Im doing some research with some panel data I have on firm output and investment.
I ran two equations.
- $$\Delta y=\alpha_0+\Delta\alpha_1x+\epsilon$$
in R these equations were prodouced using these commands
1) lm(output~investment+I(investment^2)) 2) lm(diff(output)~diff(investment))
The first equation had statistical significance on the 1% level, however with the first differenced data statistical significance was lost, and I ended up with rather high p-values as if there is no relationship between the two variables.
What is the interpretation of such results (i.e is there a relationship between investment and output in this data set) and which regression should I use in my research?