Empirical Estimation of Elasticities and Their Use

Applied research in economics contains many papers that empirically estimate an elasticity (or a set of elasticities) and uses the estimate(s) for policy analyses. These estimates are typically based on an estimated relationship (such as a demand function). If the specific functional form used in the estimation yields a constant elasticity in the form of an estimated coefficient alone, that coefficient represents the elasticity. If, on the other hand, the formula for the elasticity involves other regressors and coefficients, empirical estimation of the elasticity is based on applying the calculus-based definition of elasticity to this expression. However, a di erential change in a variable is only an approximation to the actual discrete change for small changes, and the approximation can may be quite poor when large changes are considered. This paper advocates using the actual percentage change in the predicted value of the dependent variable when the variable with respect to which the elasticity is estimated changes by one percent. The example provided shows that the difference can be substantial when elasticities are estimated this way. An empirical illustration that uses and replicates a published study to calculate price elasticities in various ways. The study then considers the impact of large changes in prices to show that simply evaluating estimated functions gives substantially different results compared to using estimated elasticities. It is better to rely on estimated relationships and predict changes as finite changes in the predicted values. The approximation errors when elasticities are used can be substantial.