Coefficient interpretation in multinomial logistic regression I am not really good in statistics so please bear with me here :)
I was reading an article regarding financial advisors in mergers and acquisition deals and couldn't quite understand how the authors interpret the coefficients from a multinomial logistic regression and reach the percentage increase/decrease in likelihood (see image and quote below): I assume this is a relatively easy question but did not manage to come to the answer by myself or by googling. Is there a command in STATA that gives you these percentages after running a mlogit?

"Deal size is an important determinant in the acquirer's selection of advisors. The coefficient of -0.514 (Column 1) on deal size means that, when the size of the deal doubles, the likelihood of an acquirer hiring boutique advisors decreases by 5.73%."
I would be extremely thankful for any help..
Best regards!
 A: The italicized quote doesn’t deal with the results directly and thus doesn't seem especially helpful; hopefully you can use the information below to decide whether it is accurate.  It would be correct to interpret the output as follows:
 when the *natural log* (ln) of the deal size increases by *1*, the *odds* of the acquirer choosing Boutique over the Reference Category (not shown in the output) is multiplied by e^(-.514).  
This is rather abstract.  It is possible to convert this information into a more intuitive and probably more useful statement about probability.  (The authors seem to be equating “likelihood” with “probability”— not uncommon.)  For this conversion, you need to refer to some particular type of acquirer, with a particular deal size, who, based on all other values, has already been assigned a particular probability of choosing Boutique over Reference.  Then, using a standard odds-to-probability conversion, you can arrive at the probability you seek.
Example:  suppose a certain acquirer has been assigned a 20% probability of choosing Boutique over Reference.   That would mean odds of .2/(1-.2) = .25.  Then suppose another acquirer is the same in all relevant respects but one:  this company is looking at a deal size that, in terms of natural log, is greater by 1.  For this acquirer, the odds differ by a factor of exp(-.514), which means they are .6 times as great.  Thus we’d multiply .25 by .6.  These new odds of .15 can finally be converted into probability of choosing Boutique over Reference, via .15/(1+.15) = 13%.
