I7362w74 PSP Discussion Paper Series Effects of Social Security on Lifetime Income Distribution in Brazil Rafael Rofman August 1995 Poverty and Social Policy Department Human Capital Development and Operations Policy The World Bank This Booklet of Abstracts contains short summaries of recent PSP Discussion Papers; copies of specific papers may be requested from Patricia G. Sanchez via All-in-One. The views expressed in the papers are those of the authors and do not necessarily represent the official policy of the Bank. Rather, the papers reflect work in progress. They are intended to make lessons emerging from the current work program available to operational staff quickly and easily, as well as to stimulate discussion and comment. They also serve as the building blocks for subsequent policy and best practice papers. Abstract Brazil's Social Security system is organized as a very complex Pay-As-You-Go scheme, with many different structures of contributions and benefits. As of December 1992, there were 97 different types of benefits, although efforts to simplify the system are under way. This paper considers the distributive effects of the system from a lifetime income ap- proach, assessing the potential effect of different variables on the retums offered by the system. Using data on gender, residence and income level a simulation was prepared to estimate the intemal rates of return received by workers, considering not only sociodemographic and eco- nomic differences between social groups but the possibility of receiving benefits under altema- tive program rules. Our results indicate that workers retiring under the "Old Age" provisions (which grant retirement benefits to those who exceed a certain age, with very low contributions requirements) receive the best rates of retum. Instead, most workers retiring under the "Length of Service" (which grants benefits after a number of years with contributions, regardless of age) receive rates of return much closer to market interest rates. The analysis indicates that women are in better position than men and the system appears to be progressive with respect to income distribution. A number of illogical inequities, such as "special retirement" provisions, should be eliminated, since they rarely benefit those who are in worst socioeconomic situation. A more sound, multipillar model should be enacted to replace the current system. Table of Contents 1. INTRODUCTION ...............................................................1 2. THE BRAZILIAN SOCIAL SECURITY SYSTEM ........................................2 3. METHODOLOGY .........................................................6 3.1. Data Sources ...............................................................6 3.2. Methodology ..............................................................8 4. RESULTS .............................................................. 11 4.1. Differences by Program .............................................................. 11 4.2. Differences By Gender ............................................................. 15 4.3. Regional Differences: ............................................................. 17 4.4. Income Differences: .............................................................. 18 4.5. Differences for Specific Groups ......................... ..................................... 20 4.6. The Role of Survivors' Benefits ............................................................. 21 5. DISCUSSION AND CONCLUSIONS ........................................................ 24 6. POLICY RECOMMENDATIONS ........................................................ 27 7. BIBLIOGRAPHY ........................................................ 29 8. APPENDIX A. USING ALTERNATIVE MORTALITY ESTIMATES . ..... 31 9. APPENDIX B. RATES OF RETURN BY SOCIOECONOMIC CHARACTERISTICS FOR DIFFERENT RETIREMENT PROGRAMS ........ 33 10. APPENDIX C. RATES OF RETURN BY SOCIOECONOMIC CHARACTERISTICS FOR DIFFERENT RETIREMENT PROGRAMS. MARRIED MALES, INCLUDING SURVIVOR'S BENEFITS FOR SPOUSES ........ ................ 55 11. APPENDIX D. PARAMETER ESTIMATES, SAMPLE WEIGHTS AND EDUCATIONAL ATTAINMENT MEANS FOR EARNINGS FUNCTIONS ....62 1. INTRODUCTION Social Security systems are designed, throughout the world, to perform as a distributive scheme that facilitates the transfers of resources from younger to older, and richer to poorer individuals. The systems are usually based on a simple model: all active individuals contribute a proportion of their earnings (usually, wages), and retired individuals receive benefits. The most common system is known as "Pay-As-You-Go" (PAYG), and its main characteristic is that it is an unfunded scheme, since all contributions are distributed among beneficiaries and, in principle, no funds are accumulated. The analysis of the distributive effect of these systems can be approached from several viewpoints. If we consider the system a part of the general tax and transfers governmental programs, then we should look into its effects in a given period. Instead, if we analyze the systems considering them compulsory saving schemes with a distributive side, then we must look into the distributive effect from a lifetime perspective. This last approach is used in this study, where we calculate the rates of return the system would offer if the rules were to stay unchanged during a generation's lifetime, and compare them by retirement programs and socio- economic characteristics. Sections 2 and 3 present some background information, describing the Brazilian Social Security system and the data sources and methodology, respectively. Section 4 reports the results of our analysis and sections 5 and 6 discusses them and present conclusions and policy recom- mendations. A bibliography and two appendixes complete the report. 1 2.. THE BRAZILIAN SOCIAL SECURITY SYSTEM Brazil's Social Security system was started in the early 1 920s, when the first retirement funds where created for railroad workers. Since then, a number of funds, both private and public, were created, originating a disperse body of legislation and inequities of different types. The first law unifying benefits was passed in 1960, and the process of unification continues until now. Currently, the Social Security system is centrally managed by the Ministerio da Previdencia Social (NPS), and efforts continue to simplify and unify benefit rules. The MPS manages social security in a wide sense, including a range of programs that go from old age prevision to social welfare. The programs include the pay-as-you-go retirement scheme and several types of short and long term disability benefits, family benefits for active workers, maternity leave benefits, and benefits for families of imprisoned felons, among others. Overall, there are 97 types of benefits, although most of them are very small. We will limit our analysis to the urban programs directly related to old age labor earnings replacement goals. In other words, we are excluding all types of disability benefits, benefits granted under social welfare policies (that is, benefits not requiring previous contributions to qualify) and rural benefits. This last group was excluded of the analysis because, even if they are formally part of the pay-as-you-go system, in practice the rural programs are social welfare schemes. This argument can be easily understood if we consider that, by 1989, rural retirees were around 40% of all retirees and received 15% of retirement benefits, but their contributions amounted to less than 2.5% of all revenues from contributions, or about 1.7% of revenues from all sources. Thus, we concentrated our attention in the four specific programs known as Retirement for Old Age, Retirement for Length of Service and Special Retirement, always for urban workers. These three categories include 17 benefit types, comprising all benefits that could be considered part of a pay-as-you-go retirement scheme. 2 The rates of return a Social Security system offers to its affiliates are determined by five factors that can, directly or indirectly, be parametrized for the analysis. They are (1) the age at entering the labor force, (2) the age at retirement, (3) the age at death, (4) the rule used to determine contributions and (5) the rule used to determiine benefits. If different individuals are exposed to identical conditions regarding these five elements during their lifetime, those indi- viduals will receive identical rates of return. Social Security legislation is rarely neutral, in the sense that systems' rules are usually designed to generate differences in rates of retum, produc- ing income transfers between social groups. This is true for almost every system in the world, including traditional pay-as-you-go models, as the U.S. case, or systems strongly based on private capitalization, as the Chilean case. Because the distributive rules cannot affect age at death and they rarely affect age at entering labor force, in most cases they concentrated on the effect of age at retirement and benefit calculations, and, sometimes, on contribution rules. The three programs analyzed here have some characteristics in common and a few dif- ferences. All of them require identical contribution taxes, although the minimum number of contributions required to qualify varies. In fact, Brazilian legislation does not impose a minimum number of contributions in any case, but a minimum number of "years in service". This concept refers to the number of years an individual can prove he or she has worked in an activity covered by Social Security, without having to prove that actual contributions were made. Brazil's Social Security Ministry does not maintain any type of records of contributions at the individual level, and consequently, there is no possible control over contribution payments. Nevertheless, Brazil- ian officials have insisted that this type of tax evasion is minor and, in most cases, is the employ- ers and not the employees' responsibility. Thus, in the context of this report, we assume there is no evasion among workers employed in formal activities. Also, the tax rates used to determine contributions are progressive with income, and they have a ceiling. The basic tax rate is 8% for individuals earning a wage that is less than 3 minimum wages, it increases to 9% for those eaning between 3 and 5 minimum wages and then is 10% for those earning more than 5 mini- mum wages. Also, eamings over a ceiling of 10 minimum wages are excepted from contribu- tions. Additionally, self employed workers must contribute 10% of an estimated monthly income if it does not exceed 3 minimum wages, and 20% otherwise. 3 The formula used to calculate benefits is different for each program. In all cases, benefit calculations are based in a "salary of benefit", the average of the last 36 monthly wages, indexed for inflation. The actual benefit is percentage of this amount, depending on the program and number of years in service. Finally, age at retirement is a critical variable in Brazil's system, since one of the most important differences between the programs is the age at which individuals are allowed to retire. The current Social Security system in Brazil is the result of a complex process of suc- cessive modifications of a 1960 law. Following the 1988 constitution, several changes have been introduced in the system beginning in 1991. While most of them were effective immediately, some provisions (mostly those affecting the minimum number of years in service) were designed to be introduced gradually. As a consequence, this report analyzes the system as it was working in December 1994, though one of the altemative retirement programs considered adopts the new rinimum length of service, which will be fully enforced beginning in 2012. The three programs analyzed are described next: 1.- Old Age Retirement: Under this program, males aged 65 and females aged 60 can retire with a minimum of 5 years of time in service until December 1992. This minimum will be increased, at a rate of six months per year, until it reaches 15 years in 2012. The benefits amount to 70% of the "salary of benefit", plus 1% per each year in service (creating a "de facto" 75% minimum in 1992 and 85% in 2012), up to a maximum of 100%. 2.- Length of Service Retirement: Under this program, males with a minimum of 30 years in service and females with a minimum of 25 years in service can retire. They receive a benefit of 70% of the "salary of benefit" plus 6% per year in service beyond the minimum, up to a nmaximum of 100%. 3.- Special Retirement: This is a special type of "Length of Service" retirement, for which individuals working in some activities considered dangerous can retired after 15, 20 or 25 yezrs in service. The benefit is 85% of the "salary of benefit" plus 1% per each year in service, up to a maximum of 100%. As a result of this rule, the actual benefit is always 100% the "salary of benefit". 4 Based on these benefit programs, we estimated the rates of return received by different socioeconomic groups, assuming alternative labor force participation histories. As a result, seven altemative situations where analyzed: I.- Individuals with 5 years of contributions retiring under the Old Age program. (Five years of contributions was the minimum required to qualify until December 1992). 2.- Individuals with 12 years of contributions retiring under the Old Age program. (The number of 12 years was chosen considering Dataprev data indicating that, as of December 1992, that was the average time in service of those retired under the Old Age program, once excluded those with defective time in service data. (Castro et al., 1993) 3.- Individuals with 15 years of contributions retiring under the Old Age program. (Fifteen years of contributions is the minimum required to qualify, to be fully effective as of 2012). 4.- Individuals with 45 (males) or 40 (females) years of contributions retiring under the Old Age program. (Forty-five and 40 years of contributions would be the maximum possible assuming the individuals enter the labor force at age 20 and retire when they reach the minimum age). 5.- Individuals with 30 (males) or 25 (females) years of contributions retiring under the Length of Service program. (Thirty and 25 years in service are the minimum necessary to qualify for this program. All individuals are assumed to enter the labor force at age 20 and, conse- quently, retire at ages 50 and 45). 6.- Individuals with 35 (males) or 30 (females) years of contributions retiring under the Length of Service program. (Similar to previous case, but now retirement benefits are 100% of "salary of benefit" and ages at retirement are 55 and 50 years). 7.- Individuals with 25 years of service retiring under the Special Retirement program. (While some individuals may qualify to retire with as little as 15 years of time in service, more than 97% of individuals retired under this program had 25 or more years of service in December 1992 (Campos et al. 1993). 5 3. METHODOLOGY 3.1. Data Sources All data analyzed in this report was obtained from secondary sources, and corrections of the original information were made when necessary. The data on lifetime income profiles was obtained from Ricardo Paes Barros, of the "Instituto de Pesquisa Econ6mica Aplicada", IPEA. This dataset, originally developed for a study on gender discrimination (Paes de Barros et al., 1992), includes earnings function parameters for sixty combinations of gender, region of resi- dence, and occupational position. It also includes the corresponding weights necessary to estimate average earnings profiles for the total population. The functions were estimated from the 1988 PNAD (Pesquisa Nacional per Amostra de Domicilios) survey, collected in September of that year. The PNAD is an annual survey that collects data on socioeconomic characteristics of the Brazilian population, and covers most of the country. The estimations prepared by the IP'EA researchers limited the universe to ". . working men and women, 25 to 50 years old, living in urban areas and working in non-agricultural occupations. Additionally we excluded from the sample workers who either work 20 hours or less per week in their main occupation, receive no income, or are currently attending school... ." (Paes de Barros et al., 1992:7). This screening process, developed to assure reliability in the estimations, limited the universe to about 3 5% of the employed labor force, or 48% of the employed labor force in urban areas. While this limitation might introduce a bias in our analysis and conclusions, it is important to note that several of the corrections do not affect us significantly. The limits in the age interval are easily avoided by using the estimated earnings functions to assign labor income to ages between 20 and 24 and 50 to 65. Simnilarly, the exclusion of all part-time workers is necessary for our analysis, since, otherwise, our parameters would be biased by the implicit averaging made during the eslimation process. In fact, the only serious limitation is the exclusion of rural workers of the analysis. This group, that included 33% of the retired and received 25% of total benefits by December 1991 (Dataprev, 1992), presents serious difficulties to researchers who try to study rural income, due to the problems involved in the quantification of non-monetary earmnngs. Additionally, the pattem of contributions to the social security system by rural workers is highly 6 irregular and not organized as a payroll tax, but a tax on gross sales, that generates a very low revenue to the system. This study needs to use information on surviving probabilities, differentiated by socio- economic status. To obtain these data, we used the 1990-1995 life table for Brazil (CELADE, 1994), which provided an estimation of surviving probabilities by sex and age in 1985-1990. Together with these data, we used estimations of life expectancy at birth by region and income (Carvalho & Wood, 1978) to adjust the surviving probabilities and define differentials by sex, region and income. While the Carvalho & Wood estimations are rather old, we decided to adopt them due to the lack of other reliable sources. In appendix A, we present the reasons for this choice in detail. An important aspect of this study is that, while it presents results describing the lifetime effect of Social Security, it is based on cross-sectional data, that is, data observed at one unique moment. The reason for adopting this approach is mostly practical and similar to the logic of a period life table. If we wanted to prepare the analysis using the actual eamrings and surviving histories of Brazilians, we would need the complete series of annual eanings for a complete cohort already extinguished at the time of the analysis. That would imply we need information on all earnings, contributions, and benefits received by a cohort that would be, at the time of this study (1995) at least 100 years old. Clearly such data do not exist and, besides, the results would not interest us unless we want to study the Social Security system's history. As a consequence, we "created" a hypothetical cohort, in which individuals are born, live and die being exposed to mortality risks and receiving earnings corresponding to those actually received by Brazilians in 1990-1995. Of course such cohort did not and will not exist, and we should not expect to find actual individuals with these earnings and surviving probabilities. Nevertheless, this approach seems to be the most appropriate if we are interested in a "snapshot" approach; we are not really interested on what happened in the past, and we do not have enough information to know what will happen in the future. Instead, we can assess the system as it works today, considering the effects it has on today's workers and retirees. Because of this approach, we ignore possible changes in mortality or real earnings in the future, assuming the situation will remain unchanged in the future. Also, we ignore the effect of historical phenomena, such as inflation (which can have a differential effect by earnings level), since the earnings data are assumed to always 7 have a differential effect by earnings level), since the earnings data are assumed to always rnaintain their real value. Both problems could be introduced in the model, making special assumptions regarding the future, but we believe that at this stage, it is better to estimate the distributive effects assuming the simplest context. 3.2. Methodology The methodology developed for this study included three steps. First, we estimated earnings profiles for the 60 socioeconomic groups defined by Paes de Barros et al., assigning a monetary wage for each age between 20 and 65. Then, we estimated the monetary flows for each group according to each program rules. With this information, we calculated average flows by occupational position, gender, region of residence and lifetime income and, calculating the corresponding surviving probabilities, we estmated the rates of return for each of these groups and all weighted averages. The groups analyzed were defined according to the characteristics of the IPEA data. Thus, we had 60 groups, resulting from the combination of gender, region, and occupational position. The categories used for each variable, together with their relative weight in the sample are presented in table I. The weights included in table I are averages, a detailed table of weights for each group and average educational attainments is included in the appendix. Using the Paes de Barros et al.'s data, we estimated annual eamings for each of the 60 groups, given the eamings functions of equation I: In(y) = a +f61 *age +fi2 *age2 +f3 *edtc (I) The IPEA data included the values of alphas and betas for each of the sixty combinations of gender, region and occupational position. Thus, by assigning the average educational attain- ment corresponding to each group (as presented in the appendix), we estimated the earnings y for each age from 20 to 65. The second step was to estimate the surviving probabilities. The original data obtained from CELADE included the proportion of the population surviving up to age x, "Ix", for both males 8 Table I. Variables Used and their Categories |Varable ] Categories Weight (in %) Cumulative Weight Gender Male 67.4% 67.4% Female 32.6% 100.0% Region Rio de Janeiro 14.0% 14.0% Sao Paulo 31.7% 45.80% South 15.1% 60.90% East 13.5% 74.40% Northeast 17.3% 91.70% Frontier 8.4% 100.00% Occupational Informal 11.9% 11.90% Position Formal 47.1% 59.00% Public Servant 15.0% 74.00% Self-employed 20.6% 94. 60% Employer 5.4% 100.00% Source: Paes de Barros et al. (1993) and females, for five-year age intervals between ages 0 to 80. We first extended the l, series up to age 110, by applying the "Coale-Guo" technique (Coale and Guo, 1989). This method is based on the empirical observation that, after age 80, mortality rates in- crease at a constantly decreasing rate. Once the series were completed up to age 110, we calculate the values of I, for single ages by sex, using a geometric interpolation (Coale & Guo, 1989). Using these estimations, the set of differentiated surviving probabilities, Ixd was calculated adapting a technique known as "Brass-logit". This technique, created by William Brass to estimate mortality rates in societies with low-quality data, consists in defining a logit conversion of the lx function such as we can define a function 4'd as presented in equation II. 9 where changes in a produce changes in the overall level of 4,, without changing the general pattern of age-specific mortality rates. Then, based on the differentials in life expectancy at birth by region and income estimated by Carvalho & Wood (1978), we estimated the corresponding values of a and obtained 105 sets of 4l (all possible combinations of six regions by four income levels by two genders, including subtotals and totals). Finally, we estimated the rates of return offered by the systems to each social group, considerng both surviving probabilities sets. The basic equation to estimate rates of return is presented in equation Im. E' (C- Bx) * Q, +l 4X ° 5 = 0 w x=20 (ri )x where Cx' is the flow of contributions, B is the flow of benefits, lri is the probability of surviving up to age x and r' is the rate of return, while the subscripts x represents age, i repre- sents socioeconomic characteristics, and co is the age at death. The estimation of r' was made assuming no there are no differentials in mortality (that is, using the lx series estimated for the population as a whole) and assuming there is a socioecononic specific differential in mortality (that is, using the Ixi series). Then, both sets of rates of return were calculated considering each of the seven alternative retirement schemes analyzed. 10 4. RESULTS The estimations and calculations described on the methodology section produced a total of 4,844 rates of retum, as presented in Appendix B. To analyze this huge amount of informa- tion, we will first consider the different available dimensions independently, and then we will present a few significant cases. 4.1. Differences by Pro2ram We first consider the differences in rates of return offered by the system through each of its alternative programs. Table II presents the rates of return received by individuals considering each of the seven analyzed programs. It also includes a column called "Benefit Multiplier to Equalize". This column presents the necessary change in benefits necessary to assure that individuals from every program receive a rate of return equal to the rate received by those contributing for 15 years and retiring under the Old Age provisions. As we can see in this table, the Old Age program is the most generous, followed by the Special Retirement and, finally, the Length of Service altematives. The annual rates of return offered by the Old Age program are as high as 51% for those retiring with the minimum number of contributions as of 1992. The returns offered to these individuals were so high that, if we wanted the individuals retiring under this provision to receive similar rates than those retiring with 15 years of contribu- tions, their salaries of benefit should be reduced to nearly one seventh of their original value. This result implies that the benefits granted to individuals retiring with five years of contributions are mostly a matter of social welfare, in the sense that there is no actuarial justification for their magnitude. The progressive increase in the minimum number of years of contribution enacted since 1992 recognizes this fact and tends to solve it in the medium run. 11 Table II. Annual Rates of Return by type of Social Security Program Program Annual Rate of Benefit Multiplier to l_______________________________{ Return IRR= 12.12% Old Age with 5 years (Type 1) 50.81% -85.3% Old Age with 12 years (Type II) 16.26% -37.7% Old Age with 15 years (Type III) 12.12% 0.0% Old Age with 40/45 years (Type IV) 3.06% 1524.8% Length of Service with 25/30 years (Type V) 7.73% 186.0% Length of Service with 30/35 years (Type VI) 6.95% 310.9% Special with 25 years (Type VII) 11.19% 22.9% Source: Own, in base to IPEA. If we consider the situation of those retiring with the mean number of years in service as of 1992 (that is, 12 years) we can see that the differences are still significant, amounting to about 4 percentage points respect to those retiring with 15 years of service. This difference could be compensated if we reduce their salary of benefit by about 38%. On the other side, we can see the situation of an individual who started contributing when he or she entered the labor force at age 20 and continued contributing without interruption until retirement at age 60 or 65. In this case, the rate of return would amount to about 3%, a value probably close to long-term market rates. Individuals retiring under special conditions receive a high rate of return, but not as high as some of those retired under the Old Age program. The situation of those retired under special rules is very similar that of those retiring under Old Age writh 15 years of contributions. Finally, Length of Service programs do not appear to be as generous as traditionally thought, at least not if we coimpare them with other programs. The most beneficial alternative for retirement under this program offers rates of return that are clearly lower than those offered by the Old Age alterna- tives. Also, we can see that remaining in the labor force for five additional years, to increase the salary of benefit, does not appear to be a wise choice. The system is currently offering an increase in replacement rate of 30 percentage points from 70% to 100% of salary of benefit for those remaining five years after reaching the minimum nunber of years in service. This increase does not compensate the loss caused by the increase in number of contributions and decrease in 12 number of benefits. Applying the same criteria used to calculate the benefit multipliers, we estimate that benefits for those retiring five years after the minimum should be around 125% of salary of benefit to receive similar rates of return than those retiring at the minimum age. The rates presented in table II correspond to workers in both formal and informal sec- tors. Because the principal criterion to distinguish between them is the regularity of their contri- butions to Social Security, in the context of this study formal workers contribute every year during their active lifetime, while informal workers do not contribute consistently. If this were the case in reality, informal workers would never receive benefits, since they would not qualify for them. Instead, they have periods of formality and, while they stay out of the system for most of their active life, they make a few contributions. For this analysis, we want to consider what would be their returns if they contributed a minimum number of years, immediately before retirement. Assuming that formal workers retire under Length of Service while infornal workers have access only to the Old Age programs, we can reformulate table II and see table III. Table mI. Annual Rates of Return by Social Security Program and Formality in Employment Program AnMual Rate of Benefit Multiplier to Retum IRR= 14.79% Informal Workers: Old Age with 5 years (Type I) 55.91% -86.0% Old Age with 12 years (Type II) 19.25% -37.7% Old Age with 15 years (Type I) 14.79% 0.0% Old Age with 40/45 years (Type TV) 4.22% 2660.3% Formal Workers: Length of Service with 25/30 years (Type V) 8.54% 329.2% Length of Service with 30/35 years (Type VI) 7.51% 608.3% Special with 25 years (Type VIII) 12.32% 661% Source: Own, in base to IPEA. Clearly, this assumption increase the differences, specially for the programs with many years of contributions. At the same time, it does not modify the relative advantage of the pro- 13 LEIP Five Year Plan Page 34 Phase l: Commercial Buildings electrical distribution services in buildings maiy provide potential energy 2 savings if wiring and switching methods/products were improved. Industrial buildings and streetlighting should also be reviewed. The 4 reviews should include research into the size of the market, potential energy savings in the market, and the ultimate impact on the country's a electrical generating and distribution systems. Table Thirteen a Related General Issues Task Timing Estimated Local Estimated Costs Foreign Costs 10 Review Tariff and Financing Within first Rs 75,000. US$ 0. Strategies and Recommend three 12 Dispositions months Review of Other Sector Within first Rs 1,000000. USS 50,000. 14 Lghting and Lighting- three Related Energy-Saving years 16 Opportunfies and Environmental Impacts r i.b- -=7 ~Related General lssues-- VEstimated Local C ost6s Rs -1`;67&,000Y VEstistsated fbreignritn : S$i0,'O YD'eliverab1e'iitncipg'Sr"tgy X .Recommendatons, ReieoEeyln P.I Nam provisions is 30, the effect of these differences is that most individuals retiring under Old Age receive better returns than those retiring under Length of Service. Only those who contribute more than 20 but less than 30 years find themselves forced to accept the lower returns generated by the Old Age program. This group is rather small, and does not exceed a 10% of those retired under Old Age by December 1992 (Caldas de Castro et al., 1993). 4.2. Differences By Gender Gender-specific differences in rates of return are originated in three concurrent factors. First, current legislation consistently grants benefits under less demanding requirement to females than males. Both Old Age and Length of Service programs allow women to retire five years earlier than men. This rule clearly benefits women, since they are required to contribute fewer years (as in the case of Length of Service) and, because of their earlier retirement, receive benefits for a longer period. A second factor that favors women over men in the system is linked with mortality dif- ferentials. As we mentioned above, one of the five points that can affect rates of return is the age at death. Female life expectancy has been shown to be higher than male's across ages and national populations. As a result, women can expect to survive longer than men and receive benefit for a longer time. The combined effect of the two mentioned factors can be better understood if we consider some figures. According to CELADE's data, life expectancy at birth for females was close to 69 years old, nearly 4.5 years higher than males'. This difference, of about 7% does not seem to be specially large, but if we consider the ages at retirement as set, for example, by the Old Age provisions, then we will have a diffierent view. Women retiring at age 60 can expect to survive (and receive benefits) for 20.2 years, while men will not survive more than 15.3 years after they retire at 65.. In other words, the number of benefit checks received by a typical woman will be almost exactly 30% higher than the number received by a typical man'. 'While this difference is significative, it is important to note that gender-specific differentials in Brazil are not as high as in other countries. For example, life expectancy at age 65 is 1.2 years higher for females than for males in Brazil, while the difference in Argentina is almost 4 years, in Chile 3.2 years and in uruguay 15 The third factor has a direct origin in the gender differences on wages existing in Brazil. In a specific study, Barros et al. (1992) found that the gender gap reached as high as 70% during the 1980s. Because the system is designed to redistribute income through a progressive contri- bution tax rate and the existence of miniimum and maximum benefits, we can expect that, other things equal, those with lower wages (in this case, women) will receive higher returns. Table IV presents our results by gender and each of the surviving probabilities sets esti- mated. By doing this, we can disentangle the effect of the system rules (that is, the age at retirement and progressive formulas effects) and the effect of mortality differentials. Table IV. Annual Rates of Retum by Gender and Mortality Table. Gender Annual Rate of Return Difference Benefit Without mortality With Mortality Multiplier Old Age Program (12 years of Contributions) Males 14.93% 14.68% -0.25% 51.8% Females 18.13% 18.30% 0.17% 0.0% Dff. Females-Males 3.20% 3.62% 0.42% Length of Service (25/30 years of Contributions) Males 7.14% 7.04% -0.10% 93.9% Females 9.63% 9.70% 0.07% 00.0% Diff. Females-Males 2.49% 2.66% 0.17% Souirce: Own, in base to IPEA. A first observation indicates that females' rates of return are clearly higher, regardless of which program we consider. Mortality differentials introduce a relative small increase in the gap between women and men's rates of retum, reaching 0.42 percentage points in the Old Age program. The gender-specific difference is very important; if we were to design a policy to compensate males by increasing their benefits, we should increase their salaries of benefit by about 50% in the case of the Old Age Program and 95% in the case of Length of Service. Nevertheless, one important aspect to remember when considering these data is that all figures 3.8 years. As a consequence, the effect of this gender-specific differential will be relatively smaller in Brazil 16 Nevertheless, one important aspect to remember when considering these data is that all figures refer to rates of return and not absolute values. In other words, women do receive higher rates of return, but they are not high enough to make their benefits higher than males' benefits. This consideration is critical if Social Security is expected to have a role in a poverty alleviation strategy, since our data show that the system distributes in favor of females, but it does not show whether this distribution is enough to decrease poverty levels among women. 4.3. Regional Differences: The next socioeconomic characteristic of interest in our data is the residence. We have estimates of rates of return for six regions of Brazil. Because this variable represents an ecologi- cal dimension, we should treat it carefully. It is known that using ecological data (that is, assum- ing that regional differences are a reflection of individual differences) can be misleading and produce paradoxical results, especially if the internal differences in each region are important (Grushka, 1993). Brazil's regional differences are well known, and it is generally believed that they satisfactorily represent differences at the individual level. In any case, we will be able to contrast these differences with the income data also available. Table V presents our results, including the effect of mortality differentials. The data in table V show that the distributive mechanisms of the system have little effect in terms of regional transfers. The rates of return received by individuals retired under the Old Age provisions are almost identical for all regions when no mortality differentials are considered. A similar effect can be found among those retiring under the Length of Service provisions. It is very interesting to consider the effect of mortality differentials. Because the north- eastern population is exposed to higher mortality rates than the rest of the country, their rates of return are negatively affected when we drop the "equal mortality" assumption. Among those retiring under the Old Age program, the effect is such that the difference in rates of return between Rio's inhabitants and north easterners changed from nearly one third of a percentage point to almost one and a half percentage points. This difference is telling us that, because of their high mortality, individuals living in the Northeast are losing in the Social Security "game", in spite of being the poorer group in Brazil, because what they gain from the progressive rules is 17 more than overturned by mortality differences. On the other side, Rio and Sao Paulo's inhabitants are the most benefited by mortality differentials. Table V. Annual Rates of Retum by Region and Mortality Table. Region Annual Rate of Return Difference Without mortality With mortality With-Without Old Age Program (12 years of Contributions) l Rio 17.30% 17.58% 0.28% Sao Paulo 15.17% 15.58% 0.41% South 16.79% 17.27% 0.48% East 17.10% 17.22% 0.11% Northeast 16.94% 16.18% -0.76% Frontier 16.80% 17.00% 0.19% Diff. Rio-Nortieast 0.36% 1.40% 1.04% Length of Service (25/30 years of Contributions) Rio 8.15% 8.27% 0.12% Sao Paulo 7.43% 7.61% 0.18% South 7.73% 7.93% 0.20% East 8.21% 8.26% 0.05% Northeast 8.29% 7.94% -0.35% Frontier 7.24% 7.32% 0.08% Diff Rio-Northeast -0.14% 0.33% 0.47% Source: Own, in base to data from IPEA 4.4. Income Differences: Differences by income can be assessed only considering lifetime income or a satisfactory proxy for it. To define a unit that can be compared across classes and individuals, we calculated the number of minimum wages that corresponds to each group's salary of benefit. Then, we divided the population in four groups, corresponding to those with a salary of benefit of less than 2 minimum wages (group "1"), those with a salary of benefit between 2 and 3 minimum wages (group "2"), those with salary of benefit between 3 and 4 minimum wages (group "3") and those witil salary of benefit of more than 4 minimum wages (group "4"). This stratification was decided considering that the available data on mortality differentials were organized with the 18 same criteria. Also, the four groups are relatively close to represent four quartiles in the income distribution of the sampled population (they represent 23.6%, 37.5%, 15.4%, and 23.5%, respectively). The resulting rates of return are presented in table VL for those retiring under Old Age with 12 years of contributions and those retiring under Length of Service with 25/30 years of service. Table VI. Annual Rates of Return by Income and Mortality Table. I Annual Rate of Return Difference Income Group j Without mortality With mortality With -Without Old Age Program (12 years of Contributions) 1 (<2 ln. Wages) 18.02% 17.60% -0.42% 2 (2-3 Min. Wages) 17.97% 17.99% 0.02% 3 (3-4 Min. Wages) 16.57% 16.91% 0.35% 4 (> 4 Min. Wages) 13.80% 14.67% 0.87% Diff. groups 1-4 4.22% 2.93% -1.29% Length of Service (25/ 30 years of Contributions) 1 (< 2 Min. Wages) 8.96% 8.77% -0.19% 2 (2-3 Min. Wages) 8.51% 8.52% 0.01% 3 (3-4 Min. Wages) 7.64% 7.79% 0.15% 4 (> 4 Min. Wages) 6.86% 7.22% 0.36% Diff. groups 1-4 2.10% 1.55% 0.55% Source: Own, in base to data from IPEA The differences by income level are clear when we assume that no mortality differentials exist. In this case, low-income individuals receive rates of return 4.2 percentage points higher than higher-income individuals in the Old Age program, and 2.1 percentage points in the Length of Service program. The effect of mortality differentials is particularly significant in this dimen- sion, since the differences in rates of return are reduced by about 30%. Our results indicate that 19 the system remains progressive in spite of the regressive effect of mortality differentials, al- though the progressivity is seriously affected by these differentials. 4.5. Differences for Specific Groups As a final point, we will consider the rates of return received by some groups that, be- cause of some specific characteristics, such as their quantitative weight in society, or they specially high or low rates of retum, deserve our special attention. These groups are presented in table VIII. Table VIII. Annual Rates of Return for Specific Groups by Mortality Table for Males. Annual Rate of Return Difference Group Without With mortal- With vs. mortality ity Differen- Without Differentials tials differentials Old Age Program (12 years of Contributions) Group I: Formal Workers, Males, residing in 15.38% 16.45% 1.07% Sao Paulo with income="4" Group II: Civil Servants, Females, residing in 20.40% 20.95% 0.56% the East with income="3" Group III: Employers, Males, residing in the 7.83% 8.60% 1.76% East with incorne="4" Length of Service (30 years of Contributions) Group I: Formal Workers, Males, residing in 7.55% 8.06% 0.51% Sao Paulo with income="4" Group II: Civil Servants, Females, residing in 10.29% 10.66% 0.37% the East with income="3" Group III: Employers, Males, residing in the 4.86% 4.40% -0.47% East with income="4" Source: Own, in base to data from IPEA Group I was selected because it represents the largest proportion of the sampled popula- tioIn, almost 13% of our population has a formal employment, is male, resides in the Sao Paulo region and would receive a salary of benefit equivalent to more than four minimum wages. These individuals receive rates of return that appear to be slightly under those received by the whole 20 population on average, if we assume no mortality differentials exist. If, on the other hand, we include an estimation of the effect of mortality differentials, we will find that this group does receive rates of return that are somewhat higher than average. The second group is formed by female civil servants who reside in the eastem region and eam enough to have a salary of benefit that lies between 3 and 4 minimum wages. Because of their low mortality and earnings profile, they receive the highest rates of return in the system among our 60 groups, reaching over 20% for those contributing for 12 years and then retiring under Old Age and over 10% for those retiring under Length of Service with minimum contribu- tions. Finally, group m is formed by male employers living in the eastern region and earning enough to have a salary of benefit that is more than 4 minimum wages. Because of their high contribution tax rate and their higher mortality, they are the group that receives the lower rates of retur in our population, with rates that are consistently less than half of those received by the previous group. The results regarding groups II and m are generally consistent across the eight retirement programs we analyzed. 4.6. The Role of Survivors' Benefits The Social Security System in Brazil provides benefits for relatives of workers, in case the worker dies. These benefits, known as "survivor benefits", amount to 80% of the benefit the worker was receiving, in the case he was already retired, or 80% of the benefit he would receive if he had completed the minimum number of contributions. In addition, an extra 10% is added for each dependent receiving the benefits, creating a de facto 90% minimum, up to a 100% maximum. The importance of these benefits can be seen if we consider that, by December 1993, there were almost as many beneficiaries of survivors' benefits as beneficiaries of the Old Age Retirement Program. Assessing the effect of these benefits on the distributive role of Social Security is not simple. Detailed data on family structure, including age differences between spouses and children are necessary for the task, but it is rarely available. While a complete analysis of the effects of survivors benefits is not possible, we have developed a simple procedure to estimate its magnitude. 21 Considering only male workers, and assuming that all of them are married to non- working women five years younger than them and that they have no children in position to claim a survivors' benefit, we could estimate the rate of return received by these families. Equation V was used to estimate the corresponding rates of return: ECx, * Q',, + Ix1) * ° 5 - ffx * (Lx Lx'+d * °5 =o( if ~ ~ -o(IV) whlere = (I - li-male) * md-female * 0.9 v x <65 = Ii-male + (I _ ,x-male) * xi-femule * 0.9 V x 2 65 This estimation is, of course, subject to the validity of the assumptions (universal mar- riage and age gap of five years) and, most important, to the fact that these two demographic behaviors are similar across socioeconormic groups. With these restrictions in mind, we can evaluate the results, as shown in table IX. As expected, including survivors benefits increased the average rate of return received unmder all programs, since we included a new benefit without modifying contributions. The improvement is more important for those retiring under the Old Age Program, and, in both cases, the programns becamne more progressive. This last effect, that can be clearly seen in Table IX, is produced by the differences in mortality between the groups. Because poorer worker tend to die earlier than their wealthier counterparts, mortality differentials have a regressive role among single workers. Among married workers, the loss in rates of return produced by the higher probability of dying is compensated by the fact that, if the worker dies, his wife will receive a life-time benefit. Thus, mortality differentials have a contradictory role on Social Security dis- tributive effects when survivors benefits are considered. They have a regressive effect (due to the deaths among workers) and a progressive one (due to the existence of survivors' benefits). The net effect will depend on a number of variables, including the proportion of married workers, the age difference between spouses, the presence of children young enough to receive benefits and so on. [f these variables adopt similar values for all socioeconomic groups (which was assumed 22 for this exercise) then the regressive effect should be stronger. If, instead, poorer workers tend to marny more often and age differences between husband and wife is larger, then the overall effect could be progressive. Table IX. Annual Rates of Return for Male Workers by Marital Status and Income. Marital Status Difference Income Group Single i Married Married - Single Old Age Program (12 years of Contributions) TOTAL 14.68% 17.92% 3.24% 1 (< 2 Min. Wages) 16.66% 20.43% 3.77% 2 (2-3 Min. Wages) 16.52% 19.75% 3.23% 3 (3-4 Min. Wages) 14.94% 17.83% 2.89% 4 (> 4 Min. Wages) 14.57% 16.88% 2.31% Diff. groups 1-4 2.09% 3.55% 1.46% Length of Service (25/ 30 years of Contributions) TOTAL 7.04% 7.93% 0.89% 1 (< 2 Min. Wages) 7.15% 8.14% 0.99% 2 (2-3 NM. Wages) 7.64% 8.49% 0.85% 3 (3-4 Min. Wages) 6.98% 7.77% 0.79% 4 (> 4 Min. Wages) 7.15% 7.79% 0.64% Diff groups 1-4 0.00% 0.35% 0.35% Source: Own, in base to data from IPEA 23 5. DISCUSSION AND CONCLUSIONS The results presented in the previous section considered the distributive effect of Social Security considering four levels. First we analyzed the effect of differences between the pro- grams currently existing, including several alternatives for each of them. Second, we considered the effect of distributive mechanisms included in the legislation, third, we considered the effect of mortality differentials, and, finally, we assessed the role of survivors' benefits.. The analysis of the altemative systems produced results that are somehow surprising, considering other analyses and reports from qualified informants at DATAPREV. We found that, for most cases, individuals retiring under Old Age provisions receive better returns than those retiring under Length of Service and even under Special Retirement provisions. These two programs have been traditionally blamed for the financial difficulties of the Brazilian system, mostly because they are the most costly in terms of per-capita expenditures. By 1992, Dataprev estimated that the mean benefit for these retirees amounted to 3.93 minimum wages, more than two times the mean benefit of those retiring under Old Age provisions. In the same line, the "Coomissao Especial para Estudo do Sistema Previdenciario" (Comissao..., 1992) argues that the system is regressive because of the differential access to Length of Service retirement. Our data show, beyond doubt, that individuals retiring under Length of Service provi- sions receive, on average, rates of return that are lower than those received by anyone retiring under Old Age, as long as these individuals contributed for less than 20 years. Consequently, the piece of information we need to confirm which program is more generous is the actual number of years individuals contribute to the system. Unfortunately, no data are available on that question at this point. Instead, we have the number of years "in service", which is the number of years a retiring individual can prove he or she had ajob in a formal sector business. It is possible (but exTremely difficult to verify empirically) that many individuals retiring under Old Age provisions did contribute during more years than they can prove, and, if they had those years considered, they would qualify for length of Service retirement. Then, if the number of unproved years of contributions has a direct association with the socioeconomic status of the individual, we could conclude that the dual system does have a regressive effect. If, on the other hand, we accept that Dataprev's information on years in service is a good proxy for the number of years of contribu- 24 tions, then we must conclude that the dual-program scheme in place has a progressive effect. One particular aspect of the Brazilian system that should be considered is that it is possible to work and contribute for 25/30 years, retire under Length of Service, return to the labor force and then retire under Old Age. As a result, two benefits are received and returns become much higher. There are no reliable data on the number of beneficiaries in this situation, but they may be a significant proportion of the retired population. The system is designed to progressively distribute income among its affiliates. This redis- tribution operates through three mechanisms. First, the contribution tax rate is progressive, going from 8% for those with lower income to 10% to those earning more than 7 minimum wages. Second, there is a minimum benefit, equivalent to the minimum wage. Finally, a third rule that makes the system more progressive is the differential treatment received by men and women regarding the minimum age or time in service. Because females have, on average, lower income than their male counterparts, any rule benefiting them becomes a "de facto" progressive rule. Along with the three mentioned rules, there is a ceiling to taxable salaries (10 minimum wages), which is replicated on a maximum benefit. If the ceiling were set to only one of them, it would have a distributive effect. Instead, because the limit is set to both contributions and benefits, its effects are canceled out. The effect of mortality differentials must be considered. Our data show that, because Brazil's population is exposed to a wide range of mortality risks, and that range is, at least partially, determined by socioeconomic characteristics, the role of this dimension is crucial. Previous analyses had proposed that mortality differentials are not significant when considering social security issues. In a 1991 paper, Camarano et al. proposed that income-specific differ- ences in life expectancy are not important in Brazil, based in the fact that total life expectancy converges with age. They wrongly compare the total number of years an individual aged 60 years old can expect to live since birth, to conclude that differences are small (Camarano et al., 1991). In fact, if we consider the remaining expected years of life, we can see that differences among income groups are as high as 50% by age 60. The effect of these differentials, which are stronger among males, can be seen in our results, where table VII shows that mortality differentials are important enough to reverse the progressive effect of the legislation, making the system regres- 25 sive, at least among males. This result was found in both Old Age and Length of Service pro- grams, and it is present regardless of the total number of contributions. The regressive effect of mortality differentials was expected, since similar results have been found in other countries, such as the U.S. and Argentina (Rofman, 1993 & 1995). Finally, the role of survivors' benefits was considered. As expected, these benefits im- prove the returns for every program and social group, although the effect is not identical for each of ihem. Because survivors' benefits are paid when the worker dies, they have a complementary behavior with respect to retirement benefits. The higher is the mortality for any specific group, the higher will be the survivor's benefits, since there will be more beneficiaries. The available data indicate that, in general, this benefit tends to make the system more progressive, but it was not possible to determine if this progressive effect is enough to compensate the regressive effect observed above. Social Security in Brazil is going through serious financial difficulties, partly due to its unreasonable generosity. The combination of poor coverage and lack of sensible rules that would keep the system equilibrated will bring the system to a point where reform will become unavoid- able. A new system, which disentangles benefits linked to contributions from those that should be considered social welfare, maintains clear and complete records of contributions and benefits and, finally, defines contributions and benefits at a level that will assure medium and long term equilibrium will have to be developed and enacted in the near future. 26 6. POLICY RECOMMENDATIONS Social Security systems are always designed with two central objectives. First, they are expected to perform as a society wide compulsive savings scheme, that forces individuals to save for old-age years, promising fair returns once they retire. Second, they are a welfare program that provides financial resources to poor aged individuals. Because of the extreme number of com- plexities involved in the Brazilian Social Security system, none of these goals is being clearly fulfilled. The first goal is not achieved in the sense that rates of return currently paid are ex- tremely high, risking the medium and long term financial stability of the system. The second goal is not achieved because the system is distributing resources from the lower to the higher income brackets. Several policy measures should be taken to improve the performance of the system and, in the medium term, achieve the two goals aforementioned. Policy recommendations can be classified into two broad categories. The first group in- clude possible steps that would improve the performance of the current system. Second, a general overhaul of the system is recommended for the medium and long term, to insure the viability of Social Security in that period. The recommendations regarding the short term include: 1) Steps should be taken to simplify the very large number of retirement options currently in existence. This should include the administrative elimination of many benefit types and the administrative and financial independence of Retirement programs from Social Welfare prograrns. 2) A reform should be started by eliminating all type of Special Retirement programs. Several of them are not reasonable under the original justification for their existence (which allows for special provision in case of riskier activities). Moreover, if a specific activity fairly de- serves a special treatment, the cost of this should not be afforded by the Retirement system but by the Social Welfare system. 3) The increase of the minimum number of years in service necessary to qualify for Old Age benefits, which is planned to be increased until it reaches 15 years by 2012, should be ac- celerated and not limited to 15 years, but extended until the minimum reaches a level comparable with the Length of Service requirements. 27 4) 'The benefits granted to those who remain in the labor force after reaching the minimum number of years should be increased, in order to induce more workers to retire later. Finally, we believe the system should be completely overhauled to assure its stability in the long term. It is very important to realize that the only reason why it has not suffered a serious crisis so far is because it is a relatively young system, implemented in a young society. Once the system reaches a higher level of maturity and Brazil's population increases its aging process, the crisis will be unavoidable if measures are not taken to prevent it. The new system should be based on a multiple-pillar model, and could include: 1) A universal, mandatory saving and annuities.program. This program, to be successful, must ensure that benefits will be only granted to those who contributed during their active life. Moreover, the system should directly link the benefits to lifetime contributions, and not to the last few years' earnings. This program could be either public or privately managed, but, in any case, a strong control system must be designed. 2) A program that guarantees a minimum benefit to every aged individual. Funding for this program should be independent from the annuity program, and its benefits should be only granted to lower income groups, and 3) A program of fiscal and social incentives for non-mandatory savings, that would complement the first program. 28 7. BIBLIOGRAPHY Brazil (1993) A Nova Previdencia Social. Grafica Auriverde, Rio de Janeiro. Caldas de Castro, M. et al. (1993) Avalia,o da Qualidade das Variaveis data de Nascimento do Segurado e Data de J-iicio do Beneficio nos Cadastros de Beneficios em Manutencao" Dataprev, Rio do Janeiro (mimeo) Caldas de Castro, M. et al. (1993) Avalia,co da Qualidade das Variavel Tempo de Servi,o no Cadastro de Beneficios em Manutenc, o" Dataprev, Rio De Janeiro (mimeo) Camarano & Beltrao, 1993 "Dinamica demografica por nivel de renda". Relatorios Tecnicos, IBGE, Rio do Janeiro. Camarano, A.A et al. (199la) "Aposentadoria e esperan,a de vida" Cojuntura Econ6mica May 1991. pp. 41-44. Camarano, A.A et al. (1991b) "Aposentadoria por Tempo de Servico: Onde a Esperan,a de Vida o Menos hnportante" Relatorio Intemo. IPEA, Rio do Janeiro. Camarano A.A. & Beltrao, K (1993) Dindmica demogrdfica por nivel de renda. Relatorios Tecnicos, IBGE, Rio do Janeiro. Carvalho, J.A. & Wood, C. (1978) "Mortality, Income Distribution, and Rural-Urban Residence in Brazil". Population and Development Review. Vol. 4 (3). Coale, A, and Guo, G (1989), "Revised Regional Model Life Tables at Very Low Levels of Mortality". in Population Index, vol. 55 (4) Comissao Especial para Estudo do Sistema Previdenciario (i992), "Relatorio Final". in Previdencia em Dados, Rio de Janeiro, v. 7 (2) pp. 5-44. Dataprev (1992) "Indicadores Sociais. Beneficios en Manuntenco" .Previdencia em Dados, Rio de Janeiro, v. 7 (3). Dataprev (1993) Indicadores Sociais. Beneficios Concedidos. Rio de Janeiro? Mimeo Grushka, C. (1993) "Adult Mortality in Argentina". University of Pennsylvania, Mimeo. 29 Jarnes, E. (1992) Income Security for Old Age. Conceptual Background and Major Issues. Policy Research Working Papers Series # 977. The World Bank, Washington, DC Kane, C. (1992) BraziL Fiscal Implications of the Social Security System. Country Operations Division, Country Department L Latin America and the Caribbean Region, The World Bank, Washington, DC Konder, B. et al. (1992) "Perfil de renda das Aposentadorias Mantidas pela Previdencia Social". Previdencia en Dados. Rio de Janeiro, v 7 (3) Kopits, G. et al. (1992) Brazil: Optionsfor Social Security Reform. International Monetary Fund, Fiscal Affairs Department, Washington, DC Paes de Barros, R et at. (1992) "Gender Differences in Brazilian Labor Markets", Paper prepared for the Conference on Women's Human Capital and Development, Bellagio, Italy, May 18-22, 1992. Rofinan, R. (1993) Social Security and Income Distribution Ph. D. Dissertation, U. C. Berkeley. Rofinan, R (1995) "Distributive Effects of Social Security in Argentina". mimeo. 30 8. APPENDIX A. USING ALTERNATIVE MORTALITY ESTIMATES. The reliability of the conclusions presented in this paper depends on the quality of both the methodological procedures and the basic data used. While the methodology has been shown to work properly elsewhere (see Rofman, 1993, 1995), the data sources should be carefully assessed before concluding that this document is accurate. Two types of data were used. First, the earnings functions parameter estimates, obtained from Paes de Barros et al. (1992). These estimates are based on a national survey, conducted by Brazil's national statistics office (Funda,co Instituto Brasileiro de Geografia e Estadistica - IBGE) and its results have been used and tested repeatedly. On the other hand, the second data set, which includes mortality estimates, has not been used in this type of study as often and, as such, could be subject of controversy. As of the time this document was prepared, it was not possible to find a recently pub- lished estimation of unabridged life tables for Brazil including differences by socioeconomic status. As a consequence, such tables had to be estimated based on the available data. With this limitation, we decided to base our estimation on CELADE's estimated life table for the period 1990-95, published as recently as January 1994. Unfortunately, this table includes differentiated mortality rates by gender, but there is no information on differences by other socioeconomic variables, such as region of residence or income. As a consequence, we were forced to look for an altemative source for these differences, which we found in the Carvalho & Wood (1978) paper. hn their paper, Carvalho & Wood estimate life expectancy at birth by gender, region of residence and income, a criterion easily applicable to the earnings functions data. As a result, we decided to adopt their estimations, calculating their estimated differences in life expectancy at birtl and, using the Brass-Logit technique, correcting the CELADE's life table to obtain a set of 105 life tables, differentiated by gender, region of residence and income level. During our research, with the help of some of its authors, we found another estimation of mortality differentials. This estimation was prepared by a group of researchers from IPEA and IBGE, in Rio do Janeiro. Based on data from the 1980 census, they estimated life expectancy at birth and several ages, differentiated by gender and income. Their results were published in several documents (Comissao Especial para Estudo do Sistema Previdenciario, 1992; Camarano 31 & Beltrao, 1993; Camarano et al., 1991a, Camarano et al., 1991b). While these estimations are more recent and, consequently, might be more adequate than Carvalho & Wood's, we found that the lack of data on regional differences would force us to ignore a dimension that could be important. Also, we could not find a clear reference to the methodology used by the Camarano et al. group to obtain their estimates, making extremely difficult an adequate evaluation of their reliability. Considering these considerations, we decided to adopt Carvalho & Wood work as the basis for our differences estimates, recognizing that a more recent and complete data set would be desirable and hoping it will become available in the near future. 32 9. APPENDIX B. RATES OF RETURN BY SOCIOECONOMIC CHARACTERISTICS FOR DIFFERENT RETIREMENT PROGRAMS. 33 Rates of Return for Old Age Retirement with 5 years of Contributions. RATES OF RETURN (ANNUAL %/) OBS OCCUPATION GENDER REGION INCOME FREQ MORTALITY DIFFERENTIALS I_______ ______ _____ WITHOUTI WITH IDIFFERENCE 1 ALL BOTH ALL ALL 100.00 50.81 50.81 0.00 2 ALL BOTH ALL 1 23.61 53.58 53.05 -0.53 3 ALL BOTH ALL 2 37.51 54.66 54.69 0.03 4 ALL BOTH ALL 3 15.41 51.03 51.44 0.41 _ ALL BOTH ALL 4 23.46 41.90 42.93 1.03 6 ALL BOTH R0 ALL 13.98 51.44 51.78 0.34 7 ALL BOTH SAO PAULO ALL 31.76 48.83 49.31 0.48 8 ALL BOTH SOUTH ALL 15.08 52.34 52.91 0.57 9 ALL BOTH EAST ALL 13.48 53.02 53.15 0.14 10 ALL BOTH NORTHEAST ALL 17.29 52.09 51.15 -0.94 1 1 ALL BOTH FRONTIER ALL 8.40 51.97 52.20 0.23 12 ALL BOTH RIO 1 1.76 52.80 52.60 -0.20 13 ALL BOTH RIO 2 4.30 55.03 55.39 0.36 14 ALL BOTH RIO 3 5.96 53.53 54.29 0.75 15 ALL BOTH RIO 4 1.95 41.62 42.88 1.26 16 ALL BOTH SAO PAULO 1 1.54 56.18 56.12 -0.06 17 ALL BOTH SAO PAULO 2 8.44 54.56 55.04 0.48 18 ALL BOTH SAO PAULO 3 5.36 46.34 47.21 0.87 19 ALL BOTH SAO PAULO 4 16.42 41.98 43.48 1.50 20 ALL BOTH SOUTH 1 4.66 54.00 54.01 0.02 21 ALL BOTH SOUTH 2 8.24 54.68 55.29 0.61 22 ALL BOTH SOUTH 3 0.17 45.87 46.71 0.84 23 ALL BOTH SOUTH 4 2.01 43.74 45.46 1.72 24 ALL BOTH EAST 1 3.99 52.99 52.60 -0.39 25 ALL BOTH EAST 2 6.34 51.32 51.52 0.20 26 ALL BOTH EAST 3 1.27 54.42 54.93 0.51 27 ALL BOTH EAST 4 1.88 48.02 49.31 1.29 28 ALL BOTH NORTHEAST 1 8.99 52.98 51.53 -1.46 29 ALL BOTH NORTHEAST 2 5.85 54.98 54.08 -0.90 30 ALL BOTH NORTHEAST 3 1.79 53.79 53.17 -0.62 31 ALL BOTH NORTHEAST 4 0.67 33.10 33.15 0.05 32 ALL BOTH FRONTIER 1 2.67 53.38 53.07 -0.31 33 ALL BOTH FRONTIER 2 4.34 55.68 55.94 0.26 34 ALL BOTH FRONTIER 3 0.86 53.25 54.04 0.79 35 ALL BOTH FRONTIER 4 0.53 32.96 34.19 1.22 36 _ ALL MALE ALL ALL 67.40 46.26 45.94 -0.32 37 ALL FEMALE ALL ALL 32.59 52.54 52.75 0.21 38 ALL MALE ALL 1 7.50 52.51 51.52 -0.99 34 Rates of Return for Old Age Retirement with 5 years of Contributions. If I I I |RATES OF RETURN (ANNUAL °/0) OBS OCCUPATION GENDER REGION INCOME FREQ MORTALITY DIFFERENTIALS _1 ______ _________ ______ ______ _WITHOUT| WITH IDIFFERENCE 39 ALL MALE ALL 2 25.42 51.95 51.67 -0.29 40 ALL MALE ALL 3 11.51 44.11 44.29 0.18 41 ALL MALE ALL 4 22.97 44.07 44.89 0.82 42 ALL FEMALE ALL 1 16.11 53.64 53.33 -0.32 43 ALL FEMALE ALL 2 12.09 55.18 55.42 0.24 44 ALL FEMALE ALL - 3 3.90 53.53 54.12 0.59 45 ALL FEMALE ALL 4 0.49 36.10 37.09 0.99 46 ALL MALE RIO ALL 9.42 49.74 49.83 0.09 47 ALL MALE SAO PAULO ALL 21.41 42.24 42.50 0.26 48 ALL MALE SOUTH ALL 10.17 48.11 48.48 0.36 49 ALL MALE EAST ALL 9.09 49.66 49.51 -0.15 50 ALL MALE NORTHEAST ALL 11.66 49.61 48.21 -1.40 51 ALL MALE FRONTIER ALL 5.66 47.77 47.73 -0.05 52 ALL FEMALE RIO ALL 4.56 52.00 52.52 0.52 53 ALL FEMALE SAO PAULO ALL 10.35 51.46 52.11 0.65_ 54 ALL FEMALE SOUTH ALL 4.92 54.38 55.11 0.73 55 ALL FEMALE EAST ALL 4.39 53.93 54.27 0.34 56 ALL FEMALE NORTHEAST ALL 5.63 53.09 52.41 -0.68 57 ALL FEMALE FRONTIER ALL 2.74 53.80 54.23 0.42 58 ALL MALE RIO 2 2.39 51.59 51.72 0.13 59 ALL MALE RIO 3 5.17 54.25 54.85 0.61 60 ALL MALE RIO 4 1.86 41.96 43.16 1.20 61 ALL MALE SAO PAULO 2 1.56 53.87 54.18 0.32 62 ALL MALE SAO PAULO 3 3.68 32.97 33.69 0.72 63 ALL MALE SAO PAULO 4 16.16 45.14 46.51 1.37 64 ALL MALE SOUTH 1 0.81 56.51 56.21 -0.31 65 ALL MALE SOUTH 2 7.34 52.18 52.58 0.40 66 ALL MALE SOUTH 4 2.01 43.74 45.19 1.45 67 ALL MALE EAST 1 0.86 50.82 50.01 -0.81 68 ALL MALE EAST 2 6.34 51.32 51.20 -0.12 69 ALL MALE EAST 4 1.88 48.02 49.02 1.00 70 ALL MALE NORTHEAST 1 5.02 50.37 48.36 -2.01 71 ALL MALE NORTHEAST 2 4.25 53.17 51.78 -1.39 72 ALL MALE NORTHEAST 3 1.79 53.79 52.85 -0.94 73 ALL MALE NORTHEAST 4 0.59 32.40 32.16 -0.24 74 ALL MALE FRONTIER I 0.81 56.83 56.09 -0.73 75 ALL MALE FRONTIER 2 3.53 51.20 51.19 -0.01 76 ALL MALE FRONTIER 3 0.86 53.25 53.72 0.47 35 Rates of Return for Old Age Retirement with 5 years of Contributions. RATES OF RETURN (ANNUAL /%) OBS OCCUPATION GENDER REGION INCOME FREQ MORTALITY DIFFERENTIALS __ WITHOUTI WITH IDIFFERENCEI 77 ALL MALE FRONTIER 4 0.46 31.92 32.96 1.03 78 ALL FEMALE RIO 1 1.76 52.80 52.82 0.01 79 ALL FEMALE RIO 2 1.91 55.77 56.33 0.56 80 ALL FEMALE RIO 3 0.79 53.22 54.11 0.88 81 ALL FEMALE RIO 4 0.10 41.34 42.59 1.25 82 ALL FEMALE SAO PAULO 1 1.54 56.18 56.34 0.16 83 ALL FEMALE SAO PAULO 2 6.88 54.57 55.26 0.69 84 ALL FEMALE SAO PAULO 3 1.68 53.12 54.12 1.00 85 ALL FEMALE SAO PAULO 4 0.26 33.73 35.05 1.32 86 ALL FEMALE SOUTH 1 3.84 53.91 54.14 0.231 87 ALL FEMALE SOUTH 2 0.90 56.21 56.97 0.76 88 ALL FEMALE SOUTH 3 0.17 45.87 46.90 1.03 89 ALL FEMALE EAST 1 3.13 53.02 52.84 -0.18 90 ALL FEMALE EAST 3 1.27 54.42 55.14 0.72 91 ALL FEMALE NORTHEAS 1 3.97 53.48 52.25 -1.23 92 ALL FEMALE NORTHEAST 2 1.59 55.39 54.73 -0.66 93 ALL FEMALE NORTHEAST 4 0.07 34.37 34.61 0.24 94 ALL FEMALE FRONTIER 1 1.87 53.08 52.99 -0.10 95 ALL FEMALE FRONTIER 2 0.81 57.22 57.67 0.46 96 ALL FEMALE FRONTIER 4 0.07 35.78 36.92 1.14 97 INFORMAL BOTH ALL ALL 11.95 55.91 55.91 0.00 98 FORMAL BOTH ALL ALL 47.08 54.79 54.79 0.00 99 CIVIL SERV. BOTH ALL ALL 14.98 54.14 54.14 0.00 100 SELF BOTH ALL ALL 20.55 46.21 46.21 0.00 101 EMPLOYER BOTH ALL ALL 5.43 34.65 34.65 0.00 102 INFORMAL BOTH ALL 1 9.57 56.13 55.58 -0.55 103 FORMAL BOTH ALL 1 5.87 54.78 54.25 -0.53 104 SELF BOTH ALL 1 8.17 50.03 49.50 -0.53 105 INFORMAL BOTH ALL 2 2.38 54.07 54.11 0.04 106 FORMAL BOTH ALL 2 23.12 55.47 55.50 0.03 107 CIVL SERV. BOTH ALL 2 3.31 56.19 56.21 0.03 36 Rates of Return for Old Age Retirement with 12 years of Contributions. Married Males, including survivors' benefits for spouses RATES OF RETURN (ANNUAL %) OBS OCCUPATIO GENDER REGION INCOME FREQI MORTALITY DIFFERENTIALS IWITHOUTI WITH IDIFFERENCE 1 ALL BOTH ALL ALL 100.00 16.26 16.26 0.00 2 ALL BOTH ALL 1 23.61 18.02 17.60 -0.42 3 ALL BOTH ALL 2 37.51 17.97 17.99 0.02 4 ALL BOTH ALL 3 15.41 16.57 16.91 0.35 5 ALL BOTH ALL 4 23.46 13.80 14.67 0.87 6 ALL BOTH RIO ALL 13.98 17.30 17.58 0.28 7 ALL BOTH SAOPAULO ALL 31.76 15.17 15.58 0.41 8 ALL BOTH SOUTH ALL 15.08 16.79 17.27 0.48 9 ALL BOTH EAST ALL 13.48 17.10 17.22 0.11 10 ALL BOTH NORTHEAS ALL 17.29 16.94 16.18 -0.76 11 ALL BOTH FRONTIER ALL 8.40 16.80 17.00 0.19 12 ALL BOTH RIO 1 1.76 18.45 18.30 -0.15 13 ALL BOTH RIO 2 4.30 18.90 19.20 0.29 14 ALL BOTH RIO 3 5.96 17.48 18.11 0.63 15 ALL BOTH RIO 4 1.95 14.44 15.57 1.13 16 ALL BOTH SAO PAULO 1 1.54 19.40 19.36 -0.04 17 ALL BOTH SAO PAULO 2 8.44 18.60 18.97 0.37 18 ALL BOTH SAO PAULO 3 5.36 13.88 14.65 0.76 19 ALL BOTH SAO PAULO 4 16.42 13.72 15.00 1.29 20 ALL BOTH SOUTH 1 4.66 18.43 18.44 0.01 21 ALL BOTH SOUTH 2 8.24 17.18 17.69 0.51 22 ALL BOTH SOUTH 3 0.17 12.83 13.52 0.69 23 ALL BOTH SOUTH 4 2.01 15.02 16.40 1.39 24 ALL BOTH EAST 1 3.99 17.33 17.03 -0.30 25 ALL BOTH EAST 2 6.34 15.95 16.11 0.15 26 ALL BOTH EAST 3 1.27 19.46 19.86 0.39 27 ALL BOTH EAST 4 1.88 15.32 16.33 1.01 28 ALL BOTH NORTHEAST 1 8.99 17.38 16.23 -1.16 29 ALL BOTH NORTHEAST 2 5.85 17.66 16.94 -0.72 30 ALL BOTH NORTHEAST 3 1.79 19.60 19.13 -0.46 31 ALL BOTH NORTHEAST 4 0.67 9.40 9.45 0.05 32 ALL BOTH FRONTIER 1 2.67 18.31 18.06 -0.25 33 ALL BOTH FRONTIER 2 4.34 18.21 18.42 0.21 34 ALL BOTH FRONTIER 3 0.86 18.99 19.59 0.59 35 ALL BOTH FRONTIER 4 0.53 9.58 10.67 1.08 36 ALL MALE ALL ALL 67.40 14.93 14.68 -0.25 37 ALL FEMALE ALL ALL 32.59 18.13 18.30 0.17 38 ALL MALE ALL 1 7.50 17.40 16.66 -0.74 37 Rates of Return for Old Age Retirement with 12 years of Contributions. Married Males, including survivors' benefits for spouses RATES OF RETURN (ANNUAL %) ] OBS OCCUPATION GENDER REGION INCOME FREQ I MORTALITY DIFFERENTIALS ___ _______ _______ _____ WITHOUT| WITH [DIFFERENCE 39 ALL MALE ALL 2 25.42 16.75 16.52 -0.22 40 ALL MALE ALL 3 11.51 14.81 14.94 0.13 41 ALL MALE ALL 4 22.97 13.93 14.57 0.64 42 ALL FEMALE ALL 1 16.11 18.15 17.91 -0.24 43 ALL FEMALE ALL 2 12.09 18.88 19.07 0.19 44 ALL FEMALE ALL - 3 3.90 18.81 19.28 0.46 45 ALL FEMALE ALL 4 0.49 12.63 13.50 0.87 46 ALL MALE RIO ALL 9.42 16.33 16.39 0.06 47 ALL MALE SAO PAULO ALL 21.41 13.34 13.53 0.20 48 ALL MALE SOUTH ALL 10.17 15.98 16.25 0.27 49 ALL MALE EAST ALL 9.09 15.61 15.49 -0.12 50 ALL MALE NORTHEAST ALL 11.66 16.29 15.23 -1.06 51 ALL MALE FRONTIER ALL 5.66 15.87 15.83 -0.04 52 ALL FEMALE RIO ALL 4.56 18.50 18.91 0.41 53 ALL FEMALE SAO PAULO ALL 10.35 17.82 18.33 0.51 54 ALL FEMALE SOUTH ALL 4.92 18.17 18.73 0.56 55 ALL FEMALE EAST ALL 4.39 18.72 18.99 0.27 56 ALL FEMALE NORTHEAST ALL 5.63 17.87 17.36 -0.51 57 ALL FEMALE FRONTIER ALL 2.74 18.26 18.59 0.33 58 ALL MALE RIO 2 2.39 18.68 18.77 0.09 59 ALL MALE RIO 3 5.17 16.80 17.24 0.44 60 ALL MALE RIO 4 1.86 13.84 14.79 0.95 61 ALL MALE SAO PAULO 2 1.56 17.18 17.41 0.23 62 ALL MALE SAO PAULO 3 3.68 10.94 11.53 0.59 63 ALL MALE SAO PAULO 4 16.16 13.93 15.01 1.08 64 ALL MALE SOUTH 1 0.81 19.98 19.74 -0.23 65 ALL MALE SOUTH 2 7.34 16.57 16.86 0.29 66 ALL MALE SOUTH 4 2.01 15.02 16.17 1.15 67 ALL MALE EAST 1 0.86 14.01 13.39 -0.62 68 ALL MALE EAST 2 6.34 15.95 15.86 -0.10 69 ALL MALE EAST 4 1.88 15.32 16.09 0.77 70 ALL MALE NORTHEAS 1 5.02 16.32 14.81 -1.51 71 ALL MALE NORTHEAS 2 4.25 16.51 15.48 -1.03 72 ALL MALE NORTHEAST 3 1.79 19.60 18.89 -0.70 73 ALL MALE NORTHEAST 4 0.59 9.25 9.03 -0.22 74 _ ALL MALE FRONTIER 1 0.81 20.28 19.74 -0.54 75 ALL MALE FRONTIER 2 3.53 16.64 16.63 -0.02 76 ALL MALE FRONTIER 3 0.86 18.99 19.34 0.35 38 Rates of Return for Old Age Retirement with 12 years of Contributions. Married Males, including survivors' benefits for spouses RATES OF RETURN (ANNUAL %) OBS OCCUPATION GENDER REGION INCOME FREQ | MORTALITY DIFFERENTIALS | l___ | 1 . I 1WITHOUTI WITH TIFFERENCE 77 ALL MALE FRONTIER 4 0.46 9.61 10.47 0.86 78 ALL FEMALE RIO 1 1.76 18.45 18.46 0.01 79 ALL FEMALE RIO 2 1.91 19.06 19.49 0.43 80 ALL FEMALE RIO 3 0.79 18.75 19.44 0.69 81 ALL FEMALE RIO 4 0.10 16.37 17.44 1.07 82 ALL FEMALE SAO PAULO 1 1.54 19.40 19.52 0.12 83 ALL FEMALE SAO PAULO 2 6.88 18.69 19.22 0.53 84 ALL FEMALE SAO PAULO 3 1.68 18.54 19.33 0.79 85 ALL FEMALE SAO PAULO 4 0.26 11.81 13.00 1.19 86 ALL FEMALE SOUTi 1 3.84 18.25 18.43 0.18 87 ALL FEMALE SOUTH 2 0.90 18.69 19.27 0.58 88 ALL FEMALE SOUTH 3 0.17 12.83 13.69 0.86 89 ALL FEMALE EAST 1 3.13 17.51 17.37 -0.13 90 ALL FEMALE EAST 3 1.27 19,46 20.02 0.56 91 ALL FEMALE NORTHEAST 1 3.97 18.14 17.21 -0.93 92 ALL FEMALE NORTHEAST 2 1.59 18.76 18.27 -0.49 93 ALL FEMALE NORTHEAST 4 0.07 10.08 10.30 0.22 94 ALL FEMALE FRONTIER 1 1.87 17.75 17.68 -0.07 95 ALL FEMALE FRONTIER 2 0.81 20.46 20.81 0.35 96 ALL FEMALE FRONTIER 4 0.07 9.41 10.44 1.04 97 INFORMAL BOTH ALL ALL 11.95 19.25 19.25 0.00 98 FORMAL BOTH ALL ALL 47.08 17.15 17.15 0.00 99 CIVIL SERV. BOTH ALL ALL 14.98 18.88 18.88 0.00 100 SELF BOTH ALL ALL 20.55 14.77 14.77 0.00 101 EMPLOYER BOTH ALL ALL 5.43 10.47 10.47 0.00 102 INFORMAL BOTH ALL 1 9.57 19.37 18.94 -0.43 103 FORMAL BOTH ALL 1 5.87 17.99 17.59 -0.40 104 SELF BOTH ALL 1 8.17 16.87 16.45 -0.42 105 INFORMAL BOTH ALL 2 2.38 18.87 18.90 0.03 106 FORMAL BOTH ALL 2 23.12 18.02 18.04 0.02 107 CIVIL SERV. BOTH ALL 2 3.31 19.20 19.22 0.02 39 Rates of Return for Old Age Retirement with 15 years of Contributions. RATES OF RETURN (ANNUAL %) | OBS CCUPATION GENDER REGION INCOME FREQ MORTALITY DIFFERENTIALS l_______ ______ ________ _____ IWITHOUTI WITH PIFFERENCE 1 ALL MALE ALL ALL 67.40 17.73 17.92 0.19 2 ALL MALE ALL 1 7.50 20.23 20.43 0.20 3 ALL MALE ALL 2 25.42 19.55 19.75 0.20 4 ALL MALE ALL 3 11.51 17.64 17.83 0.19 5 ALL MALE ALL 4 22.97 16.70 16.88 0.18 6 ALL MALE RIO ALL 9.42 19.16 19.35 0.19 7 ALL MALE SAO PAULO ALL 21.41 16.11 16.31 0.20 8 ALL MALE SOUTH ALL 10.17 18.81 18.98 0.18 9 ALL MALE EAST ALL 9.09 18.39 18.59 0.19 10 ALL MALE NORTHEAST ALL 11.66 19.11 19.28 0.17 11 ALL MALE FRONTIER ALL 5.66 18.69 18.89 0.19 12 ALL MALE RIO 2 2.39 21.60 21.78 0.18 13 ALL MALE RIO 3 5.17 19.59 19.75 0.16 14 ALL MALE RIO 4 1.86 16.64 16.80 0.16 15 ALL MALE SAO PAULO 2 1.56 19.98 20.16 0.18 16 _ ALL MALE SAO PAULO 3 3.68 13.75 13.97 0.22 17 ALL MALE SAO PAULO 4 16.16 16.69 16.85 0.16 18 ALL MALE SOUTH 1 0.81 22.89 23.10 0.21 19 ALL MALE SOUTH 2 7.34 19.36 19.54 0.17 20 ALL MALE SOUTH 4 2.01 17.86 17.97 0.11 21 ALL MALE EAST 1 0.86 16.70 16.85 0.15 22 ALL MALE EAST 2 6.34 18.73 18.92 0.19 23 ALL MALE EAST 4 1.88 18.12 18.27 0.15 24 ALL MALE NORTHEAS 1 5.02 19.13 19.26 0.13 25 ALL MALE NORTHEAST 2 4.25 19.29 19.46 0.17 26 ALL MALE NORTHEAST 3 1.79 22.53 22.77 0.24 27 ALL MALE NORTHEAST 4 0.59 11.96 12.14 0.18 28 ALL MALE FRONTIER 1 0.81 23.21 23.44 0.23 29 ALL MALE FRONTIER 2 3.53 19.46 19.65 0.19 30 ALL MALE FRONTIER 3 0.86 21.90 22.06 0.15 31 ALL MALE FRONTIER 4 0.46 12.37 12.62 0.26 32 rNFORMAL MALE ALL ALL 6.66 22.04 22.25 0.21 33 FORMAL MALE ALL ALL 34.13 18.78 18.97 0.19 34 CMVIL SERV. MALE ALL ALL 8.06 21.24 21.45 0.21 35 SELF MALE ALL ALL 13.90 16.39 16.59 . 0.19 36 EMPLOYER MALE ALL ALL 4.65 12.61 12.79 0.18 37 INFORMAL MALE ALL 1 4.28 22.31 22.54 0.23 38 _ SELF MALE ALL 1 3.23 17.68 17.85 0.17 40 Rates of Return for Old Age Retirement with 15 years of Contributions. RATES OF RETURN (ANNUAL %) OBS OCCUPATION GENDER REGION INCOME FREQ MORTALITY DIFFERENTIALS IWITHOUTI WITH pIFFERENCE 39 INFORMAL MALE ALL 2 2.38 21.76 21.97 0.21 40 FORMAL MALE ALL 2 16.05 19.26 19.45 0.19 41 SELF MALE ALL 2 6.99 19.44 19.64 0.20 42 FORMAL MALE ALL 3 5.17 19.59 19.77 0.18 43 CIVIL SERV. MALE ALL 3 2.65 22.31 22.49 0.18 44 SELF MALE ALL 3 3.68 13.75 13.96 0.21 45 FORMAL MALE ALL 4 12.91 18.13 18.29 0.17 46 CIVIL SERV. MALE ALL 4 5.41 20.81 20.93 0.12 47 EMPLOYER MALE ALL 4 4.65 12.61 12.86 0.24 48 INFORMAL MALE RIO ALL 0.82 23.74 23.92 0.19 49 FORMAL MALE RIO ALL 5.17 19.59 19.78 0.19 50 CIVIL SERV. MALE RIO ALL 1.39 18.47 18.66 0.19 51 SELF MALE RIO ALL 1.57 20.53 20.72 0.19 52 EMPLOYER MALE RIO ALL 0.46 14.37 14.58 0.20 53 INFORMAL MALE SAO PAULO ALL 1.56 19.98 20.16 0.18 54 FORMAL MALE SAO PAULO ALL 12.91 18.13 18.31 0.19 55 CIVIL SERV. MALE SAO PAULO ALL 1.67 19.11 19.29 0.18_l 56 SELF MALE SAO PAULO ALL 3.68 13.75 13.97 0.21 l 57 EMPLOYER MALE SAO PAULO ALL 1.58 12.99 13.21 0.22 58 INFORMAL MALE SOUTH ALL 0.81 22.89 23.05 0.16_l 59 FORMAL MALE SOUTH ALL 5.26 19.84 20.01 0.17_l 60 CIVIL SERV. MALE SOUTH ALL 1.19 22.04 22.20 0.16 61 SELF MALE SOUTH ALL 2.08 18.02 18.20 0.18 62 EMPLOYER MALE SOUTH ALL 0.82 12.12 12.35 0.23 63 INFORMAL MALE EAST ALL 0.86 16.70 16.88 0.18 64 FORMAL MALE EAST ALL 4.54 18.53 18.72 0.19_l 65 CIVIL SERV. MALE EAST ALL 1.15 22.36 22.57 0.21_l 66 SELF MALE EAST ALL 1.80 19.20 19.39 0.20 67 EMPLOYER MALE EAST ALL 0.73 10.43 10.61 0.18 68 INFORMAL MALE NORTHEAST ALL 1.79 22.57 22.80 0.23 69 FORMAL MALE NORTHEAST ALL 4.25 19.29 19.46 0.16 70 CIVIL SE V. MALI NORTHEAST ALL 1.79 22.53 22.78 0.25 71 SELF MALE NORTHEAST ALL 3.23 17.68 17.82 0.15 72 EMPLOYER MALE NORTHEAST ALL 0.59 711.96 12.00 0.04 73 INFORMAL MALE FRONTIER ALL 0.81 23.21 23.40 0.20 74 FORMAL MALE FRONTIER ALL 2.00 19.12 19.31 0.19 75 CIVIL SE V. MALI FRONTIER ALL 0.86 21.90 22.10 0.20 76 SELF MALE FRONTIER ALL 1.53 19.81 20.00 0.19 41 Rates of Return for Old Age Retirement with 15 years of Contributions. RATES OF RETURN (ANNUAL %) OBS OCCUPATION GENDER REGION INCOME FREQ i MORTALITY DIFFERENTIALS l______ ______ _____ _____ WITHOUTj WITH DIFFERENCE 77 EMPLOYER MALE FRONTIER ALL 0.46 12.37 12.57 0.20 78 INFORMAL MALE RIO 2 0.82 23.74 23.92 0.18 79 SELF MALE RIO 2 1.57 20.53 20.72 0.19 80 FORMAL MALE RIO 3 5.17 19.59 19.75 0.16 81 CIVIL SE V. MALI RIO 4 1.39 18.47 18.61 0.13 82 EMPLOYER MALE RIO 4 0.46 14.37 14.58 0.20 83 INFORMAL MALE SAO PAULO 2 1.56 19.98 20.16 0.18 84 SELF MALE SAO PAULO 3 3.68 13.75 13.97 0.22 85 FORMAL MALE SAO PAULO 4 12.91 18.13 18.26 0.13 86 CIVL SE V. MALI SAO PAULO 4 1.67 19.11 19.21 0.10 87 EMPLOYER MALE SAO PAULO 4 1.58 12.99 13.23 0.24 88 INFORMAL MALE SOUTH 1 0.81 22.89 23.10 0.21 89 FORMAL MALE SOUTH 2 5.26 19.84 20.01 0.17 90 SELF MALE SOUTH 2 2.08 18.02 18.20 0.18 91 CIVIL SERV. MALE SOUTH 4 1.19 22.04 22.05 0.01 92 E.MPLOYER MALE SOUTH 4 0.82 12.12 12.40 0.28 93 INFORMAL MALE EAST 1 0.86 16.70 16.85 0.15 94 FORMAL MALE EAST 2 4.54 18.53 18.72 0.19 95 SELF MALE EAST 2 1.80 19.20 19.39 0.20 96 CIVIL SERV. MALE EAST 4 1.15 22.36 22.44 0.08 97 E,MPLOYER MALE EAST 4 0.73 10.43 10.74 0.31 98 INFORMAL MALE NORTHEAST 1 1.79 22.57 22.78 0.21 99 SELF MALE NORTHEAST 1 3.23 17.68 17.77 0.09l 100 FORMAL MALE NORTHEAST 2 4.25 19.29 19.46 0.17 101 CIVIL SERV MALE NORTHEAST 3 1.79 22.53 22.77 0.24 102 EMPLOYER MALE NORTHEAST 4 0.59 11.96 12.14 0.18 103 INFORMAL MALE FRONTIER 1 0.81 23.21 23.44 0.23 104 FORMAL MALE FRONTIER 2 2.00 19.12 19.31 0.19 105 SELF MALE FRONTIER 2 1.53 19.81 20.00 0.19 106 CIVIL SERV. MALE FRONTIER 3 0.86 21.90 22.06 0.15 107 CIVIL SERV. MALE FRONTIER 3 0.86 21.90 22.06 0.15 42 Rates of Return for Old Age Retirement with 45 years of Contributions. RATES OF RETURN (ANNUAL %) OBS OCCUPATION GENDER REGION INCOME FREQ MORTALITY DIFFERENTIALS 1WITHOUTI WITH IFFERENCE 1 ALL BOTH ALL ALL 100.00 3.06 3.06 0.00 2 ALL BOTH ALL 1 23.61 4-04 3.74 -0.30 3 ALL BOTH ALL 2 37.51 3.58 3.60 0.02 4 ALL BOTH ALL 3 15.41 3.53 3.78 0.25 5 ALL BOTH ALL 4 23.46 2.15 2.76 0.62 6 ALL BOTH RIO ALL 13.98 3.70 3.90 0.20 7 ALL BOTH SAO PAULO ALL 31.76 2.58 2.88 0.30 8 ALL BOTH SOUTH ALL 15.08 3.21 3.54 0.34 9 ALL BOTH EAST ALL 13.48 3.41 3.50 0.08 10 ALL BOTH NORTHEAST ALL 17.29 3.49 2.95 -0.54 11 ALL BOTH FRONTIER ALL 8.40 3.06 3.19 0.13 12 ALL BOTH RIO 1 1.76 4.60 4.49 -0.11 13 ALL BOTH RIO 2 4.30 4.68 4.88 0.21 14 ALL BOTH RIO 3 5.96 3.87 4.32 0.45 15 ALL BOTH RIO 4 1.95 2.26 3.07 0.80l 16 ALL BOTH SAO PAULO 1 1.54 4.95 4.92 -0.03 17 ALL BOTH SAO PAULO 2 8.44 4.55 4.82 0.27 18 ALL BOTH SAO PAULO 3 5.36 2.28 2.84 0.56 19 ALL BOTH SAO PAULO 4 16.42 2.00 2.92 0.92 20 ALL BOTH SOUTH 1 4.66 4.40 4.41 0.01 21 ALL BOTH SOUTH 2 8.24 2.87 3.23 0.36 22 ALL BOTH SOUTH 3 0.17 -0.67 -0.11 0.57 23 ALL BOTH SOUTH 4 2.01 3.23 4.19 0.96 24 ALL BOTH EAST 1 3.99 3.87 3.65 -0.22 25 ALL BOTH EAST 2 6.34 2.37 2.48 0.10 26 ALL BOTH EAST 3 1.27 5.95 6.23 0.28 27 ALL BOTH EAST 4 1.88 3.08 3.79 0.71 28 ALL BOTH NORTHEAST 1 8.99 3.51 2.68 -0.82 29 ALL BOTH NORTHEAST 2 5.85 3.49 2.98 -0.51 30 ALL BOTH NORTHEAST 3 1.79 5.37 5.07 -0.30 31 ALL BOTH NORTHEAST 4 0.67 0.40 0.44 0.03 32 ALL BOTH FRONTIER 1 2.67 4.12 3.95 -0.17 33 ALL BOTH FRONTIER 2 4.34 3.37 3.51 0.15 34 ALL BOTH FRONTIER 3 0.86 4.84 5.22 0.39 35 ALL BOTH FRONTIER 4 0.53 0.12 0.90 0.78 36 ALL MALE ALL ALL 67.40 2.48 2.30 -0.18 37 ALL FEMALE ALL ALL 32.59 4.72 4.85 0.13 38 ALL MALE ALL 1 7.50 3.15 2.65 -0.50 43 Rates of Return for Old Age Retirement with 45 years of Contributions. RATES OF RETURN (ANNUAL %) f OBS OCCUPATION GENDER REGION INCOME FREQ I MORTALITY DIFFERENTIALS l___ ________ |_____ ________ ______ JWITHOUT| WITH PDIFFERENCE 39 ALL MALE ALL 2 25.42 2.78 2.62 -0.16 40 ALL MALE ALL 3 11.51 2.88 2.96 0.08 41 ALL MALE ALL 4 22.97 2.11 2.54 0.43 42 ALL FEMALE ALL 1 16.11 4.46 4.29 -0.16 43 ALL FEMALE ALL 2 12.09 4.98 5.12 0.14 44 ALL FEMALE ALL 3 3.90 5.12 5.47 0.34 45 ALL FEMALE ALL 4 0.49 2.97 3.65 0.67 46 ALL MALE RIO ALL 9.42 3.23 3.26 0.03 47 ALL MALE SAO PAULO ALL 21.41 1.84 1.96 0.12 48 ALL MALE SOUTI ALL 10.17 2.91 3.08 0.17 49 ALL MALE EAST ALL 9.09 2.63 2.54 -0.10 50 ALL MALE NORTHEAST ALL 11.66 3.07 2.34 -0.73 51 ALL MALE FRONTIER ALL 5.66 2.67 2.63 -0.04 52 ALL FEMALE RIO ALL 4.56 4.89 5.19 0.30 53 ALL FEMALE SAO PAULO ALL 10.35 4.71 5.10 0.38 54 ALL FEMALE SOUTH ALL 4.92 4.16 4.58 0.42 55 ALL FEMALE EAST ALL 4.39 5.30 5.50 0.20 56 ALL FEMALE NORTHEAST ALL 5.63 4.80 4.44 -0.37 57 ALL FEMALE FRONTIER ALL 2.74 4.28 4.53 0.25 58 ALL MALE RIO 2 2.39 4.38 4.43 0.05 59 ALL MALE RIO 3 5.17 3.46 3.75 0.29 60 ALL MALE RIO 4 1.86 2.07 2.71 0.64 61 ALL MALE SAO PAULO 2 1.56 2.76 2.90 0.14 62 ALL MALE SAO PAULO 3 3.68 1.31 1.71 0.40 63 ALL MALE SAO PAULO 4 16.16 1.94 2.68 0.74 64 ALL MALE SOUTH 1 0.81 4.41 4.25 -0.16 65 ALL MALE SOUTH 2 7.34 2.52 2.71 0.19 66 ALL MALE SOUTH 4 2.01 3.23 4.02 0.78 67 ALL MALE EAST 1 0.86 0.65 0.21 -0.44 68 ALL MALE EAST 2 6.34 2.37 2.29 -0.08 69 ALL MALE EAST 4 1.88 3.08 3.60 0.52 70 ALL MALE NORTHEAST 1 5.02 2.78 1.75 -1.03 71 ALL MALE NORTBHEAS1 2 4.25 2.70 1.99 -0.71 72 ALL MALE N ORTHEAST 3 1.79 5.37 4.91 -0.46 73 ALL MALE NORTHEAST 4 0.59 0.23 0.06 -0.17 74 ALL MALE FRONTIER 1 0.81 4.43 4.08 -0.35 75 ALL MALE FRONTIER.- 2 3.53 2.72 2.70 -0.02 76 _ ALL MALE FRONTIER 3 0.86 4.84 5.05 0.21 44 Rates of Return for Old Age Retirement with 45 years of Contributions. RATES OF RETURN (ANNUAL %) OBS OCCUPATION GENDER REGION NCOME FREQ I MORTALITY DIFFERENTIALS _WITHOUTI WITH DIFFERENCE 77 ALL MALE FRONTIER 4 0.46 0.10 0.70 0.59 78 ALL FEMALE RIO 1 1.76 4.60 4.62 0.02 79 ALL FEMALE RIO 2 1.91 5.13 5.44 0.32 80 ALL FEMALE RIO 3 0.79 5.50 6.02 0.51 81 ALL FEMALE RIO 4 0.10 3.46 4.23 0.77 82 ALL FEMALE SAO PAULO 1 1.54 4.95 5.04 0.09 83 ALL FEMALE SAO PAULO 2 6.88 4.83 5.22 0.39 84 ALL FEMALE SAO PAULO 3 1.68 4.92 5.50 0.59 85 ALL FEMALE SAO PAULO 4 0.26 3.32 4.27 0.95 86 ALL FEMALE SOUTH 1 3.84 4.40 4.53 0.14 87 ALL FEMALE SOUTH 2 0.90 4.90 5.34 0.43 88 ALL FEMALE SOUTH 3 0.17 -0.67 0.05 0.73 89 ALL FEMALE EAST 1 3.13 4.37 4.28 -0.09 90 ALL FEMALE EAST 3 1.27 5.95 6.36 0.41 91 ALL FEMALE NORTHEAST 1 3.97 4.66 4.00 -0.65 92 ALL FEMALE NORTHEAST 2 1.59 5.40 5.05 -0.35 93 ALL FEMALE NORTHEAS 4 0.07 1.82 2.00 0.18 94 ALL FEMALE FRONTIER 1 1.87 3.95 3.90 -0.04 95 ALL FEMALE FRONTIER 2 0.81 5.49 5.74 0.25 96 ALL FEMALE FRONTIER 4 0.07 0.25 1.09 0.85 97 INFORMAL BOTH ALL ALL 11.95 4.22 4.22 0.00 98 FORMAL BOTH ALL ALL 47.08 3.08 3.08 0.00 99 CIVIL SERV. BOTH ALL ALL 14.98 4.87 4.87 0.00 100 SELF BOTH ALL ALL 20.55 2.50 2.50 0.00 101 EMPLOYER BOTH ALL ALL 5.43 0.92 0.92 0.00 102 INFORMAL BOTH ALL 1 9.57 4.36 4.06 -0.30 103 FORMAL BOTH ALL 1 5.87 4.33 4.04 -0.29 104 SELF BOTH ALL 1 8.17 3.45 3.15 -0.31 105 INFORMAL BOTH ALL 2 2.38 3.93 3.94 0.02 106 FORMAL BOTH ALL 2 23.12 3.48 3.50 0.02 107 CMVIL SERV. BOTH ALL 2 3.31 5.25 5.27 0.01 45 Rates of Return for Time in Service Retirement w/ 25/30 yrs of Contributions. RATES OF RETURN (ANNUAL %/6) | OBS OCCUPATION GENDER REGION INCOME I MORTALITY DIFFERENTIALS l __ _ ______ ______ _______ _____ _____ WITHOUT| WITH DIFFERENCE 1 ALL BOTH ALL ALL 100.00 7.73 7.73 0.00 2 ALL BOTH ALL 1 23.61 8.96 8.77 -0.19 3 ALL BOTH ALL 2 37.51 8.51 8.52 0.01 4 ALL BOTH ALL 3 15.41 7.64 7.79 0.15 5 ALL BOTH ALL 4 23.46 6.86 7.22 0.36 6 ALL BOTH RIO ALL 13.98 8.15 8.27 0.12 7 ALL BOTH SAO PAULO ALL 31.76 7.43 7.61 0.18 8 ALL BOTH SOUTH ALL 15.08 7.73 7.93 0.20 9 ALL BOTH EAST ALL 13.48 8.21 8.26 0.05 10 ALL BOT'H NORTHEAST ALL 17.29 8.29 7.94 -0.35 11 _ ALL BOTH FRONTIER ALL 8.40 7.24 7.32 0.08 12 - ALL BOTH RIO 1 1.76 9.03 8.96 -0.07 13 ALL BOTH RIO 2 4.30 8.86 8.99 0.12 14 ALL BOTH RIO 3 5.96 8.92 9.18 0.26 15 ALL BOTH RIO 4 1.95 6.28 6.75 0.47 16 ALL BOTIH SAO PAULO 1 1.54 9.79 9.78 -0.02 17 ALL BOTH SAO PAULO 2 8.44 9.60 9.76 0.16 18 ALL BOTH SAO PAULO 3 5.36 6.11 6.44 0.34 19 ALL BOTH SAO PAULO 4 16.42 7.19 7.71 0.51 20 ALL BOTH SOUTH 1 4.66 9.26 9.27 0.01 21 ALL BOTH SOUTH 2 8.24 7.80 8.01 0.21 22 ALL BOTH SOUTH 3 0.17 5.29 5.63 0.34 23 ALL BOTH SOUTH 4 2.01 6.78 7.34 0.56 24 ALL BOTH EAST 1 3.99 9.75 9.62 -0.14 25 ALL BOTH EAST 2 6.34 7.90 7.97 0.06 26 ALL BOTH EAST 3 1.27 9.97 10.13 0.17 27 ALL BOTH EAST 4 1.88 6.97 7.38 0.42 28 ALL BOTH NORTHEAST 1 8.99 8.34 7.79 -0.55 29 ALL BOTH NORTHEAS 2 5.85 9.01 8.68 -0.33 30 ALL BOTH NORTHEAST 3 1.79 8.84 8.65 -0.19 31 ALL BOTH NORTHEAST 4 0.67 5.47 5.49 0.02 32 ALL BOTH FRONTIER 1 2.67 8.59 8.48 -0.11 33 ALL BOTH FRONTIER 2 4.34 7.86 7.95 0.09 34 ALL BOTH FRONTIER 3 0.86 8.55 8.78 0.23 35 ALL BOTH FRONTIER 4 0.53 4.34 4.81 0.47 36 ALL MALE ALL ALL 67.40 7.14 7.04 -0.10 37 ALL FEMALE ALL ALL 32.59 9.63 9.70 0.07 38 ALL MALE ALL 1 7.50 7.46 7.15 -0.31 46 Rates of Return for Time in Service Retirement wI 25/30 yrs of Contributions. RATES OF RETURN (ANNUAL %) OBS OCCUPATION GENDER REGION INCOME FREQ I MORTALITY DIFFERENTIALS l __ ________ ______ ________ _____ IWITHOUTI WITH DIFFERENCE 39 ALL MALE ALL 2 25.42 7.73 7.64 -0.09 40 ALL MALE ALL 3 11.51 6.92 6.98 0.06 41 ALL MALE ALL 4 22.97 6.88 7.15 0.27 42 ALL FEMALE ALL 1 16.11 9.69 9.59 -0.10 43 ALL FEMALE ALL 2 12.09 10.12 10.20 0.08 44 ALL FEMALE ALL 3 3.90 9.60 9.80 0.20 45 ALL FEMALE ALL 4 0.49 6.45 6.84 0.39 46 ALL MALE RIO ALL 9.42 7.73 7.76 0.03 47 ALL MALE SAO PAULO ALL 21.41 6.77 6.86 0.09 48 ALL MALE SOUTH ALL 10.17 7.28 7.40 0.12 49 ALL MALE EAST ALL 9.09 7.55 7.51 -0.05 50 ALL MALE NORTHEAST ALL 11.66 7.65 7.18 -0.47 51 ALL MALE FRONTIER ALL 5.66 6.73 6.72 -0.01 52 ALL FEMALE RIO ALL 4.56 9.33 9.50 0.18 53 ALL FEMALE SAO PAULO ALL 10.35 9.71 9.93 0.22 54 ALL FEMALE SOUTH ALL 4.92 9.15 9.40 0.24 55 ALL FEMALE EAST ALL 4.39 10.14 10.26 0.12 56 ALL FEMALE NORTHEAST ALL 5.63 10.39 10.16 -0.23 57 ALL FEMALE FRONTIER ALL 2.74 8.88 9.03 0.14 58 ALL MALE RIO 2 2.39 7.67 7.71 0.04 59 ALL MALE RIO 3 5.17 8.59 8.77 0.18 60 ALL MALE RIO 4 1.86 6.58 6.97 0.39 61 ALL MALE SAO PAULO 2 1.56 7.67 7.77 0.10 l 62 ALL MALE SAO PAULO 3 3.68 4.86 5.12 0.26 63 ALL MALE SAO PAULO 4 16.16 7.17 7.60 0.43 64 ALL MALE SOUTH 1 0.81 7.82 7.73 -0.09 65 ALL MALE SOUTH 2 7.34 7.52 7.64 0.13 66 ALL MALE SOUTH 4 2.01 6.78 7.25 0.47 67 ALL MALE EAST 1 0.86 7.24 6.98 -0.26 68 ALL MALE EAST 2 6.34 7.90 7.87 -0.03 69 ALL MALE EAST 4 1.88 6.97 7.29 0.33 70 ALL MALE NORTHEAST 1 5.02 7.39 6.70 -0.69 71 ALL MALE NORTHEASI 2 4.25 8.27 7.82 -0.45 72 ALL MALE NORTHEAST 3 1.79 8.84 8.55 -0.28 73 ALL MALE NORTHEAST 4 0.59 5.20 5.11 -0.09 74 ALL MALE FRONTIER 1 0.81 7.60 7.38 -0.22 75 ALL MALE FRONTIER 2 3.53 7.43 7.43 0.00 76 ALL MALE FRONTIER 3 0.86 8.55 8.69 0.14 47 Rates of Return for Time in Service Retirement w/ 25/30 yrs of Contributions. RATES OF RETURN (ANNUAL %) OBS OCCUPATION GEDER REGION ICOME FREQ I MORTALITY DIFFERENTIALS IWITHOUTI WrrH PIFFERENCE 77 ALL MALE FRONTIER 4 0.46 4.18 4.56 0.38 78 ALL FEMALE RIO 1 1.76 9.03 9.04 0.01 79 ALL FEMALE RIO 2 1.91 10.47 10.65 0.18 80 ALL FEMALE RIO 3 0.79 10.53 10.82 0.29 81 ALL FEMALE RIO 4 0.10 3.29 3.82 0.53 82 ALL FEMALE SAO PAULO 1 1.54 9.79 9.85 0.06 83 ALL FEMALE SAO PAULO 2 6.88 9.95 10.18 0.22 84 ALL FEMALE SAO PAULO 3 1.68 9.69 10.02 0.33 85 ALL FEMALE SAO PAULO 4 0.26 7.83 8.34 0.52 86 ALL FEMALE SOUTH 1 3.84 9.56 9.64 0.08 87 ALL FEMALE SOUTH 2 0.90 9.81 10.05 0.25 88 ALL FEMALE SOUTH 3 0.17 5.29 5.71 0.42 89 ALL FEMALE EAST 1 3.13 10.32 10.26 -0.06 90 ALL FEMALE EAST 3 1.27 9.97 10.20 0.24 91 ALL FEMALE NORTHEAST 1 3.97 9.99 9.57 -0.43 92 ALL FEMALE NORTHEAST 2 1.59 11.30 11.08 -0.21 93 ALL FEMALE NORTHEAST 4 0.07 7.96 8.06 0.10 94 ALL FEMALE FRONTIER 1 1.87 9.05 9.02 -0.03 95 ALL FEMALE FRONTIER 2 0.81 9.70 9.84 0.15 96 ALL FEMALE FRONTIER 4 0.07 5.62 6.09 0.48 97 INFORMAL BOTH ALL ALL 11.95 8.41 8.41 0.00 98 FORMAL BOTH ALL ALL 47.08 8.54 8.54 0.00 99 CIVIL SERV. BOTH ALL ALL 14.98 9.12 9.12 0.00 100 SELF BOTH ALL ALL 20.55 6.53 6.53 0Q00 101 EMPLOYER BOTH ALL ALL 5.43 5.17 5.17 0.00 102 INFORMAL BOTH ALL 1 9.57 8.62 8.43 -0.19 103 FORMAL BOTH ALL 1 5.87 10.17 9.99 -0.18 104 SELF BOTH ALL 1 8.17 8.10 7.90 -0.20 105 INFORMAL BOTH ALL 2 2.38 7.98 8.00 0.01 106 FORMAL BOTH ALL 2 23.12 8.86 8.87 0.01 107 CIVIL SERV. BOTH ALL 2 3.31 10.31 10.32 0.01 48 Rates of Return for Time in Service Retirement w/ 30/35 yrs of Contributions. RATES OF RETURN (ANNUAL %) OBS OCCUPATION GENDER REGION INCOME FREQ MORTALITY DIFFERENTIALS IWITHOUTI WITH ITIFFERENCE I ALL BOTH ALL ALL 100.00 6.95 6.95 0.00 2 ALL BOTH ALL 1 23.61 8.04 7.83 -0.22 3 ALL BOTH ALL 2 37.51 7.62 7.63 0.01 4 ALL BOTH ALL 3 15.41 7.05 7.22 0.17 5 ALL BOTH ALL 4 23.46 6.09 6.51 0.42 6 ALL BOTH RIO -ALL 13.98 7.44 7.58 0.14 7 ALL BOTH SAO PAULO ALL 31.76 6.62 6.82 0.21 8 ALL BOTH SOUTH ALL 15.08 6.97 7.20 0.23 9 ALL BOTH EAST ALL 13.48 7.33 7.39 0.06 10 ALL BOTH NORTHEAST ALL 17.29 7.46 7.06 -0.40 11 ALL BOTH FRONTIER ALL 8.40 6.58 6.68 0.10 12 ALL BOTH RIO 1 1.76 8.24 8.16 -0.08 13 ALL BOTH RIO 2 4.30 8.21 8.35 0.14l 14 ALL BOTH RIO 3 5.96 8.04 8.34 0.31 15 ALL BOTH RIO 4 1.95 5.71 6.26 0.55 16 ALL BOTH SAO PAULO 1 1.54 8.86 8.84 -0.02 17 ALL BOTH SAO PAULO 2 8.44 8.64 8.82 0.19 18 ALL BOTH SAO PAULO 3 5.36 5.64 6.02 0.39 19 ALL BOTH SAO PAULO 4 16.42 6.29 6.90 0.61 20 ALL BOTH SOUTH 1 4.66 8.33 8.34 0.01 21 ALL BOTH SOUTH 2 8.24 6.92 7.17 0.25 22 ALL BOTH SOUTH 3 0.17 4.09 4.48 0.40 23 ALL BOTH SOUTH 4 2.01 6.37 7.02 0.65 24 ALL BOTH EAST 1 3.99 8.54 8.38 -0.16 25 ALL BOTH EAST 2 6.34 6.86 6.94 0.07 26 ALL BOTH EAST 3 1.27 9.32 9.52 0.19 27 ALL BOTH EAST 4 1.88 6.34 6.83 0.49 28 ALL BOTH NORTHEAST 1 8.99 7.50 6.87 -0.63 29 ALL BOTH NORTHEAST 2 5.85 7.98 7.60 -0.38 30 ALL BOTH NORTHEAS 3 1.79 8.43 8.22 -0.22 31 ALL BOTH NORTHEAST 4 0.67 4.69 4.71 0.03 32 ALL BOTH FRONTIER 1 2.67 7.78 7.65 -0.13 33 ALL BOTH FRONTIER 2 4.34 7.09 7.20 0.11 34 ALL BOTH FRONTIER 3 0.86 8.08 8.35 0.27 35 ALL BOTH FRONTIER 4 0.53 3.77 4.32 0.54 36 ALL MALE ALL ALL 67.40 6.37 6.25 -0.12 37 1 ALL FEMALE ALL ALL 32.59 8.71 8.79 0.09 38 ALL MALE ALL 1 7.50 6.74 6.38 -0.36 49 Rates of Return for Time in Service Retirement w/ 30/35 yrs of Contributions. RATES OF RETURN (ANNUAL %/0) | OBS OCCUPATION GENDER REGION INCOME FREQ MORTALITY DIFFERENTIALS l______ ______ _______ _____ IWITHOUTI WITH PIFFERENCE 39 ALL MALE ALL 2 25.42 6.85 6.74 -0.10 40 ALL MALE ALL 3 11.51 6.37 6.44 0.07 41 ALL MALE ALL 4 22.97 6.08 6.39 0.31 42 ALL FEMALE ALL 1 16.11 8.65 8.53 -0.12 43 ALL FEMALE ALL 2 12.09 9.12 9.22 0.10 44 ALL FEMALE ALL 3 3.90 8.80 9.03 0.23 45 ALL FEMALE ALL 4 0.49 6.14 6.60 0.45 46 ALL MALE RIO ALL 9.42 7.01 7.05 0.03 47 ALL MALE SAO PAULO ALL 21.41 5.95 6.05 0.10 48 ALL MALE SOUTH ALL 10.17 6.57 6.71 0.13 49 ALL MALE EAST ALL 9.09 6.64 6.58 -0.06 50 ALL MALE NORTHEAST ALL 11.66 6.88 6.34 -0.53 51 ALL MALE FRONTIER ALL 5.66 6.13 6.12 -0.02 52 ALL FEMALE RIO ALL 4.56 8.59 8.79 0.20 53 ALL FEMALE SAO PAULO ALL 10.35 8.77 9.03 0.26 54 ALL FEMALE SOUTH ALL 4.92 8.17 8.46 0.29 55 ALL FEMALE EAST ALL 4.39 9.21 9.34 0.14 56 ALL FEMALE NORTHEAST ALL 5.63 9.29 9.02 -0.27 57 ALL FEMALE FRONTIER ALL 2.74 8.02 8.19 0.17 58 _ ALL MALE RIO 2 2.39 7.32 7.36 0.05 59 ALL MALE RIO 3 5.17 7.69 7.90 0.21 60 ALL MALE RIO 4 1.86 5.88 6.33 0.45 61 ALL MALE SAO PAULO 2 1.56 6.79 6.90 0.11l 62 ALL MALE SAO PAULO 3 3.68 4.48 4.78 0.30 63 ALL MALE SAO PAULO 4 16.16 6.26 6.77 0.51 64 ALL MALE SOUTH 1 0.81 7.39 7.29 -0.10 65 ALL MALE SOUTH 2 7.34 6.63 6.78 0.14 66 ALL MALE SOUTH 4 2.01 6.37 6.92 0.55 67 ALL MALE EAST 1 0.86 5.85 5.54 -0.30 68 ALL MALE EAST 2 6.34 6.86 6.82 -0.04 69 ALL MALE EAST 4 1.88 6.34 6.72 0.38 70 ALL MALE NORTHEAST 1 5.02 6.62 5.84 -0.78 71 ALL MALE NORTHEAST 2 4.25 7.22 6.71 -0.51 72 ALL MALE NORTE1EAST 3 1.79 8.43 8.11 -0.33 73 ALL MALE NORTHEAST 4 0.59 4.44 4.33 -0.11 74 ALL MALE FRONTIER 1 0.81 7.23 6.98 -0.25 75 ALL MALE FRONTIER 2 3.53 6.63 6.62 0.00 76 ALL MALE FRONTIER 3 0.86 8.08 8.24 0.16 50 Rates of Return for Time in Service Retirement w/ 30/35 yrs of Contributions. RATES OF RETURN (ANNUAL %) OBS OCCUPATION GENDER REGION INCOME FREQ I MORTALITY DIFFERENTIALS || IWITHOUTI WITH DIFFERENCE 77 ALL MALE FRONTIER 4 0.46 3.66 4.09 0.43 78 ALL FEMALE RIO 1 1.76 8.24 8.25 0.01 79 ALL FEMALE RIO 2 1.91 9.41 9.63 0.21 80 ALL FEMALE RIO 3 0.79 9.59 9.93 0.34 81 ALL FEMALE RIO 4 0.10 4.27 4.84 0.57 82 ALL FEMALE SAO PAULO 1 1.54 8.86 8.92 0.06 83 ALL FEMALE SAO PAULO 2 6.88 8.96 9.22 0.26 84 ALL FEMALE SAO PAULO 3 1.68 8.80 9.19 0.39 85 ALL FEMALE SAO PAULO 4 0.26 7.24 7.86 0.61 86 ALL FEMALE SOUTH 1 3.84 8.53 8.63 0.09 87 ALL FEMALE SOUTH 2 0.90 8.86 9.15 0.29 88 ALL FEMALE SOUTH 3 0.17 4.09 4.58 0.50 89 ALL FEMALE EAST 1 3.13 9.08 9.01 -0.07 90 ALL FEMALE EAST 3 1.27 9.32 9.60 0.28 91 ALL FEMALE NORTHEAST 1 3.97 8.95 8.46 -0.49 92 ALL FEMALE NORTHEAST 2 1.59 10.11 9.86 -0.25 93 ALL FEMALE NORTHEAST 4 0.07 6.81 6.93 0.12 94 ALL FEMALE FRONTIER 1 1.87 8.04 8.01 -0.03 95 ALL FEMALE FRONTIER 2 0.81 8.95 9.12 0.17 96 ALL FEMALE FRONTIER 4 0.07 4.65 5.22 0.56 97 INFORMAL BOTH ALL ALL 11.95 7.70 7.70 0.00 98 FORMAL BOTH ALL ALL 47.08 7.51 7.51 0.00 99 CIVIL SERV. BOTH ALL ALL 14.98 8.43 8.43 0.00 100 SELF BOTH ALL ALL 20.55 5.97 5.97 0.00 101 EMPLOYER BOTH ALL ALL 5.43 4.61 4.61 0.00 102 INFORMAL BOTH ALL 1 9.57 7.89 7.66 -0.22 103 FORMAL BOTH ALL 1 5.87 8.95 8.74 -0.21 104 SELF BOTH ALL 1 8.17 7.30 7.07 -0.23 .i105 INFORMAL BOTH ALL 2 2.38 7.33 7.34 0.01 106 FORMAL BOTH ALL 2 23.12 7.84 7.85 0.01 107 CIVIL SERV. BOTH ALL 2 3.31 9.34 9.35 0.01 51 Rates of Return for Special Retirement with 25 years of Contributions. H_I JNcOME RATES OF RETURN (ANNUAL %) OBS OICCUPATION GENDER REGION INCOME FREQ I MORTALITY DIFFERENTIALS _WITHOUTI WITH TDIFFERENCE I ALL BOTH ALL ALL 100.00 11.19 11.19 0.00 2 ALL BOTH ALL 1 23.61 11.33 11.15 -0.17 3 ALL BOTH ALL 2 37.51 11.82 11.83 0.01 4 ALL BOTH ALL 3 15.41 10.88 11.01 0.12 5 ALL BOTH ALL 4 23.46 10.81 11.09 0.27 6 ALL BOTH RIO ALL 13.98 11.49 11.59 0.10 7 ALL BOTH SAO PAULO ALL 31.76 10.94 11.09 0.14 8 ALL BOTH SOUTH ALL 15.08 11.14 11.31 0.16 9 ALL BOTH EAST ALL 13.48 11.82 11.86 0.04 10 ALL BOTH NORTHEAST ALL 17.29 11.80 11.50 -0.30 11 ALL BOTH FRONTIER ALL 8.40 10.46 10.53 0.07 12 ALL BOTH RIO 1 1.76 10.60 10.53 -0.06 13 ALL BOTH RIO 2 4.30 11.59 11.70 0.11 14 ALL BOTH RIO 3 5.96 12.75 12.96 0.21 15 ALL BOTH RIO 4 1.95 9.82 10.18 0.36 16 ALL BOTH SAO PAULO 1 1.54 11.39 11.37 -0.02 17 ALL BOTH SAO PAULO 2 8.44 11.61 11.76 0.15 18 ALL BOTH SAO PAULO 3 5.36 9.16 9.44 0.27 19 ALL BOTH SAO PAULO 4 16.42 11.28 11.67 0.39 20 ALL BOTH SOUTH 1 4.66 11.21 11.22 0.00 21 ALL BOTH SOUTH 2 8.24 11.60 11.77 0.17 22 ALL BOTH SOUTH 3 0.17 6.78 7.09 0.32 23 ALL BOTH SOUTH 4 2.01 10.53 10.95 0.42 24 ALL BOTH EAST 1* 3.99 11.95 11.82 -0.13 25 ALL BOTH EAST 2 6.34 12.22 12.27 0.05 26 ALL BOTH EAST 3 1.27 11.63 11.79 0.16 27 ALL BOTH EAST 4 1.88 11.08 11.40 0.31 28 ALL BOTH NORTHEAST 1 8.99 11.45 10.96 -0.49 29 ALL BOTH NORTHEAST 2 5.85 12.70 12.42 -0.28 30 ALL BOTH NORTHEAST 3 1.79 12.56 12.41 -0.15 31 ALL BOTH NORTHEAST 4 0.67 9.25 9.26 0.02 32 ALL BOTH FRONTIER 1 2.67 10.78 10.68 -0.10 33 ALL BOTH FRONTIER 2 4.34 11.40 11.48 0.07 34 ALL BOTH FRONTIER 3 0.86 12.37 12.54 0.18 35 ALL BOTH FRONTIER 4 0.53 7.51 7.87 0.36 36 ALL MALE ALL ALL 67.40 11.18 11.10 -0.08 37 ALL FEMALE ALL ALL 32.59 11.25 11.32 0.07 38 _ ALL MALE ALL 1 7.50 11.39 11.13 -0.25 52 Rates of Return for Special Retirement with 25 years of Contributions. RATES OF RETURN (ANNUAL %) OBS OCCUPATION GENDER REGION INCOME FREQ MORTALITY DIFFERENTIALS l IWITHOUTI WITH 7DIFFERENCE 39 ALL MALE ALL 2 25.42 11.86 11.79 -0.07 40 ALL MALE ALL 3 11.51 10.76 10.81 0.05 41 ALL MALE ALL 4 22.97 10.93 11.13 0.21 42 ALL FEMALE ALL 1 16.11 11.30 11.20 -0.10 43 ALL FEMALE ALL 2 12.09 11.75 11.83 0.08 44 ALL FEMALE ALL 3 3.90 11.24 11.43 0.19 45 ALL FEMALE ALL 4 0.49 7.98 8.34 0.37 46 ALL MALE RIO ALL 9.42 11.70 11.72 0.03 47 ALL MALE SAO PAULO ALL 21.41 10.83 10.90 0.07 48 ALL MALE SOUTH ALL 10.17 11.27 11.36 0.09 49 ALL MALE EAST ALL 9.09 11.83 11.80 -0.03 50 ALL MALE NORTHEAST ALL 11.66 11.72 11.34 -0.38 51 ALL MALE FRONTIER ALL 5.66 10.46 10.46 -0.01 52 ALL FEMALE RIO ALL 4.56 10.90 11.07 0.17 53 ALL FEMALE SAO PAULO ALL 10.35 11.34 11.55 0.21 54 ALL FEMALE SOUTH ALL 4.92 10.75 10.98 0.23 55 ALL FEMALE EAST ALL 4.39 11.80 11.91 0.11 56 ALL FEMALE NORTHEAST ALL 5.63 12.07 11.85 -0.22 57 ALL FEMALE FRONTIER ALL 2.74 10.45 10.59 0.14 58 ALL MALE RIO 2 2.39 11.22 11.26 0.04 59 ALL MALE RIO 3 5.17 12.85 13.00 0.14 60 ALL MALE RIO 4 1.86 10.41 10.70 0.30 61 ALL MALE SAO PAULO 2 1.56 11.75 11.83 0.08 62 ALL MALE SAO PAULO 3 3.68 8.41 8.62 0.21 63 ALL MALE SAO PAULO 4 16.16 11.33 11.66 0.33 64 ALL MALE SOUTH 1 0.81 11.44 11.37 -0.07 65 ALL MALE SOUTH 2 7.34 11.63 11.72 0.10 66 ALL MALE SOUTH 4 2.01 10.53 10.89 0.36 67 ALL MALE EAST 1 0.86 11.84 11.63 -0.21 68 ALL MALE EAST 2 6.34 12.22 12.20 -0.02 69 ALL MALE EAST 4 1.88 11.08 11.33 0.25 70 ALL MALE NORTHEAST 1 5.02 11.36 10.78 -0.57 71 ALL MALE NORTHEAST 2 4.25 12.61 12.24 -0.36 72 ALL MALE NORTHEAST 3 1.79 12.56 12.33 -0.23 73 ALL MALE NORTHEAS 4 0.59 9.19 9.13 -0.07 74 ALL MALE FRONTIER I 0.81 11.12 10.95 -0.18 75 ALL MALE FRONTIER 2 3.53 11.43 11.43 0.00 76 ALL MALE FRONTIER 3 0.86 12.37 12.48 0.11 53 Riates of Return for Special Retirement with 25 years of Contributions. RATES OF RETURN (ANNUAL %) OBS )CCUPATION GENDER REGION INCOME FREQ I MORTALITY DIFFERENTIALS l______ _____ _______ _____ IWITHOUTI WITH jIFFERENCE 77 ALL MALE FRONTIER 4 046 7.56 7.85 0.29 78 ALL FEMALE RIO 1 1.76 10.60 10.60 0.01 79 ALL FEMALE RIO 2 1.91 12.12 12.29 0.17 80 ALL FEMALE RIO 3 0.79 12.21 12.49 0.27 81 ALL FEMALE RIO 4 0.10 4.51 5.01 0.50 82 ALL FEMALE SAO PAULO 1 1.54 11.39 11.44 0.05 83 ALL FEMALE SAO PAULO 2 6.88 11.58 11.80 0.21 84 ALL FEMALE SAO PAULO 3 1.68 11.32 11.63 0.31 85 ALL FEMALE SAO PAULO 4 0.26 9.54 10.02 0.48 86 ALL FEMALE SOUTH 1 3.84 11.16 11.24 0.08 87 ALL FEMALE SOUTH 2 0.90 11.42 11.66 0.23 88 ALL FEMALE SOUTH 3 0.17 6.78 7.17 0.39 89 ALL FEMALE EAST 1 3.13 11.98 11.93 -0.05 90 ALL FEMALE EAST 3 1.27 11.63 11.85 0.23 91 ALL FEMALE NORTHEAST 1 3.97 11.63 11.21 -0.41 92 ALL FEMALE NORTHEAS 2 1.59 13.01 12.81 -0.21 93 ALL FEMALE NORTHEAST 4 0.07 9.74 9.83 0.10 94 ALL FEMALE FRONTIER 1 1.87 10.62 10.59 -0.03 95 ALL FEMALE FRONTIER 2 0.81 11.28 11.42 0.14 96 ALL FEMALE FRONTIER 4 0.07 7.10 7.54 0.44 97 INFORMAL BOTH ALL ALL 11.95 11.57 11.57 0.00 98 FORMAL BOTH ALL ALL 47.08 12.32 12.32 0.00 99 CIVIL SERV. BOTH ALL ALL 14.98 12.08 12.08 0.00 100 SELF BOTH ALL ALL 20.55 9.81 9.81 0.00 101 EMPLOYER BOTH ALL ALL 5.43 8.52 8.52 0.00 102 INFORMAL BOTH ALL 1 9.57 11.40 11.23 -0.17 103 FORMAL BOTH ALL 1 5.87 11.81 11.64 -0.17 104 SELF BOTH ALL 1 8.17 10.82 10.64 -0.17 105 'INFORMAL BOTH ALL 2 2.38 11.90 11.91 0.01 106 FORMAL BOTH ALL 2 23.12 12.38 12.38 0.01 107 CIVIL SERV. BOTH ALL 2 3.31 11.95 11.96 0.01 54 10. APPENDIX C. RATES OF RETURN BY SOCIOECONOMIC CHARACTERISTICS FOR DIFFERENT RETIREMENT PROGRAMS. MARRIED MALES. INCLUDING SURVIVOR'S BENEFITS FOR SPOUSES 55 Rates of Return for Old Age Retirement with 12 years of Contributions. Married Males, including survivors' benefits for spouses }OCUPAiON~ GENDER INCOME} RATES OF RETURN (ANNUAL %)|| | OBS OCCUPATION GENDER REGION INCOME FREQ I MORTALITY DIFFERENTIALS I__ _______ I_____ _______ _____ jWITHOUT| WITH JDIFFERENCE 1 ALL MALE ALL ALL 67.40 17.73 17.92 0.19 2 ALL MALE ALL 1 7.50 20.23 20.43 0.20 3 ALL MALE ALL 2 25.42 19.55 19.75 0.20 4 ALL MALE ALL 3 11.51 17.64 17.83 0.19 5 ALL MALE ALL 4 22.97 16.70 16.88 0.18 6 ALL MALE RIO - ALL 9.42 19.16 19.35 0.19 7 ALL MALE SAO PAULO ALL 21.41 16.11 16.31 0.20 8 ALL MALE SOUTH ALL 10.17 18.81 18.98 0.18 9 ALL MALE EAST ALL 9.09 18.39 18.59 0.19 10 ALL MALE NORTHEAST ALL 11.66 19.11 19.28 0.17 11 ALL MALE FRONTIER ALL 5.66 18.69 18.89 0.19 12 ALL MALE RIO 2 2.39 21.60 21.78 0.18 13 ALL MALE RIO 3 5.17 19.59 19.75 0.16 14 ALL MALE RIO 4 1.86 16.64 16.80 0.16 15 ALL MALE SAO PAULO 2 1.56 19.98 20.16 0.18 16 ALL MALE SAO PAULO 3 3.68 13.75 13.97 0.22 17 ALL MALE SAO PAULO 4 16.16 16.69 16.85 0.16 18 ALL MALE SOUTH 1 0.81 22.89 23.10 0.21 19 ALL MALE SOTTH 2 7.34 19.36 19.54 0.17 20 ALL MALE SOUTH 4 2.01 17.86 17.97 0.11 21 ALL MALE EAST 1 0.86 16.70 16.85 0.15 22 ALL MALE EAST 2 6.34 18.73 18.92 0.19 23 ALL MALE EAST 4 1.88 18.12 18.27 0.15 24 ALL MALE NORTHEAST 1 5.02 19.13 19.26 0.13 25 ALL MALE NORTHEAST 2 4.25 19.29 19.46 0.17 26 ALL MALE NORTHEAST 3 1.79 22.53 22.77 0.24 27 ALL MALE NORTHEAST 4 0.59 11.96 12.14 0.18 28 ALL MALE FRONTIER 1 0.81 23.21 23.44 0.23 29 ALL MALE FRONTIER 2 3.53 19.46 19.65 0.19 30 ALL MALE FRONTIER 3 0.86 21.90 22.06 0.15 31 ALL MALE FRONTTIER 4 0.46 12.37 12.62 0.26 32 INFORMAL MALE ALL ALL 6.66 22.04 22.25 0.21 33 FORMAL MALE ALL ALL 34.13 18.78 18.97 0.19 34 CIVIL SERV. MALE ALL ALL 8.06 21.24 21.45 0.21 35 SELF MALE ALL ALL 13.90 16.39 16.59 0.19 36 EMPLOYER MALE ALL ALL 4.65 12.61 12.79 0.18 37 INFORMAL MALE ALL 1 4.28 22.31 22.54 0.23 38 SELF MALE ALL 1 3.23 17.68 17.85 0.17 56 Rates of Return for Old Age Retirement with 12 years of Contributions. Married Males, including survivors' benefits for spouses lCCUPATIO~.j l_______ lNCMEI |RATES OF RETURN (ANNUAL %)|| OBS OCCUPATION GENDER REGION INCOME FREQ | MORTALITY DIFFERENTIALS || l_______ ______._______ ____ I WlTHOUTI WITH DIFFERENCE 39 INFORMAL MALE ALL 2 2.38 21.76 21.97 0.21 40 FORMAL MALE ALL 2 16.05 19.26 19.45 0.19 41 SELF MALE ALL 2 6.99 19.44 19.64 0.20_ 42 FORMAL MALE ALL 3 5.17 19.59 19.77 0.18 43 CIVIL SERV. MALE ALL 3 2.65 22.31 22.49 0.18 44 SELF MALE ALL 3 3.68 13.75 13.96 0.21 45 FORMAL MALE ALL 4 12.91 18.13 18.29 0.17 46 CIVIL SERV. MALE ALL 4 5.41 20.81 20.93 0.12 47 EMPLOYER MALE ALL 4 4.65 12.61 12.86 0.24 48 INFORMAL MALE RIO ALL 0.82 23.74 23.92 0.19 49 FORMAL MALE RIO ALL 5.17 19.59 19.78 0.19 50 CIVIL SERV. MALE RIO ALL 1.39 18.47 18.66 0.19 51 SELF MALE RIO ALL 1.57 20.53 20.72 0.19l 52 EMPLOYER MALE RIO ALL 0.46 14.37 14.58 0.20 53 INFORMAL MALE SAO PAULO ALL 1.56 19.98 20.16 0.18 54 FORMAL MALE SAO PAULO ALL 12.91 18.13 18.31 0.19 55 CIVIL SERV. MALE SAO PAULO ALL 1.67 19.11 19.29 0.18 56 SELF MALE SAO PAULO ALL 3.68 13.75 13.97 0.21 57 EMPLOYER MALE SAO PAULO ALL 1.58 12.99 13.21 0.22 58 INFORMAL MALE SOUTH ALL 0.81 22.89 23.05 0.16 59 FORMAL MALE SOUTH ALL 5.26 19.84 20.01 0.17 60 CIVIL SERV. MALE SOUTH ALL 1.19 22.04 22.20 0.16 61 SELF MALE SOUTH ALL 2.08 18.02 18.20 0.18 62 EMPLOYER MALE SOUTH ALL 0.82 12.12 12.35 0.23 63 INFORMAL MALE EAST ALL 0.86 16.70 16.88 0.18 64 FORMAL MALE EAST ALL 4.54 18.53 18.72 0.19 65 CIVIL SERV. MALE EAST ALL 1.15 22.36 22.57 0.21 66 SELF MALE EAST ALL 1.80 19.20 19.39 0.20 67 EMPLOYER MALE EAST ALL 0.73 10.43 10.61 0.18 68 INFORMAL MALE NORTHEAST ALL 1.79 22.57 22.80 0.23 69 FORMAL MALE NORTHEAST ALL 4.25 19.29 19.46 0.16 70 CML SE V. MAL NORTHEAST ALL 1.79 22.53 22.78 0.25 71 SELF MALE NORTHEAST ALL 3.23 17.68 17.82 0.15 72 EMPLOYER MALE NORTHEAST ALL 0.59 11.96 12.00 0.04 73 INFORMAL MALE FRONTIER ALL 0.81 23.21 23.40 0.20 74 FORMAL MALE FRONTIER ALL 2.00 19.12 19.31 0.19 75 CIVIL SE V. MAL FRONTIER ALL 0.86 21.90 22.10 0.20 76 SELF MALE FRONTIER ALL 1.53 19.81 20.00 0.19 57 Rates of Return for Old Age Retirement with 12 years of Contributions. Married Males, including survivors' benefits for spouses RATES OF RETURN (ANNUAL %3|) } OBS OCCUPATION GENDER REGION INCOME FREQ I MORTALITY DIFFERENTIALS l __ _ _______ ______ ________ _____ _____ WITHOUTI WITH JDIFFERENCE 77 EMPLOYER MALE FRONTIER ALL 0.46 12.37 12.57 0.20 78 INFORMAL MALE RIO 2 0.82 23.74 23.92 0.18 79 SELF MALE RIO 2 1.57 20.53 20.72 0.19 80 FORMAL MALE RIO 3 5.17 19.59 19.75 0.16 81 CIVIL SE V. MALI RIO 4 1.39 18.47 18.61 0.13 82 E]MPLOYER MALE RIO 4 0.46 14.37 14.58 0.20 83 INFORMAL MALE SAO PAULO 2 1.56 19.98 20.16 0.18 84 SELF MALE SAO PAULO 3 3.68 13.75 13.97 0.22 85 FORMAL MALE SAO PAULO 4 12.91 18.13 18.26 0.13 86 CIVIL SE V. MAL SAO PAULO 4 1.67 19.11 19.21 0.10 87 E1MPLOYER MALE SAO PAULO 4 1.58 12.99 13.23 0.24 88 INFORMAL MALE SOUTH .1 0.81 22.89 23.10 0.21 89 FORMAL MALE SOUTH 2 5.26 19.84 20.01 0.17 90 SELF MALE SOUTH 2 2.08 18.02 18.20 0.18 91 CIVIL SERV. MALE SOUTH 4 1.19 22.04 22.05 0.01 92 EMPLOYER MALE SOUTH 4 0.82 12.12 12.40 0.28 93 ]NFORMAL MALE EAST 1 0.86 16.70 16.85 0.15 94 FORMAL MALE EAST 2 4.54 18.53 18.72 0.19 95 SELF MALE EAST 2 1.80 19.20 19.39 0.20 96 C'IVIL SERV. MALE EAST 4 1.15 22.36 22.44 0.08 97 EMPLOYER MALE EAST 4 0.73 10.43 10.74 0.31 98 INFORMAL MALE NORTHEAST 1 1.79 22.57 22.78 0.21 99 SELF MALE NORTHEAST 1 3.23 17.68 17.77 0.09 100 FORMAL MALE NORTHEAST 2 4.25 19.29 19.46 0.17 101 CIVIL SERV. MALE NORTHEAST 3 1.79 22.53 22.77 0.24 102 EMPLOYER MALE NORTHEAST 4 0.59 11.96 12.14 0.18 103 INFORMAL MALE FRONTIER 1 0.81 23.21 23.44 0.23_ 104 FORMAL MALE FRONTIER 2 2.00 19.12 19.31 0.19 105 SELF MALE FRONTIER 2 1.53 19.81 20.00 0.19 106 CIVIL SERV. MALE FRONTIER 3 0.86 21.90 22.06 0.15 107 E MPLOYER MALE FRONTIER 4 0.46 12.37 12.62 0.26 58 Rates of Return for Time in Service Retirement w/ 30 years of Contributions. Married Males, including survivors' benefits for spouses RATES OF RETURN (ANNUAL %) OBS OCCUPATION GENDER REGION INCOME FREQ MORTALITY DIFFERENTIALS l__ ________ ______ _______ _____ IWITHOUTI WITH DIFFERENCE 1 ALL MALE ALL ALL 67.40 7.91 7.93 0.02 2 ALL MALE ALL 1 7.50 8.19 8.14 -0.06 3 ALL MALE ALL 2 25.42 8.47 8.49 0.02 4 ALL MALE ALL 3 11.51 7.70 7.77 0.07 s ALL MALE ALL 4 22.97 7.66 7.79 0.13 6 ALL MALE RIO ALL 9.42 8.47 8.53 0.05 7 ALL MALE SAO PAULO ALL 21.41 7.55 7.63 0.08 8 ALL MALE SOUTH ALL 10.17 8.04 8.12 0.08 9 ALL MALE EAST ALL 9.09 8.32 8.36 0.03 10 ALL MALE NORTHEAST ALL 11.66 8.40 8.30 -0.10 11 ALL MALE FRONTIER ALL 5.66 7.49 7.53 0.04 12 ALL MALE RIO 2 2.39 8.40 8.46 0.06 13 ALL MALE RIO 3 5.17 9.32 9.41 0.09 14 ALL MALE RIO 4 1.86 7.35 7.52 0.16 15 ALL MALE SAO PAULO 2 1.56 8.40 8.47 0.07 16 ALL MALE SAO PAULO 3 3.68 5.71 5.86 0.15 17 ALL MALE SAO PAULO 4 16.16 7.94 8.10 0.16 1 8 ALL MALE SOUTH 1 0.81 8.53 8.55 0.02 19 ALL MALE SOUTH 2 7.34 8.26 8.34 0.08 20 ALL MALE SOUTH 4 2.01 7.58 7.76 0.18 21 ALL MALE EAST 1 0.86 7.99 7.95 -0.04 22 ALL MALE EAST 2 6.34 8.65 8.68 0.04 23 ALL MALE EAST 4 1.88 7.78 7.92 0.14 24 ALL MALE NORTHEAST 1 5.02 8.13 7.94 -0.19 25 ALL MALE NORTHEAST 2 4.25 9.00 8.90 -0.09 26 ALL MALE NORTHEAST 3 1.79 9.55 9.51 -0.04 27 ALL MALE NORTBHEAST 4 0.59 6.06 6.09 0.03 28 ALL MALE FRONTIER 1 0.81 8.30 8.28 -0.03 29 ALL MALE FRONTIER 2 3.53 8.17 8.22 0.05 30 ALL MALE FRONTIER 3 0.86 9.28 9.36 0.08 3 1 ALL MALE FRONTIER 4 0.46 5.02 5.22 0.20 32 INFORMAL MALE ALL ALL 6.66 8.48 8.50 0.01 33 FORMAL MALE ALL ALL 34.13 8.81 8.83 0.02 34 CIVIL SE V. MAL ALL ALL 8.06 9.05 9.07 0.02 35 SELF MALE ALL ALL 13.90 6.77 6.78 0.02 36 EMPLOYER MALE ALL ALL 4.65 5.85 5.87 0.02 37 INFORMAL MALE ALL 1 4.28 8.28 8.22 -0.06 38 SELF MALE ALL 1 3.23 8.10 8.04 -0.05 59 Rates of Return for Time in Service Retirement w/ 30 years of Contributions. Married Males, including survivors' benefits for spouses RATES OF RETURN (ANNUAL %) OBS OCCUPATION GENDER REGION INCOME FREQ MORTALITY DIFFERENTIALS l _______ _______ _____ IWITHOUT| WITH DIFFERENCE 39 INFORMAL MALE ALL 2 2.38 8.70 8.72 0.02 40 FORMAL MALE ALL 2 16.05 8.92 8.94 0.02 41 SELF MALE ALL 2 6.99 7.43 7.45 0.02 42 FORMAL MALE ALL 3 5.17 9.32 9.38 0.06 43 CIVIL SE V. MAL ALL 3 2.65 9.44 9.50 0.06 44 SELF MALE ALL 3 3.68 5.71 5.79 0.08 45 FORMAL MALE ALL 4 12.91 8.58 8.70 0.11 46 CIVIL SE V. MAL ALL 4 5.41 8.92 9.03 0.11 47 EMPLOYER MALE ALL 4 4.65 5.85 6.00 0.15 48 INFORMAL MALE RIO ALL 0.82 9.40 9.45 0.05 49 FORMAL MALE RIO ALL 5.17 9.32 9.37 0.05 50 CIVIL SE V. MALI RIO ALL 1.39 8.67 8.73 0.05 51 SELF MALE RIO ALL 1.57 8.03 8.08 0.06 52 EMPLOYER MALE RIO ALL 0.46 5.22 5.29 0.07 53 INFORMAL MALE SAO PAULO ALL 1.56 8.40 8.47 0.07 54 FORMAL MALE SAO PAULO ALL 12.91 8.58 8.65 0.07 55 CIVL SE V. MAL SAO PAULO ALL 1.67 8.50 8.57 0.07 56 SELF MALE SAO PAULO ALL 3.68 5.71 5.80 0.09 57 EMPLOYER MALE SAO PAULO ALL 1.58 5.88 5.97 0.09 58 INFORMAL MALE SOUTH ALL 0.81 8.53 8.61 0.08 59 FORMAL MALE SOUTH ALL 5.26 8.66 8.74 0.08 60 CIVIL SE V. MAL SOUTH ALL 1.19 9.69 9.76 0.07 61 SELF MALE SOUTH ALL 2.08 7.25 7.33 0.09 62 EMPLOYER MALE SOUTH ALL 0.82 6.04 6.14 0.10 63 INFORMAL MALE EAST ALL 0.86 7.99 8.02 0.03 64 FORMAL MALE EAST ALL 4.54 9.16 9.19 0.03 65 CIVL SE V. MAL EAST ALL 1.15 9.11 9.14 0.03 66 SELF MALE EAST ALL 1.80 7.31 7.34 0.03 67 E1MPLOYER MALE EAST ALL 0.73 6.60 6.65 0.04 68 INFORMAL MALE NORTHEAST ALL 1.79 8.24 8.13 -0.11 69 FORMAL MALE NORTHEAST ALL 4.25 9.00 8.90 -0.10 70 CIVIL SE V. MAL NORTHEAST ALL 1.79 9.55 9.45 -0.09 71 SELF MALE NORTHEAS ALL 3.23 8.10 7.99 -0.11 72 EIMPLOYER MALE NORTHEAST ALL 0.59 6.06 5.94 -0.12 73 INFORMAL MALE FRONTIER ALL 0.81 8.30 8.35 0.04 74 FORMAL MALE FRONTIER ALL 2.00 9.00 9.04 0.04 75 CIVIL SE rV. MAL FRONTIER ALL 0.86 9.28 9.32 0.04 76 _ SELF MALE FRONTIER ALL 1.53 7.20 7.24 0.04 60 Rates of Return for Time in Service Retirement w/ 30 years of Contributions. Married Males, including survivors' benefits for spouses RATES OF RETURN (ANNUAL %) OBS OCCUPATION GENDER REGION INCOME FREQ I MORTALITY DIFFERENTIALS l IWITHOUTI WITH DIFFERENCE 77 EMPLOYER MALE FRONTIER ALL 0.46 5.02 5.07 0.05 78 INFORMAL MALE RIO 2 0.82 9.40 9.45 0.05 79 SELF MALE RIO 2 1.57 8.03 8.09 0.06 80 FORMAL MALE RIO 3 5.17 9.32 9.41 0.09 81 CIVIL SE WV MAL RIO 4 1.39 8.67 8.81 0.14 82 EMPLOYER MALE RIO - 4 0.46 5.22 5.43 0.21 83 INFORMAL MALE SAO PAULO 2 1.56 8.40 8.47 0.07 84 SELF MALE SAO PAULO 3 3.68 5.71 5.86 0.15 85 FORMAL MALE SAO PAULO 4 12.91 8.58 8.74 0.15 86 CIVIL SE V. MAL SAO PAULO 4 1.67 8.50 8.66 0.15 87 EMPLOYER MALE SAO PAULO 4 1.58 5.88 6.09 0.21 88 INFORMAL MALE SOUTH 1 0.81 8.53 8.55 0.02 89 FORMAL MALE SOUTH 2 5.26 8.66 8.74 0.08 90 SELF MALE SOUTH 2 2.08 7.25 7.34 0.09 91 CIVIL SE V. MALI SOUTH 4 1.19 9.69 9.83 0.14 92 EMPLOYER MALE SOUTH 4 0.82 6.04 6.25 0.22 93 INFORMAL MALE EAST 1 0.86 7.99 7.95 -0.04 94 FORMAL MALE EAST 2 4.54 9.16 9.20 0.04 95 SELF MALE EAST 2 1.80 7.31 7.35 0.04 96 CMIL SE V. MALI EAST 4 1.15 9.11 9.23 0.12 97 EMPLOYER MALE EAST 4 0.73 6.60 6.76 0.16 98 INFORMAL MALE NORTHEAST 1 1.79 8.24 8.04 -0.20 99 SELF MALE NORTHEAST 1 3.23 8.10 7.91 -0.19 100 FORMAL MALE NORTHEAST 2 4.25 9.00 8.90 -0.09 101 CIVIL SE V. MAL NORTHEAST 3 1.79 9.55 9.51 -0.04 102 EMPLOYER MALE NORTHEAST 4 0.59 6.06 6.09 0.03 103 INFORMAL MALE FRONTIER 1 0.81 8.30 8.28 -0.03 104 FORMAL MALE FRONTIER 2 2.00 9.00 9.04 0.04 105 SELF MALE - FRONTIER 2 1.53 7.20 7.25 0.05 106 CIVIL SE V. MALI FRONTIER 3 0.86 9.28 9.36 0.08 107 EMPLOYER MALE FRONTIER 4 0.46 5.02 5.22 0.20 61 11. APPENDIX D. PARAMETER ESTIMATES, SAMPLE WEIGHTS AND EDUCATIONAL ATTAINMENT MEANS FOR EARNINGS FUNCTIONS. 62 Sample Weights, Mean Educational Attainment and Parameter Estimates for Earnings Functions by Occupational Position, Gender and Region of Residence. SAMPLE MEAN PARAMETER ESTIMATES POSITION GENDER REGION WEIGHT EDUCATION Intercept Age 7 AgeA2 j Education (in Yrs.) INFORMAL MALE RIO 0.82% 6.22 4.9756 0.03731 -0.0001216 0.09792 INFORMAL MALE SAO PAULO 1.56% 5.33 4.1747 0.10910 -0.001 2815 0.12569 INFORMAL MALE SOUTH. 0.81% 5.38 5.0344 0.03648 -0.0002827 0.13057 INFORMAL MALE EAST 0.86% 4.92 2.4065 0.18731 -0.0024048 0.11516 INFORMAL MALE NORTHEAST 1.79% 3.48 5.0246 0.03278 -Q0-02921 0.10137 INFORMAL MALE FRONTIER 0.81% 4.84 5.6018 0.01905 -0.0000942 0.10328 INFORMAL FEMALE RIO 0.84% 4.81 4.1143 0.06676 -0.0007061 0.114591 INFORMAL FEMALE SAO PAULO 1.54% 4.54 4.1410 0.07628 -0.0008775 0.14433 INFORMAL FEMALE SOUTH. 0.70% 4.28 3.6710 0.09227 -0.0011512 0.12944 INFORMAL FEMALE EAST 0.67% 4.25 3.5571 0.07809 -0.0006220 0.10664 INFORMAL FEMALE NORTHEAST 1.00% 3.29 2.5963 0Q11172 -0-0013111 0.12799 INFORMAL FEMALE FRONTIER 0.53% 4.57 3.2798 0.10324 -0.0012459 0.11541 FORMAL MALE RIO 5.17% 7.29 3.1502 0.13835 -0.0014584 0.14807 FORMAL MALE SAO PAULO 12.91% 6.62 3.5753 0.15756 -0.0018178 0.12900 FORMAL MALE SOUTH. 5.26% 6.35 3.6770 0.12941 -0.0014734 0.14033 FORMAL MALE EAST 4.54% 6.52 2.2979 0.18865 -0.0021552 0.15876 FORMAL MALE NORTHEAST 4.25% 6.26 2.9306 0.15365 -0.0017534 0.14524 FORMAL MALE FRONTIER 2.00% 6.58 2.8239 0.16303 -0.0018564 0.14987 FORMAL FEMALE RIO 1.91 % 8.36 3.3122 0.1 1430 -0.0012806 0.14960 FORMAL FEMALE SAO PAULO 5.17% 7.21 4.0953 0.10195 -0.0011499 0.13410 FORMAL FEMALE SOUTH. 2.22% 7.14 3.7821 0.10775 -0.0013361 0.13632 FORMAL FEMALE EAST 1.55% 7.49 1.6157 0.19654 -0.0023713 0.17512 FORMAL FEMALE NORTHEAST 1.42% 7.74 3.1640 0.11985 -0.0014072 0.14159 FORMAL FEMALE FRONTIER 0.69% 7.84 3.7371 0.10826 -0.0013684 0.13651 CIVIL SERV. MALE RIO 1.39% 9.86 3.1138 0.15239 -0.0017140 0.14509 CIVIL SERV. MALE SAO PAULO 1.67% 8.67 4.0581 0.12141 -0.0013659 0.11578 CIVIL SERV. MALE SOUTH. 1.19% 8.49 4.5081 0.05645 -0.0002807 0.15430 CIVIL SERV. MALE EAST 1.15% 8.09 5.1697 002326 0.0000428 0.16772 CIVIL SERV. MALE NORTHEAST 1.79% 7.65 42957 0.05794 -0.0003629 0.15276 CIVIL SERV. MALE FRONTIER 0.86%0/ 8.23 44874 006811 -0.0005312 0.13306 CIVIL SERV. FEMALE RIO 0.790o 11.03 3.5481 010453 -0.0010739 0.14529 CIVIL SERV. FEMALE SAO PAULO 1.68% 11.28 4.6710 007680 -0003485 0.10385 CIVIL SERV. FEMALE SOUTH. 0.90% 10.58 4.3361 0.07957 -0.0009011 0.12147 CIVIL SERV~ FEMALE EAST 1.15% 10.62 43328 0.05525 -Q0003682 0.14206 CIVIL SERV. FEMALE NORTHEAST 1.59%° 9.55 2.0126 0.15757 -0.0017265 0.14970 CIVIL SERV. FEMALE FRONTIER 0.81% 9.68 4.8775 0.04266 -0.0)4065 0.12822 SELF MALE RIO 1.57% 6.36 4.9252 0.05590 -0.0004780 0.11497 SELF MALE SAO PAULO 3.68% 6.20 5.6213 0.05407 -0.0005646 0.10601 SELF MALE SOUTH. 2.08% 5.81 4.6219 0.09443 -0.0011545 0.11257 SELF MALE EAST 1.80% 5.56 5.1245 o006284 -0.0007204 0.10186 SELF MALE NORTHEAST 3.23% 4.04 3.2972 0.14162 -0.0016028 0.09258 SELF MALE FRONTIER 1.53% 5.24 5.7325 0.04083 -0.0Q04492 0.09056 SELF FEMALE RIO 0.92% 6.22 4.4240 0.06032 -00007177 0.13203 SELF FEMALE SAO PAULO 1.71% 6.41 3.9112 0.09970 -0.0011694 0.15514 SELF FEMALE SOUTH. 0.92% 5.61 4.5120 0.05731 -0.0006022 0.11677 SELF FEMALE EAST 0.91% 5.19 4.0779 0.06853 -0.0007499 0.13359 SELF FEMALE NORTHEAST 1.54% 3.93 2.8800 0.10728 -0.0011888 0.17065 SELF FEMALE FRONTIER 0.65% 5.49 5.0Q05 0.05138 -0.0007226 0.11324 EMPLOYER MALE RIO 0.46% 9.43 5.9458 0.04140 -0.0003554 0.08946 EMPLOYER MALE SAO PAULO 1.58% 9.51 4.7433 0.12325 -0.0012775 0.07645 EMPLOYER MALE SOUTH. 0.82% 8.85 4.2874 0.14782 -0.0016334 0.05375 EMPLOYER MALE EAST 0.73% 8.84 1.8774 0.25244 -0.0028981 0.08951 63 Sample Weights, Mean Educational Attainment and Parameter Estimates for Earnings Functions by Occupational Position, Gender and Region of Residence. SAMPLE MEAN PARAMETER ESTIMATES POSITION GENDER REGION WEIGHT EDUCATION Intercept Age AgeA2 Education (in Yrs. EMPLOYER MALE NORTHEAST 0.59% 7.72 3.7763 0.14995 -0.0016958 0.10747 EMPLOYER MALE FRONTIER 0.46% 8.29 5.4330 0.10215 -0.0012047 0.0750S EMPLOYER FEMALE RIO 0.10% 10.51 12.9791 -0.36459 0.0D47031 0.15399 EMPLOYER FEMALE SAO PAULO 0.26%h 10.22 3.6402 0.15028 -0.0015097 0.10006 EMPLOYER FEMALE SOUTH. 0.17% 9.38 3.8450 0.18165 -0.0026130 0.08038 EMPLOYER FEMALE EAST 0.11% 10.49 4.3479 0.13304 -0.0016789 0.06769 EMPLOYER FEMALE NORTHEAST 0.07% 9.57 1.9438 0.20205 -0.0023746 0.16975 EMPLOYER FEMALE FRONTIER 0.07% 10.01 4.7828 0.15874 -0.0021368 0.03744 Source: Paes de Barros et al. (1992) and IPEA, Unpublished data. 64