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.Engel curves, Fieller method, Tobit, robust regression, semiparametric

Providing intuition to the Fieller Methodwith two geometric representationsusing STATA and Eviews

Research paper no. 992, ISBN 0 7340 2650 1The Fieller Method for the construction of confidence intervals for ratios of the expectedvalue of two normally distributed random variables has been shown by a number of authorsto be a superior method to the delta approximation. However, it is not widely used due inpart, to the tendency to present the intervals only in a formula context. In addition, potentialusers have been deterred by the potential difficulty in interpreting non-finite confidenceintervals when the confidence level is less than 100%. In this paper we present two graphicalmethods which can be easily constructed using two widely used statistical software packages(Eviews and Stata) for the representation of the Fieller intervals. An application is presentedto assess the results of a model of the non-accelerating inflation rate of unemployment(NAIRU)