We have N companies. For our research, we aim to run monthly cross$-$sectional regression, in our regression, we regress excess stock returns on the Tax planning measure, and other control variables. Our tax planning measure is Cash effective tax rate $($CETR$),$where lower the rate means aggressive tax planner the company is$.$

Then we extract coefficients from monthly regression for Tax planning measure $($Monthly betas for tax planning$)$ and regress them on Fama French five factors in step $2$ as time series regression to analyse if Tax planning pays premia. We think if we get significant negative alpha it would mean that tax planning is associated with premia. Is this possible that beta coefficients from step $1$ are insignificant whereas, intercept in the step $2$ is significant. If yes why, if no why?

What is the economic reason behind these results? Our approach is cross sectional regression approach which is not similar to fama$-$mac beth approach. Could you also explain the approach which we have used? Would it be correct to say that our approach is$,$ second step of the fama mac beth approach as the first step of the fama mac beth approach fetch the factor exposure which in our case is the CETR, thus we employ the second step of the fama mac beth approach. How can we economically explain this cross sectional approach which we have applied?