The statistics on the total number of pensioners in the INSS statistical report consider only those pensions recorded as currently registered on December (31{mathrm{st}}), so a comparison between the distributions of pensioners (by type of pension, gender and age) in the CSWL as of December (31{mathrm{st}}) and the INSS makes sense, because the moment in time considered is the same.
The SR sample obtained seems to be the best at representing the population of pensioners by age, gender and type of pension, with the larger one being better.
In the case of the CSWL the distribution of the population of pensioners by age, gender, and type of pension is known from the statistical report of the INSS (INSS, 2006 2014).
The procedure should therefore include a goodness of fit test on the distribution of the number of pensioners by age, gender and type of pension that takes into account the associated p values.
Even though the researcher does not have the entire population, the distributions of the population of pensioners organized by age, gender and type of pension on the last day of each year are available.
We have the information on the distribution of pensioners organized by age, gender and type of pension and we know the number of pensions and the mean pension expenditure in each group, so in this section we check whether stratification matters by looking at the total expenditure estimated using a stratified random sample.
This methodology enables us to obtain quite a large dataset included in the CSWL which is much more representative of the pensioner population in terms of type of pension, gender, and age, as would be the case with an SR.
The aim is to find a subsample for the more general case of fit to the distribution of the CSWL to the pensioner population by age, gender and type of pension.
However, given that the CSWL is not a stratified sample, it is advisable to check whether it covers the correct proportion of the population in each stratum to be considered in the study of the pensioner population categorized by age, gender and type of pension.
Another practical reason is that the information available to us about the population of pensioners is the distribution of this population organized by age, gender and type of pension.
For pensioners, the data set offers detailed information about the type of pension received.
