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

[Peter Schmid]

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

[Phil Bromiley]

You are more likely to obtain a helpful answer if you follow the FAQ on asking questions - provide Stata code in code delimiters, Stata output, and sample data using dateex. Also, try to simplify your presentation to the core issues.

Variance decomposition has a whole literature of its own. A lot of it appears in the anova context. Note that by using variance and r-squared, you're really dealing with the square of importance. This can make the size of effects look more different than they are.

These models are very different than the approach most commonly used for regression. The dummy variables are very coarse proxies for underlying constructs (which is why we moved to regression from anova as soon as it became computationally easy).

If you're going to work on this, you should look at the literature. I did a little (c.f., Brush & Bromiley, Strategic Management Journal, 1997; Brush Bromiley, and Hendrickx, SMJ, 1999) but many folks have done related studies. McGahan and Porter did several related papers. Others have used CEO dummies. Most do not consider the endogeneity issue.

Yes, there is an endogeneity issue. Suppose low performance resulted in CEO turnover. Then we have the rhs CEO dummy being influenced by the dv ROA.

[Carlo Lazzaro]

Peter:
you can also be interested in -estat esize-.
Endogeneity biases your regression model; hence, any subsequent post estimation procedure will refer to a biased regression model.