I have panel data with approx. 20,000 observations on different firms and years. In each observation, a firm makes a business decision, deciding for either $A$ and/or $B$ (both are continuous from 0 to 1).
My hypothesis is that firms will decide for one, not both of these options, i.e. combine a larger $A$ with a lower $B$ or reverse, as opposed to going both high or both low. The null hypothesis is that these are not correlated.
Using Stata, I tried
corr A B
which gave me a correlation coefficient of 0.24. However, I can clearly not include my independent and control variables that I have in other models.
I read about the commands
mvreg, and implemented them, following this link. In particular,
mvreg, noheader notable corr
displays the correlation matrix of residuals. It is 0.09 (p-Value > 0.0001). Is this number a better use to investigate my proposed positive correlation?
I noticed that the
mvreg-regression with some independent and control variables $X_1,X_2,C_1,...$
mvreg A B X1 X2 C1
is just a combined display of
reg A X1 X2 C1 reg B X1 X2 C1
Hence, nothing in there is actually telling me whether or not $A$ increases at a cost of $B$ or not (or am I not seeing something?)
Also, if I understand correctly,
manova is telling me whether the independent variables are suitable to be included in the model, by displaying the results of four statistical tests for each independent variable. Again, nothing that tells me if the two dependent variables are substitutes for each other or going hand in hand.
My question is: Is there a way for the "correlation question" to include independent variables and make use of the fact that I have panel data, or is the correlation coefficient
corr A B actually "sufficient" and "elaborated enough" for my hypothesis test?
The only other thing that comes to my mind is to divide the whole sample into subsamples by firm size, age, etc., and check if the correlation coefficient is consistent across subsamples.