I estimat a multinomial logit model in Stata. Is it possible to compute elasticities from the MLogit model? If so, do I need to take the logarithm of the y and x variable, or only the log of x?
I ask because the mlogit model is non-linear, so I don't know what it means to compute d(lny)/d(lnx). (In Stata this would be mfx, eyex after mlogit model).
A similar question was asked in a lengthier form but was never answered:
Income and price elasticity for multinomial logit/probit and alternative-specific conditional logit/multinomial probit in Stata?
Thomas
Best Answer
Stata has the
margins
command that makes this as easy as pie to get elasticities for continuous variables (% change in probability of each outcome for a % change in x) and semi-elasticities for dummy variables (% change in probability of each outcome when x goes from 0 to 1).mfx
has been superseded bymargins
.Having said that, I find these elasticities hard to interpret and prefer to look at the change in probability for a % change in x or unit change in x. I will do that below as well, and try to connect the dots between the two ways of doing this.
Here's example of Stata code with interpretation for what you want:
For interpretation, a 1% increase in age gives you .25% increase in the probability of choosing indemnity insurance (inelastic). Being male lowers the that probability by almost a third.
Personally, I find this much easier to interpret:
This says that 1% increase in age boost the probability of indemnity insurance by 11.8 percentage points and being a year older would give you a 2/10 of percentage point boost.
Let make sure the former agrees with what we did before. The baseline for indemnity is:
An 11.8 percentage point increase expressed as percentage change over the baseline is .118/.476=.24789916, which is pretty close to 0.25.