<p>Coming from a different background, I can't quite get my head around around estimation of price elasticity from observational data.
It seems that most of the materials online suggest using a log-log model of demand vs price, and then using linear regression to find the elasticity: <span class="math-container">$\log(Q)=\epsilon\log(P)+\beta$</span>. As far as I understand, this is the point estimate.</p>
<p>Another method that I had been suggested is using linear regression with log-log <em>rate of change</em>: <span class="math-container">$\log(Q_t/Q_{t-1})=\epsilon\log(P_t/P_{t-1})+\beta$</span> instead. This is something which is used for instance in <a href="https://drive.google.com/file/d/1CPe_Zm3ajCTbWlJIBNh36mdAZ0J9iPe_/view?usp=sharing" rel="nofollow noreferrer">this paper</a> and as far as I understand is related to arc elasticity.</p>
<p>I wasn't able to find much on the topic of difference between these approaches, except <a href="https://economics.stackexchange.com/questions/55215/different-methods-to-calculate-price-elasticity?newreg=949e6f9da6514b5db3c465d4f3cafee6">another question,</a> the answers to which seem to suggest that the point elasticity is more applicable to the data with small price changes, and the latter method would be more relevant for larger changes.</p>
<p>Am I right in assuming this? If not what are differences between these methods and also what is the implication of the term <em>elasticity</em> for each?</p>
<p>EDIT: Uploaded <a href="https://drive.google.com/file/d/1CPe_Zm3ajCTbWlJIBNh36mdAZ0J9iPe_/view" rel="nofollow noreferrer">the paper</a> to my Google Drive for easy access, also available <a href="https://www.sciencedirect.com/science/article/abs/pii/S0378437110008320" rel="nofollow noreferrer">here</a> for those with institutional access to the journal.</p>

CC BY-SA 4.0
2024-10-22T15:40:38.910Z
The first method is closer to the definition of price elasticity of demand (just apply the formula and you'll see that $\epsilon$ captures the PED). I can't access the paper related to the second method, but it seems that $\epsilon$ there captures the elasticity of the *growth in $Q$* with respect to the *growth in $P$*, which is different from how PED is typically understood.
Herr K.
CC BY-SA 4.0
2024-10-22T19:29:03.230Z
Im downvoting and voting to close bc the question needs more focus and bc the paper cited is unaccesible.
Jesper Hybel
CC BY-SA 4.0
2024-10-22T20:40:22.640Z
Hello, I have updated the paper link, so should be accessible now - apologies.
shiftyscales
CC BY-SA 4.0
2024-10-23T09:11:25.077Z
Asking: What are the differences between these methods? is very unspecific. What are the differences between apples and oranges? There are many. One difference is that the second equation uses the first differences which has some merits from an econometric point of view. But this is just one difference ... Also paper is behind paywall so I still can't see econometric estimation equation, data used and assumption of exogeneity.
Jesper Hybel
CC BY-SA 4.0
2024-10-23T09:23:34.180Z
Thank you, please use the link that I posted above https://drive.google.com/file/d/1CPe_Zm3ajCTbWlJIBNh36mdAZ0J9iPe_/view to access
shiftyscales
<econometrics><elasticity><price>
Point estimate or rate of change for price elasticity using observational data
shiftyscales
# Point estimate or rate of change for price elasticity using observational data

(Asked by: username_0 on 2024-10-21)

Coming from a different background, I can't quite get my head around around estimation of price elasticity from observational data.
It seems that most of the materials online suggest using a log-log model of demand vs price, and then using linear regression to find the elasticity: $\log(Q)=\epsilon\log(P)+\beta$. As far as I understand, this is the point estimate.

Another method that I had been suggested is using linear regression with log-log *rate of change*: $\log(Q\_t/Q\_{t-1})=\epsilon\log(P\_t/P\_{t-1})+\beta$ instead. This is something which is used for instance in [this paper](https://drive.google.com/file/d/1CPe_Zm3ajCTbWlJIBNh36mdAZ0J9iPe_/view?usp=sharing) and as far as I understand is related to arc elasticity.

I wasn't able to find much on the topic of difference between these approaches, except [another question,](https://economics.stackexchange.com/questions/55215/different-methods-to-calculate-price-elasticity?newreg=949e6f9da6514b5db3c465d4f3cafee6) the answers to which seem to suggest that the point elasticity is more applicable to the data with small price changes, and the latter method would be more relevant for larger changes.

Am I right in assuming this? If not what are differences between these methods and also what is the implication of the term *elasticity* for each?

EDIT: Uploaded [the paper](https://drive.google.com/file/d/1CPe_Zm3ajCTbWlJIBNh36mdAZ0J9iPe_/view) to my Google Drive for easy access, also available [here](https://www.sciencedirect.com/science/article/abs/pii/S0378437110008320) for those with institutional access to the journal.

**Tags:** econometrics, elasticity, price

> **Comments:**
> **username_1**: The first method is closer to the definition of price elasticity of demand (just apply the formula and you'll see that $\epsilon$ captures the PED). I can't access the paper related to the second method, but it seems that $\epsilon$ there captures the elasticity of the *growth in $Q$* with respect to the *growth in $P$*, which is different from how PED is typically understood.  
> **username_2**: Im downvoting and voting to close bc the question needs more focus and bc the paper cited is unaccesible.  
> **username_0**: Hello, I have updated the paper link, so should be accessible now - apologies.  
> **username_2**: Asking: What are the differences between these methods? is very unspecific. What are the differences between apples and oranges? There are many. One difference is that the second equation uses the first differences which has some merits from an econometric point of view. But this is just one difference ... Also paper is behind paywall so I still can't see econometric estimation equation, data used and assumption of exogeneity.  
> **username_0**: Thank you, please use the link that I posted above https://drive.google.com/file/d/1CPe_Zm3ajCTbWlJIBNh36mdAZ0J9iPe_/view to access  

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## 0 answers

