The Cost of Minimum Pension Guarantee

1. The Cost of Minimum Pension Guarantee

2. What is the problem we study? • Governments often promise a minimum level of benefits under an accumulation scheme • If future does not turn out to be rosy, what is the likelihood that the government has to foot the bill of this guarantee? • Using the actual experience of the past eight years, and including actual features of the Mexican system, we calculate the probability distribution of such promises

3. Pension System in Mexico • Investment Regime • Minimum Pension Guarantee • Model • Results • Conclusions

4. Current Mexican pension regime (for the formal sector) In 1997, Mexico moved from a defined benefits system (a la US Social Security) to a defined contribution system (a la Chile) The system is publicly mandated but funds are privately managed The funds are called AFORES (Administradoras de Fondos para el Retiro) There are three components to each fund: government component, private compulsory component and private voluntary component There is a government contribution There is also a government guarantee

5. Contribution is 6.5% of the base salary (SBC)There are three component Monthly Contribution as percentage of SBC Other Contributions • Each individual can also make voluntary contribution to the system. But such funds are maintained separately • 1.125% Worker • 5.150% Employer • This is called Cuota Social (cs). • 5.5% of minimum wage • indexed for inflation • 0.225% Govt TOTAL 6.5% Note: There is an upper limit to the SBC equivalent to 25 times the minimum wage

6. Pension System in Mexico • Investment Regime • Minimum Pension Guarantee • Model • Results • Conclusions

7. Investment regime under the new system The AFORES invest in special funds called SIEFORES. Until 2004, the SIEFORES had extremely restricted investment regimes. For example, investment in anything other than high grade inflation protected bonds were not allowed In January 2005, new investments were allowed such as foreign bonds in currencies other than pesos as well as in other instruments provided that capital is protected from erosion (through synthetic instruments such as futures and options)

8. ACTUAL INVESTMENT STRUCTURE IN THE PENSION SYSTEM Allowed Financial Instruments & Limits Affiliated Workers • Debt Instruments with inflation protection – lower limit 51% • Foreign Debt – up to 20% • Assigned Workes • Workers over 56 years old • Workers who choose to invest under this SIEFORE SIEFORE-1 • Foreign Instruments – up to 20% • Equity Notes – up to 15% • Workers under 56 years SIEFORE-2

9. Pension System in Mexico • Investment Regime • Minimum Pension Guarantee • Model • Results • Conclusions

10. The nature of minimum pension guarantee The government promises to pay a minimum level of benefits if the amount of money accumulated in the worker’s account does not reach certain minimum value What does the government promise? The Federal Government promises the equivalent of one minimum wage to any worker who has contributed to the new system for 1250 weeks or 24 years (even if it is not continuous) The government promises to pay an annuity of one minimum salary for life for each worker in the system

11. Although small today, the number of people who become beneficiaries of this promise is rising Number of people entitled to minimum pension guarantee thousands,2005 Government burden of such a guarantee is rising... (millions of pesos) 86 4.3 4 66 3.5 2.8 49 2.2 35 1.7 25 1.3 17 .9 8 .19 Source: IMSS data

12. ....and this will continue to rise because the workers under the regime largely have low wages (with over half earning no more than 3 times the minimum wage) Salary level of workers under the IMSS system 2004 8.6% 15.06% More than 10 MW 20.65% 6 to 10 MW 4 to 5 MW 55.68% 1 to 3 MW M.W.= Minimum Waves Source: IMSS

13. Pension System in Mexico • Investment Regime • Minimum Pension Guarantee • Model to Calculate the Cost of the M.P.G. • Results • Conclusions

14. The model is as follows: The first element describes the distribution of the variable rate of return, the second describes the law of motion, the third is a contribution at each period taking into account the commission charged Equity Returns Accumulation Contribution

15. The rate of return is the actual rate that prevailed during 1997-2005 in Mexico mM = 0.00757452 equivalent of 9.48% annual sM = 7.12315% Adjusted Log Likelihood = 135.017 For the riskless rate, we took the real rate of return of Bondes182 (a government bond with inflation indexation) rf = 4.63% annual

16. Monthly rate of return of the Mexican broad market index IPC was indeed Normal during 1997-2005 We assume that a fraction l is invested in the broad stock index and the other fraction (1- l) is invested in government bonds Where: ComAFOREi,t Fee charged by AFORE i at time t cs Cuota Social

17. Underlying assumptions for running simulations • Retirement Age. 65 years • Contribution period. 25 and 40 years respectively • Contribution Rate. 6.5% of base salary • Contribution frequency. Monthly • Commissions. We use the actual and projected commission structure taking into account the loyalty discounts offered by some AFORES • Inflation. We calculate everything in real terms

18. Measuring the guarantee costWe can conceptually think of the guarantee cost as an implicit put option for the government at the retirement age Payoff (T) = max{ PMG – VT , 0} Payoff VT PMG Where PMG: Price of a contingent annuity that pays the equivalent of one minimum salary in real terms VT: Funds accumulated in the worker’s individual account at retirement

19. We could value the option using traditional Black Scholes option pricing model (it requires risk neutral valuation and the assumption of complete contingent markets) Simulation • 1,000 realizations of the final amount for each level of salary assuming different levels of investment in equity Cashflows • We calculate the present value for each trajectory Average • The average payment is the value of the option

20. We need to calculate the single premium contingent annuity of one minimum salary (the government guarantee) The net premium for such an annuity is calculated using the following euqation Where SM97: Minimum salary current in 1997 but brought forward to 2005 f : Administrative and acquisition fee 1% sm: Security Margin of 2% We also assume that at retirement the worker is married and his spouse is four years younger than him (average in Mexico) *We use the mortality table used by the Mexican Social Security

21. Pension System in Mexico • Investment Regime • Minimum Pension Guarantee • Model to Calculate the Cost of the M.P.G. • Results • Conclusions

22. PROBABILITY TO EXERCISE THE GUARANTEE UNDER THE ASSUMPTION THAT THE WORKER CONTRIBUTES TO THE SYSTEM DURING 40 YEARS Probability *Measured in multiples of minimum wage Equity Fraction Income*

23. WHEN WE REDUCE THE CONTRIBUTION TIME TO 25 YEARS, THE RESULTS CHANGE DRAMATICALLY Probability *Measured in multiples of minimum wage Income* Equity Fraction

24. We also calculate the cost of the option for the government Option Price Option price, 25 years thousands Income* Equity Fraction *Measured in multiples of minimum wage

25. LOS COSTOS DERIVADOS SON REDUCIDOS DE FORMA IMPORTANTE CON UNA MAYOR FLEXIBILIDAD DE INVERSIÓN EN EQUITIES Guarantee Price for a worker who earns 3 M.W. SIEFORE-1: $ 147, 491 53% Cost Reduction SIEFORE-2: $119,804 If the SIEFORES could invest up to 50% in Equity: $63,913 Equity Fraction

26. Pension System in Mexico • Investment Regime • Minimum Pension Guarantee • Model to Calculate the Cost of the M.P.G. • Results • Conclusions

27. CONCLUSIONS • Minimum pension guarantee is present to serve a social purpose: protecting low income individuals from falling into poverty • But it also binds the government to future costs • High commission (between 20% and 30% of contribution) directly affect the minimum pension guarantee: therefore, governments should seriously consider strategies for reducing commissions • The capital protection regulation currently in place does not eliminate all downside risks • While allowing for investment in broad stock indexes can increase upside for the workers, it can significantly increase the burden for the government especially for low income workers

28. Income profile of AFORE affiliates who contribute regularly Tapen Sinha

29. How did income increase during 1997-2005 among affiliates? • Main question • Why is it important? • To know how much affiliates would have in their AFOREs during their lifetimes • To have an idea of how income changes in a life cycle context in Mexico in the formal sector • To disentangle the gender gap in income

30. Limitations • There are few observations in some of the cells – thus, they are not reliable (example: women in the highest quintile) • We do not get a picture of all who are contributing – only the ones that are contributing regularly • We only have data for 1997-2005 much less than lifetime data

31. Original study • With macroeconomic data • Modigliani Bloomberg life cycle hypothesis • Milton Friedman permanent income hypothesis • Both posit that people smooth consumption over lifetime income • Income has less volatility than consumption

32. Income Consumption income consumption borrow? working life retire death

33. “Typical” income consumption profile

34. Age consumption income profile in the US matches the typical one......

35. ....but the Japanese data does not match the typical...

36. Data • For men and women separate samples • For each quintile, 1000 persons for each age group • 20 or below, 21-25, 26-30, 31-35, 36-40, 41-45, 46-50, 51-55, 56-60, 61 and above • Total ten categories • Thus, (in theory) we have 50,000 observations for men and women – we have less numbers • Each person has a salary figure for August 1997 to February 2005 every two months (46 obs)

37. Simple analysis • We can collapse all the observations by examining the average salary over (almost) eight years and examine how average salary changes with all the persons put together taking into account sex of the person and the age of the person • This will be similar to the analysis of the US and Japan (we saw in the OECD Report in the previous slides)

38. Estimating for the entire sample • Estimation Equation: • Log(SalProm) = c0 +c1.sexo +c2edad +c3edad2 • LOG(SalProm) = 4.482169548 - 0.1617908224*SEXO + 0.0318998435*EDAD - 0.0003307339208*EDAD*EDAD • Highly significant coefficients

39. Separate estimates • Males • SalProm = -9.935 + 9.311*EDAD - 0.0887*EDAD*EDAD • Females • SalProm = 18.471 + 6.712*EDAD - 0.06534*EDAD*EDAD

40. When does the income starts to decline • From separate estimates: • Male 52.47 • Female 51.35 • From combined estimate: • Highest income at 48.23

42. What is wrong with the pictures? • They are calculated from by combining all the people of different age groups • They do not tell us anything about cohort effect • Here, we can actually observe the real trajectory of persons over eight years • What we need to know for constructing income profiles of actual workers is what they earn over their lifetimes – we have segments in our data

43. Household Savings and Income Distribution in Mexico Orazio P. Attanasio and Miguel Székely, 1998

44. Analyzing data controlling for cohorts and gender • Now examine the data, controlling for "starting income" (which is a proxy for cohort) and follow them for eight years • How should it look like? • Logically, it should depend on the economic performance (more about that at the end) • It should also depend on cohort • For young higher growth than old

45. Wage Observations from data….that leads to…. Old Young 1997 2005 Time

46. …the following lifetime wage profile Wage 20s 30s 40s 50s 60s

47. Males in Quintile 1 Each point is average

48. Males in Quintile 2

49. Males in Quintile 3

50. Males in Quintile 4