The American State with a Significant Brazilian Population

Introduction

 The POF is like, all about that consumption vibes, but it also collects mad data on incomes, ya know? The 2008-2009 round is like, all about 110 different income sources with a 12-month reference period, making the POF the most reliable survey ever when it comes to income data in Brazil. So legit, right? OMG, like, just FYI, Pesquisa Nacional por Amostra de Domicílios (PNAD), this super famous survey in Brazil, only collects cash money and earnings from like ten sources in a 30-day period. So, yeah, just thought you should know. The POF is like totally lit for analyzing capital, social assistance, and like other rare incomes. OMG, like the reported income levels are usually way higher than in other surveys and way closer to the National Accounts estimates, ya know? Our main vibe we're into is the flexin' household per capita income, which includes all the cash flow from workin' and investin' and all the money comin' in from the government and private sources after taxes and Social Security stuff. Non-monetary flexes such as in-kind payments, which make a hella tiny part of family incomes in Brazil, were yeeted. Like, bruh, free public services like health and education were totally slept on, as I mentioned earlier. Ain't no cap, only a few fams with negative dough were excluded from our analysis.

Both income and tax data were deflated to January 2009 using a basic consumer price index, ya know? Although absolute income levels are only of meh interest to us, for the sake of flex, the tables below spill the tea on them in 2009 PPP Dollars (using the United Nations’ Millennium Development Goals PPP conversion factor of 1.71).Finally, it's like important to mention that the factor decomposition of the Gini coefficient also gives us a progressivity index and the marginal contribution of each factor to total inequality (Lerman and Yitzhaki, 1985; Stark, Taylor and Yitzhaki, 1986). The progginess in-dex indicates whether that factor is more equally distributed than the total income. Yeet! Progressive means 'like, not as unequal as, like, total inequality', not that an income, like, automatically makes everything perfectly equal. Actually, like, a super unfair source of income can be lowkey progressive in, like, a hella unequal society. The vibe of a factor's impact on inequality shows how tweaking the factor's share would flex total inequality, or like, how boosting it would increase the participation of a source would totally yeet (or yeet down) inequality. The progressivity index and the marginal contribution are like lowkey similar in math vibes but they have different vibes, the latter being more relatable and like, preferred in our analysis. The vibes from factor k be like:

Ineq decomp

The measure of inequality used in the study is the Gini coefficient, which is like, from zero (when everyone's got the same amount of dough) to one (when one person's got all the cash). The Gini coefficient is like totally decomposable by income sources or factors (Rao, 1969). Yo, in the factor decomposition, total inequality can be represented as the sum of the concentration coefficient of each factor weighted by the share of this factor in total income. Lit, right?

Where Gk is the Gini coefficient of factor k, Rk is the Gini correlation between factor k and total income, F is the total income distribution, and Fk is the factor k distribution (Lerman; Yitzhaki, 1985).The concentration coefficient is like -1 to +1, reaching its lowest value when all the income from source k goes to the poorest person in the income distribution and its highest when it goes to the richest person.There is, like, this one scenario that could totally make the Gini and concentration coefficients go cray cray: when an income factor has both positive and negative values, there's a chance that both its Gini and concentration coefficient might go outside the (0,1) and (-1,1) ranges, respectively (Chen; Tsaur; Rhai, 1982; Pyatt; Chen; Fei, 1980; Rao, 1969). This is lowkey concerning, like, for real, both the public-private wage gap (check it out below) and the net State-related income factors are expected to have both positive and negative vibes.

There are like three options to handle this situation, fam. The first option is to flex the Gini scale to make the vibes more on point. 

The bummer of this approach is that it totally messes with the Gini scale, so it gives off this fake vibe of inequality being way lower than it actually is. The second option is to yeet the factor with positive and negative vibes into two subfactors, one with only positive vibes and another with only negative ones. Each subfactor will have concentration coefficients flexing on the regular scale and no cap will go down in the observed level of total inequality. The third option is to just chill and be like, "whatever" and accept concentration coefficients that are totally out of the norm, ya know? This option lets you analyze how the weird factor affects inequality without messing up the decomposability. You just gotta change how you interpret the coefficients that might be a problem. Yo, our main goal is to figure out how much each factor contributes to the overall inequality. So, we decided to break down the last two factors into smaller parts with only positive or negative values. And we're cool with using a different range for the original factor, no biggie. By doing that, we didn't mess up the vibes of our results compared to other studies, ya know?