Semi-Parametric Analysis of Shape-Invariant Engel Curves with Control Function Approach

An extended generalised partially linear single-index (EGPLSI) model provides flexibility of a partially linear model and a single-index model. Furthermore, it also allows for the analysis of the shape-invariant specification. Especially, since it does not only provide the flexibility of a partially linear (PL) and a single-index (SI) models, but also enables an analysis of the shape-invariant specification. Nonetheless, the model's practicality in the empirical studies has been hampered by lack of appropriate estimation procedure and method to deal with endogeneity. In the current paper, we establish an alternative control function approach to address the endogeneity issue in the estimation of the EGPLSI model. We also show that all attractive features of the EGPLSI model discussed in the literature are still available under the proposed estimation procedure. Economic literature suggests that semiparametric technique is an important tool for an empirical analysis of Engel curves, which often involves endogeneity of the total expenditure. We show that our newly developed method is applicable and able to address the endogeneity problems in semiparametric analysis of the empirical Engel curves