# simple linear regression causality

lets say we have a perfect linear regression, i.e. we have included all relevant variables (to prevent OVB: omitted variable bias), and also such that there is no other problems like mutli-collinearity.

in this case, can we infer causality between a predictor variable x and the outcome variable y?

i understand that in normal cases, we cannot assume causality due to the possibility of there being a confounding varaible. however, if we solve OVB, we naturally solve for the lack of confounding variable, since it will be included.

therefore in this case, is it okay to infer causality?

• i ask this because i also understand that when we choose y and x, we try to choose it in a way that makes logical, casual sense e.g. wage as y, education as x and not the other way around Oct 9, 2020 at 12:31
• ALSO since, from an economic POV, coefficient of a predictor variable captures the effect of xi on y, holding all else i.e. other variables constant Oct 9, 2020 at 12:45
• Having a baby is a beautiful explanatory variable for gender. Would you conclude that one's gender is caused by giving birth??
– whuber
Oct 9, 2020 at 15:01
• OVB is related to causality, however the problems are deeper. See here: stats.stackexchange.com/questions/493211/… Sep 13, 2021 at 7:12
• Even if you have measured all the variables causally related to the two variables you're invested in, this does not solve your problem. Among them, there could be a set of variables that, if adjusted for, you would bias your estimate of the effect between your variables of interest, X and Y, for example. The identification step in causal inference is much more complicated than just having all these variables measured. Dec 11, 2021 at 23:58