Hello everyone, the following question may sound a bit silly but I have been a bit puzzled about this and wanted to share it with you - also for pedagogical reasons to whoever reads any potential answers.

I am using firm-level data and want to estimates the returns of advertising on revenue. Every variable in my model is in logarithmic form and I estimate the following:

Code:
xtreg lnrevenue lnage lnemployment lnadvertising, fe vce(robust)
The estimated coefficient on lnadvertising is 0.014 (p=0.000). This means that a 1% increase in advertising expenditure can increase revenue by 0.014%. To calculate the return, I multiply the ratio of the median value of revenue over the median value of advertising expenditure of the firms in my sample (which is 7,300,000/680,000 ≈ 10.74) with the coefficient on lnadvertising (0.014) to yield:

advertising return = 0.014*7,300,000/680,000 ≈ 0.15

This means that for every $1 spent on advertisement, there is a $0.15 increase in revenue (or a return of 15%).

My question is: can I use the estimated coefficient on lnadvertising (i.e. 0.014) and multiply it with the ratio of the revenue over advertising expenditure for each of the firms in my sample and get individual firm advertising returns on revenue? In other words, does the advertising_returns variable created as below capture individual firm advertising returns?

Code:
generate advertising_returns = 0.014*revenue/advertising
I understand that the value of an estimated coefficient in a regression model is the mean change in the dependent variable due to a 1-unit change in the independent variable (ceteris paribus) and therefore it refers to ALL firms in the sample and does not apply to each firm individually. Of course, my assumption here is that effect of advertising on revenue is the same for each firm (which is not plausible indeed from a theoretical perspective; but if we assume this holds, is my rationale for calculating advertising_returns correct)?