Identification and Estimation of Engel Curves with Endogenous and Unobserved Expenditures

When dealing with the estimation of Engel curves, measurement errors in expenditure data and simultaneity are likely sources of endogeneity. In this paper we study identification of the parameters that characterize an Engel curve in the presence of both. We consider specifications where budget shares are polynomials in the logarithm of total expenditure, which is the case frequently encountered in empirical applications. We propose an estimation procedure which is an extension of that in Lewbel (1996) and exploits a control function assumption to correct for the endogeneity of the true unobserved total expenditure.