Statistical interpretation of the GDP, the PNAD and the minimum wage

Why has household income in the National Household Survey (PNAD) grown so much faster than household consumption in Brazil's GDP from 2011 to 2012? To provide an answer to this question, we start from a visualization of the importance of the minimum wage in PNAD's income distribution and from a hypothesis that the underestimation of incomes in the PNAD surveys is concentrated in those families whose incomes do not follow the minimum wage. We then derive an equation to explain the difference between household income growth in the PNAD and household consumption growth in the national accounts as a function of the change in the minimum wage. Our empirical estimates of this equation suggest that the behavior of the minimum wage has been an important component in the explanation of differences in income growth between the PNAD and the GDP accounts.