Why many papers when testing different hypothesis with one dataset they tend to separate in different models to analyse?
Example Model 1: $y = c + \beta_1 Ctrl1 + \beta_2 Ctrl2 + \beta_3 Expla1 + \beta_4 Expla2 + \beta_5 (Expla1*Expla2) $
Model 2: $y = c + \beta_1 Ctrl1 + \beta_2 Ctrl2 + \beta_3 Expla1 + \beta_4 Expla3 + \beta_5 (Expla1 * Expla3) $
and not: $y = c + \beta_1 Ctrl1 + \beta_2 Ctrl2 + \beta_3 Expla1 + \beta_4 Expla2 + \beta_5 Expla3 + \beta_6 (Expla1 * Expla2) + \beta_7 (Expla1*Expla3) $
In the real case they use 8 control variables, and test 3 different models where they always use Expla1 and change for the other while they also try an interaction.
Is it just because too many variables to analyse can lead to a multiple regression less powerful?
I think a image speak better than words. This is an extract from Deb, P., David, P., & O'Brien, J. (2016). When is cash good or bad for firm performance?. Strategic Management Journal.
Each model use the same dataset. I personnally use the same control and explanatory variables (except square of cash) but with a different dataset. Also, I have to use in my case GMM/DPD method with Eviews 9 (to correct for autocorrelation).
My results are inconsistent for "cash", only 2B significant. For the explanatory variables industry competition (positive significance) and industry growth (negative significance). In the interactions I only have cash*industry growth who is statistically significant.
So I did try an multiple regression adding all models (all explanatory and interactions together). In this case cash is not significant, while 2/3 explanatory are significant and 2/3 as well for the interaction.
It's why I'm wondering which way to conduct the analysis is more reliable? Carry independent models as the paper did or doing all variables together.