnokutskaya, Elena, Yiyang Li, and Petra Todd, “Product Choice under Government Regulation: The Case of Chile’s Privatized Pension System,” Technical Report August 2016. Madrian, Brigitte C. and Dennis F. Shea, “The Power of Suggestion: Inertia in 401(k) Participation and Savings Behavior,” The Quarterly Journal of Economics, 2001, 116 (4), pp. 1149–1187. Marinovic, Iv´ an and Salvador Vald´ es, “La Demanda de las AFP Chilenas: 1993-2002,” Technical Report, Pontificia Universidad Cat´olica de Chile 2005. Marzilli Ericson, Keith M, “Consumer inertia and firm pricing in the Medicare Part D prescription drug insurance exchange,” American Economic Journal: Economic Policy, 2014, 6 (1), 38–64. Miravete, Eugenio J. and Ignacio Palacios-Huerta, “Consumer Inertia, Choice Dependence and Learning from Experience in a Repeated Decision Problem,” The Review of Economic Studies, July 2014, 96 (3). Nosal, Kathleen, “Estimating switching costs for medicare advantage plans,” Unpublished manuscript, University of Mannheim, 2012. Polyakova, Maria, “Regulation of Insurance with Adverse Selection and Switching Costs: Evidence from Medicare Part D.,” American Economic Journal: Applied Economics, july 2016, 8 (3), 165– 195.

32

Pordes, Ruth, Don Petravick, Bill Kramer, Doug Olson, Miron Livny, Alain Roy, Paul Avery, Kent Blackburn, Torre Wenaus, W Frank et al., “The open science grid,” in “Journal of Physics: Conference Series,” Vol. 78 IOP Publishing 2007, p. 012057. Sfiligoi, Igor, Daniel C Bradley, Burt Holzman, Parag Mhashilkar, Sanjay Padhi, and Frank Wurthwein, “The pilot way to grid resources using glideinWMS,” in “Computer Science and Information Engineering, 2009 WRI World Congress on,” Vol. 2 IEEE 2009, pp. 428–432. Shcherbakov, Oleksandr, “Measuring consumer switching costs in the television industry,” The RAND Journal of Economics, 2016, 47 (2), 366–393. Sudhir, K and Nathan Yang, “Exploiting the Choice-Consumption Mismatch: A New Approach to Disentangle State Dependence and Heterogeneity,” Technical Report October 2015. Thaler, Richard H and Cass R Sunstein, Nudge: Improving Decisions About Health, Wealth, and Happiness, Yale University Press, 2008. Train, Kenneth, Discrete Choice Methods with Simulation, Cambridge University Press, 2009.

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 α ˆ it . 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

ηˆitk k ∈ {M, E}

M and η E (a) Distribution of ηˆit ˆit

0 -50

0

50

100

U.S. dollars of December 2001

(b) Distribution of

M η ˆit α ˆ it

and

E η ˆit α ˆ it

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

βˆit

α ˆ it

(b) Distribution of βˆit

(a) Distribution of α ˆ it

The left figure reports the distribution of the marginal utility of income (ˆ α) by gender and the right figure reports the distribution of preferences over the ranking of returns (β) also by gender.

50