Errors in Variables and Engel Curve Analysis

The traditional method of estimating Engel curve parameters uses either (recorded) income or total expenditure as an independent variable in least squares analysis. Neither of these variables is, however, a satisfactory index of the true economic position of the family. This results in biased estimates of the income elasticities of the various consumption categories. The bias can, however, be eliminated in large samples by using both income and total expenditures in the estimation procedure. This can be accomplished by applying the method of "instrumental variables" to Engel curve analysis, with recorded income serving as the instrumental variable. Having formulated consistent estimation procedures, we use empirical data to investigate and analyze the direction and size of the biases in the traditional estimates of income elasticities of various commodity groups. IT IS COMMON practice to use current income, Y, or perhaps more often, total expenditures, C, as independent variables in least squares analysis of Engel curves. Strong objections, however, have recently been raised against the applications of the least squares procedures to family budget studies. Friedman [3] argued that spending decisions are based on "permanent income," a concept which is generally inadequately represented by Y as obtained from household records. The divergence between the empirical measure of income and its theoretical counterpart leads in Friedman's model to biased estimates of the "true" parameters. The objection to the use of C as regressor has been raised and analysed by Summers [9]. The main point of Summers' contribution is that C and its components (the "dependent variables") are endogenous to the consumer and are determined simultaneously. As is well known, the classical method of least squares leads in the above circumstances to biased estimates of the "true" parameters, i.e., the parameters of the relation between the systematic parts of C and its components. In this paper we shall present a method of obtaining consistent estimates of the "true" parameters of Engel curves when C is used as an explanatory variable. Our method consists of using Y (as recorded in budget studies) as an instrumental variable which eliminates the simultaneous equations bias from the relation between C and its components. Some empirical estimates