metadata: authors: 0: author: Joubert,Clement Jean Edouard
count: Chile
docna: 0: docna: Gender Pension Gaps in a Private Retirement
            Accounts System : A Dynamic Model of Household Labor Supply
            and Savings
docty: Policy Research Working Paper
subtopic: Pensions & Retirement Systems,Gender and Development,Labor Markets,Health Care Services Industry
teratopic: Gender,Social Protections and Labor,Industry
abstracts: cdata!: This paper develops and estimates a
            dynamic model of individuals' and couples' labor
            supply, savings, and retirement decisions to analyze how the
            design of a privatized pension system affects gender pension
            gaps. Chile has one of the longest running nationwide
            private retirements accounts systems in the world, operating
            since 1980. It has served as a model for many countries and
            was reformed in 2008 to alleviate old- age poverty and
            reduce gender pension gaps. The paper estimates the dynamic
            model using pre-reform data and compares the model's
            short-term predictions with available evidence on the
            reform's causal impacts. The analysis finds that
            household structure is an important determinant of the
            behavioral and distributional impacts of the reform. The
            paper evaluates how actual and counterfactual changes in the
            pension system design affect men's and women's
            economic decisions, pension receipts, and program costs over
            a longer time horizon. Three design features significantly
            reduce gender pension gaps: expanding minimum pension
            benefit eligibility, providing a per-child pension bonus,
            and increasing women's retirement age to be equal to men's.
geo_reg_key: 119228,517191
repnme: repnme: Gender Pension Gaps in a Private Retirement
            Accounts System : A Dynamic Model of Household Labor Supply
            and Savings
display_title: Gender Pension Gaps in a Private
            Retirement Accounts System : A Dynamic Model of Household
            Labor Supply and Savings
listing_relative_url: /research/2020/07/32249694/gender-pension-gaps-private-retirement-accounts-system-dynamic-model-household-labor-supply-savings
topicv3: Gender m1327621 615,Retirement m1504007 2896,Labor Supply m1504055 2751,Health m1504661 3480
publishtoextweb_dt: 2020-07-16T00:00:00Z
historic_topic: Gender,Social Protections and Labor,Industry
origu: DECRG: Human Development (DECHD)
no_of_pages: 70
author_keys: 0: author_key: 1411340
model_extractions: Policy Research Working Paper 9322 Gender Pension Gaps in a Private Retirement Accounts System A Dynamic Model of Household Labor Supply and Savings _Clément Joubert Petra Todd_ Development Economics Development Research Group July 2020
Policy Research Working Paper 9322

# **Abstract**

This paper develops and estimates a dynamic model of individuals’ and couples’ labor supply, savings, and retirement decisions to analyze how the design of a privatized pension system affects gender pension gaps. Chile has one of the longest running nationwide private retirements accounts systems in the world, operating since 1980. It has served as a model for many countries and was reformed in 2008 to alleviate old- age poverty and reduce gender pension gaps. The paper estimates the dynamic model using pre-reform data and compares the model’s short-term predictions with available evidence on the reform’s causal impacts. The analysis finds that household structure is an important determinant of the behavioral and distributional impacts of the reform. The paper evaluates how actual and counterfactual changes in the pension system design affect men’s and women’s economic decisions, pension receipts, and program costs over a longer time horizon. Three design features significantly reduce gender pension gaps: expanding minimum pension benefit eligibility, providing a per-child pension bonus, and increasing women’s retirement age to be equal to men’s.

This paper is a product of the Development Research Group, Development Economics. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The author may be contacted at cjoubert@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
Gender Pension Gaps in a Private Retirement Accounts System: A Dynamic Model of Household Labor Supply and Savings Clement Joubert and Petra E. Todd<sup>_∗_</sup>

# **JEL Classification: J240, J260, E210, E260, O170**

**Keywords:** Private pensions, Gender Gaps, Household labor supply, retirement, savings, structural estimation

> _∗_ Petra E. Todd is the Edmund J. and Louise W. Kahn Term Professor of Economics at the University of Pennsylvania and Clement Joubert is an economist at the World Bank’s research group. This research uses data from the EPS survey. We would like to thank the Subsecretar ́ıa de Previsi ́on Social of Chile for granting permission to use the data base. The Subsecretar ́ıa is not responsible for the results presented in this paper. This paper builds on an initial study that Todd and Joubert did as consultants to the Budget Office in the Chilean government. A preliminary version of the paper was presented at the LACEA meetings in Santiago, Chile, Nov., 2011, at NYU, Washington University-St. Louis, University of Minnesota, and University of Chicago. We would like to thank Alberto Arenas, David Bravo, Santiago Levy, Evelyn Matthei, Beatriz Moraga, Roy Rogers, the Superintendencia de Pensiones and seminar participants for helpful comments. We also are grateful for funding for research assistants from the National Institutes of Health - National Institute on Aging, Grant number P30 AG12836, the Boettner Center for Pensions and Retirement Security at the University of Pennsylvania, and National Institute of Child Health and Development Population Research Infrastructure Program R24 HD-044964, all at the University of Pennsylvania.
# **1 Introduction**

Many traditional pay-as-you-go social security systems face impending insolvency as the number of pensioners per worker rises. The kinds of reforms being considered include, for example, increasing the required contribution per worker, raising the standard retirement age, or completely overhauling the pension system by transiting to a private accounts system. Chile has been at the forefront of pension reform, having switched to a private retirement accounts system in 1980.<sup>1</sup> Many plans proposed in the United States and Europe are similar to Chile’s current pension system.<sup>2</sup> They outline a system in which workers are mandated to contribute part of their income to a pension account that is managed by a money manager, either a government owned company or a private firm. Under the proposed plans and also under the Chilean system, the government serves as a last resort guarantor, supplementing pension income if pension accumulations are insufficient, either due to low income or unfavorable investment returns.

A potential drawback of a private retirement accounts-based system is that it can leave women vulnerable to old-age poverty. This is because women typically experience lower wages, careers interrupted by child bearing, and longer life spans.<sup>3</sup> In 2008, Chile undertook a major reform of its pension system largely out of concerns about old age poverty and gender gaps in pension accumulations and pension receipt. The reform incorporated more generous noncontributory pension benefits into the pension system design, and other features likely to benefit women such as a pension supplement for each child born, or pension fund transfers between divorcing spouses. However, policy makers were concerned that these changes may reduce working and savings incentives for both men and women.

This study develops and estimates a dynamic structural model to examine how pension system design affects gender gaps in pensions and household economic decisions. The

> 1The Chilean pension fund system is known as the _Administradoras de Fondos de Pensiones_ or _AFP_ system.

> 2In the U.S., President G.W.Bush in 2005 and Republican Party presidential primary candidate Herman Cain in 2011 invoked the Chilean model as a blueprint to reform Social Security. Chile’s system served as a model for pension reform in many other countries (dates of adoption in parentheses), including Peru (1993), Argentina (1994), Colombia (1994), Uruguay (1995), Bolivia (1996), Mexico (1997), El Salvador (1998), Costa Rica (2000), Czech Republic (1994), Hungary(1998), Poland (1999), Bulgaria (2000), Estonia (2002), and Kazakhstan (1998).

> 3See discussions in Bertranou (2001), James et al.(2003), and Fajnzylber (2012)

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households, which can be either couples or individuals, make choices over time with regard to labor supply, private savings and retirement in an environment with uncertainty about future wages, returns on pension savings, fertility, divorce or widowhood and own survival. Men and women choose not only whether to work or not but also whether to work in the formal sector where pension contributions are mandatory or in the informal sector. The distinction between formal and informal sector work is important in Chile (and most countries across the world) because many individuals work in the informal sector and reach old age having contributed little to the system. In addition, women choose whether to work part-time or full-time. The model is estimated on longitudinal microdata from the _Encuesta de Protecci ́on Social (EPS)_ merged with administrative data on pension funds.<sup>4</sup> We use the estimated model to study how labor supply and savings behavior changes with the introduction of the 2008 pension reform in comparison to the previous pension system behavior and in comparison to alternative pension system designs. We estimate model parameters by the method of simulated moments using pre-reform data from the 2004 and 2006 EPS Surveys. The estimation results reveal substantial heterogeneity in how individuals value pecuniary and non-pecuniary dimensions of formal and informal work. Some individuals have strong comparative advantages to working in the formal or informal sectors, which dampens behavioral responses to pension rule changes.

Incorporating the pension rules explicitly in our model allows us to construct counterfactual simulations in which the reform did not happen, keeping everything else constant. In this way, we perform an ex ante prediction of the short-run behavioral impacts of the pension reform and compare our predictions to some evidence from other causal impact studies of the reform’s impacts. Consistently with other studies, we find that the more generous safety net induces negative wealth effects on the labor supply of men and women at older ages. Contrary to other studies that model reform changes at the individual level, our simulations show that household structure is an important determinant of pension policy reform responses. Even though many of the reform features were targeted at women, we find that men’s responses are sometimes greater than those of women, as men respond to the wealth effect of an increase in pension benefits accruing to their wives. In addition, household-level

> 4The longitudinal household survey data were collected by the Microdata Center under the supervision of David Bravo and the administrative data come from Chile’s _Superintendencia de Pensiones_ .

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means-tests cause some men to increase their labor force participation at younger ages. We do not observe any crowding-out of private savings.

We then use the model to perform simulations over longer time horizons to analyze the effects of actual and counterfactual pension program designs on a range of outcomes including pension gender gaps, labor force participation rates, years of pension contributions, benefit receipt levels and household assets. We focus on design features that have been proposed by policy-makers as possible ways of reducing gender gaps, such as, requiring individuals to make pension contributions to their spouse’s account in years when their spouse does not work or increasing the mandatory retirement age of women to match that of men. We predict the effects of the actual pension reform and of alternative scenarios by simulating our sample households’ decision-making over a 20-year time horizon. We also report the cost to the government of various alternatives.

The results indicate that the changes in the pension system design introduced with Chile’s 2008 pension reform dramatically improve pension saving and receipt levels for women, bridging a sizable part of the male-female pension benefit gap. In addition, the short-term behavioral responses do not compound into large changes to pension accumulations in the longer run. The reduction in the gender pension gap is attributable mainly to the large expansion in eligibility for a minimum pension guarantee, the so-called basic solidarity pension ( _Pensi ́on B ́asica Solidaria_ , or PBS) and from an increase in the generosity of the minimum pension benefit.<sup>5</sup> The work requirements for receiving the minimum pension benefit guarantee were also removed through the reform. The per-child bonus also emerges as an important feature in increasing women’s pensions relative to men’s, particularly for less educated women who have more children and tend to participate less in formal sector work. Raising the retirement age of women does not result in an increase in years contributed but does significantly increase female pension benefits, by reducing their expected longevity at retirement and allowing pension funds to accrue interest longer.

The paper proceeds as follows. Section 2 discusses the related literature on modeling behavioral effects of social security and pension rules. Section 3 gives some background on the Chilean pension system and describes the features of the 2008 pension reform that we incorporate in our analysis. Section 4 describes the model and section 5 summarizes

> 5The Chilean pension system and the 2008 reform are described in detail in section 3

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the data used in estimation. Section 6 discusses parameter estimates, provides evidence on within-sample model fit, and compares the short-run impacts predicted by the model with the available post-reform evidence. Section 7 uses the model to analyze how different policy features, included or not in the reform, impact gender equity and household decisions. Section 8 concludes.

# **2 Related literature**

This study builds on a literature, pioneered by Fields and Mitchell (1984) and Mitchell and Fields (1984) that models how the structure of earnings, social security, and pension benefits affect retirement behavior. Their model assumed that individuals make a one time retirement age decision, taking into account future expected earnings and retirement benefits. They found that wealthier individuals retire earlier, and those who expect to gain more by postponing retirement retire later. Subsequent research developed and implemented fully dynamic modeling approaches that incorporate uncertainty in decision-making over time. An early dynamic model by Gustman and Steinmeier (1986) showed how pension benefits affect the lifetime budget constraint and alter the price of leisure at different ages, thus influencing the choice of retirement age. Stock and Wise (1990) analyzed the effect of pension plan provisions on the retirement age and also emphasized the importance of modeling uncertainty in accurately capturing the option value embedded in the decision to retire. Their estimation was based on a retirement decision rule that was motivated by a dynamic programming rule, but was computationally less complex. Berkovec and Stern (1991) estimated the first dynamic discrete choice model of individual retirement decisions using a dynamic programming set-up. Subsequent papers additionally incorporated into the basic dynamic discrete choice modeling framework other aspects, such as health expenditure risk, savings and detailed institutional pension rules to provide a fuller accounting of retirement determinants.<sup>6</sup> The more recent literature estimates dynamic structural models of the joint retirement decisions of husbands and wives. Our modeling framework is most closely related to that of 6See, e.g., Rust and Phelan (1997), French (2005), Blau and Gilleskie (2008), French and Jones (2011) and Blundell et al. (2016) for a survey.

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Van der Klaauw and Wolpin (2008) who study how the design of U.S. social security rules affects decision-making within a collective household model. As in their model, we allow households to accumulate private savings in addition to pension benefits for consumption in retirement. One important difference is that we focus on gender aspects of pension design, so we incorporate into our model divorce and separation. These events are major financial risks for women with low private and pension savings and low attachment to the labor force. We do not incorporate health or health insurance, in part because Chile has a public health insurance program. Also, we allow only women and not men to work part-time. Another important difference is that our model allows workers to make a choice about being employed in the informal sector, in which they do not contribute to their pensions or make progress towards qualifying for a minimum pension. This is a crucial margin from a public finance point of view in Chile and a majority of countries around the world. Other recent collective models of joint retirement include Blau and Gilleskie (2006), who focus on retirement incentives related to spousal health benefits, and Casanova (2010), who investigates the timing of retirement between two married individuals. Because these papers are not concerned with the difference in financial risk borne by each spouse individually, they model divorce and death through a terminal value, instead of following, as we do, individuals after separation or death has dissolved the household.<sup>7</sup> Many individuals, especially women, spend a significant part of their retirement as widows, so following them after their spouse dies is important to understanding old age poverty.

This paper also builds on a previous study by Joubert (2015) of the relationship between pension design and labor force participation decisions with regard to informal/formal sector work using the same Chilean data that we use. This study extends Joubert (2015) by using a collective household model and by allowing for divorce and fertility, which make the model suitable for studying the differential impact of the 2008 pension reform on men and women.

Lastly, this study is more broadly related to a literature initiated by Auerbach and Kotlikoff (1987) that examines the welfare effects of pension reform using life cycle and

> 7Other notable papers are Gustman and Steinmeier (2000, 2002) who consider a non-cooperative game solution to the household joint decision, and Gallipoli and Turner (2011) who compare non-cooperative and collective models of joint retirement. In the macroeconomic literature, Nakajima (2011) calibrates an equilibrium collective model of joint retirement, focusing on spousal and survivor benefit policies.

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overlapping generations models.<sup>8</sup> Two recent related papers in that strand are O’Dea (2018) who computes the optimal level of means-tested non-contributory pensions and McKiernan (2018) who models the Chilean transition from pay-as-you-go to a privatized pension system.

# **3 Background on the Chilean pension system and the 2008 reform**

When it was introduced in 1980, the privatized Chilean pension system, called the AFP system, replaced a heterogeneous pay-as-you-go system composed of many different institutions (called _Cajas de Prevision_ ) that covered different professions and subsets of the population.<sup>9</sup> Individuals in the old pension system (now known as the INP system) had the option of transferring to the new AFP system based on individual capitalization or to remain in the old system.<sup>10</sup> To encourage transfers, workers who opted for the new system received a 12.6 percent increase in net income (the new contribution rate plus commissions or fees) and the benefits accrued under the old system were recognized through the issuing of a “recognition bond,” payable upon retirement. Labor force entrants after 1980 were required to affiliate to the new system.<sup>11</sup> By the end of 1983, 77 percent of workers from the old system had switched to the new one (Acu ̃na and Iglesias (2001)).

The AFP Pension system is a savings program based on defined-contribution individual accounts. The program is mandatory for salaried workers and voluntary for self-employed. Affiliated workers pay a 10 percent contribution of their monthly wages (up to a cap) into a tax-deferred pension account, which is for the most part inaccessible until retirement.<sup>12</sup> A pension system affiliate can choose to invest his/her pension funds in one of a number of pension fund administrators (the AFP firms) who manage and invest the savings in the markets.

> 8A partial list of notable papers in this branch of the literature includes Conesa and Krueger (1999), Kotlikoff et al. (1999), Huggett and Ventura (1999), Nishiyama and Smetters (2007)

> 9AFP = _Administradoras de Fondos de Pensiones_

> 10INP= _Instituto de Normalizacion Previsional_

> 11Government and military workers are exempted and have separate pension systems.

> 12The restrictions on fund withdrawal are more stringent in Chile than they are for US 401K plans. The contributions are capped at 60 Unidades de Fomento, a monetary unit that is indexed to inflation. The value of the UF as of December 2004 was $17,317 pesos (US$31). In addition, workers must pay a contribution of 7 percent for health services, 0.8 percent for a disability and survivorship insurance, and an average of 2.6 percent to the pension fund manager as a commission or fee.

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Individuals can access their pension savings at age 65 for men and 60 for women, with three withdrawal options: Programmed Withdrawals ( _Retiro Programado_ ), purchase an annuity from an insurance company ( _Renta Vitalicia_ ), or a mix of phased withdrawals for a period of time and a deferred lifetime annuity. The law also allows for early retirement, provided that the worker has pension funds sufficient to generate a pension amount equal to or greater than 110 percent of the minimum pension guaranteed by the state.<sup>13</sup> Prior to the 2008 pension reform, the state provided noncontributory retirement income transfers through two mechanisms. First, a welfare or assistance pension, known as the _PASIS_ pension, equal a little less than a third of the minimum wage was available for program applicants above 65 years of age, irrespective of their contribution history, was allocated based on an index of economic vulnerability, called “ficha CAS”.<sup>14</sup> The second transfer was a minimum pension guarantee (MPG) equal to about twice the PASIS pension. Individuals with more than 20 years of contributions received the MPG if their accumulated contributions could not finance a higher pension. Both of these benefits took the form of a top-up, that is, the benefit was equal to the difference between the guaranteed level and the pension financed by the worker’s account.

# **3.1 Gender pension gaps and the 2008 reform**

In 2008, the pension system underwent significant reforms aimed at alleviating old age poverty and reducing gender gaps in pension accumulations. An analysis of pension contribution histories at the micro level (e.g. Arenas de Mesa et. al. (2007)) showed that most individuals were expected to have low pension accumulations upon retirement.<sup>15</sup> Only 37 percent of women were projected to have a pension above the MPG level, in comparison with 67 percent for men. The average projected replacement rate for women under the pre-reform pension system was 28 percent of the last wage in comparison to 51 percent for men.

An important factor underlying gender gaps in projected pensions is that labor force

> 13The pension must also be equal to or greater than 50 percent of the average taxable income for the last 10 working years.

> 14In August 2007, the minimum wage was 159,000 pesos per month, while the PASIS was 44,186 pesos for retirees between 65 and 70 years of age, 47,103 pesos between 70 and 75 and 51,503 pesos if older than 75.

> 15The micro-level data on pension contribution histories were obtained from a database of the pension fund regulatory agency, the _Superintendency of Pensions_ or SP. These are the same data as used in this paper.

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participation is lower and more sporadic among women. Arenas de Mesa and Montecinos (1999) note that the direct link between lifetime earnings and pensions in the AFP system largely accounts for the lower average pensions for women, who tend to retire at earlier ages, participate less often in the labor-force and earn lower salaries. A statistic that is sometimes used as a measure of pension program participation is the _density of contributions_ , which is the number of years the individual makes pension contributions divided by the number of potential working-age years. The density of contribution for women is 41 percent in comparison with 61 percent for men. Additionally, lower wages, earlier retirement ages and projected longer life spans, which affect annuity pay-outs, all serve to reduce the level of women’s pensions relative to men’s.

# **3.2 The new safety net**

Reducing the gender gap in pension benefits/accumulations was a significant objective of the 2008 pension reform. The reform replaced the PASIS pension and the minimum pension guarantee (MPG) with a so-called “New Solidarity Pillar” that augments pension levels of workers with relatively few years of contributions. The new safety net implements a meanstested welfare pension, which will eventually guarantee to all individuals in the 60 percent least affluent households a pension of 75,000 pesos per month called _Pension Basica Solidaria_ , or PBS. This feature was introduced gradually over July 2008-July 2011.<sup>16</sup> The PBS represents an increase of nearly 50 percent with respect to the former PASIS pension. In addition to providing a minimum pension level, the new system augments low contributory pensions through the Solidarity Pension Supplement or APS.<sup>17</sup> The APS benefit corresponds to a fraction of the PBS that is gradually reduced for workers with relatively larger contributory pensions according to the formula:<sup>18</sup>

> 16The level of the PBS was initially 60,000 pesos and reached 75,000 pesos in July 2009. The coverage of the PBS was started at 40 percent with eligibility being based on an existing poverty index, the Social Protection Index ( _Ficha de Proteccion Social)_ . After September, 2009, eligibility was based on the household’s income.

> 17Aporte Previsional Solidario

> 18The Maximum Supplemented Pension (PMAS or _Pension Maxima con Aporte Solidario_ ) was gradually increased through the phased implementation from 70,000 pesos per month to 255,000 pesos per month in July 2011

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In effect, this means that the APS tapers off at a rate that reached 0.3 in July 2011. For example, a worker who can finance a pension of one 100,000 pesos per month with the _−_ funds accumulated in his/her individual account will receive a supplement equal to 75 _,_ 000 (100 _,_ 000 _∗_ 0 _._ 3) = 45 _,_ 000. His/her total pension will then be 145,000 pesos per month.<sup>19</sup> James et al. (2003) note that state-financed minimum pension benefits that are targeted toward low earners often women.

Figure 1 graphically shows the effect of the pension reform on the pension level that people qualify for as a function of the total number of years in which they made pension contributions. The two vertical lines show the PASIS pension benefit and also the minimum pension guarantee available to those with 20 years of contributions under the pre-reform system. The diagonal line that intersects with (0,0) shows the pension benefit financed with the accumulated pension savings. The diagonal line that intersects with the y axis represents the pension amounts under the reformed system.

# **3.3 Other features of the reform**

A second important feature of the 2008 pension reform with regard to gender equity is the introduction of a pension subsidy for mothers that depends on their number of children. The subsidy seeks to compensate for contribution history interruptions due to pregnancy and infant care. The subsidy level retroactively accounts for children born before the reform. When a woman turns 65, the state augments her pension savings with a benefit equal to a year and a half of pension contributions at the minimum wage (about 280,000 pesos in 2008), plus interest accrued since the child’s birth minus commissions paid to the pension fund administrator. A third feature of the pension reform is a change in the rules for dividing pension balances in the case of divorce or annulment. Before the reform, an individual would lose access to their spouse’s pension upon divorce.<sup>20</sup> A judge can now rule that up to 50 percent of one of the spouse’s pension balance be transferred to the other spouse’s account

> 19Before the reform, eligible workers effectively faced an implicit marginal tax rate of 100 percent on contributions over some range, in that additional contributions would not increase the level of pension upon retirement. The new pension system design ensures that additional contributions always increase the level of the retirement pension; it maintains a constant implicit marginal tax rate of about 37 percent on additional contributions.

> 20However, divorce only became legal in Chile in 2004.

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after a divorce or annulment as a form of alimony. A fourth feature is a change in the premium for disability and survivorship benefits. Prior to 2008, women and men both paid about 1 percent of their wages towards disability and survivorship benefits, which is actuarially unfair to women. As of July 2009, men and women pay contributions that correspond to men’s premium, but the difference in premiums is added back to a woman’s pension account. Lastly, the pension reform also made it possible for someone who is not working (for example a stay-at-home mother) to make pension contributions. The contributions can be deducted from the taxable income of a third party, such as a spouse, who can contribute towards the voluntary affiliate’s account.

# **4 A dynamic model of household labor supply and savings**

The dynamic behavioral model that we develop and estimate describes how households make decisions over their lifetime with regard to work and savings. The model does not have an analytic solution and is therefore solved numerically by backwards recursion. Details of the solution method are provided in section A.1.

In the model, a household may consist of either a couple or a single individual. In each period, couples face an exogenous probability of separation (described in detail below) or of one member of the couple dying, in which case the couples’ problem changes to that of a single-headed household. It is important to recognize the existence of permanent unobservable sources of heterogeneity affecting decision-making, so the model incorporates unobserved discrete types (see, e.g, Heckman and Singer (1984) and Keane and Wolpin (1997)) that index couples. Individuals are indexed by the type of couple they form (if married) or would be part of (if single).<sup>21</sup>

> 21In the empirical work, we incorporate four unobserved types. The number of types we could allow was limited due to the computational complexity of the model. The type probability is modeled as a logit function of schooling, marital status and birth cohort. Parameter estimates are presented in table B6

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# **4.1 Timing and initial conditions**

The superscript _j ∈{m, f }_ denotes gender, and the superscript 2 denotes a couple.<sup>22</sup> Periods in the singles’ problem are indexed by the individual’s age ( _t_ = _a_<sup>_j_</sup> _t_<sup>),whilethecouples’</sup> problem is indexed by the age of the female ( _t_ = _a_<sup>_f_</sup> _t_<sup>).Forsingles,thedecisionproblem</sup> begins at age _t_ 0 = 35.<sup>23</sup> For couples, the decision problem begins when the wife turns _t_ 0. Thus, the age of the husband in the first period, _a_<sup>_m_</sup> _t_ 0<sup>ispartoftheinitialconditionsand</sup> becomes a state variable thereafter. Any household assets ( _At_ 0) or work experience ( _Xt_<sup>_m_</sup> 0<sup>_, X_</sup> _t_<sup>_f_</sup> 0<sup>)</sup> accumulated prior to the first model period, as well as any children born prior to female age _t_ 0 ( _Nt_ 0) are also taken as initial conditions. The initial conditions also include pension savings ( _Bt_<sup>_m_</sup> 0<sup>_, B_</sup> _t_<sup>_f_</sup> 0<sup>),whichincludeanypensionrightsaccumulatedbythetwospousesunder</sup> the earlier INP retirement system prior to age _a_<sup>_j_</sup> _t_ 0<sup>(“Bonosdereconocimiento”)orunder</sup> the new AFP system. Finally, the initial conditions include two permanent characteristics: completed schooling levels of men and women ( _e_<sup>_j_</sup> ), and their birth cohorts ( _bc_<sup>_j_</sup> ). We denote the set of initial conditions for a single household by: The set of initial conditions for a couple is then: At ages _t_<sup>_f_</sup> _C_<sup>=60and</sup><sup>_tm_</sup> _C_<sup>=65yearsoldrespectively(orsooneriftheyqualifyforearly</sup> retirement), males and females begin to withdraw money from their pension savings accounts. For tractability, we did not incorporate the choice about whether to take retirement savings as an annuity or as a phased withdrawal. Rather, we assume phased withdrawal, because the formula is a simple function of age.<sup>24</sup> The level of pension benefits is calculated according

> 22 We use the terms husband and wife, but the model applies to cohabiting, non-married couples 23 Singles are assumed to remain single after age _t_ 0. Married couples are able to transition to being divorced or widowed, as further described below. We estimate the model for singles on people who remain single after age _t_ 0.

> 24In computing the programmed withdrawals, we used the life tables RV-2004 published by the _Superintendencia de Pensiones_ . The 2009, 2010 and 2011 rates of return were used for the corresponding years. To discount years more than 20 years in the future, the 20th discount rate was repeated. For years after 2011, the 2011 vector was used. For years before 2009, a single discount rate of 5 percent was used. If a couple qualifies for the PASIS pension, our simulation assigns the PASIS pension to the woman (only one member of the household can get the PASIS).

11
to the rules of the pension system in place, including the minimum pension guaranty (MPG) in the years when applicable. After age 65, either spouse may receive the government pension transfers (PASIS, PBS, APS) for which they qualify, given their individual and family incomes, and according to the rules to which they are subject at that time (prereform until 2008, phased implementation of the reform from 2009 to 2011, post-reform after 2011).

By age _tR_ =75, it is assumed that all individuals stop working, at which point they take leisure for all remaining periods.<sup>25</sup> The last period of the model is age _tD_ = 90. When both spouses turn _tR_ and no longer have the option of working, the model assumes that households run down their accumulated savings by optimally consuming until they die or reach the last period. We assume that bequests (savings left after death of both spouses) are involuntary and do not generate utility.

# **4.2 Decisions**

In each period of the model prior to _tR_ , a two-person household makes a saving decision for the household ( _st_ ), a labor force participation decision for each individual ( _d_<sup>_m_</sup> _t_<sup>_, d_</sup> _t_<sup>_f_)and</sup> a part-time work decision for the woman ( _p_<sup>_f_</sup> _t_<sup>),untilage</sup><sup>_tR_.Theincomethatisnotsaved</sup> is split evenly into the two spouses’ consumption levels _c_<sup>_m_</sup> _t_<sup>_, c_</sup> _t_<sup>_f_.</sup><sup>_st_isthefractionofincome</sup> that is saved and not consumed in period _t_ . The three employment options available to both men and women are to work in the formal sector ( _d_<sup>_j_</sup> _t_<sup>=</sup><sup>_F_),toworkintheinformalsector</sup> ( _d_<sup>_j_</sup> _t_<sup>=</sup><sup>_I_),orinhomeproduction(</sup><sup>_dj_</sup> _t_<sup>=</sup><sup>_H_)for</sup><sup>_j∈{m, f}_.Inaddition,femaleworkerscan</sup> choose to work part-time ( _p_<sup>_f_</sup> _t_<sup>=1)orfull-time(</sup><sup>_pj_</sup> _f_<sup>=0).26Aone-personhouseholdmakes</sup> the same saving and work decisions relevant to his/her gender, but consumes the full amount of income minus savings.

> 25This assumption reduces computational complexity by reducing the number of choices needed to be evaluated each decision period.

> 26In the model, part-time work is only an option for females so we set _pmt_ = 0. In the data, part-time work, defined as working fewer than 31 hours per week is relatively marginal for men (5.6 percent of working men at 35, 10.3 percent at age 60), and is likely to be related to disability, which is not modeled. In contrast, the fraction among women is two to three times as high (14.2 percent at 35, 23.5 percent at 60) and might be related to household joint decisions that are relevant to our model.

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# **4.3 Preferences**

Individuals derive utility from consumption and from leisure, if not working or working parttime. The utility of leisure is allowed to depend on unobserved type, _k_ . Other variables that affect utility are grouped in _St_<sup>_j_=</sup> � _c_<sup>_j_</sup> _t_<sup>_, d_</sup> _t_<sup>_j, dj_</sup> _t−_ 1<sup>_, p_</sup> _t_<sup>_j, Nt, ε_</sup> _t_<sup>_j_</sup> � for _j ∈{m, f }_ . We denote the union of _St_<sup>_m_and</sup><sup>_S_</sup> _t_<sup>_f_by</sup><sup>_S_</sup> _t_<sup>2.</sup> The per period utility function of a couple is the weighted sum of the utility of a single male and the utility of a single female, where the weights represent bargaining power (the weight is set to 0.5 in the simulations reported below): The terms _u_<sup>_m_</sup> ( _._ ) and _u_<sup>_f_</sup> ( _._ ) represent the utility from consumption, leisure, and number of children for a single household formed by a male and a female respectively.

The leisure preference shocks are assumed to be jointly distributed normally and to be uncorrelated over time: The period utility function is specified below. Dummy variables for participation in each sector _s ∈{F, I, H}_ are created as follows: _d_<sup>_j_</sup> _s,t_<sup>=</sup><sup>_I_</sup> � _d_<sup>_j_</sup> _t_<sup>=</sup><sup>_s_</sup> �, where _I_ ( _._ ) denotes the indicator function.

This formulation allows the marginal utility of consumption to depend on the number of children and on labor market participation. The utility from not being employed is stochastic, type-specific and depends on the number of children ( _Nt_ ) and marital status ( _mt_ ).<sup>27</sup> We allow

> 27To reduce the number of parameters to estimate, we set the coefficients on the number of children and marital status to 0 in the case of men since these factors have a smaller impact on men’s labor force participation in Chile.

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for the utility of leisure to change after the pension system’s retirement age ( _t_<sup>_j_</sup> _C_<sup>), which could</sup> capture social norm effects on the supply and/or demand for labor. _δp_<sup>_j_capturesthefraction</sup> of the utility of leisure received if employed part-time (an option only for women). Nonpecuniary benefits (or penalties) associated with the informal sector are captured by _φ_<sup>_j_</sup> 2 _,k_<sup>,</sup> and the costs of switching sectors and entering (or re-entering) the labor force are denoted by _φ_<sup>_j_</sup> _s_<sup>and</sup><sup>_φj_</sup> _r_<sup>respectively.</sup>

# **4.4 Household income**

The labor market consists of two sectors, a formal sector where pension contributions are mandatory, and an informal sector. Each working age individual (whether part of a couple or single) receives an earnings offer from the informal sector in every period with probability one. In addition, with a probability Γ<sup>_j_</sup> _t_<sup>,individualsmayreceiveanofferfromtheformal</sup> sector. The probability depends on his/her gender, level of schooling, age, and whether employed in the formal sector in the previous period.

The log-earnings offers (for gender _j ∈{m, f }_ , in sector _s ∈{F, I}_ of type _k ∈{_ 1 _..K}_ and with completed schooling levels _e_<sup>_j_</sup> ) are: where _θ_ 0<sup>_j_</sup> _sk_<sup>isagender-,sector-,type-specificconstant,</sup><sup>_θ_</sup> 1<sup>_j_</sup> _es_<sup>agender-,sector-,schooling-</sup> specific cohort effect, _θ_ 2<sup>_j_</sup> _s_<sup>the sector-specific returns to schooling, and</sup><sup>_θ_</sup> 3<sup>_j_</sup> _es_<sup>and</sup><sup>_θ_</sup> 4<sup>_j_</sup> _es_<sup>the sector-</sup> and schooling-specific returns to experience. _ε_<sup>_j_</sup> _s,t_<sup>are i.i.d.sector-specific earnings offer shocks</sup> that are uncorrelated across time-periods and across members of the same household. The earnings offer specification allows returns to experience to differ in both sectors.

The total household disposable labor income of a couple, _yt_<sup>2,isthesumofaccepted</sup> earnings offers, net of income taxes and mandatory pension contributions: 14
where _τ_ is the pension contribution rate. Household income for a single household, _yt_<sup>_j_,is</sup> defined similarly.

Formal labor earnings net of pension contributions and private savings returns are subject to a progressive income tax. Taxes due at period _t_ are denoted by _T_ ( _At, wF,t_<sup>_m, w_</sup> _F,t_<sup>_f, d_</sup> _t_<sup>_m, d_</sup> _t_<sup>_f_),</sup> and depend on the household’s stock of private savings, formal sector earnings offers and labor force participation decisions.<sup>28</sup> Net borrowing and borrowing against pension savings are not allowed. It is assumed that individuals working in the informal sector do not pay taxes on their labor income.

# **4.5 Separation and mortality**

In each period, the a probability of the man or woman (whether in a couple or single) surviving to the next period, _π_<sup>_sj_</sup> = _π_<sup>_sj_</sup> ( _at_ ), is assumed to be exogenous with respect to the other aspects of the model.<sup>29</sup> Widows inherit a portion of their former spouse’s pension funds to finance a survivorship pension.

Household separation (for reasons other than widowhood) is modeled as an exogenous event. Conditional on both spouses surviving, the probability of becoming separated in period _t_ is assumed to depend on the man’s level of education ( _e_<sup>_m_</sup> ), and the ages of the spouses ( _a_<sup>_m_</sup> _t_<sup>_, a_</sup> _t_<sup>_f_).Until2004,divorcedidnotexistinChile.Forsimplicitywetreatdivorce,</sup> marriage annulment and de facto separation as equivalent in the model. The separation probability is specified as a logistic model, Upon separation, a couple’s non-pension assets _At_ are split evenly between the two individuals who then become single households.

Recall that one feature of the pension reform was a change in the rules governing pensions upon divorce. Prior to the reform, divorce could lead to a loss of rights to a spouse’s pension benefits. After the reform, in the event of a divorce or annulment, a judge can rule that

> 28See table B8 for the actual bracket values and corresponding marginal tax rates.

> 29We obtain these probabilities from life tables that are specific to Chile and are conditional on age and gender (RV-2004, from Circular 1314, published by the Superintendencia de Pensiones).

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up to 50 percent of one of the spouse’s pension balance be transferred to the other spouse’s account as a form of alimony. In our model, we assume that before the reform, divorced individuals only have access to their own pension funds and do not get to keep their former spouse’s pension. After the reform, each spouse gets one-half of the pooled pension savings of the wife and husband. To reduce computational complexity and because separation in old age is relatively rare, we assume that no separation occurs after the woman turns age 60.

# **4.6 Fertility**

The number of children _Nt_ is assumed to evolve stochastically. The probability of having another child is modeled as a logistic model, that depends on the woman’s age, marital status, schooling level and number of children in the previous period.

There are assumed to be no births after the woman turns age 40.<sup>30</sup>

# **4.7 Evolution of other state variables**

The model’s other time-varying state variables, _At_ , _Bt_<sup>_m_,</sup><sup>_B_</sup> _t_<sup>_f_,</sup><sup>_X_</sup> _t_<sup>_m_,</sup><sup>_X_</sup> _t_<sup>_f_aredeterminedbythe</sup> saving, labor supply decisions and asset return shocks. Private savings are assumed to earn the risk-free rate _r_ , assumed to be 5 percent.<sup>31</sup> . The balances on each spouse’s pension account accrue interest stochastically and are augmented by the current period’s contribution. Returns on the pension accounts are modeled as an iid process: _rB ∼ iidN_ ( ̄ _rB, σB_<sup>2).32</sup>

# **4.8 Recursive formulation of the household’s problem**

The optimization problem faced by a single individual of gender _j_ has the following recursive formulation:

> 30This assumption is made in part to reduce computational complexity.

> 31Chile’s 10-year government bond yields oscillated between 4 and 6 percent over the period 2008-2018

> 32Individual returns will differ in part because people can choose different firms to administer their pension funds and choose different funds within those firms. These decisions are not incorporated into the model. Also, allowing for serial correlation in the returns would require adding past returns as additional continuous state variables, which would significantly complicate the model’s numerical solution.

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s.t.

where _Bt_<sup>_j_</sup> +1<sup>accruespensioncontributionsintheformalsector.</sup><sup>_y_</sup> _t_<sup>_j_isthehousehold’sincome</sup> defined earlier, and ̃ _ε_<sup>_j_</sup> _t_<sup>is a vector of shocks to wage offers, preferences for leisure, and pension</sup> asset returns. In addition to the constraints above that describe the evolution of pension and non-pension assets, the model includes the wage offer equations and the income/tax equation specified earlier.<sup>33</sup> For couples, the continuation value embeds five possible events. Either both spouses die (the continuation value is 0 in this case), or the husband dies and the maximization problem continues with the wife, or the wife dies and the maximization problem continues with the husband, or both spouses survive and remain together, or both spouses survive and separate.

Incorporating greater detail about the different possible next period options, the recursive formulation of the couple’s problem can be written as: 33 When we estimate the model, we constrain household consumption to be above a floor _Cmin_ . This avoids technical issues associated with infinitely negative utility levels and captures un-modeled government programs and private transfers that are available to families with extremely low earnings.

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s.t.

The variables on which the separation and divorce probabilities depend were omitted above to ease notation.

# **4.9 Discussion of the model**

## **4.9.1 Incorporating the 2008 pension reform**

We introduce the following key features of the 2008 pension reform into the model: (i) _The New Solidarity Pillar_ . The NSP is most beneficial to workers with low pension savings accumulations who otherwise would not have contributed long enough to qualify for the MPG under the old system. The NSP is expected to disproportionately benefit women. (ii) _The per-child bonus_ . The child bonus is provided only to women, regardless of whether they actually experience career interruptions upon giving birth. (iii) _Change in rules for divorce_ . Wives can receive up to 50 percent of the husband’s pension savings upon divorce.

Two aspects of the reform cannot be evaluated given our methodology. The first is the change in the premium paid by women per the Survivorship and Disability insurance, because the model does not incorporate health status, other than death. The second is the ability to make voluntary pension contributions. Under the current system, the percentage of the population making voluntary contributions to their pension account above the mandated 10 percent level is very small: fewer than 2 percent of the system’s affiliates had positive balances in their voluntary contributions account in 2005 (own calculations). Given the additional complexity required and given the infrequency of voluntary contributions in the data, we did not incorporate this aspect into the model. The model does incorporate decisions 18
about private savings, but not the decision of whether to place the private savings into a tax-deferred pension account.

The model is dynamic and explicitly incorporates forward-looking behavior under a rational expectations assumption. It also incorporates uncertainty and incomplete information. Specifically, individuals are uncertain about future wage shocks, future fertility, future divorce or widowhood, future survival and investment returns at the time of making labor supply and savings decisions. In solving the model, we assume that the 2008 pension reform came as a surprise and was not anticipated. We assume this, in part, because our discussions with the Budget Office in Chile indicated that the reform was not anticipated.<sup>34</sup> Thus, decisions up until 2008 are governed by a pre-reform decision model and decisions after 2009 are governed by a post-reform model. This requires solving two different versions of the model. First, we solve the dynamic programming problem (obtain the Emax values) assuming no reform and we estimate the structural model parameters only using pre-pension reform data. Then, fixing those parameters, we resolve the dynamic programming problem (i.e. obtain the Emax values that individuals use to form expectations) with the reform in place. These new Emax values are then used to simulate decision-making after the reform was introduced.

To a limited extent, the model incorporates business cycle effects in that returns on pension investments vary over time. Two limitations of the model are that investment returns are assumed to be i.i.d. and that there are otherwise no aggregate earnings shocks. However, aggregate demographic changes in the economy are incorporated in a few ways. First, the initial conditions include the education levels of the husband and wife and rising levels of education with successive birth cohorts will lead to different decision-making for different cohorts. For example, more recent cohorts of women who have higher education levels on average and the model will generate that they have fewer children and participate more in the labor force. Also, the model takes marital sorting patterns as initial conditions, so any changes over time in marital sorting patterns can also generate differences in behaviors across birth cohorts.

34Modeling the reform as anticipated would have also been feasible, but would require somewhat arbitrary assumptions about when the details of the reform became known to workers.

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## **4.9.2 Incorporating labor market regulations**

The model also incorporates some important labor market regulations. For example, the progressive tax structure is taken into account in computing after-tax income. Fees that workers pay for health and disability insurance are also taken into account. Lastly, the model incorporates the fact that informal sector workers typically do not pay these taxes and fees.<sup>35</sup>

# **5 Description of the data**

The estimation and simulations are based on data from three sources: the _Encuesta de Protecci ́on Social_ (EPS) longitudinal survey, linked administrative records of pension balances and contributions to retirement accounts (obtained from the Chilean supervising agency for pension fund administrators (the _Superintendency of Pensions_ or SP) and data on the returns achieved by Chile’s pension fund administrators (the _Administradoras de Fondos de Pensiones_ ).

The EPS survey was first administered in 2002 (originally under the name _Historia Laboral y de Seguridad Social_ ) by the Microdata Center of the University of Chile. Originally, the sampling frame was individuals affiliated with the AFP or the older INP pension systems. The survey data were then linked to the administrative records of the pension accounts of the sampled individuals. In 2004, 2006 and 2009 three follow-up surveys were administered, and the sample was augmented to include individuals that were not affiliated to any pension program, to obtain a total sample of 20,114 individuals, representative of the Chilean population in 2004. We use information on the 16,150 respondents who were interviewed in the 2006 round and use the survey weights to correct for attrition and non response.

The EPS questionnaire was designed specifically to study Chile’s social protection programs including the pension system. It contains rich longitudinal information on sociodemographic variables, household composition, employment histories, earnings and assets. The data include retrospective employment histories back to 1981 as well as earnings from

> 35 We use information on reported earnings and do not explicitly incorporate minimum wage regulation. However, we trim out reported monthly wages over 100 million pesos as they are likely to be reported with error.

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2002 to 2006 and household assets in 2004-2006. The main variables used in our estimation are age, schooling level, schooling level of the spouse, an indicator for the birth of a child in the current year, ages of all children, number of years the respondent worked in the formal sector, number of years the respondent worked in the informal sector, labor sector choice, labor sector choice of the spouse, annual earnings and private household wealth.<sup>36</sup> We merge the household survey data with the administrative data on pension savings accumulations.

To arrive at our estimation sample, we impose the following sample restrictions: (i) Our model incorporate the rules of the AFP pension system. We excluded from the estimation sample workers who reported only making contributions to a pension system other than AFP. We do, however, incorporate those workers who worked before 1980 and accumulated some pension rights under the previous pension system and then switched to the AFP system. In the model, the value of these rights is captured through the value of their Recognition Bond (“bono de reconocimiento”), which we add to the funds accumulated in the AFP account upon retirement.<sup>37</sup> (ii) Incorporating marriage decisions is not feasible given the model’s complexity. To limit the impact of this abstraction, we set the initial age in our model to 35, an age at which most people’s marital status has been determined. We use in estimation individuals who are 35 or older in 2004, the initial year of our sample. We excluded respondents who reported getting married after the age of 35.

(iii) We excluded households with missing information on key variables and with inconsistencies across survey rounds with respect to age, education and civil status (2,502 respondents).

The final sample contains 6109 households, some consisting of a single person and some of a couple, for a total of 5482 women and 4843 men.

Tables 1 and 2 present summary statistics for the estimation sample and for all EPS respondents, imposing the age restriction only. Table 1 shows demographic and labor force participation information whereas table 2 describes the distribution of earnings, non-pension 36We construct a wealth measure that also includes the reported value of equity in major household assets, such as the home and car.

> 37We obtained a dataset on the recognition bond values from the Superintendence of Pensions, which we linked to the survey data.

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assets and pension assets, in millions of Chilean pesos.<sup>38</sup> A potential concern with regard to sample restrictions is whether we might disproportionately be excluding poorer households, who are the target of the pension policies we are evaluating. As table 2 shows, the distributions are very similar, except in the right tail of the earnings distribution. The estimation sample contains a slightly smaller proportion of high earning individuals households, which is unlikely to affect our conclusions.

The rest of sample characteristics are also very similar before and after sample restrictions. Two thirds of the sample are couples, and most of the single households are women. Women are a lot less likely than men to be working (31.9 percent versus 73.5 percent). Among workers, women are slightly less likely to be working in the formal sector than men. The high average age of the sample (51.5 for men and 50.9 for women) is due to the fact that the estimation only incorporates workers over 35 years of age at the time of the first survey (2004).

# **6 Estimation results**

Model parameters are estimated by the Method of Simulated Moments (MSM). This method was chosen, in part, because it more easily accommodates missing state variables than does simulated maximum likelihood, which would require numerical integration over all possible missing state variable values. Details of the estimation procedure and standard error computation are provided in section A.2.

This section first discusses the estimated values obtained for key parameters of interest and the model’s within-sample fit. Then, we describe the out-of-sample pension reform predictions and discuss how they compare to reform impacts estimated in other studies.

## **6.1 Parameter estimates**

Tables 3 and 4 provide the parameter estimates and associated standard errors governing preferences and labor market opportunities. The main parameters governing preferences for work and saving align with estimates reported in the literature. The coefficient of risk

> 38The responses for each type of asset holding (housing, cars, etc.) have been top coded at 1 percent to reduce the effect of outliers/miscoding.

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aversion (1- _σ_ ) is estimated to be 2.7. The structural labor literature typically estimates values between 1 and 5 (van der Klaauw and Wolpin (2008)) and the discount factor is estimated at 0.999 (French and Jones (2011) report estimates between 0.85 and 1.12). The estimated utility of leisure (Ul) parameters indicate that females value leisure (i.e., nonmarket work) more than males. Also, married women, women with children and women who work part-time derive greater utility of leisure.

The parameter estimates provide some insights into what leads individuals to work formally or informally, which is helpful in understanding heterogeneous behavioral responses to pension policies. First, we find significant costs to switching between the formal and informal sectors for both men and women. The costs are similar in magnitude to the cost of re-entering the labor market after a period of not working. Both entry costs and switching costs are higher for women. These labor market frictions will tend to mitigate labor supply responses to pension policy changes, particularly for women.

Second, we find heterogeneity in the way individuals value informal sector work, as captured by the estimated unobserved type coefficients. Some types incur non-pecuniary costs when working informally (types 1, 2 and 3 for women and type 2 for men), while other types perceive benefits. This heterogeneity may reflect differences in individuals’ attributes that affect suitability for informal sector work as well as preference heterogeneity. Turning to the estimated parameters of the formal and informal log earnings offer equations, we find that the estimated intercept varies significantly across types. For example, for a given schooling and experience level, type 4 males have higher earnings offers in the formal sector, but their informal earnings offers are similar to other types. Thus, type 4 males have a comparative advantage in the formal sector.

Additionally, the estimated returns to schooling and experience, both allowed to be quadratic, differ in the formal and informal sectors. For example, for men, the informal sector offers lower returns to experience. The returns to schooling are initially higher in the informal sector and then lower as schooling levels increase in comparison to the formal sector. Heterogeneity in schooling levels is an additional source of comparative advantage to working in the formal sector.<sup>39</sup> Moreover, once a worker accumulates sufficient levels of

> 39Younger birth cohorts have higher schooling levels on average and therefore tend to have stronger attachment to the formal sector.

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formal sector experience, he would be unlikely to switch to the informal sector where the returns are much lower. Taken together, these sources of heterogeneity in demographics and in how individuals value pecuniary and non-pecuniary dimensions of formal and informal work will influence whether they adjust their labor supply in response to pension system changes. In particular, if many individuals have a strong comparative advantage in the formal sector, their behavioral response to pension system changes will be muted.

Lastly, we estimate a significant non-pecuniary cost to working past the legal retirement age (LRA) for men. The discontinuous drop in labor force participation at the legal retirement age observed in the data could, in principle, be explained in two ways within our model. The first is that borrowing constrained individuals have to wait until their pension benefits become available. However, conditions for early pension claiming in the Chilean system are relatively easy to satisfy (see section 3) and do not carry a discontinuous penalty in pension benefits as is typical under defined benefit schemes. This suggests that there may be non-financial motives to retiring exactly at the legal retirement age. The estimated cost of working past the legal retirement age (LRA) for women is smaller and statistically insignificant; the labor force participation drop off at the LRA is less pronounced for women than for men.

# **6.2 Model**

To evaluate the ability of the model to capture the key patterns in the data, we use the estimated model to simulate each sampled household’s labor supply and savings behavior in years 2004-2008 from the observed 2004 initial conditions. Figure 2 shows the labor force participation rates for men and women as they approach the standard retirement age. The model captures the low female labor force participation rate in Chile in comparison to males, and the decline of employment for both men and women near retirement. It slightly overpredicts the labor force participation rate for men at some ages.

Figure 3 shows the fraction of workers in the formal sector with different levels of formal sector experience. The model captures the “lock-in effect” observed in the data, namely that individuals become less likely to switch sectors the longer they work in one sector. The higher the formal sector work experience level, the higher the proportion working in that sector for both males and females.

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Figure 4 shows the distribution of earnings in both sectors as observed in the data and as simulated by the model. The model captures that formal sector wages are substantially higher and have greater variance. It also captures the skewness in both the formal and informal sector distributions. The model does not capture the small group of informal sector workers with very high earnings (who tend to be self-employed). This group is unlikely to be much affected by reforms to the pension safety net and therefore are not the primary focus of this study.

Figure 5 shows the distribution of non-pension assets in the model and in the data. The model fits the basic features of the wealth distribution, although the proportion with wealth holdings in the lowest category is somewhat higher in the model than in the data.

# **6.3 Predicted short-run reform impacts and comparison with existing studies**

We next evaluate the short-term impact of the 2008 pension reform and also compare our predictions to reform impacts that have been estimated in a few studies. To this end, we simulate decision-making and outcomes in each year up until 2015 under two scenarios. In the first scenario, we incorporate the reform as it was implemented. In the second, we simulated behavior under the old system as if there had been no reform. The difference in pension levels, labor force participation patterns (including the formal/informal sector break-down) between those two sets of simulations can be attributed to the changes in the pension rules, keeping other factors (including any general demographic time trends) constant.

Figure 6 shows the distribution of simulated pension levels under the old system (without the 2008 reform) and with the reform for both men and women and by marital status. The four graphs on the right from figure 6 show that the fraction of women with no pension is dramatically reduced as a result of the reform. Moreover, a significant number of unmarried men and women who qualified only for PASIS under the old system now receive the higher PBS pension. Less intuitively, two-person middle-class households appear to be the main beneficiaries of the reform. Married women who did not contribute to the system often did not qualify for any benefits prior to the reform, because their household income was too high to be eligible for the PASIS pension. Many of these women receive the PBS pension after the reform, due to the much larger coverage of the PBS (the first six deciles of the household 25
income distribution).

Figure 7 (left panel) plots a Lorenz curve to analyze inequality in individual pension receipt (combining men and women). It shows that the reform strongly impacts inequality at all deciles above 10%. However, if we consider a household-level inequality measure (figure 7, right panel), the impacts are significantly smaller. The right panel figure shows that households just above the median level household (in terms of combined pension benefits) benefit more from the reform than the poorest households.

Table 5 shows the simulated effect of the reform on labor force participation at different ages. There is evidence of substantial heterogeneity with respect to age, schooling levels and marital status. At younger ages (age 50-59), men increase their labor force participation in response to the reform, but at older ages (ages 60-74) they decrease it. For women, we observe a pronounced decrease in labor supply at older ages. There is also heterogeneity in labor force participation responses with respect to schooling levels. Men without high school increase labor supply, but as the level of education increases the effect on labor force participation becomes negative. For women, the negative impact of labor force participation is greatest for those with less education (who also tend to be older). Disaggregating by marital status, we see that the reform increased the labor supply of single men but decreased it for married men.

The positive labor force participation impacts are concentrated among those who were most likely to qualify for the old system safety net. This is consistent with the fact that the old system was characterized by stringent means-testing and a higher implicit marginal tax rate in comparison to the new system. The new system is also more generous, which explains why the wealth effect dominates at older ages, allowing individuals to stop working earlier than they would have under the old system.

The differential response by marital status is not surprising when considered in relation to household-level pension benefits. Recall that the largest jump in pension benefits occurs for married women in households who are not poor enough to receive PASIS but who are eligible for the PBS (i.e. they are under the 60% PBS means-test threshold). Our simulations show that their husbands respond to the additional pension income by retiring earlier. Women’s labor supply decreases but to a lesser extent. Formal sector participation (unconditional on working) shows similar patterns as overall labor force participation (the previous table), but 26
with slightly larger magnitudes (Table 6). The fact that the formal sector work decrease is larger than the labor force participation decrease shows that there is some switching from formal to informal work.

Despite a large descriptive literature on the 2008 reform, thus far only a few studies have attempted to isolate the behavioral responses to the 2008 Chilean pension reform using either quasi-experimental or structural estimation methods.<sup>40</sup> Behrman, Calderon, Mitchell, Vasquez, and Bravo (2011) analyze the effects of the PBS (the Basic Solidary Pension) on household income as well as on outcomes related to household work, health status, expenditures on alcohol and cigarettes, health insurance and ownership of consumer durables. They use a difference-in-difference approach to compare the change in income/outcomes over time for treated families that qualify for the PBS (by virtue of being poor and having a family member over age 65) and households that are either non-poor or do not have a family member over age 65 and therefore do not qualify for PBS. The pre-treatment year is 2006, two years before the reform, and the post-treatment year is 2009, one year after the reform.<sup>41</sup> Behrman et al. (2011) find that PBS eligible households had 2.4 percent more household annual income relative to non-targeted households, with little evidence of crowding out of private transfers. In addition, targeted households report more leisure hours, which is consistent with the lower labor force participation we predict at older ages.

Using the same data, Encina (2013) applies a difference-in-difference with matching methodology to PASIS recipients, and finds that receiving the more generous PBS benefit causes them to reduce their labor force participation by 18 percentage points relative to eligible households who do not report receiving PBS. This negative wealth effect in a sample of individuals above 65 is qualitatively consistent with our simulations. The larger magnitude is not surprising since the estimate corresponds to the subsample of the elderly whose increase the most.

> 40Packard (2002) was the first to study the frequency of contributions over the life-cycle and their determinants in Chile, using limited dependent variable models of self-reported contribution densities elicited in PRIESO, a cross-sectional household survey.

> 41An implicit assumption of Behrman et. al.’s (2011) difference-in-difference approach is that households who do not qualify for the program at a point in time do not anticipate that they may qualify at some future time period, which could affect their current behavior even if they are not actively receiving benefits. The dynamic structural modeling framework used in this study explicitly incorporates such possible anticipatory

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Another study by Attanasio, Meghir and Otero (2011) examines the effects of Chile’s pension reform on formal and informal labor market participation. Following an approach previously used by Attanasio and Rohwedder (2003) and Attanasio and Brugiavini (2003), the study exploits variation in the intensity with which different groups were affected by the reform to estimate the relationship between expected pension wealth, expected accrual rates and a variety of outcomes. Using forecast equations to predict future wages and labor supply, they build expected pension wealth and accrual rates with and without the reform. Attanasio et. al. (2011) find that the increase in pension wealth upon retirement implemented by the reform reduced the rate of participation in formal sector jobs, by around 4.1 percent for older workers, which aligns with our results on older workers. Two differences with our results are that their estimated behavioral changes are larger for women than for men and that they do not find increases in labor supply at younger ages. The first difference can be explained by the fact that they do not model, as we do, the income effects that impact married men through increased government transfers to their spouses. As for the second difference, they do not model the loosening of the basic pension’s means-test to which we attribute the predicted increased labor supply at younger ages.

As Attanasio et. al. (2011) note, relying on reduced-form forecast equations can miss part of the reform impacts: “One important difficulty in calculating pension wealth is that future labor supply will change as well as current one, as a result of the reform. In order to capture the relationship completely, a fully specified dynamic model should be used.” Our structural framework allows us to go beyond short-term impact evaluation to make predictions about long-term pension reform impacts and study the effects of hypothetical pension program designs that differ significantly from the one implemented. Such analyses are the object of our next section.

# **7 Analysis of the reform design**

A major benefit to estimating a structural model is that we can use the model to evaluate the effects of alternative pension policy designs. We focus on design changes that have been proposed by policy makers as possible ways to achieve further reductions in the gender pension gap. We consider the impacts not only on pension benefits but also on labor supply, 28
formal sector work, government costs, and private savings.

For each actual and hypothetical pension system design, we assume that the reform (if any) took place in the year 2008 and we report outcomes for years 2009-2028, which is when the youngest cohort in our sample reaches the female retirement age.<sup>42</sup> Therefore, these simulations assume that the youngest cohorts in our estimation sample are exposed to the new pension rules at most half of their career. The simulations do not capture the effect of being subject to the new pension system over one’s entire working life. However, governments are often interested in how populations are affected over medium-term horizons.

# **7.1 Sources of gender pension gaps and reform designs**

Our baseline scenario for purposes of comparison is the 2008 pension reform as implemented (described in the section 3). We analyze which features of the pension reform are most important to achieving the gender pension gap reductions by perturbing the current pension system design in various ways. We also consider the cost to the government of these alternative designs.

We examine the following scenarios, where the last seven represent modifications to the existing (2008) pension system.

0. The old pension system is kept in place (i.e. no reform)

1. The actual 2008 pension reform is implemented (baseline)

2. The retirement age of women is raised to 65 (equal to men’s) 3. When a married woman does not contribute, half of her husband’s contribution goes to her account (5% to each) 4. When a married woman does not contribute, her husband has to make a full contribution to her account in addition to his own (10% each) 5. Gender neutral tables are used to compute pension benefits 6. The reform is implemented without the child bonus

> 42As previously discussed, we assume that the reform was not anticipated.

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7. The reform is implemented without the divorce rule 8. The reform combines all features above (equal retirement age, split contributions, gender neutral tables, child bonus, divorce rule) In Chile, the retirement age is lower for women than for men (60 vs. 65). When women reach their retirement age (60), they have a lower accumulated balance and must finance a longer retirement period than if they claimed a pension starting at age 65. This results in lower monthly benefits and contributes to the gender pension gap. Scenario 2 simulates the effect of equating the retirement age for men and women. The difference in the gender pensions gap in scenarios 1 and 2 shows how much of the gap is attributable to the gender difference in retirement ages in the post-2008 system. Under the current system, women have the option to delay claiming their pension benefits until age 65. Thus, raising the retirement age of women places a constraint on behavior and, in the context of our model, would lower welfare for women (and for their husbands) despite increasing their pension benefit levels.

Scenarios 3, 4, 6 and 7 are concerned with the fact that women, particularly married women, tend to have lower contribution densities than men. That is, they reach retirement having contributed fewer months, because they are much more likely to have spent time caring for children or dependent adults. In Chile, the labor force participation rate of women was particularly low by international standards among the cohorts considered for this study.<sup>43</sup> As a way to fill the gaps in contribution histories, scenarios 3 and 4 require married men to contribute on behalf of their wives if they are working and their wives are not.<sup>44</sup> In scenario 3, the 10% contribution is allocated equally (split) to the husband and wife’s account. In scenario 4, two 10% contributions are subtracted from the husband’s formal income and put in each of their accounts.

The 2008 reform adopted a different approach to the problem of career interruptions related to childbearing. The child bonus subsidizes women’s pension accounts in proportion to the number of children they had. To isolate the effect of this feature of the pension system

> 43In the early 2000s, female labor force participation was still only in the upper 30s. It has since reached 50% with the addition of younger cohorts into the labor force.

> 44To simplify the interpretation, we do not require working women to contribute for their non-working husbands.

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design, we simulate the reform without the child benefit in scenario 6, and contrast it to the baseline reform. Lastly, scenario 7 simulates the 2008 reform without the provision that pension savings can be split between spouses in the event of a divorce, particularly if the wife is facing a drop in her living standards.

In a pension system based on individual capitalization accounts, women’s greater longevity reduces their monthly pension benefits relative to men. The capital accumulated on the account at retirement must cover a greater number of years in expectation. An alternative that would potentially favor women at the expense of men is to use gender-neutral life tables for the purpose of computing monthly pension benefits. That is, the probabilities of survival for an individual of either sex at each age are estimated from all individuals of that age rather than being computed separately for men and women. As a result, survival probabilities are overestimated for men and underestimated for women. In scenario 5, we simulate a simplified version of this change in which women’s pension benefits are computed using the male life tables.

In scenario 8, we combine all considered reform features: equal retirement age, an extra 10% contribution (as in scenario 4), gender neutral tables, child bonus, and the divorce rule.

# **7.2 Impacts of reform designs on the gender pension gap**

Table 7 shows the male female gender pension gap for new retirees in different subgroups. Comparing columns 0 and 1, it is clear that the pension reform significantly reduced the gender pension gap from 46% to 24%. The main impact is found in terciles 1 and 2 of the pension benefits distribution, as women with low contribution densities benefit the most from the more generous safety net. Examining gender pension gaps by schooling reveals that women with the lowest education levels had the highest gender pension gaps prior to the reform. The 2008 reform had the largest impact on this group, reducing the gap by over 30 percentage points.

One of the notable features of the 2008 pension reform was the reduction in the number of years of formal work experience required to qualify for a minimum pension. For this reason, workers with lower levels of formal work experience (both men and women) became eligible for greater pension benefits. Women are more likely to have low levels of formal sector work experience, because of lower rates of labor force participation and careers interrupted by 31
childbearing. Table 7 shows that the largest reduction in the gender pension gap, from 26% to 2% occurred for women with less than 10 years of formal work experience. Given the low labor supply among married women we therefore also observe that the gap for married individuals exhibits a bigger reduction than for singles. For women with strong formal work attachment (more than 20 years), the initial gap was much lower and the pension reform all but eliminates it.

In addition to more generous transfers for workers with sparse contribution histories, the 2008 pension reform included provisions in which women are compensated for the time spent in childbearing and we would naturally expect this aspect of the reform to have the greatest impact on women with more children. Women with 3 or more children saw a large reduction in the gender pension gap (from 62% to 32%), whereas women with no children saw a small increase in the gap (from 4% to 15%). However, as seen in column 6, the bulk of the reduction in the gender gap would have been accomplished with the reform even without the child bonus feature.

Turning to features not included in the reform, model simulations in column 2 show that the gender pension gap could be reduced further by delaying the standard retirement age for women to be the same as that for men (from 24% to 13%). Of note, these gains are concentrated in very different subgroups than those affected by the actual reform. The gap diminishes the most at higher terciles (of pension benefits), schooling and formal experience levels.

The other design changes shown in the table also reduce the average gender gap but have more modest impacts. However, when all of the features are combined (column (8)), the gender benefit gap is reduced to 4%. The pension system design that combines all the features leads to a pension surplus for more educated women and for women with a lot of formal sector experience.

# **7.3 Impacts of reform designs on labor supply, savings and program costs**

Table 8 examines how the 2008 pension reform and the various perturbations of its design described above affect labor supply and savings behavior over the 20 years following the reform. Each table entry shows the outcome measure as a percentage of the outcome observed 32
in column 1.

For example, as shown in columns 0 and 1, the pension reform has a modest negative effect on male or female labor supply (at ages 60-65). In contrast, raising the female retirement age from 60 to 65 (column 2) increases female labor force participation by 20.7% between those ages as liquidity-constrained households substitute pension income with labor income. Interestingly, this only results in a very modest (.8%) increase in the stock of years contributed. This is because the labor supply increase is limited to this age group, and happens mostly in the informal sector. As shown in the row labeled “pension assets,” pension assets for women increase substantially by 37.7% if the standard age of retirement for women is increased. Given that years contributed are not impacted, this effect can be attributed to the fact that pension assets accrue interest for up to five additional years before women start withdrawing them.

Other pension features have little impact on labor supply and years contributed. In particular, though mandating that husbands contribute to their nonworking spouse’s pension (columns 3 and 4) is an implicit tax on wages, it does not appear to substantially affect their labor supply. In the absence of large behavioral responses, spousal contributions impact the accumulated pension assets of men (upwards) and women (downwards) in the expected way.

Column 6 reveals the quantitative importance of the per child bonus: removing it reduces pension assets by 16.9% on average. Imposing gender neutral life tables also substantially reduces pension assets at age 65. However, this is because the programmed withdrawals made by women between age 60 and 65 are larger than in the baseline scenario, resulting in more depleted pension accounts by age 65.

The row labeled “household assets” shows that the pension reform did not decrease household assets, so there does not appear to be a problem of the pension system crowding out private savings. This is not surprising since the population segments that were targeted by the reform accumulate very little savings to start with. Changing the divorce rule about division of assets appears to reduce incentives to save outside the pension system. Theoretically, splitting pension assets upon divorce should reduce the marginal benefit of saving outside the pension system for women (who will benefit from the asset transfer) and increase it for men. Therefore, the impact of incentives for a married couple faced with divorce risk are a priori ambiguous. Our simulations predict that household assets are lower under the 33
prior divorce rule, i.e. when pensions were not divided between spouses.

The last row compares the different pension system designs in terms of government costs. Increasing eligibility for the minimum pension had significant costs. A comparison of columns 1 and 0 shows that the old pension system had 48% of the costs of the post-reform pension design. The child bonus also significantly increased costs: excluding this feature would have resulted in 7.6% lower costs.

# **8 Conclusion**

This paper develops and estimates a dynamic discrete choice model of household labor supply, pension and non-pension savings, and retirement. The model incorporates that individuals may work in the formal sector, where they pay taxes and make mandatory pension contributions, in the informal sector or not at all. The consideration of how government policies affect incentives to work in the formal or informal sector is important to most economies around the world, including among so-called developed countries.

The model that we develop and estimate is detailed enough to capture important institutional features of the 2008 Chilean pension reform, such as how the pension benefit levels depend on numbers of children, changes in the rules for dividing pensions upon divorce and changes in the payout formulae for pensions (based on actuarial life tables for men and women). A unique aspect of our model relative to other models estimated in the retirement, pension, and savings literature is that we continue to follow individuals after they become widowed or separate. This is important, because separation and widowhood are among the major economic risks facing women at older ages.

Two primary goals of the 2008 pension reform in Chile were to reduce old age poverty and to reduce the gender pension gap. We use our estimated model to explore the heterogeneous impacts of the 2008 pension reform and to study implications for gender pension gaps and household inequality. We also use the model to analyze the impact of changing the current pension system design along various dimensions. Lastly, the model is used to simulate the government cost of alternative pension system designs.

Model parameter estimates show that the returns to education and the returns to experience are higher in the formal labor market sector. Once individuals gain substantial 34
formal sector experience, they are unlikely to switch sectors. The model captures this observed sector-specific “lock-in” effect seen in the data. The parameter estimates also reveal significant sector switching costs. These labor market frictions have implications for how individuals respond to pension reforms. Once individuals develop a comparative advantage in a certain sector, their labor supply behavior will be relatively inelastic in response to pension reforms.

Results based on simulating the estimated model show that the 2008 pension reform substantially decreased the pension gender gap, especially for women with lower levels of education, lower levels of formal sector work experience and for women with children. However, for some of these groups a sizable gap remains even after the reform (e.g. the 27%-39% gap for women with less than a high school degree). Two of the most important features of the current pension system design that reduced the gender pension gap are the expansion in eligibility for the basic solidarity pensions and the per child bonus.

The model simulations show that household structure is an important determinant of pension policy reform responses. Even though many of the reform features were targeted at women, we find that men’s responses are sometimes greater than those of women as men respond to the wealth effect of an increase in pension benefits accruing to their wives. Younger men (age 50-59) increased their labor supply and older men decreased it. We observe little impact on women’s labor force participation at younger ages but significant negative impacts at older ages. In addition, the reform generates some switching from formal to informal sector work, particularly for older and more educated individuals.

The main beneficiaries of the reform appear to be married couples with joint pension benefits just above the median level. These tend to be households in which the husband earned a sizeable pension—excluding them from for the PASIS minimum pension prior to the reform—but the wife did not contribute to the pension system and thus qualifies for the PBS benefit after the reform. Inferences about changes in pension inequality differ substantially when the analysis is done at the individual or the household level (as seen in Figure 7). The 2008 pension reform had heterogeneous effects on labor force participation with respect to education and number of children. The gender pension gap is reduced substantially for less education women with three or more children.

Theoretically, increasing government transfers later in life could discourage private sav35
ings. However, the population segments that were targeted by the reform accumulate very little savings and we do not find any evidence that the pension reform crowded out private savings.

An analysis of the costs associated with the 2008 reform shows that the new pension system design is about twice as expensive as the old system. The cost of the new pension system could be reduced by about 8 percent by increasing the retirement age of women to be the same as that of men (age 65 instead of age 60) and/or by mandating that men make extra pension contributions to their spouse’s pension account if they have a nonworking spouse.

Overall, our analysis shows that the 2008 pension reform largely achieved the government’s stated goals of reducing old-age poverty, inequality and gender pension gaps. However, these benefits came at some cost, as the post-2008 pension reform is on average double the cost of the old system. The counterfactual simulations showed that increasing the mandatory retirement age of women to be the same as that of men would be a design change that would further reduce the gender pension gap and also substantially reduce monetary costs.

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