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Elasticities in MNL

Ask general questions about model specification and estimation that are not Apollo specific but relevant to Apollo users.
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jbas
Posts: 6
Joined: 18 Feb 2021, 10:57

Elasticities in MNL

Post by jbas » 09 Jun 2021, 10:24

Hi all,

I came up with a doubt taking a look at the calculation of elasticities in a multinomial logit. Shouldn't the elasticities and cross-elasticities sum up to 1 due to the IIA property? It can be seen in Apollo_example_3.r that this is not the case. And it is certainly not in my models either.

Elaborating a bit more my question; since in a MNL an improvement in the attributes of an alternative reduces the probabilities for all the other alternatives by the same percentage, and elasticities show how the probabilities change when the attribute changes, they should sum up to 1. Shouldn't they?

Thanks for your help!

BR,

J.

stephanehess
Site Admin
Posts: 440
Joined: 24 Apr 2020, 16:29

Re: Elasticities in MNL

Post by stephanehess » 09 Jun 2021, 16:39

Hi

First, you should note that the proportional substitution that results from the IIA assumption applies only at the observation level, not after aggregating the probabilities across observations.

The elasticities calculated in those files are for the total demand, not for an individual observation. For the latter, you would have that the cross-elasticities would all be the same.

Second, this property relates to relative changes in probabilities, not absolute changes.

I’m not sure why there would be interest in summing the elasticities and cross-elasticities, but the value of that sum would be a function of the probabilities, the attribute in question, and the associated marginal utility. So it would not need to be equal to 1. See chapter 3.6 in Train’s book

Hope this helps

Stephane
--------------------------------
Stephane Hess
www.stephanehess.me.uk

jbas
Posts: 6
Joined: 18 Feb 2021, 10:57

Re: Elasticities in MNL

Post by jbas » 14 Jun 2021, 16:23

Hi, thanks for your reply.

It was precisely reading Train's that I wondered if my results were wrong. But I didn't clearly understood it.

Thanks a lot for the clarification.

J.

svenne
Posts: 22
Joined: 26 Apr 2020, 16:20
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Re: Elasticities in MNL

Post by svenne » 04 Oct 2021, 16:24

Dears,

This is an interesting issue. I wonder whether there is a textbook or any other reference that discusses the relationship between the elasticity at the individual level and the market level (total demand)?
Any hint is appreciated.

Best
Sven

stephanehess
Site Admin
Posts: 440
Joined: 24 Apr 2020, 16:29

Re: Elasticities in MNL

Post by stephanehess » 07 Oct 2021, 08:16

Sven

I've not seen any discussion of it, but it would depend on attribute levels, availabilities, etc

Stephane
--------------------------------
Stephane Hess
www.stephanehess.me.uk

svenne
Posts: 22
Joined: 26 Apr 2020, 16:20
Contact:

Re: Elasticities in MNL

Post by svenne » 07 Oct 2021, 10:36

Hi Stephane,

thanks a lot for getting back.

Best
Sven

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