# Question about using elasticities to compare difference rates but with different normalization

Lets say I am estimating a regression of a death rate per 100k people on an economic shock, so:

$$y = \beta_o + \beta_1 * X+ error$$ where the dependent variable is the death rate, and x is the measure of the shock.

First, I can calculate an arc elasticity by doing $$\hat{\beta}$$ * $$\frac{\bar{x}}{\bar{y}}$$, correct?

and given this, I want to compare this elasticity to another paper in the literature that uses a different shock by creating the same arc elasticity given their regression results and summary statistics. However, their dependent variable is a death rate per 100k people aged 18-54. Since elasticities are unitless, if I calculate my elasticity, and say it is 2, and their elasticity is 2.5, are these still roughly comparable measures?

• if you do not mind me asking, why are you interested specifically in arc elasticity? As far as I know arc elasticity is used mostly in entry level econ textbooks. Typically in empirical estimations people estimate point elasticity. Is that perhaps a typo or do people in your field actually estimate arc elasticities?
– 1muflon1
Mar 24 at 21:42
• The only reason I am asking about arc elasticities is just because if say I am comparing an elasticity I got to a measure from another report, but I do not have their data, the arc can be a crude way to get a measure of the elasticity from their regression coefficient and summary statistics Mar 25 at 16:40