Nonlinear errors in variables Estimation of some Engel curves

The most common solution to the errors in variables problem for the linear regression model is the use of instrumental variable estimation. However, this methodology cannot be applied in the nonlinear regression framework. In this paper we develop consistent estimators for nonlinear regression specifications when errors in variables are present. We apply our methodology to estimation of Engel curves on household data. First, we find that the ‘Lesser-Working’ specification of budget shares regressed on the log of income or expenditure should be generalized to higher-order terms in log income. Also, we find that errors in variables in either reported income or expenditure should be accounted for. Lastly and perhaps most interesting, we find rather strong support for the Gorman rank restriction on the matrix of coefficients for the polynomial terms in income.