Measuring the impact of the public expenses on the well-being level, which stands through the Human Development Index (HDI) and the Poverty Index (POVI, constitutes the central focus of this work, which will take the state of Piauà as reference. This has been a hypothesis tested in relevant international empirical works of the literature, initiated by Aschauer (1989) and intensely tested by Barro (1990; 1991), from where arose the term "Barroâs Regressions" due to their importance, and in Brazil, Ferreira (1994) began the empirical testing. Official data base from the National Treasury regarding public expenses with health, education, housing and welfare of 219 municipalities gave support to the analysis in order to test whether or not these expenses provokes well-being increase and reduces the social inequalities of the population. For doing this, an econometric modeling has been built up through which it could be inferred, with reliable statistical significance, that the effect of the expenses with health, education, housing and welfare on the HDI is positive, and the more developed is the municipality the greater is such an effect. On the other hand, in spite of the effect of the expenses on the POVI being as well as positive, its magnitude is inversely related to the development stage of the municipality. / Medir o impacto dos gastos pÃblicos sobre o nÃvel de bem-estar, aferido atravÃs do Ãndice de Desenvolvimento Humano (IDH) e do Ãndice de Pobreza (IPOB), constitui o foco central deste trabalho, o qual tomarà como referÃncia o estado do PiauÃ. Esta tem sido uma hipÃtese testada em trabalhos empÃricos relevantes da literatura internacional, iniciada por Aschauer (1989) e intensamente testada por Barro (1990; 1991), de onde se originou o termo âRegressÃes de Barroâ devido a sua importÃncia, e no Brasil, Ferreira (1994) iniciou as verificaÃÃes empÃricas. Dados da Secretaria do Tesouro Nacional referentes a gastos pÃblicos com saÃde, educaÃÃo, habitaÃÃo e previdÃncia de 219 municÃpios piauienses deram suporte à anÃlise a fim de testar se esses gastos provocam aumento de bem-estar e reduz as desigualdades sociais da populaÃÃo. Para tanto, foi utilizado um instrumental economÃtrico atravÃs do qual se pode concluir, com elevada significÃncia estatÃstica, que as despesas com saÃde, educaÃÃo, habitaÃÃo e previdÃncia quando incrementadas marginalmente em municipios mais desenvolvidos impactam mais fortemente no IDH, e menos no IPOB, do que impactariam em municÃpios menos desenvolvidos.