Oaxaca help - mean wage generated does not match the one given by sum command

[Lucy Colbert]

Good afternoon,

I am using the oaxaca command to decompose the ethnic pay gap, in the example here I am comparing the pay of Bangladeshi men to White British men. My code used is

oaxaca LogHOURPAY varlist, by(Bangladeshi) pooled categorical(varlist) eform

I have been using a Jann guide https://core.ac.uk/download/pdf/6442665.pdf which has the following in it on page 18:

So it appears this value should give the mean wage for the given group. However when I do this I get the following mean wages for the groups:
so it appears they are £13.37 for White British & £9.02 for Bangladeshi men.

However when I use the sum command mean hourly pay is £15.74 and £10.40 to White British and Bangladeshi men respectively.


I'm using the same data and the number of observations are the same so I am uncertain as to where this discrepancy could come from.

Thanks so much for any help provided, have a great day!

[FernandoRios]

Hi Lucy
That is indeed a puzzling result. Do you mind posting the results that you obtain to see if indeed the same data is being used, and what transformations are being applied.
Based on the command line you provide, it seems to me that when using oaxaca, you are estimating average wages, using the exponential of the average log(wage). But when using sum, you are directly summarizing wage.
They are not supposed to be the same. E(log(y)) is not the same as log(E(y)), and EXP( E(logY)) is not the same as E(Y).
HTH
Fernando

[Lucy Colbert]

Hi Fernando, thanks so much for your help! I think I have realised where the discrepancy stems from - the oaxaca command appears to generate the geometric mean whereas sum provides the arithmetic mean. Sorry if I wasted your time, have a great day!