Ratios of Parameters: Some Econometric Examples

Abstract

Ratios of parameter estimates are often used in econometric applications. However, constructing confidence intervals (CIs) for these ratios can cause difficulties since the ratio of asymptotically normally distributed random variables are Cauchy distributed and thus have no finite moments. This article presents a method for the estimation of CIs based on the Fieller approach that has been shown to be preferable to the usual Delta method. Using example applications in Stata and R, we demonstrate that a few extra steps in the examination of the estimate of the ratio can provide a CI with superior coverage.