Difference in Interpretation Between Regression Output and Marginal Effects

[Jeff Thompson]

Hi,

I've read a lot of articles about how to interpret marginal effects, but have never really seen their interpretations compared to a regression output. Plus, I haven't seen very many interpretations on margins after -regress- as most articles on marginal effects are related to probabilities. I think it would help me get my head around the differences between the two interpretations if someone could use this as an example in the variations in the interpretations.

*Networking restrictions prevent me from copy/pasting Stata outputs. Screenshots are the only option for me*

xtreg log_avg_pay_change size_cat##c.emp_change if growth==1, fe vce (cluster lbdnum)

log_avg_pay_change- log(average payt)-log(average payt-1)

 margins, dydx(emp_change) over(size_cat)

For size category 3, would these be the differences in reading the regression output and the marginal effects?

• Regression output:
  • size_cat: Firms in size category 3, see a 7.5% higher average pay change than firms in size category 1 (the base).
  • emp_change: 1 unit increase in employment change results in a 75% decrease in average pay change across all sizes.
  • size_cat#c.emp_change: 1 unit of employment change increases average pay change 9.8% for firms in category 3.
• Margins: If all firms were in size category 3, their average pay change would decrease 65% for every one unit increase in employment change. Could it also be said that the slope coefficient between average pay change and employment change is -.65?

[Weiwen Ng]

I just came into some idiotic networking restrictions myself yesterday, so this is said in sympathy: your networking restrictions are idiotic, and your screenshots didn't attach.

Without being able to see your output, I am a bit confused as to what scale you're working on.

[*]size_cat: Firms in size category 3, see a 7.5% higher average pay change than firms in size category 1 (the base).[*]emp_change: 1 unit increase in employment change results in a 75% decrease in average pay change across all sizes.[*]size_cat#c.emp_change: 1 unit of employment change increases average pay change 9.8% for firms in category 3.

That said, your interpretations for the first point sounds correct. But for the second point, it's rather that a 1-unit increase in employment change results in a 75% decrease in pay change in size category 1, and for the third, the differential increase in the dependent variable for size category 3 was +9.8%.

Allowing for some rounding error, if you took 75% and deducted 9.8%, you get around 65%, which is what you got from margins.

You're right that people have mainly talked about margins in the context of probability models, but they're still useful for linear models with interaction terms. You will nonetheless find that the results you get from margins are the same as adding up all the correct coefficients (this is a property of an OLS or xtreg model).

[Jeff Thompson]

Hey Weiwen Ng,

Glad you were able to decipher the problem even though the images weren't attached. They showed up correctly on my end, but I'll repost them below. Let me know if there's anything else you'd like to add. I'm still having a hard time wrapping my mind around these.

 xtreg log_avg_pay_change size_cat##c.emp_change if growth==1, fe vce (cluster lbdnum)

margins, dydx(emp_change) over(size_cat)

For size category 3, would these be the differences in reading the regression output and the marginal effects?

• Regression output:
  • size_cat: Firms in size category 3, see a 7.5% higher average pay change than firms in size category 1 (the base).
  • emp_change: 1 unit increase in employment change results in a 75% decrease in average pay change across all sizes.
  • size_cat#c.emp_change: 1 unit of employment change increases average pay change 9.8% for firms in category 3.
• Margins: If all firms were in size category 3, their average pay change would decrease 65% for every one unit increase in employment change. Could it also be said that the slope coefficient between average pay change and employment change is -.65?