<p>If you totally differentiate both the sides you will get:
<span class="math-container">$\frac{1}{h}d(h) = e_1 \frac{1}{w}d(w)$</span></p>
<p><span class="math-container">$\Rightarrow e_1 = \frac{w}{h}\frac{d(h)}{d(w)} = \frac{\frac{d(h)}{h}}{\frac{d(w)}{w}} = \frac{\frac{d(h)}{h}*100}{\frac{d(w)}{w}*100} = \frac{\% \triangle h}{\% \triangle w} $</span></p>
<p>Which is the expression used to give elasticity of h with respect to w , hence <span class="math-container">$e_1$</span> is the elasticity.</p>

CC BY-SA 4.0
2023-07-01T19:07:24.233Z
2023-07-01T19:07:24.233Z
Agrim Rana
<p>Suppose that we have the following regression:</p>
<p><span class="math-container">$$ln (h) = e_{0} + e_{1} ln (w) + u$$</span>.</p>
<p>Isn't elasticity <span class="math-container">$e_{1}$</span>? in other words: <span class="math-container">$\frac{\delta ln (h)}{\delta ln (w)}$</span>? I am a bit confused since I have seen in some papers they take the first difference and then calculate elasticity, i.e.,
<span class="math-container">$\frac{\Delta ln (h)}{\Delta ln (w)}$</span> Which one is the correct way of calculating elasticity?</p>

CC BY-SA 4.0
2023-06-23T23:32:52.030Z
could you please link to concrete examples?
1muflon1
CC BY-SA 4.0
2023-06-27T13:02:10.117Z
Suppose that we want to calculate the elasticity of labor supply. $h$ is the number of hours worked and $w$ is the wage. According to the standard definition, the estimated coefficient must be the elasticity, no?
Giordano
CC BY-SA 4.0
2023-06-27T14:38:50.703Z
the reason why I am asking is that you could calculate elasticity not just between level variables but also growth rates and your post might just have slightly incorrect notation, already your notation $\delta \ln(h)/\delta \ln(w)$ is non standard as in econ people would typically use $\partial \ln(h)/ \partial \ln(w)$ or $d \ln(h)/ d \ln(w)$, my best guess is that you just mistakenly $\Delta ln(h)/ \Delta ln(w)$ when the paper maybe said $d\Delta \ln(h)/ d\Delta \ln(w)$ which would be elasticity between growth rates or something like that. In that case taking first difference makes sense
1muflon1
<regression><elasticity>
Elasticity computation
Giordano
# Elasticity computation

(Asked by: username_0 on 2023-06-23)

Suppose that we have the following regression:

$$ln (h) = e\_{0} + e\_{1} ln (w) + u$$.

Isn't elasticity $e\_{1}$? in other words: $\frac{\delta ln (h)}{\delta ln (w)}$? I am a bit confused since I have seen in some papers they take the first difference and then calculate elasticity, i.e.,
$\frac{\Delta ln (h)}{\Delta ln (w)}$ Which one is the correct way of calculating elasticity?

**Tags:** regression, elasticity
> **Comments:**
> **username_1**: could you please link to concrete examples?  
> **username_0**: Suppose that we want to calculate the elasticity of labor supply. $h$ is the number of hours worked and $w$ is the wage. According to the standard definition, the estimated coefficient must be the elasticity, no?  
> **username_1**: the reason why I am asking is that you could calculate elasticity not just between level variables but also growth rates and your post might just have slightly incorrect notation, already your notation $\delta \ln(h)/\delta \ln(w)$ is non standard as in econ people would typically use $\partial \ln(h)/ \partial \ln(w)$ or $d \ln(h)/ d \ln(w)$, my best guess is that you just mistakenly $\Delta ln(h)/ \Delta ln(w)$ when the paper maybe said $d\Delta \ln(h)/ d\Delta \ln(w)$ which would be elasticity between growth rates or something like that. In that case taking first difference makes sense  

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## 1 answers

### Answer by username_2 on 2023-07-01. Score: 2

If you totally differentiate both the sides you will get:
$\frac{1}{h}d(h) = e\_1 \frac{1}{w}d(w)$

$\Rightarrow e\_1 = \frac{w}{h}\frac{d(h)}{d(w)} = \frac{\frac{d(h)}{h}}{\frac{d(w)}{w}} = \frac{\frac{d(h)}{h}\*100}{\frac{d(w)}{w}\*100} = \frac{\% \triangle h}{\% \triangle w} $

Which is the expression used to give elasticity of h with respect to w , hence $e\_1$ is the elasticity.


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