I am running an asset pricing test (Fama MacBeth); regressing one month ahead excess stock returns on market beta and some firm-level variables (e.g. MAX and EISKEW shown below). My object is to evaluate the (if any) effect of controlling for two variables MAX and/or EISKEW on the third variable market beta (theory predicts a positve coefficient on market beta and returns).
I have included a picture of my results, where model (1) exclude the control variables and model (8) include them. My interpretation is that they both seem to have a meaningful effect as the coefficient is shrinking towards zero, but not in a substantial way.
Are there any more formal way of analyzing/interpreting the effect of control variables on another independent variable?