Margins after REGHDFE with log dependent variable

[Katherine Pham]

I am using the reghdfe command with a log dependent variable. Then, I am using the margins command for postestimation. However, I would like to "contextualize" the result by putting the margins answers back into the magnitudes of the original variables. There is a lot going on here so I was hoping to get some validation: is this the correct approach and interpretation? Here is an MWE.

sysuse auto, clear
drop if rep78==.
gen lprice = log(price)
reghdfe lprice mpg i.foreign, absorb(FE=rep78) resid
margins foreign, expression(exp(predict(xb)+FE))


Predictive margins Number of obs = 69
Model VCE : OLS

Expression : exp(predict(xb)+FE)

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
foreign |
Domestic | 5492.019 287.0945 19.13 0.000 4929.324 6054.713
Foreign | 6576.807 604.7936 10.87 0.000 5391.434 7762.181
------------------------------------------------------------------------------


margins r.foreign, expression(exp(predict(xb)+FE))


Contrasts of predictive margins
Model VCE : OLS

Expression : exp(predict(xb)+FE)

------------------------------------------------
| df chi2 P>chi2
-------------+----------------------------------
foreign | 1 2.26 0.1328
------------------------------------------------

------------------------------------------------------------------------
| Delta-method
| Contrast Std. Err. [95% Conf. Interval]
-----------------------+------------------------------------------------
foreign |
(Foreign vs Domestic) | 1084.789 721.7383 -329.7924 2499.37
------------------------------------------------------------------------

It is a bit silly to do causal interpretation in this scenario, but setting that concern aside: "we assume that for the average car in the dataset, we could charge $5492 if the car is labeled as domestic, whereas it would have a price of $6577 if it was labeled as foreign. Although changing a car's classification to foreign is estimated to increase its value by about $1085, this difference is not statistically significant."

Questions:

• Is this the right way to convert my estimates back into $? (As I understand it reghdfe does not allow xbd prediction option: https://github.com/sergiocorreia/reghdfe/issues/138. Also, I am using the "expression" option because my understanding is that the typical recommended solution -- raw dependent variable with poisson or GLM before margins -- will be harder to implement in the high-dimensional fixed effects scenario).
• Is this the right interpretation of the results? e.g. are the estimates and confidence intervals coming out of these commands OK or are there issues with my transformation that I should be aware of?
• Has anyone experienced any problems with this type of postestimation using reghdfe? As Sergio notes on github, not all examples have been checked: https://github.com/sergiocorreia/reghdfe/issues/32

Thanks in advance!

[Phil Bromiley]

Your approach looks ok to me, but I don't do many log models. You might try it out in xtreg and see if it comes out the same.

[Katherine Pham]

Thanks Phil! I followed your advice and actually had some problems replicating, which I've raised as a separate issue on GitHub. So think I'll wind up manually implementing the predictions for now. However it was helpful advice...if I gain any more insight on the matter I'll follow up in another post.

Best, Katherine