Elasticity Coefficients as Effects Measures in Model Formulations

When dealing with mathematical or statistical models involving one or more explanatory (independent) variables, one often wants to determine the effects of such variables on a response (independent) variable. In the case of linear regression models, one such effects measure is the so-called standardized regression coefficients used in various statistical software packages and discussed in regression textbooks. However, since strong reservations have been expressed against the use of standardized regression coefficients because of various limitations, the objective or initial working hypothesis behind the present research was that some alternative measure without such limitations ought to be explored. Consequently, elasticity coefficients are formulated and proposed as both relative and absolute such measures. While the standardized regression coefficients lack any convenient interpretation, the proposed elasticity coefficients have the particularly desirable property of having a logical and intuitively appealing interpretation in terms of the relative change in the value of the response variable as a consequence of a relative change (of 1 percent) in the value of one or more of the explanatory variables. Those elasticity measures have the flexibility of being applicable to individual or to all explanatory variables and to individual or to all observations or data sets. A numerical example is used to illustrate the use of these new measures. Comparison between values of the standardized regression coefficients and those of the corresponding elasticity coefficients based on reported data from various sources is provided. Also, the form of the elasticity coefficients for a variety of different types of models is presented. Statistical inferences are also discussed.