How the Design of a Pension System Influences Old Age Poverty and Gender Equity

Transcription

1 How the Design of a Pension System Influences Old Age Poverty and Gender Equity A Study of Chile s Private Retirement Accounts System Clement Joubert (U. of North Carolina) and Petra E. Todd (U. of Pennsylvania) January 23, 2015

2 Chile at the forefront of pension reform Population aging is threatening traditional pay-as-you-go pension systems (e.g. U.S. s Social Security). While younger, developing countries are aging faster than developed countries. 1980: Chile first country to switch to a fully-funded, privately-managed, individual pension accounts system. Blueprint for wave of privatization reforms around the world Examples

3 Chile s privatized pension system Main features of the individual pension accounts: Mandatory monthly contributions (10% of wages in a tax-deferred pension account) Private pension fund managers (the Administradoras de Fondos de Pensiones (AFP)) Restricted access to funds until retirement (age 60 for women, 65 for men) A minimum pension guarantee (MPG) provides insurance against lifetime income risk and asset return risk.

4 Perceived shortcomings of Chile s system Low projected benefits for workers with discontinuous contribution histories Average replacement ratio: 28% for women (vs. 51% for men)) Only 37% of women above the MPG (vs. 67 % of men). Few women eligible for the MPG (20 years of contributions required) 2008: Major reform of the safety net with strong emphasis on reducing gender gaps. source: Arenas de Mesa et. al. (2007)

5 Goals of this paper Evaluate the shorter-term and longer-term effects of the 2008 pension reform: Impact on stated policy goals: poverty and gender gaps, Potential distortions on labor supply and formality, Program costs, net of changes in tax revenue. Compare to alternative reform designs.

6 Methodology Develop a dynamic model of the lifetime labor and saving decisions of single and two-person households. Estimate the model s parameters using a simulated method of moments on panel data on Chilean households. Compare the model predictions to post-reform (2009) data not used in estimation. Simulate the short- and long-term impacts of the actual reform Conduct policy experiments on the reform design.

7 Related literature Extend framework from Joubert (2012) to study gender gaps unitary model collective model of the household allow for divorce, widowhood, and fertility. Behrman, Calderon, Mitchell, Vasquez, and Bravo (2011): use a triple-difference approach (pre/post-reform, age eligibility, income eligibility) Attanasio, Meghir and Otero (2011): Models formal work as a function of the expected pension wealth (EPW) at retirement and the expected pension accrual rate (EPA). Exploits variation in how the reform changes EPW and EPA for different cohorts and genders.

8 Results preview In the short-run (5 years), the model predicts: large reductions in old-age poverty and gender inequality in pensions. modest short-run decrease in labor supply and formality. effects are consistent with diff-in-diff studies Long-run simulations suggest: Labor supply distortions do not persist in the long run. Poverty and gender inequality reduction goals could be achieved at lower cost by using a simpler minimum pension formula.

9 Outline Chile s 2008 reform The model Data sources and empirical strategy Short-run reform impacts Long-run reform impacts Conclusion

10 Section 1 Chile s 2008 reform

11 Pre vs. post 2008 pension system s safety net Pre-2008: PASIS - Welfare pension about 30% of minimum income. restricted eligibility: 20% most vulnerable households. Pre-2008: MPG - Minimum Pension Guarantee about 75% of minimum income. eligibility: need to contribute more than 20 years. Post-2008: PBS - Solidarity pension about 50% of minimum income. Large eligibility: 60% least affluent households. Tapered benefit formula.

12 PENSION Pre vs. post-2008 minimum pension benefits Contributory pension TOTAL YEARS OF CONTRIBUTIONS

13 PENSION Pre vs. post-2008 minimum pension benefits Contributory pension Pre-2008 safety net MPG PASIS 20 years TOTAL YEARS OF CONTRIBUTIONS

14 PENSION Pre vs. post-2008 minimum pension benefits Contributory pension Pre-2008 safety net Post-2008 safety net PMAX MPG PBS PASIS 20 years TOTAL YEARS OF CONTRIBUTIONS

15 2008 pension reform: other relevant features Per child pension supplement for mothers: Bono por hijo (Child bonus) Pension asset division upon divorce or annulment: Up to 50% of one of the spouse s pension balance can be transferred to the other spouse s account. Premium for disability and survivorship benefits made actuarially fair for women (not modeled). Non-workers can make pension contributions as a "voluntary affiliate" (not modeled).

16 Section 2 The model

17 Key Model features Life-cycle model with endogenous saving and employment decisions: Potential shortage of formal jobs Endogenous retirement and early benefits claims. Exogenous risks: divorce, widowhood, fertility individual heterogeneity: observed (gender, age, schooling, experience, assets, pension savings, kids) unobserved (two discrete types affect productivity and preferences permanently) Rich model designed to capture heterogeneous responses to policy.

18 Model: Life cycle (women) or 65 (men) Initial conditions: - Assets - Experience - Schooling - Marital status - Permanent unobserved type Collect pension benefits Stop working Death

19 Individual preferences ( ct ) 1 σ u(c t,d t,p t ;N t,ε t,type = k) = MUC 1 σ + MUL (d 3,t + δ p p t ) Notation: + φ 2k d 2,t + φ s (d 1,t d 2,t 1 + d 2,t d 1,t 1 ) + φ r (d 1,t d 3,t 1 + d 2,t d 3,t 1 ) d1 :Formal, d 2 :Informal, d 3 :Home, p t :Part-time, c:consumption, N:kids, m:married Marginal utility of consumption: MUC = 1 + e ν 0N t +ν 1 d 3,t Utility of leisure: MUL = δ lk + δ n N t + δ m m t + ε t, with ε t jointly normal and iid. Non-pecuniary benefits from informal work: φ 2,k Costs of switching sectors and entering the labor force, φ s and φ r.

20 Recursive formulation of a couple s problem V 2 t (Ω 2 t ; ε 2 t ) = max + β s t,d m t,d f t,p f t [ θu m (c m t,d m t ) + (1 θ)u f (c f t,d f t,p f t ) ( π sf (1 π sm )(1 θ)ev f t (Ω f t+1 ) + π sm (1 π sf )θev m t (Ω m t+1 ) + π sm π sf (1 π d )EV 2 t+1(ω 2 t ) + π sm π sf π d [ θev m t+1 (Ωm t+1 ) + (1 θ)evf t (Ω f t+1 ) ]) ] s.t. c t = (1 s t )(y 2 t + A t (1 + r)) A t+1 = s t (y 2 t + A t (1 + r)), A t+1 0 B j t+1 = B j t(1 + r B ) + τw j C,t dj 1,t, j {m,f } Notation: y 2 t : household labor income, A t : non-pension assets, B m t,b f t : husband s, wife s pension wealth

21 Solution method Solving the model requires calculating the EV t (.) functions: i.e. the expected maximized utility achieved at any state that is reachable by some sequence of decisions. No analytic solution numerical backwards recursion. Continuous state variables Keane and Wolpin (1994, 1997) approximation method The EV t (.) functions are evaluated at 3000 states The function is approximated at other states by a polynomial regression. Model Details

22 Section 3 Data sources and empirical strategy

23 Data sources EPS (Encuesta de Proteccion Social) - longitudinal survey (2002, 2004, 2006, 2009 rounds), 16,150 respondents Linked administrative records of pension balances and contributions to retirement accounts, obtained from the Chilean regulatory agency Time series on the returns of Chile s pension fund administrators (Administradoras de Fondos de Pensiones firms) Sample restrictions Summary statistics

24 Empirical strategy

25 Empirical strategy

26 Empirical strategy MSM estimator

27 Empirical strategy

28 Empirical strategy Out-of-sample

29 Empirical strategy Reform impacts

30 Estimation method Method of Simulated Moments (MSM): Adapted to allow for moments computed on a subset of the sample (e.g. LFP transitions) Moments describe joint distribution of decisions and outcomes conditional on state variables: Employment by age, schooling, gender Employment transitions Distribution of savings accumulations by age and schooling Distribution of earnings by age, schooling, gender and experience first-difference in earnings by type of employment transition Estimation Details

31 Model fit Table: Within sample model fit (2006 data) - Couples variable mean sd p10 p25 p50 p75 p90 Men s earnings (model) Men s earnings (data) Wom. s earnings (model) Wom. s earnings (data) Savings (model) Savings (data)

32 Model fit Table: Model fit (2006 and 2009) - Couples variable Men s LFP (model) Men s LFP (data) Wom s LFP (model) Wom s LFP (data) Men in formal sect. (model) Men in formal sect. (data) Wom. in formal sect. (data) Wom. in formal sect. (model)

33 Model fit conclusions The model provides a realistic description of a rich set of decisions and outcomes: Good fit of distributions important to capture distributional impacts of the reform. Exceptions: Underestimates participation in the formal sector for men. Misses the very right tail of earnings and assets.

34 Model fit conclusions Simulations also consistent with post-reform Caveats: Data were collected shortly after the reform started to be phased-in and individuals may be uninformed about the rules of the new system. Model incorporates macroeconomic fluctuations only through asset returns.

35 Section 4 Short-run reform impacts

36 Short-run impact of the pension reform Use the estimated model to simulate outcomes 5 years ahead, with and without the reform, holding everything else constant. Assumes that the reform was introduced in 2008 and was unanticipated at the time. For the years , use actual market returns on assets as the return on pensions in the simulation, but for years 2010 or later we use an average of the returns, which equals 6.3%.

37 Pension withdrawals Table: Predicted annual pension withdrawal amounts for women age 60-79, without and with reform (in thousands of pesos) Without reform age group mean P10 P25 P50 P75 P With reform age group P10 P25 P50 P75 P

38 Pension withdrawals Table: Predicted annual pension withdrawal amounts for men age 60-79, without and with reform (in thousands of pesos) Without reform age group mean P10 P25 P50 P75 P With reform age group mean P10 P25 P50 P75 P

39 Labor force participation and formality Minimum pensions affect incentives to work through two channels: Wealth effect: Larger government transfers reduce labor force participation. Substitution effect: Higher pension accrual rates increase labor force participation and formality.

40 PENSION Short-run impact: mechanisms Contributory pension Pre-2008 safety net Post-2008 safety net PMAX MPG PBS PASIS 20 years TOTAL YEARS OF CONTRIBUTIONS

41 PENSION Short-run impact: mechanisms Contributory pension Pre-2008 safety net Post-2008 safety net PMAX MPG PBS PASIS 20 years TOTAL YEARS OF CONTRIBUTIONS

42 PENSION Short-run impact: mechanisms Contributory pension Pre-2008 safety net Post-2008 safety net PMAX MPG PBS PASIS 20 years TOTAL YEARS OF CONTRIBUTIONS

43 ΔLFP (Reform-No reform) Short-run impact: fraction working Age Males Females

44 Section 5 Long-run reform impacts

45 Long-run impact of the pension reform and alternative designs Simulate the younger cohorts in the sample until their death This takes into account the expected increase in average schooling, esp. among women Assumes that the reform was introduced in 2009 and was unanticipated at the time.

46 Long-run impact of the pension reform = Reform - No reform Men Women Years worked Years formal Government receipts Taxes collected Government outlays Old MPG Old PASIS New Minimum Pension Child bonus Net Gvt. outlays in million Chilean pesos per capita (2009 present discounted value). Source: Simulations based on estimated model

47 Short-run vs. Long-run Short-term effects differ significantly from long-term effects: Effect on older cohorts are overstated in the short-run due to surprise effect. Effect on younger cohorts are magnified in the long-run due to state dependence Human capital accumulation Savings accumulation Switching costs

48 PENSION Alternative designs - no tapering Assume policy goal is to provide consumption floor equal to the poverty line in old age, at the lowest cost to the government Take into account impact of distortions on tax revenue Contributory pension Post-2008 safety net No Tapering YEARS OF CONTRIBUTION

49 Alternative designs: LFP and government costs = Reform - No tapering Men Women Years worked Years formal Government receipts Taxes collected Government payments Old MPG Old PASIS Child bonus New Minimum Pension Total Gvt. payments in million Chilean pesos per capita (2009 present discounted value). Source: Simulations based on estimated model

50 Section 6 Conclusion

51 Conclusion We evaluate a large expansion of a privatized pension system s safety net. Our estimated behavioral model generates reasonable predictions when compared to the data within-sample and out-of-sample. Consistent with reduced-form studies, the model predicts: large reductions in old-age poverty and gender inequality in pensions small short-run labor supply distortions. Short-run effects can differ significantly from long-run effects Poverty and gender inequality reduction goals could be achieved at lower cost by using an untapered design.

52 Other projects and Future work Social insurance design: Effect of pension systems (mandatory contributions, minimum pension programs) on household saving behavior? Combine structural estimation with diff-in-diff identification e.g. exploit policy variation in mandatory pension contribution rate Model imperfect information about pension rules and information acquisition: Exploit survey questions on knowledge of pension rules

53 Other projects and Future work Overeducation and labor market mismatch: Little work in developing countries but very relevant: Tunisia (2008): Unemployment rate for college graduates is four times larger than for youth with no formal education Currently two projects on overeducated workers : 1. What are the career implications of being overeducated/underemployed (future wages, employment)? 2. What are the economic mechanisms underlying overeducation? search frictions unobserved (lack of) skills non-pecuniary benefits

54 Other projects and Future work Informality: Nature of informality: barriers to entry/frictions comparative advantage considerations non-pecuniary benefits Document transitions in informality status and wages along the life cycle and the business cycle: What happens to workers who loose their formal jobs during a crisis? What happens to youth who graduate during a recession: are they more likely to work informally?

55 Sample restrictions Incorporates: Excludes: Individuals who are 35 or older in 2004, the initial year (to avoid considering marriage) workers in pre-1980 INP system (pre-1980 pension rights accounted for through Recognition Bond ). Workers contributing to pension systems other than AFP (2,152 EPS respondents). Respondents who reported getting married after the age of 35 (1,183 cases) or those with missing info or inconsistencies (2,502 cases) Final sample contains 5,314 households (some single, some married), a total of 4,809 women and 4,309 men.

56 Sample restrictions Table: Effect of Sample Exclusions on the Distribution of Earnings Ann. Earnings (mil. pesos) mean p10 p25 p50 p75 p90 Before exclus. Married men Single men Married wom Single wom After exclus. Married men Single men Married wom Single wom Note: Minimum annual wage around 1.5 million pesos Back

57 Table: Predicted mean and percentiles of pension savings distribution in 2014 for women at age 60, without and with the reform, in thousands of pesos Without reform age group mean P10 P25 P50 P75 P With reform age group mean P10 P25 P50 P75 P Back

58 Table: Predicted mean and percentiles of pension savings distribution in 2014 for men at age 65, without and with reform in thousands of pesos Without reform age group mean P10 P25 P50 P75 P With reform age group mean P10 P25 P50 P75 P Back

59 Table: Predicted annual pension withdrawal amounts for women age 60-79, without and with reform (in thousands of pesos) Without reform age group mean P10 P25 P50 P75 P With reform age group mean P10 P25 P50 P75 P Back

60 Table: Predicted annual pension withdrawal amounts for men age 60-79, without and with reform in thousands of pesos Without reform age group mean P10 P25 P50 P75 P With reform age group mean P10 P25 P50 P75 P Back

61 Table: Ratio of predicted women s and men s annual pension withdrawals in 2014, mean and percentiles age 60-79, without and with the reform Without reform age group mean P10 P25 P50 P75 P With reform age group mean P10 P25 P50 P75 P *A value of. indicates that men s pension withdrawal value was zero. Back

62 Table: Predicted Percent of households living in poverty in 2014, without and with the reform Without reform age group poverty rate #1 poverty rate # With reform age group poverty rate #1 poverty rate # *A household is defined as poor under measure #1 if household income, including pension withdrawals, is less then pesos. Poverty measure #2 uses a cut-off of pesos.

63 Table: Predicted percent not working or working in formal or informal jobs in 2014 for women, age 45-69, without and with the reform Without reform age group not working work in formal sector work in inf. sector With reform age group not working work in foraml sector work in inf. sector *The model imposes the restriction that people aged 70 and older do not work. Back

64 Table: Predicted percent not working or working in formal or informal jobs in 2014 for men, age 45-69, without and with the reform Without reform age group not working work in formal sector work in inf. sector With reform age group not working work in formal sector work in inf. sector *The model imposes the restriction that people aged 70 and older do not work. Back

65 Table: Working patterns around the age of retirement in 2014 for women age 55-70, without and with the reform Without reform age group not working working full-time working part-time With reform age group not working working full-time working part-time *The model restricts individuals age 70 and older to not work

66 Table: Working patterns around the age of retirement in 2014 for men age 55-70, without and with the reform Without reform age group not working working full-time With reform age group not working working full-time *The model restricts individuals age 70 or older to not work

67 Table: Mean and percentiles of predicted contribution density distribution in 2014 for women age 45-59, without and with reform Without reform age group mean P10 P25 P50 P75 P With reform age group mean P10 P25 P50 P75 P *density = ratio of years of contribution divided by age-18 Back

68 Table: Mean and percentiles of predicted contribution density distribution in 2014 for men age 45-64, without and with the reform* Without reform age group mean P10 P25 P50 P75 P With reform age group mean P10 P25 P50 P75 P *density=ratio of years of contribution divided by age-18 Back

69 Chile-inspired pension system reforms Latin America: (Peru (1993), Argentina (1994), Colombia (1994), Uruguay (1995), Bolivia (1996), Mexico (1997), El Salvador (1998), Costa Rica (2000)) Eastern Europe: (Czech Republic (1994), Hungary(1998), Poland (1999), Bulgaria (2000), Estonia (2002)) Central Asia: (Kazakhstan (1998)) Back

70 Related literature on Chile s pension program Joubert (2012): Develops a structural empirical framework to study pension design in the presence of a large informal/uncovered sector incentive-compatibility of pension rules is crucial This paper extends his methodology to study gender pension gaps: allows for divorce, widowhood, and fertility. unitary model collective model of the household Extend the estimation sample to singles, divorced and widows/ers

71 Related literature on Chile s 2008 pension reform Behrman, Calderon, Mitchell, Vasquez, and Bravo (2011): use a triple-difference approach (pre/post-reform, age eligibility, income eligibility) Find that minimum pension eligibility increases household annual income by 2.4%, Small increases in health care expenditures and improved self-reported health. Decline in labor supply (insignificant).

72 Related literature on Chile s pension program Attanasio, Meghir and Otero (2011) Models formal work as a function of the expected pension wealth (EPW) at retirement and the expected pension accrual rate. Forecasts EPW combining a reduced-form model of labor supply, hours and wages, with the pre- or post-reform pension benefit rules. Instruments EPW with time dummies interacted with group (cohort, gender) dummies Also find a small decrease in the rate of participation in formal sector jobs at older ages. Literature review

73 Related literature on labor market segmentation Two models of the informal sector in the development literature: Segmented model (Harris & Todaro (70), Fields (90)) Excess labor supply in the formal sector (e.g. from minimum wage regulation) Informal work is an alternative to unemployment Competitive (Maloney (99)) Voluntary informal employment to avoid labor taxes or to enjoy higher flexibility Formal-informal sector choice and retirement: Valdes-Prieto (2008), Robalino, Zylberstajn, Zylberstajn and Eduardo Alfonso (2008), Velez-Grajales (2009). Literature review

74 Related literature on savings, retirement and pension reform Dynamic discrete choice models of individual and joint retirement decision: Fields and Mitchell (1984), Rust and Phelan (1996), Gustman and Steinmeier (2000), Gustman and Steinmeier (2002), Blau and Gilleskie (2006), Jiménez Martín and Sánchez Martín (2007), Van der Klaauw and Wolpin (2008). Lifecycle portfolio choice with tax-deferred retirement accounts: Gale and Scholz (1994), Engen, Gale and Scholz (1996), Dammon, Spatt and Zhang (2004), Gomes, Michaelides and Polkovnichenko (2005). Pension reform Auerbach and Kotlikoff (1987), Conesa and Krueger (1999), Nishiyama and Smetters (2007) Literature review

75 Model details Initial conditions Mortality Fertility Decisions Retirement State variables Preferences Single s problem Couple s problem Wage offers Solution method Household Income back

76 The Model: Timing and Initial conditions The superscript j {m,f } denotes gender, superscript 2 denotes a couple. For singles: Decision problem begins at ages t m 0 = t f 0 = 35 (assumed to remain single). Periods indexed by individual s age (t = a j t); For married couples: Decision problem begins when wife turns t f 0 = 35 Problem indexed by female age (t = a f t ). Age of the husband in the first period, a m t 0 is an initial condition. Can transition to being divorced or widowed and then solve single s problem.

77 Initial Conditions Initial conditions (at age 35): Initial household assets (A t0 ), work experience (Xt m 0,Xt f 0 ), children born prior to age 35 (N t0 ). Pension savings (B m t0,b f t 0 ), pension rights accumulated by the two spouses under the earlier INP retirement system prior to age a j t 0 ( Bonos de reconocimiento ) or under the new AFP system. Completed schooling levels of men and women (e j ), and birth cohorts (bc j ). We denote the set of initial conditions for a couple by Ω 2 t 0 and for a single household by Ω j t 0 : Ω 2 t 0 = {a m t 0,A t0,b m t 0,B f t 0,X m t 0,X f t 0,N t0 ;e m,e f,bc m,bc f } Ω j t 0 = {A j t 0,B j t 0,X j t 0,N t0 ;e j,bc j } Model

78 Decisions In each period such that a m t < t R and a f t < t R, a two-person household makes a saving decision for the household (s t ) a labor force participation decision for each individual (d m t,dt f ) a part-time work decision for the woman (part-time (p j t = 1) or full-time (p j t = 0)) Income that is not saved is split evenly into the two spouses consumptions c m t,c f t. s t is the income that is saved in period t. Three employment options available to both men and women are to work in the formal sector (d j t = 1), the informal sector (d j t = 2), or stay home (d j t = 3) for j {m,f }. Model

79 Earnings offer probability Each working age individual receives in every period: an offer from the informal sector with probability one an offer from the formal sector with probability Γ j t : j {m,f },t {t 0,t R } Γ j t = (1 + exp{ (γ j 0 + γj 1 I {d j t 1 =1} + γj 2 ej + γ j 3 Xj t)}) 1 I {d j t 1 =1}: lagged formal sector participation e j : education level X j t: labor force experience

80 Earnings offers The log-earnings offers (for males and females j {m,f }, in sector s {C,U} of type k = 1..K and with completed schooling levels e j ) are: w j s,t,k = K k=1θ j 0sk + θ j 1s ej + θ j 2s Xj t + θ j 3s (Xj t) 2 + ε j s,t θ j 0,s is a gender- and sector-specific constant, θ j 1es θ j 2s a gender-, sector-, schooling-specific cohort effect, the sector-specific returns to schooling, and θ j 3es and θ j 4es the gender-specific returns to experience. ε j s,t (j {m,w},s {C,U}) are iid sector-specific earnings offer shocks. Model

81 Household income Total household disposable labor income net of taxes: y 2 t = (1 τ)w i C,t I {dt=1} i + wi U,t I {dt=2} i i {H,W} I {i=h} ) + I {i=w} (1 + p f T(A t,w m C,t t ),wf C,t,dm t,dt f,p f t ) where τ is the pension contribution rate (10%). Household income for a single household is defined similarly.

82 Covered labor earnings net of pension contributions and private savings returns are subject to a progressive income tax. Taxes due at period t are denoted T(At,w m C,t,wf C,t,dm t,d f t ), They depend on the household s stock of private savings, formal sector earnings offers and labor force participation decisions. 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. Model

83 Separation and mortality Exogenous probability of surviving to the next period as π sj = π sj (a t ) for j {m,f } (taken from life tables for Chile). Household separation is modeled as an exogenous logistic probability π d t = π d (e m,e f,n t,a m t,t). Upon separation, non-pension assets A t split evenly between individuals who become single households. Model

84 Fertility The number of children N t evolves stochastically (pregnancies) up to woman s age 40. Modeled as a logistic model, depending on the woman s age, schooling, and number of prior children. π N t (N t N t 1,a j t,e f,marital status) Model

85 Retirement At ages t f C = 60 and tm C = 65 years old, males and females receive the pension benefits for which they qualify. Withdraw pension funds using phased withdrawal. Can start withdrawing earlier than 60 (resp. 65), if eligible. People can choose to work until age t R =70 when they are assumed to take leisure (d j t = 3) for remaining periods. Model

86 Evolution of other state variables Other time-varying state variables, A t, B m t, B f t, X m t, X f t are determined by the saving, labor supply decisions and asset return shocks. Private savings earn the risk-free rate r (assumed 5%.) Pension account balances accrue interests stochastically and increase with contributions. Returns on the pension accounts are iid process: r B iidn( r B,σB 2). Model

87 Recursive formulation of the single household problem The optimization problem faced by a single individual of gender j has the following recursive formulation: Vt(Ω j j t; ε t j ;type) = ] [u j (c j t,dt,p j j t,n t,εt j ;type) + βπ sj (t)ev j t+1 (Ωj t+1 ; εj t+1 ;type) s.t. max s t,d j t,p j t c j t = (1 s t ) (y j t + A t (1 + r)) A t+1 = s t (y j t + A t (1 + r)) A t+1 0 w j C,t B j t+1 = B j t (1 + r B ) + τ 1 + p j I {d j t =1} t

88 τ w j C,t I {dt=1} j is the pension contribution made by workers in the formal sector. y j t is the household s income defined earlier. ε j t is a vector of shocks to wage offers, preferences for leisure, and pension asset returns. Model

89 Couples problem For couples the continuation value accounts for five possible events: 1. Both spouses die (continuation value =0 ) 2. Husband dies and the maximization problem continues with the wife 3. Wife dies and the maximization problem continues with the husband 4. Both spouses survive and remain together 5. Both spouses survive and separate and the problem continues with the sampled individual (either male or female)

90 Solution method At age t D (age 90), there is no decision and the household consumes all savings plus any pension benefits. At age t D 1 (age 89), a household collects pension benefits and decides on consumption, which together imply a level of private savings, to maximize the weighted sum of current and future period utilities, taking into account the possibilities of widowhood or death next period. For any given value of the deterministic and shock components of the state space, optimal consumption is obtained by comparing utility on a grid of possible savings choices.

91 Solution method At any deterministic state point, the expected value of V td 1 is obtained by Monte Carlo integration over the preference, earnings, and asset shocks and by analytical integration over fertility, divorce and survival shocks to obtain EV td 1(S td 1). This expectation (the so-called Emax(t D 1) function)is calculated at a subset of 3000 deterministic state points and the function is approximated at other points by a polynomial regression (following the approach of Keane and Wolpin (1994, 1997)). This procedure is repeated at age t d 2. Using the recursive formulation of the value function, substituting the Emax(t D 1) function for the future component, the optimal decision is computed. At age 69 and younger, the option to work in the formal or informal sectors becomes available.

92 Estimation method (2) Denote by xi m an outcome measure of individual i, i 1..N, pertaining to the mth moment, m = 1..M. The MSM estimator is defined as: ˆθ N = argmax θ Θ [ 1 N [ n xi m D m i i=1 [ [ n 1 N xi m D m i i=1 ( N N m 1 R N N m )]] R K ˆx irk m (θ) ˆD m irk (θ) N r=1 k=1 N m Pr(k Ω) 1 M ( R K 1 R W 1 N )]] ˆx irk m (θ) ˆD m irk (θ) N r=1 k=1 N m Pr(k Ω) M 1 D m i is an indicator for whether observation i is included in calculating moment condition m, and N m = n i=1 Dm i, ˆD m irk is an indicator for whether the observation is included in moment m under simulation r when the individual is type k, The sum over k integrates over the unobserved types. The weighting matrix WN is an M by M diagonal matrix with the m th diagonal elements equal to the sample variance of x m i.

93 Estimation method (3) Integrate over the unobservables, k, and assume that R, so that the simulation error goes to zero and the simulator converges to the limit µ m i (θ) = E(ˆx irk (θ) m ˆD m i (θ) = 1)Pr( ˆD m i (θ) = 1) N N m. Defining: µ m i = x m i D m i Rewrite the objective function as: ˆθ N = argmax θ Θ [ 1 N ] n µ i m µ i m (θ) i=1 N N m, 1 M W 1 N [ 1 N ] n µ i m µ i m (θ) i=1 M 1

94 Estimation method (4) Following Hansen (1981), we can obtain the estimator s asymptotic variance-covariance matrix as: where D 0 = E V 0 = E [ δ µ m ( ) 1 ( 1 Asy.Var( ˆθ N ) = D 0 W 1 0 D 0 D 0 W0 1 V 0W0 1 D 0 D 0 W 1 0 0) D, δθ θ 0 ], ( [ ] ) [µ i m µ i m (θ 0 )] µ j m µ j m (θ 0 ). D 0 is estimated using numerical derivatives, V[ 0 is approximated ] by the sample variance-covariance of µ j m ˆµ j m (θ 0 ). Back

95 Key parameter estimates Because only a few rounds of data, we set the discount factor at CRRA coefficient is in line with other estimates in the savings literature: 1 σ= Returns to experience are 3.2%(M) and 3.9%(F) in the formal sector; 1% and 1.8% in the informal sector Probability of a formal offer is approx 1 for men with > 10 years of schooling, but declines rapidly for men with 5 years of schooling or less, especially from older cohorts Probability of a formal offer is.93 for women with no strong age or schooling trend Type 1 men and women have relatively higher formal wage.

96 Table: Summary statistics variable mean Couples (%) 66.9 Single Women (%) 22.0 Single Men (%) 11.1 Lab. Force Part. (women, %) 36.2 Lab. Force Part. (men %) 74.9 Formal sector* (women %) 59.5 Formal sector* (men %) 61.4 Age (men) 51.4 Age (women) 50.8 Schooling (men, years) 8.7 Schooling (women, years) 8.5 Children 3.0 Source: Encuesta EPS, Superintendencia de Pensiones * as a fraction of those working

97 Table: Summary statistics (earnings and assets in MM PS) variable avg p10 p25 p50 p75 p90 Annual Earnings (women) Annual Earnings (men) Non-Pension assets** Pension assets** (women) Pension assets** (men) Source: Encuesta EPS, Superintendencia de Pensiones Note: MM PS = Million Pesos ** The top 2% of pension values were trimmed to avoid sensitivity to outliers. Back