Confidence Intervals for Estimates of Elasticities

Elasticities are often estimated from the results of demand analysis however, drawing inferences from them may involve assumptions that could influence the outcome. In this paper we investigate one of the most common forms of elasticity which is defined as a ratio of estimated relationships and demonstrate how the Fieller method for the construction of confidence intervals can be used to draw inferences. We estimate the elasticities of expenditure from Engel curves using a variety of estimation models. Parametric Engel curves are modelled using OLS, MM robust regression, and Tobit. Semiparametric Engel curves are estimated using a penalized spline regression. We demonstrate the construction of confidence intervals of the expenditure elasticities for a series of expenditure levels as well as the estimated cumulative density function for the elasticity evaluated for a particular household.