Artículos

## Life tables of disability beneficiaries by morbidity cause. Brazil, 1999-2002

Marília Miranda Forte Gomes mariliamfg@gmail.com
Universidade de Brasília (UnB, Campus Gama), Brasil
Everton Emanuel Campos de Lima everton.emanuel@gmail.com
Universidade Estatual de Campinas, Brasil
Moema Gonçalves Bueno Fígoli moema@cedeplar.ufmg.br
Centro de Desenvolvimento e Planejamento Regional (CEDEPLAR), Brasil
Marcos Roberto Gonzaga mrcs.roberto@gmail.com
Universidade Federal do Rio Grande do Norte (UFRN), Brasil

Abstract: The main goal of this paper is to estimate a Disability Beneficiaries Life Table from the General Social Security Regime for Private Sector Workers (RGPS) by sex, age and disability cause in Brazil using multiple-decrement models. We used administrative records from Technological Enterprises and Social Security Information (DATAPREV 1999- 2002), and the information of social beneficiaries given by National Records of Social Information (CNIS 1999-2002).The results show that –in contradiction with the disability life tables used in the private sector– the male disability retirement hazard increases steadily until age 65 and decreases afterwards. However, for females, these risks increase continuously up to the oldest age. More sex differentials show that, among women, the risk of disability retirement is larger due to circulatory diseases, musculoskeletal diseases and neoplasms. Among males, mental disorders are the most responsible for an overweight in the number of pensioners, especially among the young and adult age groups. This paper contributes to a better understanding of work and disability, especially in the field of social security and retirement.

Keywords: Life Tables, Disability, Social Security, Brazil.

### Introduction

The Brazilian demographic transition process, during the last half century, caused expressive changes in the Brazilian population age structure (Carvalho, 2004). The first important change is characterized by a fast child mortality decline beginning in the 1940s. The direct consequence of this process of mortality decline was the increase in life expectancy (Prata, 1992; Carvalho e Garcia, 2003). In a period of almost sixty years, the country’s life expectancy rose from 44 years in 1940 to 73 years in 2009 (Carvalho, 2004; Ministério da Saúde, 2010). In the Southern and Southeastern parts of Brazil, the most socioeconomic developed regions of the country, it has been verified that there is an increase in the number of deaths by external causes and non-transmissible diseases, but a decrease in the number of deaths by transmissible diseases (Ferreira and Castiñeiras, 1996, 1998; Gawryszewski and Jorge, 2000; Nunes, 2004; Schramm et al., 2004). Moreover, fertility has followed a similar path of continuous decline. Total Fertility Rate (FFR) fell from 6.3 to 5.8 in 1970 and to 4.4 in 1980. After the end of the 1980s, the reduction in the national TFR was more pronounced, achieving the value of 2.9 in 1991. Finally, in 2006, the TFR reached the below replacement level (Rios-Neto, 2005; Ministério da Saúde, 2010; Alves, 2008).

This demographic transition process had important implications to labor market and social security system due to the changes in the age structure. In addition to that, due to the Brazilian demographic transition process characterized by a fast fertility decline and an increase in life expectancy, the country might experience a shortage in future active population together with an increase population aging. Therefore, the amount of taxpayers decreases as the number of social beneficiaries’ increases, and the social security system becomes deficient (Brito, 2007).

The social security system becomes more fragile in the extent that occurs early retirements. In many cases, the main cause of this early withdraw is commonly associated with any kind of disability. In Latin-American countries, the costs with social security associated with disability withdraws range from 8% to 18% at the beginning of this century (Grushka and Demarco, 2003), while in Brazil this cost currently is round 17% (AEPS, 2011).

Due to distinguished ways to manage the pension systems and different definitions adopted, it is very difficult to establish international comparison. According to Grushka and Demarco (2003), many Latin-American pension systems followed the Chilean experience, since the 1981 pension reform. The criteria for retirement disability depends of the country pension used definition –such as partial or total disability, permanent or temporary work disability– and whether or not the disability cause is related to work (Grushka and Demarco, 2003).

In Brazil, the public social security allows early retirement and it also covers any income lost to all insured laborers and victims of permanent work disability due to illness or work injuries. This retirement benefit shall be granted to the employee, even if he or she does not have illness assistance (Gomes, 2008). In this case, the work disability is defined as the incapacity to develop any kind of labor activity, without the possibility of recovering or exercising any payment work activity and the illness assistance is a benefit given in the cases of temporary incapacity to work, due to illness or injury that exceeds 15 days (Brazil, 1999). The state of work incapacity is verified by periodical medical evaluation. For the worker, the possibility of a health evaluation by his own trusted physician is permissible. In any case, there is no possibility to get retirement disability when the disease or injury was notified on the day of social security membership. However, there is an exception in the case of incapacity due to progression or aggravation of this disease or injury (Brasil, 1999).

According to the regulation of Brazilian Social Security (Brasil, 1999), the benefit of retirement disability is granted for those who pay at least twelve months to the pension public system, this being the minimum time length of contribution until the pensioner starts to receive social retirement benefits. For those who lost the benefit of retirement, and instead, renew their membership to Brazilian General Social Security Regime (RGPS), the retirement disability is given after four months of payment to the social security system. However, in two cases the benefit of retirement is independent of the time of contribution: first, the benefit is given to employees victims of work accidents of any nature; second, the worker is qualified to retire when he falls victim to any specific illness or injury, according to the disease list of the Health Ministry and Social Security (Brasil, 1999).

According to the Ministerial Decree n° 2.998, 23 August 2001 (Brasil, 2001), the following list of diseases allows early disability retirement: active tuberculosis, leprosy, mental alienation, malignant neoplasm, blindness, irreversible and disabling paralysis, serious cardiopathy, advanced state of the illness of Paget, Syndrome of the Acquired Immune Deficiency –AIDS–, radiation contamination, serious liver diseases, Parkinson’s disease, Ankylosing spondylosis and Severe nephropathy. In addition to that, the Brazilian Annual Social Security Statistics (AEPS), the disabilities withdraw benefit can be classified into accidental or social security retirement. The main distinction among these two is that retirement by accident occurs when the worker exercises his work activity inside the occupational environment or during transportation to and from work. Moreover, the accidental withdraw is independent from the number of former financial contributions to the RGPS. Nonetheless, this benefit will be available once the worker has paid the minimum pension contribution established by law (AEPS, 2007).

In this context, the objective of this paper is to bring a better understanding and knowledge of the retirement benefit flows. In this context, it is important to investigate labor markets withdraw according to distinguished morbidity causes since Brazil lacks in studies related to this matter. As methodological approach, we estimate multiple decrement life tables for different morbidity causes, for each sex, between 1999 and 2002. We call these tables “disability beneficiaries’ life tables”. These tables contain the transition hazards from an occupational state to the status of permanent disability withdraw. Concerning the construction of these tables, it is remarkable that population age composition is highly correlated with the transition hazards (Gomes, 2008). The knowledge of these transition hazards of retirement, in relation to the disease and injury, can serve as guide for policy makers once they can apply this information in the labor environment to develop work and health prevention policies. This information can also be applied to forecast the costs of early labor market exits, since earlier withdraws generally create more costs for the social security system (Ribeiro, 2006). Therefore, our main goal is to estimate disability beneficiary life tables by sex, age and disability causes. Theses tables consider only the laborers who are insured by the public social security regime (RPSS) during the period of January 1st, 1999 to December 31st, 2002. The method applied in this paper is multi-decrement life tables. These tables allow us to study the effects of every disability cause, separately or together, and the resultant effect on the general retirement pattern.

It is important to say that these tables represent only the disability retirement experience of each individual. They do not include the entire population of disabled individuals. Therefore, these life tables include only the pensioners who retire due to some disability. All the other beneficiaries are not considered in the analysis. We also excluded from the analysis other beneficiaries who receive benefits from continuous payment since the Ministry of Social Security (INSS) does not recognize their benefits as a disability retirement. The benefits from continuous payment are characterized by continuous monthly payments, until some cause (for example, death) ceases it. In this category of retirement are pensions for death, lifetime monthly incomes, allowances of permanence in service, the wage-family and maternity, etc. (AEPS, 2007).

Furthermore, those who chose other pension system are discarded from the analyses as well. It is important to say that the risks of retirement are competitive, since there are different kinds of benefits offered by the security system. For this reason, the values of the disability retirement hazards may be affected by these competitive benefits. In order to get better estimates, we try to adjust the disability life table considering only the beneficiaries from the RGPS (Gomes, 2008).

### Data and methods

#### Data set and population of study

The data is built up by administrative records gathered by Technological Enterprises and Social Security Information (DATAPREV 1999-2002) and combined with the information of beneficiaries given by the Social Information of National Social Security Registers (CNIS 1999-2002). The mortality tables, by sex and age, are estimated according to data from the Population Division and Social Indicators (DEPIS 1999-2002) and the Brazilian Institute of Geography and Statistics (IBGE 1999-2002).

The period of analyses is from 1999 to 2002. This period was chosen because it best represents the recent experiences of retirees. According to the Statistical Yearbook of Social Security (2007), in 2000, 22% of retirements occurred due to disability. In 2005, this proportion increased to over 30%. Moreover, between 1990 and 1995 it is observed an increase of 0.7% in the number of permanent disability retirees. The following periods of 1995-2000 and 2000-2005, the number of disability retirees increases respectively to 5.6% and 11.6%. At the same time, it is also a short period, which reduces the effects of changes in the benefits rules on the transitions from activity to disability state. The changes in benefit rules came after the Constitutional Emend n° 20, from 16 December 1998 (Brasil, 1998). It is important to mention that we do not analyze recent disability retirements, due to the lack of data. However, 1999-2002 is an important period of analysis since during those years it is observed a remarkable increment in disability retirement outflows.

For the estimation of the transition rates, both rural and urban beneficiaries are considered. However, the group of special retirees is discarded, once these pensioners make up part of the crude rural production, therefore they may be underestimated. This group comprehends the producers, the partners, the sharecroppers and the agricultural leaseholders, the artisan fishermen who exercise these activities individually or in familiar economy regime, receiving eventual assistance from a third party. Also it is taken to account the respective spouses, friends and children older than 16 years, since they work with the respective familiar group (AEPS, 2007). For the most part, these workers receive social security benefit after a minimum time of work exercise in some rural occupation. For these rural workers, the social security system guarantees health assistance or disability retirement according to the country’s minimum wage rates (Brasil, 1999; AEPS, 2007; Gomes et al., 2010). Depending on which beneficiary group is considered, the transition rates will be biased, due to a lack of information about the exact number of employees who belongs to this group (Gomes, 2008).

#### Classifications of disabilities according to the ICD 10

In accordance with the 10th International Classification of Diseases (ICD10) (Ministério da Saúde-DATASUS, 2006) the disability retirement tables for the period of 1999-2002 were established. Among the disability withdraws in 1999, barely 20% were classified following the ICD 9. For the following periods, the classification of diseases by ICD 10 was applied. For this reason, the analyses of the retirement tables did not go to more disaggregated levels of illness, according to the ICD 10, since it is expected that more detailed levels of analyses might bring incorrect classifications (Ribeiro, 2006).

The data was processed following the footsteps of a previous work by Ribeiro (2006). This way, the structure of disability causes included information from the initial physician visit until the last physician visit. If information from the first medical visit was not available, such that a comparison could not be made, then only information from the last medical record was considered.

During the classification of diseases, two important changes that occurred between the 9th and 10th ICD were taken into account. The first change concerns the split of the single chapter on nervous and sensory system diseases from the former ICD 9 into three new chapters in the ICD 10. Chapter VI now contains diseases of the nervous system, Chapter VII diseases of the eye and adnexa, and Chapter VIII contains information on the diseases of the ear and mastoid process. The second change concerns Chapters I, III and IV from ICD 10. In the former classification the immune deficiency disorders, including hiv disorders involving the immune mechanism). In the new classification of ICD 10, hiv infection became part of other chapters, namely Chapter I detailing certain infectious and parasitic diseases, and Chapter III which covers diseases of the blood and bloodforming organs and certain disorders involving the immune mechanism. The endocrines, nutritionals and metabolic diseases have been placed in a separate chapter in ICD 10 (Grassi and Laurenti, 1998). Furthermore, the retirement disability causes from Chapter VI in ICD 9 have been divided into other chapters in the ICD 10.

To facilitate the construction of the transition tables, we introduce the category of “non-information”, gathering all unexpected disability retirement causes. For example, the causes of disability classified in Chapter XV concerning pregnancy, childbirth and puerperium and in Chapter XVI covering certain conditions originating in the perinatal period and Chapter XX detailing external causes of morbidity and mortality were placed into the category “non- information” because there were no retirement benefits concerning these causes (see Table 1). We also create the category of “others” gathering less representative disability information. The category contains the following chapters and diseases: Chapter III: diseases of the blood and blood, forming organs and certain disorders involving the immune mechanism; Chapter VIII: diseases of the ear and mastoid process; Chapter XI: diseases of the digestive system; Chapter XII: diseases of the skin and subcutaneous tissue; Chapter XVII: congenital malformations, deformations and chromosomal abnormalities; Chapter XVIII: symptoms, signs and abnormal clinical and laboratory findings not elsewhere classified; and Chapter XXI: factors influencing health status and contact with health services. The Table 1 brings the disability causes according to ICD chapter.

Table 1. Disability cause according to Chapter ICD 10

##### Table 1
Disability cause according to Chapter ICD 10

Disability causes | Chapter ICD 10
Infectious/parasitic | I
Neoplasms | II
Nutritional/metabolic | IV
Mental disorders | V
Nervous system | VI
Eye diseases | VII
Circulatory | IX
Respiratory | IX
Musculoskeletal | X
Genitourinary | XIII
Injuries | XIX
Non-information | XV, XVI, XX
Others | III, VIII, XI, XII, XVII, XVIII, XXI

##### Source: Ministério da Saúde-DATASUS, 2006.

#### Decrement life tables: disability retirement life tables according to morbidity causes

In order to estimate the multi-decrement life table, we assume that the workers are at risk of labor market exit due to different morbidity causes, and each singular cause of retirement can be regarded as decrement or transition rates. We also assume that, at the time of retirement, every possible cause of morbidity could be experienced by the retiree (Seal, 1977; Winklevoss, 1993).

Once all transition states are known, the next step is to estimate the whole life table and the retirement hazards. Thus, disability retirement hazards by a particular cause are estimated, as well as the gain in years after a singular morbidity cause is discarded (Namboodiri and Suchindran, 1987). The estimates are obtained via the following steps:

First step: it is estimated the disability retirement probabilities for all morbidity causes, according to the information on the Table A.1 (in Appendix). The main idea behind it is to estimate the disability retirement rates according to all morbidity causes – nrx,C+ – between the ages x and x+n, in the time interval t:

Equation 1

[Equation 1]

where:

nIx,C+: Number of pensioners among the ages x and x+n, at the observation period, according to the all causes C+;

nLx: Number of person-years exposed to the risk disability withdraw in ages x and x+n, during the observation period.

It is important to mention that the number of permanent disabled pensioners is estimated by the number of social benefits given during the period between January 1st, 1999 and December 31st, 2002, regarding the time of exposure to the risk of retirement disability (see Gomes, 2008).

Once the disability retirement rates are estimated ( nrx,C+ ), the next step is to estimate the disability retirement probabilities , – nrx,C+' – according to following specification, given by Namboodiri and Suchindran (1987):

Equation 2

[Equation 2]

Considering a table of initially 100.000 insured workers exposed to these disability retirement risks, the number of disabilities retirees nix,C+ is estimated by all causes and between the ages x e x+n, according to the following specifications.

Equation 3

[Equation 3]

Equation 4

[Equation 4]

n1x,C+ : The number of insured workers at the exact age x for the initial cohort of 100.000 individuals exposed to all combined morbidity causes C+;

n1x+n,C+ : The number of insured workers at the exact age x+n for the initial cohort of 100.000 individuals exposed to all combined morbidity causes C+.

Second step: after estimating the total numbers of retirees ( nix,C+ ), this amount is distributed into distinguished disability causes – Ca – in each age. It is done considering the proportional distribution of the number of retirees by each observed morbidity reason:

Equation 5

[Equation 5]

where:

nix,Ca : Estimated number of pensioners by each disability cause Cα, between the ages x and x+n, in the period of study;

nix,C+: Estimated number of pensioners submitted to the disabilities probabilities (1) exposed to all combined disability causes C+, between the ages x and x+n, in the period of study;

nIx,Ca: Number of observed pensioners, between the ages x and x+n and in the study period according to cause a Ca;

nIx,C+ : Number of observed pensioners, between the ages x and x+n and in the study period, by cause a Ca according to cause C+.

Step three: we estimate the retirement probabilities according to each morbidity cause, by the ratio of nix,Ca to lx,C+ . The assumption behind rationality is that the whole population at risk to survive until exact age x can retire due to any disability cause Ca since each cause of morbidity can be experienced by the pensioner (Namboodiri and Suchindran, 1987). These estimated probabilities are then so-called “crude disability retirement probabilities according to morbidity cause”.

It is important to note, however, the RGPS beneficiary is at risk of disability withdraw at the commencement of his membership. This can happen as long as he is aged 15 (while the employee is a trainee) or aged 17 and above for the other beneficiaries. Although, in this paper we consider just those who retire between the age limits of 20 and 70 years old. The choice of 20 as lowest age limit was due to the small number of pensioners below that age during the observation period. The upper limit was chosen based on the same idea proposed by Ribeiro (2006). We consider the age for retirement as the highest age limit; however, the population in our sample contains rural and urban retirees, and these two population groups have distinguished ages to retire. Moreover, we verified an overweight in the number of pensioners after the age of 60. For that reason, we found it reliable to consider age 70 as a consistent upper limit, although after this age we verify a small number of labor market exits –barely 1.4% of all retirement benefits. Once the retirement probabilities were estimated, the next step was to build up the disability life table by sex and age for the period of analysis.

### Results

Figure 1 shows the distribution of the disability labor market exits by sex and disability causes. As we can see, for both sexes, circulatory diseases were the most responsible for an overwhelming number of retirement benefits, corresponding to 29.2% of the total amount of retirees. In other countries, like Canada, this number is somewhat lower, representing only 13% to 12% of the disability causes from 1998 to 2000 (Office of the Chief Actuary, 2002), being it the third most incident morbidity causes that leads to early retirement. However, in the us, according to Dwyer and Mitchell (1999), the likelihood of retirement is greatest for chronic health conditions such as functional limitations and circulatory disorders.

Figure 1. Disability labor market by sex and causes. Brazil. 1999-2002

#####
Figure 1
Disability labor market by sex and causes. Brazil. 1999-2002

##### Source: Microdata from MPS/DATAPREV.

Moreover, in Brazil between 1999 and 2002, the musculoskeletal diseases and mental disorder are the second and third more prevalent diseases, representing, respectively, 19.5% and 12.4% of the total number of conceived pension benefits. In North American countries like Canada, between 1980 and 2000, these two diseases are also the most responsible for granted early retirement benefits. During this period, the musculoskeletal disorders have increased from 24% to 29% and the mental disorders double its incidence from 11% to 23% (Office of the Chief Actuary, 2002). These findings are also very consistent with other international study. Zayatz (2005), for example, affirms that in the United States, during the period 1998-2002, the musculoskeletal diseases and the mental disorders were also the most responsible diseases in granting retirement benefits. In many European countries, the mental illnesses are becoming more and more responsible for inflows into disability (OECD, 2009). In countries like Netherlands, Denmark, Sweden and Switzerland, in 2007, more than 40% of the inflow into disability happened due to bad mental health conditions. On the other hand, in the same countries, the musculoskeletal diseases have reduced its contribution to disability retirements between 2000 and 2007 (OECD, 2009).

Among the sexes, men have higher percentages of injuries than women; however, it is clearly visible that musculoskeletal diseases affect a larger percentage of women than men. The same findings are reported in many European countries. According to European Community (2000), the reason for it is that many workplaces are designed for the physical characteristics of men rather than women, leaving women more prone to repetitive strain injuries related complaints.

Other important point to highlight is relationship between disability benefits and its progression with age. According to Zayatz (1999 and 2005), the distribution of retirement benefits by disability causes are highly correlated with the age of the pensioner. In Brazil, Ribeiro (2006) also verifies that the health conditions of a laborer tend to deteriorate once the individual becomes older. As a direct consequence, we expect that the number of other disabilities increases with the age of the employee. According to OECD (2011), the same situation is found in European countries as Finland, the Slovak Republic, Spain, Sweden and the United Kingdom, where half of workers aged 50-64 leaves jobs through either unemployment or disability.

The Figure 2 and Tables A.2 and A.3 (in Appendix) show the disability hazards progression by age and sex of the retirees.

As we can see in the Figure 2, generally, the male retirement hazards by disability cause increases steadily until age 65 and after that it decreases. For females, however, these risks increase continuously up to the oldest age. If all insured workers had satisfied the minimum requirements to retire (like time of contribution and age), considering the minimum age of retirement and that every retiree will receive retirement benefits, we should expect neither the existence of entries in disability retirement for insured females aged over 60 years old nor insured men over 65 years old since this benefit is not granted to retirees. However, there are still entries on disability retirements after these ages. This is probably due to the fact that a high proportion of insured workers, especially women, do not meet the minimum requirements needed to retire (minimum age and/or years of service) and, thus, they remain insured and at risk of disability retirement (Gomes et al., 2010). This happens either because they have later joined the RGPS or due to the fact that they have very irregular trajectories of retirement contribution (Gomes et al., 2010). Additionally, it is also found that the majority of surveyed women enjoyed an individual and voluntary insurance program, especially after the age 60.

Figure 2. Disability retirement probabilities for RGPS insured workers, by sex and age. Brazil. 1999-2002

#####
Figure 2
Disability retirement probabilities for RGPS insured workers, by sex and age. Brazil. 1999-2002

##### Source: Microdata from MPS/DATAPREV.

Other factor to highlight is the dropping risk of disability retirement among men after age 65. This seems to indicate that these workers –who remain active after this age– are belonging to a selective group, characterized by employees with good health conditions. It may also indicate that many workers who are presenting vulnerable health characteristics are granted with a regular retirement benefit (or a care benefit), because these individuals are unable to work and, therefore, cannot contribute and maintain their membership. In addition to that, the drop in male probabilities after 65 years old might occur due to the overestimation of the denominator at these ages, possibly because it includes insured workers who meet the minimum period necessary to planned retirement, but they are delaying the application of this benefit.

In Tables A.2 and A.3 we see that, for both sexes, the risk of disability retirement is larger due to circulatory and musculoskeletal diseases. Among women, the crude disability retirement risk due to neoplasm is somewhat larger than for men. Among men, however, mental disorders are the most responsible for an overwhelming number of pensioners, especially among the young adult age groups. Moreover, the two tables also show that the risk of retirement due to injuries and mental disorders decreases with age. On the other hand, circulatory and musculoskeletal illnesses, especially among women, tend to increase with age.

### Discussion

In this paper, we try to describe the transition from occupational status to disability retirement for all workers from the Social Security Regime. In order to fulfill this objective, we estimate multi-decrement disability retirement life tables by sex and age for the period of 1999-2002, using the DATAPREV/MPS and administrative information from the CNIS as sources for our analysis.

After we analyzed the intrinsic pattern of the table, we observed that for men the disability hazards increase progressively until age 65 and after that they decrease, although they still show high values until the age 70. Among women we observed that these risks increase continuously up to the oldest age. The decline in the male retirement hazards after age 65 may guide us to two conclusions. First, there is some kind of selective group among the retirees with better health conditions keeping them active in the labor market. Second, it is because the fragile retirees acquire another sort of benefit, or they simply cannot financially contribute to RGPS and keep their social benefit. Moreover, there are still a number of labor market exits, even after the upper age limit to retire. This can be explained by the presence of female employees who did not fulfill the prerequisites to retire until the minimum age of pension. In this way, they still belong to the risk group of disability retirement for a longer period.

During the period of analysis, we verified that for both sexes the risk of disability retirement is largest due to circulatory diseases and musculoskeletal diseases. As the employee age increases injuries, mental disorders and nervous system illnesses tend to decrease. However, other illnesses like circulatory and musculoskeletal diseases become more common, especially among women. Differences in the pattern of disability retirement between the sexes can be partially explained by the age structure of retirement.

A word of caution is necessary since comparison with other studies regarding the same subject are difficult to be carried out, either because of the distinguished retirement definition adopted in each study and country or due to pre-requisites for the grant of retirement benefits. In addition to that, many studies are limited by displaying only graphics, not providing the values of probabilities by age and sex. Additionally, as Grushka (2010) notes, the people exposed to the risk of disability retirement can be affected by different levels of selectivity. Thus, the aim of this work was only to present results of disability retirement in Brazil and, when possible, establishes short comparisons with other countries; however, given the difficulty to define disability retirement in each country, we have avoided further deeper assessments.

The knowledge of these disability retirement hazards creates opportunity to develop policies of work prevention and health and to promote a better work environment. In this way, we expect that these tables can be used to forecast or simulate the numbers of beneficiaries in later periods. Thus, we can predict the future social security costs. The retirement hazards are another utility provided by this work. They can be used by the social security market as a reference point for planning future pension costs because our disability life tables better replicate the reality of the country than the tables used by the private sector. This makes sense given that all beneficiaries from private security are linked with the RGPS (Coletânea, 2007).

Last but not least, this study also hopes to give an initial understanding about the disability retirement hazards in Brazil, since in international as well as in national literature few studies are known concerning these matters (Gomes, 2008; Zayatz, 2005).

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### Appendix Table A.1

##### Table A.1
Number and population at risk of disability retirement, by sex and age. Brazil. 1999-2002

Age | Male | Female | Total
| nLx | nIx,C+ | nLx | nIx,C+ | nLx | nIx,C+
20 | 2,383,343 | 218 | 1,550,307 | 72 | 3,933,650 | 290
21 | 2,732,673 | 408 | 1,754,625 | 94 | 4,487,297 | 502
22 | 2,873,070 | 578 | 1,834,833 | 175 | 4,707,903 | 753
23 | 2,949,847 | 883 | 1,899,026 | 268 | 4,848,873 | 1,151
24 | 2,955,062 | 1,123 | 1,892,079 | 355 | 4,847,141 | 1,478
25 | 2,931,142 | 1,504 | 1,872,079 | 445 | 4,803,988 | 1,949
26 | 2,915,927 | 1,726 | 1,852,846 | 627 | 4,768,378 | 2,353
27 | 2,812,059 | 2,083 | 1,778,895 | 707 | 4,590,953 | 2,790
28 | 2,831,066 | 2,368 | 1,775,255 | 900 | 4,606,322 | 3,268
29 | 2,701,811 | 2,652 | 1,704,224 | 1,007 | 4,406,035 | 3,659
30 | 2,685,729 | 3,043 | 1,668,074 | 1,210 | 4,353,803 | 4,253
31 | 2,582,866 | 3,410 | 1,610,934 | 1,423 | 4,193,800 | 4,833
32 | 2,576,920 | 3,697 | 1,587,976 | 1,581 | 4,164,896 | 5,278
33 | 2,479,184 | 4,059 | 1,550,378 | 1,793 | 4,029,563 | 5,852
34 | 2,455,349 | 4,457 | 1,535,355 | 1,958 | 3,990,704 | 6,415
35 | 2,416,227 | 4,950 | 1,529,315 | 2,310 | 3,945,542 | 7,260
36 | 2,358,543 | 5,270 | 1,494,809 | 2,562 | 3,853,352 | 7,832
37 | 2,288,525 | 5,532 | 1,461,067 | 2,838 | 3,749,592 | 8,370
38 | 2,186,709 | 6,012 | 1,400,606 | 3,112 | 3,587,315 | 9,124
39 | 2,066,345 | 6,452 | 1,330,716 | 3,435 | 3,397,061 | 9,887
40 | 2,025,729 | 7,100 | 1,295,443 | 3,716 | 3,321,172 | 10,816
41 | 1,901,729 | 7,693 | 1,228,440 | 4,089 | 3,130,169 | 11,782
42 | 1,852,413 | 8,071 | 1,185,313 | 4,421 | 3,037,726 | 12,492
43 | 1,767,359 | 8,538 | 1,127,801 | 4,945 | 2,895,160 | 13,483
44 | 1,674,091 | 9,056 | 1,065,845 | 5,075 | 2,739,936 | 14,131
45 | 1,588,079 | 9,554 | 1,006,006 | 5,425 | 2,594,084 | 14,979
46 | 1,506,724 | 10,035 | 946,860 | 5,655 | 2,453,583 | 15,690
47 | 1,387,377 | 10,173 | 873,079 | 5,995 | 2,260,456 | 16,168
48 | 1,320,524 | 10,526 | 812,139 | 6,050 | 2,132,663 | 16,576
49 | 1,186,692 | 10,463 | 730,480 | 6,077 | 1,917,173 | 16,540
50 | 1,124,173 | 10,948 | 687,060 | 6,666 | 1,811,234 | 17,614
51 | 1,002,048 | 11,000 | 620,084 | 7,025 | 1,622,132 | 18,025
52 | 932,610 | 10,776 | 581,704 | 7,376 | 1,514,315 | 18,152
53 | 818,965 | 10,372 | 525,887 | 7,296 | 1,344,852 | 17,668
54 | 726,839 | 10,304 | 479,607 | 7,596 | 1,206,446 | 17,900
55 | 640,154 | 10,200 | 435,405 | 7,632 | 1,075,560 | 17,832
56 | 574,503 | 9,925 | 403,588 | 7,926 | 978,091 | 17,851
57 | 513,728 | 10,032 | 372,847 | 8,302 | 886,575 | 18,334
58 | 466,054 | 9,758 | 436,988 | 8,456 | 813,041 | 18,214
59 | 399,515 | 9,898 | 320,895 | 8,776 | 720,411 | 18,674
60 | 378,723 | 10,311 | 251,940 | 9,096 | 630,663 | 19,407
61 | 326,992 | 10,315 | 181,138 | 8,063 | 508,129 | 18,378
62 | 298,878 | 10,013 | 149,369 | 7,364 | 448,247 | 17,377
63 | 260,019 | 9,730 | 120,324 | 6,816 | 380,343 | 16,546
64 | 241,781 | 9,240 | 97,477 | 5,961 | 339,259 | 15,201
65 | 172,179 | 7,738 | 75,180 | 5,073 | 247,359 | 12,811
66 | 125,690 | 5,689 | 57,649 | 4,218 | 183,339 | 9,907
67 | 95,643 | 4,053 | 42,395 | 3,648 | 138,038 | 7,701
68 | 78,122 | 2,652 | 32,272 | 2,711 | 110,395 | 5,363
69 | 61,127 | 1,901 | 24,387 | 2,120 | 85,514 | 4,021
70 | 54,681 | 1,329 | 19,699 | 1,668 | 74,381 | 2,997
71 | 42,257 | 857 | 14,845 | 1,196 | 57,102 | 2,053
72 | 35,860 | 530 | 11,915 | 956 | 47,775 | 1,486
73 | 28,488 | 295 | 9,467 | 657 | 37,956 | 952
74 | 22,954 | 193 | 7,542 | 491 | 30,496 | 684
75 | 18,498 | 127 | 5,934 | 383 | 24,432 | 510
76 | 14,896 | 83 | 4,661 | 260 | 19,557 | 343
77 | 11,687 | 51 | 3,763 | 197 | 15,450 | 248
78 | 9,438 | 39 | 3,023 | 143 | 12,461 | 182
Total | 77,869,616 | 329,993 | 49,242,221 | 216,392 | 127,111,838 | 546,385

##### Source: Microdata from MPS/DATAPREV.

### Appendix Table A.2

##### Table A.2
Male probability disability retirement hazards according to health cause and age (by 10.000). Brazil. 01/01/1999 to 31/12/2002

Age | Probability | Total
| Infectious | Neoplasms | Nutritional/metabolic | Mental disorders | Nervous system | Eye diseases | Circulatory | Respiratory | Musculoskeletal | Genitourinary | Injuries | Others | Non-information |
20 | 0.025 | 0.101 | 0.000 | 0.185 | 0.164 | 0.080 | 0.034 | 0.000 | 0.029 | 0.021 | 0.252 | 0.000 | 0.025 | 0.915
21 | 0.050 | 0.150 | 0.011 | 0.388 | 0.221 | 0.128 | 0.146 | 0.005 | 0.020 | 0.077 | 0.414 | 0.006 | 0.047 | 1.661
22 | 0.104 | 0.184 | 0.019 | 0.627 | 0.293 | 0.176 | 0.213 | 0.011 | 0.038 | 0.127 | 0.565 | 0.011 | 0.065 | 2.433
23 | 0.182 | 0.207 | 0.026 | 0.893 | 0.379 | 0.228 | 0.257 | 0.018 | 0.082 | 0.172 | 0.712 | 0.016 | 0.081 | 3.253
24 | 0.280 | 0.227 | 0.035 | 1.177 | 0.476 | 0.283 | 0.296 | 0.027 | 0.149 | 0.216 | 0.858 | 0.022 | 0.098 | 4.144
25 | 0.396 | 0.252 | 0.044 | 1.470 | 0.583 | 0.344 | 0.351 | 0.038 | 0.235 | 0.259 | 1.010 | 0.027 | 0.119 | 5.130
26 | 0.530 | 0.277 | 0.055 | 1.779 | 0.701 | 0.411 | 0.409 | 0.049 | 0.344 | 0.302 | 1.163 | 0.033 | 0.143 | 6.195
27 | 0.686 | 0.296 | 0.066 | 2.109 | 0.831 | 0.481 | 0.456 | 0.062 | 0.476 | 0.341 | 1.315 | 0.038 | 0.166 | 7.323
28 | 0.861 | 0.318 | 0.078 | 2.452 | 0.970 | 0.556 | 0.512 | 0.076 | 0.629 | 0.380 | 1.470 | 0.044 | 0.193 | 8.539
29 | 1.049 | 0.348 | 0.093 | 2.798 | 1.118 | 0.638 | 0.598 | 0.091 | 0.800 | 0.421 | 1.634 | 0.050 | 0.226 | 9.865
30 | 1.247 | 0.394 | 0.112 | 3.141 | 1.273 | 0.729 | 0.733 | 0.108 | 0.986 | 0.465 | 1.812 | 0.056 | 0.268 | 11.324
31 | 1.465 | 0.458 | 0.132 | 3.466 | 1.430 | 0.834 | 0.897 | 0.124 | 1.172 | 0.514 | 2.007 | 0.062 | 0.318 | 12.877
32 | 1.707 | 0.533 | 0.154 | 3.780 | 1.591 | 0.951 | 1.075 | 0.140 | 1.359 | 0.565 | 2.214 | 0.067 | 0.373 | 14.510
33 | 1.956 | 0.620 | 0.180 | 4.101 | 1.762 | 1.073 | 1.300 | 0.158 | 1.571 | 0.619 | 2.430 | 0.073 | 0.437 | 16.280
34 | 2.196 | 0.715 | 0.213 | 4.450 | 1.947 | 1.194 | 1.603 | 0.180 | 1.832 | 0.673 | 2.652 | 0.080 | 0.509 | 18.246
35 | 2.410 | 0.819 | 0.256 | 4.846 | 2.150 | 1.306 | 2.018 | 0.207 | 2.166 | 0.728 | 2.878 | 0.091 | 0.591 | 20.466
36 | 2.600 | 0.918 | 0.302 | 5.304 | 2.378 | 1.401 | 2.484 | 0.232 | 2.576 | 0.780 | 3.100 | 0.104 | 0.677 | 22.858
37 | 2.775 | 1.016 | 0.347 | 5.814 | 2.629 | 1.483 | 2.982 | 0.256 | 3.044 | 0.832 | 3.322 | 0.118 | 0.767 | 25.384
38 | 2.935 | 1.128 | 0.405 | 6.348 | 2.891 | 1.566 | 3.598 | 0.286 | 3.568 | 0.886 | 3.551 | 0.135 | 0.868 | 28.167
39 | 3.080 | 1.270 | 0.487 | 6.883 | 3.157 | 1.665 | 4.420 | 0.334 | 4.145 | 0.942 | 3.797 | 0.156 | 0.992 | 31.327
40 | 3.208 | 1.459 | 0.606 | 7.392 | 3.415 | 1.794 | 5.534 | 0.409 | 4.770 | 1.005 | 4.065 | 0.182 | 1.148 | 34.988
41 | 3.311 | 1.693 | 0.763 | 7.888 | 3.650 | 1.947 | 6.922 | 0.517 | 5.440 | 1.068 | 4.362 | 0.217 | 1.346 | 39.125
42 | 3.390 | 1.963 | 0.949 | 8.389 | 3.868 | 2.116 | 8.525 | 0.652 | 6.158 | 1.129 | 4.681 | 0.258 | 1.579 | 43.658
43 | 3.457 | 2.269 | 1.164 | 8.874 | 4.094 | 2.308 | 10.373 | 0.804 | 6.928 | 1.198 | 5.016 | 0.303 | 1.833 | 48.621
44 | 3.526 | 2.612 | 1.404 | 9.326 | 4.352 | 2.533 | 12.492 | 0.965 | 7.757 | 1.283 | 5.362 | 0.346 | 2.092 | 54.050
45 | 3.610 | 2.995 | 1.670 | 9.725 | 4.665 | 2.800 | 14.910 | 1.124 | 8.651 | 1.394 | 5.713 | 0.383 | 2.342 | 59.980
46 | 3.699 | 3.415 | 1.964 | 10.057 | 5.040 | 3.114 | 17.569 | 1.252 | 9.519 | 1.545 | 6.059 | 0.405 | 2.579 | 66.215
47 | 3.784 | 3.873 | 2.286 | 10.336 | 5.463 | 3.469 | 20.449 | 1.355 | 10.357 | 1.730 | 6.404 | 0.414 | 2.813 | 72.732
48 | 3.881 | 4.369 | 2.633 | 10.581 | 5.921 | 3.857 | 23.640 | 1.478 | 11.301 | 1.927 | 6.763 | 0.425 | 3.049 | 79.824
49 | 4.001 | 4.904 | 3.000 | 10.811 | 6.405 | 4.270 | 27.230 | 1.666 | 12.486 | 2.113 | 7.152 | 0.453 | 3.293 | 87.787
50 | 4.161 | 5.480 | 3.382 | 11.048 | 6.905 | 4.701 | 31.311 | 1.965 | 14.049 | 2.266 | 7.586 | 0.513 | 3.550 | 96.915
51 | 4.360 | 6.043 | 3.779 | 11.272 | 7.416 | 5.107 | 35.712 | 2.368 | 15.921 | 2.378 | 8.028 | 0.617 | 3.809 | 106.807
52 | 4.590 | 6.593 | 4.194 | 11.470 | 7.946 | 5.494 | 40.376 | 2.844 | 18.012 | 2.462 | 8.465 | 0.753 | 4.067 | 117.266
53 | 4.848 | 7.210 | 4.628 | 11.670 | 8.500 | 5.925 | 45.553 | 3.404 | 20.423 | 2.533 | 8.957 | 0.906 | 4.339 | 128.895
54 | 5.132 | 7.972 | 5.080 | 11.898 | 9.083 | 6.460 | 51.496 | 4.059 | 23.255 | 2.602 | 9.562 | 1.058 | 4.642 | 142.298
55 | 5.440 | 8.958 | 5.548 | 12.181 | 9.702 | 7.160 | 58.458 | 4.820 | 26.610 | 2.681 | 10.337 | 1.193 | 4.990 | 158.077
56 | 5.809 | 10.209 | 6.027 | 12.505 | 10.277 | 8.010 | 66.475 | 5.617 | 30.368 | 2.752 | 11.304 | 1.309 | 5.394 | 176.056
57 | 6.241 | 11.674 | 6.516 | 12.852 | 10.806 | 8.969 | 75.380 | 6.444 | 34.462 | 2.808 | 12.423 | 1.416 | 5.841 | 195.833
58 | 6.680 | 13.290 | 7.027 | 13.243 | 11.405 | 10.061 | 85.116 | 7.403 | 39.070 | 2.874 | 13.664 | 1.518 | 6.320 | 217.672
59 | 7.067 | 14.994 | 7.569 | 13.702 | 12.192 | 11.309 | 95.627 | 8.599 | 44.370 | 2.980 | 14.996 | 1.618 | 6.818 | 241.840
60 | 7.346 | 16.724 | 8.154 | 14.249 | 13.285 | 12.738 | 106.857 | 10.133 | 50.537 | 3.152 | 16.385 | 1.719 | 7.320 | 268.601
61 | 7.556 | 18.911 | 8.953 | 15.131 | 15.099 | 14.741 | 121.456 | 12.439 | 59.124 | 3.465 | 18.186 | 1.841 | 7.946 | 304.847
62 | 7.736 | 21.595 | 9.961 | 16.331 | 17.555 | 17.300 | 139.461 | 15.446 | 70.014 | 3.901 | 20.418 | 1.981 | 8.705 | 350.403
63 | 7.825 | 24.132 | 10.918 | 17.484 | 20.030 | 19.828 | 156.898 | 18.509 | 80.877 | 4.347 | 22.553 | 2.109 | 9.419 | 394.929
64 | 7.766 | 25.877 | 11.566 | 18.221 | 21.903 | 21.736 | 169.788 | 20.979 | 89.386 | 4.693 | 24.065 | 2.198 | 9.909 | 428.087
65 | 7.498 | 26.186 | 11.645 | 18.177 | 22.551 | 22.437 | 174.157 | 22.210 | 96.391 | 4.828 | 24.425 | 2.215 | 9.997 | 439.539
66 | 7.062 | 25.488 | 11.328 | 17.595 | 22.388 | 22.322 | 172.654 | 22.633 | 103.397 | 4.826 | 23.985 | 2.182 | 9.803 | 436.177
67 | 6.496 | 24.213 | 10.788 | 16.721 | 21.831 | 21.783 | 167.931 | 22.680 | 95.819 | 4.760 | 20.580 | 2.119 | 9.444 | 424.893
68 | 5.742 | 21.717 | 9.765 | 15.187 | 20.256 | 20.233 | 156.012 | 21.704 | 88.242 | 4.520 | 17.530 | 1.994 | 8.743 | 395.348
69 | 4.741 | 17.354 | 8.002 | 12.627 | 17.041 | 17.083 | 132.919 | 19.057 | 77.221 | 3.994 | 14.479 | 1.780 | 7.521 | 337.206
70 | 3.433 | 10.480 | 5.240 | 8.673 | 11.564 | 11.744 | 94.677 | 14.093 | 57.638 | 3.072 | 12.467 | 1.445 | 5.601 | 240.126

##### Source: Microdata from MPS/DATAPREV.

### Appendix Table A.3

##### Table A.3
Female probability disability retirement hazards according to health cause and age

Age | Probability | Total
| Infectious | Neoplasms | Nutritional/metabolic | Mental disorders | Nervous system | Eye diseases | Circulatory | Respiratory | Musculoskeletal | Genitourinary | Injuries | Others | Non-information |
20 | 0.026 | 0.090 | 0.000 | 0.071 | 0.052 | 0.013 | 0.026 | 0.000 | 0.032 | 0.013 | 0.071 | 0.026 | 0.045 | 0.464
21 | 0.052 | 0.093 | -0.003 | 0.151 | 0.051 | 0.040 | 0.002 | 0.017 | 0.065 | 0.042 | 0.081 | 0.027 | 0.042 | 0.610
22 | 0.093 | 0.097 | 0.003 | 0.217 | 0.077 | 0.004 | 0.009 | 0.027 | 0.103 | 0.070 | 0.100 | 0.027 | 0.046 | 0.873
23 | 0.147 | 0.105 | 0.016 | 0.287 | 0.125 | 0.042 | 0.042 | 0.032 | 0.152 | 0.097 | 0.129 | 0.027 | 0.056 | 1.256
24 | 0.209 | 0.123 | 0.032 | 0.374 | 0.188 | 0.094 | 0.096 | 0.037 | 0.215 | 0.125 | 0.165 | 0.026 | 0.071 | 1.756
25 | 0.278 | 0.155 | 0.048 | 0.497 | 0.262 | 0.149 | 0.166 | 0.043 | 0.299 | 0.155 | 0.208 | 0.027 | 0.091 | 2.376
26 | 0.354 | 0.197 | 0.067 | 0.642 | 0.349 | 0.215 | 0.255 | 0.048 | 0.399 | 0.186 | 0.259 | 0.027 | 0.116 | 3.114
27 | 0.440 | 0.247 | 0.090 | 0.801 | 0.453 | 0.297 | 0.367 | 0.051 | 0.513 | 0.218 | 0.319 | 0.028 | 0.146 | 3.970
28 | 0.533 | 0.309 | 0.114 | 0.990 | 0.570 | 0.386 | 0.497 | 0.054 | 0.645 | 0.252 | 0.386 | 0.029 | 0.181 | 4.945
29 | 0.629 | 0.387 | 0.137 | 1.222 | 0.692 | 0.471 | 0.640 | 0.060 | 0.800 | 0.288 | 0.460 | 0.031 | 0.221 | 6.039
30 | 0.725 | 0.485 | 0.156 | 1.516 | 0.815 | 0.539 | 0.791 | 0.072 | 0.983 | 0.330 | 0.539 | 0.036 | 0.264 | 7.251
31 | 0.826 | 0.604 | 0.167 | 1.883 | 0.937 | 0.587 | 0.921 | 0.084 | 1.175 | 0.377 | 0.626 | 0.042 | 0.311 | 8.538
32 | 0.933 | 0.739 | 0.172 | 2.312 | 1.062 | 0.621 | 1.032 | 0.095 | 1.374 | 0.430 | 0.720 | 0.048 | 0.362 | 9.900
33 | 1.040 | 0.892 | 0.176 | 2.785 | 1.192 | 0.649 | 1.169 | 0.113 | 1.606 | 0.486 | 0.821 | 0.057 | 0.417 | 11.403
34 | 1.140 | 1.064 | 0.185 | 3.284 | 1.327 | 0.679 | 1.379 | 0.144 | 1.899 | 0.542 | 0.925 | 0.069 | 0.475 | 13.112
35 | 1.228 | 1.255 | 0.203 | 3.790 | 1.470 | 0.719 | 1.705 | 0.196 | 2.280 | 0.595 | 1.032 | 0.085 | 0.536 | 15.093
36 | 1.299 | 1.450 | 0.224 | 4.300 | 1.619 | 0.760 | 2.105 | 0.278 | 2.742 | 0.642 | 1.132 | 0.106 | 0.594 | 17.253
37 | 1.358 | 1.651 | 0.246 | 4.828 | 1.774 | 0.798 | 2.546 | 0.386 | 3.266 | 0.686 | 1.226 | 0.130 | 0.652 | 19.547
38 | 1.410 | 1.877 | 0.276 | 5.377 | 1.936 | 0.844 | 3.097 | 0.505 | 3.864 | 0.729 | 1.329 | 0.158 | 0.714 | 22.116
39 | 1.462 | 2.149 | 0.322 | 5.950 | 2.105 | 0.911 | 3.824 | 0.622 | 4.547 | 0.777 | 1.455 | 0.190 | 0.788 | 25.101
40 | 1.519 | 2.490 | 0.393 | 6.552 | 2.282 | 1.010 | 4.795 | 0.725 | 5.326 | 0.832 | 1.619 | 0.224 | 0.879 | 28.644
41 | 1.576 | 2.900 | 0.480 | 7.213 | 2.450 | 1.148 | 5.963 | 0.800 | 6.146 | 0.899 | 1.822 | 0.260 | 0.991 | 32.648
42 | 1.629 | 3.367 | 0.576 | 7.931 | 2.611 | 1.318 | 7.284 | 0.857 | 6.999 | 0.974 | 2.055 | 0.299 | 1.119 | 37.018
43 | 1.687 | 3.886 | 0.696 | 8.659 | 2.786 | 1.508 | 8.826 | 0.914 | 7.969 | 1.053 | 2.316 | 0.341 | 1.259 | 41.900
44 | 1.756 | 4.454 | 0.853 | 9.352 | 3.002 | 1.710 | 10.658 | 0.989 | 9.140 | 1.130 | 2.603 | 0.387 | 1.406 | 47.440
45 | 1.844 | 5.066 | 1.061 | 9.963 | 3.281 | 1.913 | 12.848 | 1.100 | 10.598 | 1.200 | 2.915 | 0.436 | 1.556 | 53.781
46 | 1.948 | 5.746 | 1.319 | 10.456 | 3.657 | 2.087 | 15.278 | 1.230 | 12.229 | 1.260 | 3.251 | 0.483 | 1.712 | 60.656
47 | 2.062 | 6.498 | 1.617 | 10.860 | 4.112 | 2.237 | 17.904 | 1.364 | 13.980 | 1.316 | 3.614 | 0.527 | 1.875 | 67.967
48 | 2.193 | 7.284 | 1.958 | 11.233 | 4.599 | 2.411 | 20.900 | 1.533 | 16.015 | 1.369 | 4.003 | 0.579 | 2.043 | 76.119
49 | 2.344 | 8.071 | 2.341 | 11.630 | 5.070 | 2.654 | 24.443 | 1.764 | 18.503 | 1.422 | 4.415 | 0.646 | 2.211 | 85.513
50 | 2.520 | 8.821 | 2.767 | 12.109 | 5.475 | 3.013 | 28.708 | 2.086 | 21.611 | 1.477 | 4.852 | 0.739 | 2.375 | 96.554
51 | 2.721 | 9.431 | 3.203 | 12.636 | 5.760 | 3.456 | 33.306 | 2.488 | 24.956 | 1.530 | 5.265 | 0.867 | 2.514 | 108.133
52 | 2.941 | 9.924 | 3.650 | 13.175 | 5.956 | 3.953 | 38.120 | 2.950 | 28.428 | 1.577 | 5.655 | 1.023 | 2.629 | 119.982
53 | 3.185 | 10.458 | 4.156 | 13.773 | 6.148 | 4.551 | 43.734 | 3.490 | 32.600 | 1.628 | 6.093 | 1.194 | 2.753 | 133.762
54 | 3.456 | 11.188 | 4.767 | 14.480 | 6.419 | 5.297 | 50.732 | 4.125 | 38.043 | 1.691 | 6.651 | 1.366 | 2.921 | 151.135
55 | 3.757 | 12.272 | 5.533 | 15.345 | 6.853 | 6.238 | 59.697 | 4.872 | 45.330 | 1.776 | 7.399 | 1.525 | 3.165 | 173.762
56 | 4.075 | 13.907 | 6.497 | 16.389 | 7.474 | 7.377 | 70.383 | 5.738 | 54.276 | 1.894 | 8.322 | 1.631 | 3.464 | 201.426
57 | 4.408 | 15.990 | 7.628 | 17.577 | 8.226 | 8.680 | 82.402 | 6.709 | 64.499 | 2.041 | 9.370 | 1.691 | 3.798 | 233.020
58 | 4.776 | 18.223 | 8.859 | 18.881 | 9.074 | 10.146 | 96.123 | 7.779 | 76.278 | 2.197 | 10.570 | 1.769 | 4.196 | 268.869
59 | 5.197 | 20.309 | 10.121 | 20.271 | 9.982 | 11.776 | 111.913 | 8.937 | 89.891 | 2.342 | 11.947 | 1.925 | 4.687 | 309.300
60 | 5.692 | 21.950 | 11.346 | 21.716 | 10.917 | 13.568 | 130.143 | 10.176 | 105.619 | 2.456 | 13.529 | 2.222 | 5.302 | 354.637
61 | 6.361 | 23.178 | 12.592 | 23.486 | 11.922 | 15.646 | 152.255 | 11.626 | 125.023 | 2.549 | 15.436 | 2.767 | 6.132 | 408.974
62 | 7.191 | 24.191 | 13.905 | 25.600 | 13.020 | 18.012 | 178.004 | 13.294 | 147.916 | 2.634 | 17.652 | 3.518 | 7.157 | 472.094
63 | 8.031 | 24.942 | 15.197 | 27.655 | 14.146 | 20.478 | 205.224 | 14.982 | 171.957 | 2.697 | 19.993 | 4.315 | 8.240 | 537.857
64 | 8.729 | 25.386 | 16.382 | 29.249 | 15.233 | 22.857 | 231.750 | 16.493 | 194.803 | 2.724 | 22.276 | 4.997 | 9.245 | 600.125
65 | 9.136 | 25.477 | 17.371 | 29.981 | 16.213 | 24.963 | 255.416 | 17.628 | 214.112 | 2.702 | 24.319 | 5.404 | 10.037 | 652.759
66 | 9.351 | 25.246 | 20.918 | 32.917 | 17.131 | 29.439 | 277.667 | 18.520 | 231.445 | 2.640 | 26.243 | 6.192 | 10.704 | 699.851
67 | 9.475 | 24.722 | 22.389 | 35.053 | 18.033 | 33.922 | 299.945 | 19.300 | 248.365 | 2.548 | 28.171 | 7.237 | 11.340 | 745.494
68 | 9.357 | 23.861 | 24.979 | 37.766 | 18.850 | 37.469 | 320.086 | 19.771 | 262.527 | 2.410 | 29.919 | 7.745 | 11.806 | 783.549
69 | 8.847 | 22.616 | 26.329 | 35.368 | 19.517 | 41.262 | 335.924 | 19.735 | 271.592 | 2.215 | 31.304 | 6.245 | 11.968 | 807.878
70 | 7.792 | 20.942 | 19.968 | 23.377 | 19.968 | 32.630 | 345.294 | 18.994 | 273.215 | 1.948 | 32.143 | 4.383 | 11.688 | 812.341

##### Source: Microdata from MPS/DATAPREV

### Author notes

Marília M. F. Gomes has graduated in Statistics at the University of Brasilia (2005). She holds an M.Sc (2008) and PhD (2011) in Demography at the Center of Regional Planning and Development CEDEPLAR/FACE/UFMG. She is currently Associate Professor at the University of Brasilia (Campus Gama), Research Scientist at the Laboratory of Population& Development (LP&D/NEUR/CEAM/UNB) and Assistant Professor at the Graduate Program in Biomedical Engineering (UNB/ Campus Gama). Her research interests are: Probability and Statistics, Applied Statistics, Population and Health, Technical Analysis Population, Aging, Mortality and Welfare.
Everton E. C Lima has graduated in Political and Social Sciences at the Université Libre de Bruxeles in 2005. He holds an M.Sc in Sociology granted by the Université Libre de Bruxeles in 2006, and Ph.D. in Demography, CEDEPLAR/UFMG, in 2010. He worked as a Research Scientist at the Max Planck Institute for Demographic Research, 2008-2009; he is currently Assistant Professor at the Philosophy Institute and Human Science IFCH/UNICAMP and Research Scientist at the Center for Population Studies-NEPO/UNICAMP. His research interests are Fertility, Formal Demography, Small Area Estimation and Spatial Demography. Recent publications: B. L. Queiroz, E. E. Campos de Lima, F. H. Freire and M. R. Gonzaga, “Adult mortality estimates for small areas in Brazil, 1980-2010: a methodological approach”, The Lancet, vol. 381, 2013; E. E. Campos de Lima y B. L. Queiroz, “A evolução do sub-registro de mortes e causas de óbitos mal definidas em Minas Gerais:diferenciais regionais”, Rev. Bras. Estud. Popul, vol. 28, num.2, 2011, pp. 303-320. [On line].
Moema G. B. Fígoli is graduated in Mathematics at the University of Brasilia (1976). She holds an undergraduate Bachelors degree in Statistics at the University of Brasilia (1982) and a Ph.D. in Demography at the Demography at the Center of Regional Planning andDevelopment CEDEPLAR/FACE/UFMG (1997). She worked as Research Scientist at the University of Chicago (1995), and she holds two postdoctoral residences at International Institute for Applied Systems Analysis (2006) and at the University of Michigan (2002). She is currently Associate Professor at the Federal University of Minas Gerais (UFMG). She has interests in the area of demography, social security and the population forecasting. Recent publications: M. M. F. Gomes, C. M. Turra, M. G. B. Fígoli, Y. Duarte y M.Lebrao, “Associação entre mortalidade e estado marital: uma análise para idosos residentesno Município de São Paulo, Brasil, Estudo sabe, 2000 e 2006”, Cadernos de Saúde Pública (ENSP Impresso), vol. 29, 2013, pp. 566-578; M. M. F. Gomes, M. G. B. Fígoli y A. J.F. Ribeiro, “Da atividade à invalidez permanente: um estudo utilizando dados do Regime geral de Previdência Social (RGPS) do Brasil no período 1999-2002”, in Revista Brasileira deEstudos de População (Impresso), vol. 27, 2010, pp. 1-20.
Marcos R. Gonzaga holds a M.Sc and PhD in Demography granted by the Centre for Development and Regional Planning at the Federal University of Minas Gerais (CEDEPLAR/UFMG). He is graduated in Statistics at the Federal University of Minas Gerais. He has worked as Visiting Researcher at the University of Wisconsin-Madison (USA) and developed activities in the population forecast laboratory at CEDEPLAR. Currently, he is Assistant Professor at the Department of Demography and Actuarial Science at the Federal University of Rio Grande do Norte. He conducts research on methods of population forecasting and estimates of mortality for small areas. Recent publications: M. R. Gonzaga, B. L. Queiroz y C. J. Machado, “Compressão da mortalidade: um estudo da variabilidade da idade à morte na população do Estado de São Paulo, Brasil, 1980-2005”, Cadernos de Saúde Pública, vol. 25, 2009, pp. 1475- 85; H. M. Assis, M. R. Gonzaga, R. N. Rodrigues y C. J. Machado, “Utilização da história clínica perinatal para compreensão da saúde materna e do recém-nascido: enfoque na qualidade da informação”, Cadernos Saúde Coletiva (UFRJ), vol. 18, 2010, pp. 385-391.