# **Annex 2:  Moving from Cross-Sectional to Longitudinal Cohorts**

The main source of information used in this paper are the microdata from the Pesquisa Nacional por Amostra de Domicílios (PNAD) –National Household Sample Survey. This survey is goes to the field each year (except the years of the Census) and is managed by the Instituto Brasileiro de Geografia e Estatística (IBGE) - Brazilian Institute of Geography and Statistics. It is a comprehensive research on socio-economic characteristics of the population and households in Brazil. The issues include topics such as income, occupations, social security, education, fertility, etc. Each year are interviewed around 0.25% of the Brazilian population, which corresponds to just over 420,000 records. For this exercise we used the PNADs for years 1990, 1996, 2001, and 2006. In addition, we relied on aggregate data from the Statistical Yearbook of Social Security, published yearly by the Ministry of Social Security.

For the analysis the population was divided in the following groups: a) _Workers "with carteira."_ This group includes all individuals that work in the formal private sector. Or, for the purposes of this paper, which contribute to the social security system. Thus, civil servants and military are excluded from our analysis b) _Workers "without carteira."_ This group includes all workers who are in the informal sector. Or, for the purposes of this paper, which do not contribute to the basic social security system.

c) _Unemployed._ This group included all unemployed individuals. It means they are not working they are looking for a job.

d) _Retired workers._ This group includes all who receive old-age benefits and are not in the labor market. This caveat is important, because in Brazil a worker can retire, receive their benefit and continue working, without any changes, either in his situation in the labor market, either in his situation as beneficiary.

People were then divided by cohorts of 5 years, according to the following division: 16-20 years; 21-25 years;...; 66-70; and 71+. All persons under the age of 16 years were excluded from the dataset because that is the legal age of initiation of work and contribution to social security.

The main complication at this stage was with the retirees. The PNAD does not provide information on whether the person receives his retirement from the Regime Geral de Previdência Social (RGPS) - General Social Security System or the National Social Security Institute (i.e., if the person is a retiree from the private or public sector). To this end, the data from the survey was matched to the data from the Anuário Estatístico de Previdência Social (AEPS) - Statistical Yearbook of Social Security, which contains retirees by sector and age groups. Given that the age groups are not the same some additional adjustments were necessary. As the age-cohorts made by AEPS start from an age x and our cohorts from an age x + 1, the two information have only 4 years in common (80% of data). Thus, we built a new cohort x’, composed of 0.8 * (similar cohort of AEPS) + 0.2 * (previous cohort of AEPS).

## **Moving from cross-sectional to longitudinal cohorts**

With the pseudo-panel formed by the PNADs it is possible to describe the behavior along the life cycle of a _few_ cohorts. For example, the cohort aged x in 2006 was x-5 years old in 2001, x-10 years old in 1996 and so on. But the question we want to answer is: what will happen with that cohort in 5 years from now? And in n years from now? This means trying to predict the percentage of individuals of that cohort that will be in each of the four groups that defined above in the next n years. We considered two methods.

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