I am testing the statistical significance of some explanatory variables in a factor model, using the Fama-MacBeth two-pass regression (also known as the Cross-Sectional Approach).
Assuming my dependent variables are stock returns, and that my explanatory variables are macro factors, such as Inflation, Oil prices, Industrial Production:
I first run a rolling-time-series regression (60 months window) of each stock with respect to all my explanatory variables. This will result in a time-series of sensitivities of each stock to the macro variables.
Then, I run a cross-sectional regression for each month of my sample period, using stock returns as dependent variables, and the estimated sensitivities as independent variable. When the cross-sections are ran, we obtain the time-series factor values. For each factor, I test whether significantly different from zero.
Consider the following cross-sectional regression:
$R_i,t = \alpha_i,t + \beta_{i,1}(t)F_1,t + \beta_{i,2}(t)F_{2,t} + ... + \beta_{i,n}(t)F_{n,t} + \epsilon_i,t $
where the betas are estimated in previous periods, using time-series regression. The purpose of the cross-sectional regressions is to get time-series values of $F_1$, ..., $F_n$.
After I test for significance, I only collect the k significant variables, and include them in a regression. I redo the same test as above (time-series and cross-sectional regressions), only using my selected k variables.
BUT NOW, none of my k variables are significant!!
I am not sure how to construct my final model based on these results. Any help would be appreciated! Thank you!
