Nonparametric and Semiparametric Regressions: An Empirical Investigation of Engel’s Law in the Context of Brazil

The primary rationale for using nonparametric or semiparametric methods is to avoid limitations or misspecifications stemming from specific and erroneous functional forms, which can produce biased estimates. Most empirical studies in economics use parametric specifications to analyze the linear relationship between the dependent and independent variables of interest. Semi- or nonparametric regression models offer a significant advance, as they allow checking whether the estimated function is adequately specified according to the nature of the data. This chapter provides a brief theoretical discussion on the use of nonparametric and semiparametric models. It also contains a semiparametric application based on the well-known Engel’s Law for food expenditures in the metropolitan regions of Brazil by using the R language programming. While the parametric model shows almost no difference in the implicit bias in the price index based on estimated Engel curves of households headed by the elderly vis-à-vis the non-elderly; for the same consumption group, the semiparametric estimators adopted for this exercise indicated that price indices overestimate the annual rate of increase in the cost of living and that the bias is marginally greater for the elderly compared to the non-elderly.