Consistent Estimation of Expenditure Elasticities from Cross-Section Data on Households Producing Partly for Subsistence

Abstract

JN estimating Engel curves, it is common to use total expenditure in place of income as an explanatory variable. Summers [6] has shown that least-squares estimators will then be inconsistent. More recently, Liviatan [4] has shown that using income as an instrumental variable will permit consistent and relatively efficient estimation of the expenditure elasticities. However, when the sample consists of households in a less-developed country (LDC) that produce partly for subsistence, there are further sources of bias. Estimates may be asymptotically biased because of the spread between the buying and selling price of many food items in a partial subsistence economy; a household that is a net buyer of an item is confronted with a higher effective price than a household that is a net seller. Also, the arbitrary valuation of home-produced goods introduces possibly serious errors of observation with respect to both the regressand and regressor, resulting in the usual errors-in-variables bias. This paper discusses these sources of bias, presents a method for obtaining consistent estimates of the parameters in the Engel relationship, and applies the method to a sample of 816 households in rural Kenya.'