Estimation and Testing An Additive Partially Linear Model in a System of Engel Curves.

The form of the Engel curve has long been a subject of discussion in applied econometrics and until now there has no been de\u85nitive con-clusion about its form. In this paper an additive partially linear model is used to estimate semiparametrically the e¤ect of total expenditure in the context of the Engel curves. Additionally, we consider the non-parametric inclusion of some regressors which traditionally have a non linear e¤ect such as age and schooling. To that end we compare an additive partially linear model with the fully nonparametric one using recent popular test statistics. We also provide the p-values computed by bootstrap and subsampling schemes for the proposed test statistics. Empirical analysis based on data drawn from the Spanish Expendi-ture Survey 1990-91 shows that modelling the e¤ects of expenditure, age and schooling on budget share deserves a treatment better than that adopted in simple semiparametric analysis