This may be due to a suppression effect. Suppression can occur when some of the independent variables are highly correlated.

I see three possible scenarios: first, you might get a direct effect of the independent variable on the dependent variable. That is, your control variable may contain a mediating variable, which leads to a suppression effect; second, you may get a coefficient that is closer to the true causal effect, which means that your control variable eliminates the non-causal correlation due to the presence of confounding factors. Finally, your control variable may contain a collider, thus opening a back-door path, which is the worst-case scenario. Exactly which is the case requires further analysis; for example, a variable that is only influenced by the independent variable is more likely to be a mediating variable. This is my personal view for your reference.

If your library has it, take a look at Chapter 13 (Woes of Regression Coefficients) in the classic book by Mosteller & Tukey (1977).

• https://www.pearson.com/us/higher-education/program/Mosteller-Data-Analysis-and-Regression-A-Second-Course-in-Statistics/PGM154255.html

And see slide 16 here:

• https://hastie.su.domains/MOOC-Slides/linear_regression.pdf

As the first bullet point on that slide notes, "predictors usually change together!"

HTH.

Previous answers are entirely correct, but the question was also how of why this may occur. Say the ‘real’ or ‘direct’ effect of ESG on ROA is +0,20. Now say ‘Assets’ has a positive effect of +0,60 on ESG, but a negative effect of −0,50 on ROA. In that case the ‘total’ relation between ESG and ROA is the ‘direct’ effect of +0,20 plus the ‘indirect’ effect caused by the covariate ‘Assets’. The latter ‘indirect’ effect is +0,60*−0,50=−0,30. The ‘total’ relation between ESG and ROA then becomes: Direct effect=+0,20 + Indirect effect=−0,30 = Total effect=−0,10. This ‘total’ effect is the original uncorrected correlation between ESG and ROA (r=−0,10). Then after ‘subtracting’ the indirect effect, the corrected regression coefficient beta=+0,20. So in practice this will happen when a control variable is e.g. positively related to the predictor (Assets->ESG=+0,60), but negatively related to the dependent variable (Assets->ROA=−0,50), or any of the other so called imbalanced triangles (two positive relations and one negative relation or two negative relations and one positive relation).

In such situations, there are two possibilities, the first is that there is a problem. Usually called multicollinearity. That is, the correlations between all predictors as a whole is too high. Most software has indices to measure this, such as the Variance Inflation Factor (VIF). A rule of thumb is that there is multicollinearity if this VIF is 2,5 or more, in which case the ‘responsible’ control variable(s) should be deleted from the equation.

The other possibility is that you have found something very interesting. For instance to explain all this in their book ‘Quasi Experimentation’, Cook and Campbell described at page 306 that ‘Head Start’ to help children at school, was unexpectedly negatively related to the school success of the children (r was negative, Head Start appeared to make things even worse!). However, when they controlled for Social Economic Status (SES), the beta was positive and Head Start turned out to be beneficial after all. Underlying process was that SES was negatively related to receiving Head Start (this support-program was primarily given to underprivileged children), but SES was positively related to school success. So because Head Start was more often given to underprivileged children who are often less successful at school, Head Start appeared to be detrimental… until the researchers decided to control for SES. Then they found that, GIVEN the level of SES, Head Start was successful after all!

To get a better idea of what is going on, make a partial regression plot for the coefficient you are concerned about. That plot shows the relationship between, in your case, ROA and ESG *after removing the effects of the other predictors in the model from both variables*. Because your predictors are correlated, you can't easily tell what removing their effects leaves behind. The coefficient you see in the multiple regression doesn't measure the effects of ESG on ROA, but instead measures what is left of that effect after removing the (linear) effects of the other predictors. You are likely to find the plot surprising and informative.

Paul F Velleman's post suggests a little exercise you could try. It entails

estimating 3 models, as follows. You need to be careful to use the same

estimation sample each time.

Model 1

ROA = b0 + b1*ESG + {adjustment variables} + error

Model 2

ESG = b0 + {adjustment variables} + error

Save the residuals from Model 2--call the variable Res2, for example.

Model 3

ROA = b0 + b1*Res2 + error

COMPARE b1 from Models 1 and 3. If you used the same estimation sample each time, they will be the same. The SE and t-test will not match because the model df will be wrong in Model 3. But the coefficients will match, and that should give you some insight into what b1 means in Model 1. Variability in the residuals from Model 2 (Res2) is variability in ESG that is not accounted for by the adjustment variables. So in both Models 1 and 3, b1 is showing you the "effect" of ESG on ROA with the effects of the adjustment variables partialled out of ESG.

Here is an example using Stata's auto dataset. Even if you do not use

Stata, it should give you an idea about how to proceed.

* Example using Stata's auto.dta dataset

clear

sysuse auto

* Model 1

* Y=mpg, X=length, turn & weight are adjustment variables

regress mpg length turn weight, noheader

* Model 2

* Regress length on the adjustment variables and save the residuals.

regress length turn weight, noheader

predict res_L_tw, residuals

* Model 3

* Regress mpg on res_mpg_tw

regress mpg res_L_tw, noheader

* Model 1 coefficient for length in full model = -0.074.

* Model 3 coefficient for res_L_tw in last model = -0.074.

HTH.