# Does endogeneity affect the R-squared estimated in variance partitioning?

#### Peter Schmid

##### New Member
Hi,

I have a likely very simple question but I can’t get my head around the answer. I want to estimate which part of the variance in a firm's return on asset (ROA) can be attributed to year effects, industry effects, firm effects and finally CEO effects. I run an OLS regression to which I sequentially add each group (first year dummies, then industry dummies, firm dummies, CEO dummies). I use the incremental increase in R-squared as the measure of the variance of ROA a group explains. I got the comment today that because there are many time varying factors on the industry (e.g., industry specific temporary shocks), firm (e.g., change in firm size) or CEO (age) level that I don’t include in the model, endogeneity from an omitted variable is present and the coefficients are biased. While this is certainly true, I don't see how it would affect the incremental R-squared attributed to each group (year, industry, firm, CEO). More generally, is endogeneity an issue at all for variance partitioning?

Many thanks in advance and my apologies for the simplicity of the question

Peter

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#### spunky

##### Super Moderator
.... endogeneity from an omitted variable is present and the coefficients are biased. While this is certainly true, I don't see how it would affect the incremental R-squared attributed to each group (year, industry, firm, CEO). More generally, is endogeneity an issue at all for variance partitioning?
Well, OLS multiple regression's R-squared can be expressed as a function of the regression coefficients and the correlations among the dependent and independent variables. To be more specific:

$$R^{2}=r_{xy}^{t}\beta$$

Where [MATH]r_{xy}[/MATH] is the vector containing the pairwise correlations between the dependent variable Y and each predictor X and [MATH]\beta[/MATH] is the vector containing the regression coefficients. Since endogeneity biases correlations and regression coefficients I can't see how it wouldn't negatively affect R2, with the exception of the extremely contrived cases where for some reason the biases are just going in the exact opposite directions for the exact amount so that they end up cancelling out.