Significant coefficient change after adding time fixed effects

[Geert Smits]

For my master thesis I am running a time series pannel regression of the total ESG score of russel 3000 firms on the compensation of their CEO, controlling for a few different variables.

This results in the following regression eqauation:

Total_Comp _i,t = α + β₁ Tot_Scr _i,t + β₂ Contol_i,t+ µ_t + ai_t + Ɛ _i,t,

After running a regression in stata with (1) without time fixed effects and (2) with time fixed effects i get the following results (full stata results added as picture)

(1) xtreg $ylist1 $xlist1, fe

(2) xtreg $ylist1 $xlist1 i.year, fe

	(1)		(2)
	Tot_Comm		Tot_Comm
Tot_Scr	20.041**		-30.004***
	2.31		-3.05
Comp_Comm	228.27		1346.25*
	0.29		1.72
CSR_Comm	1520.59***		780.33***
	5.28		2.58
Sales_Growth	2.788		1.190
	0.89		0.37
ROA	48.366***		44.001***
	4.30		3.91
Size	23.287***		15.663***
	6.00		4.00
Lev	6.708		0.394
	1.25		0.07
Owner	92.732**		146.69***
	2.15		3.40
_cons	5090.13***		4815.59***
	5.78		5.22
Firm fixed effects	Yes		Yes
Time fixed effects	No		Yes
R-squared	0.058		0.020
F-test	15.42***		15.65***

The sign of the total score completely changes after adding Time fixed effects. I am having trouble interpretating the economic implications of the difference between the two coefficients after adding the time fixed effect.

At first a 1point increase in score, ceteris paribus, results in a 20K expected increase in CEO salary, whilst after time fixed effects a 1 point increase in score, ceteris paribus, results in a 30K expected decrease in CEO salary.

How can this difference be interpreted?

Thank you in advance for your help, Kind Regards,
Geert Smits

[Clyde Schechter]

What's going on here is that there are secular trends in both Tot_Scr and Total_Comp. The model without the time variables fails to account for this and its results are contaminated by omitted variable bias (also known as confounding). In effect, the model without the time variable is allowing the Tot_Scr variable, which is trending up over time, to "take credit" for an ongoing upward time-trend in Total_Comp. Once you include the time variables, the model is able to separate out the effects of time from the effects of Tot_Scr. To see those trends directly, I suggest you run -tabstat Tot_Scr Total_Comp, by(year)-.