<p>Lets say I am estimating a regression of a death rate per 100k people on an economic shock, so:</p>
<p><span class="math-container">$y = \beta_o + \beta_1 * X+ error$</span>
where the dependent variable is the death rate, and x is the measure of the shock.</p>
<p>First, I can calculate an arc elasticity by doing <span class="math-container">$\hat{\beta}$</span> * <span class="math-container">$\frac{\bar{x}}{\bar{y}}$</span>, correct?</p>
<p>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 <em>aged 18-54</em>.
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?</p>

CC BY-SA 4.0
2021-03-24T21:42:27.500Z
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
CC BY-SA 4.0
2021-03-25T16:40:40.463Z
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
Steve
<econometrics><elasticity><regression><reduced-form-estimation>
Question about using elasticities to compare difference rates but with different normalization
Steve
# Question about using elasticities to compare difference rates but with different normalization

(Asked by: username_0 on 2021-03-15)

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?

**Tags:** econometrics, elasticity, regression, reduced-form-estimation

> **Comments:**
> **username_1**: 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?  
> **username_0**: 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  

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## 0 answers

