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.
Important: Read this before posting to this forum
- This forum is for questions related to the use of Apollo. We will answer some general choice modelling questions too, where appropriate, and time permitting. We cannot answer questions about how to estimate choice models with other software packages.
- There is a very detailed manual for Apollo available at http://www.ApolloChoiceModelling.com/manual.html. This contains detailed descriptions of the various Apollo functions, and numerous examples are available at http://www.ApolloChoiceModelling.com/examples.html. In addition, help files are available for all functions, using e.g. ?apollo_mnl
- Before asking a question on the forum, users are kindly requested to follow these steps:
- Check that the same issue has not already been addressed in the forum - there is a search tool.
- Ensure that the correct syntax has been used. For any function, detailed instructions are available directly in Apollo, e.g. by using ?apollo_mnl for apollo_mnl
- Check the frequently asked questions section on the Apollo website, which discusses some common issues/failures. Please see http://www.apollochoicemodelling.com/faq.html
- Make sure that R is using the latest official release of Apollo.
- Users can check which version they are running by entering packageVersion("apollo").
- Then check what is the latest full release (not development version) at http://www.ApolloChoiceModelling.com/code.html.
- To update to the latest official version, just enter install.packages("apollo"). To update to a development version, download the appropriate binary file from http://www.ApolloChoiceModelling.com/code.html, and install the package from file
- If the above steps do not resolve the issue, then users should follow these steps when posting a question:
- provide full details on the issue, including the entire code and output, including any error messages
- posts will not immediately appear on the forum, but will be checked by a moderator first. This may take a day or two at busy times. There is no need to submit the post multiple times.
Elasticities in MNL
-
- Site Admin
- Posts: 1068
- Joined: 24 Apr 2020, 16:29
Re: Elasticities in MNL
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
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
Re: Elasticities in MNL
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.
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.
Re: Elasticities in MNL
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
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
-
- Site Admin
- Posts: 1068
- Joined: 24 Apr 2020, 16:29
Re: Elasticities in MNL
Sven
I've not seen any discussion of it, but it would depend on attribute levels, availabilities, etc
Stephane
I've not seen any discussion of it, but it would depend on attribute levels, availabilities, etc
Stephane
Re: Elasticities in MNL
Hi Stephane,
thanks a lot for getting back.
Best
Sven
thanks a lot for getting back.
Best
Sven