Depending on the goal of your analysis, you may want to take a different approach; but, often, more regressors do not necessarily improve a model. Rather than throwing in as many potentially relate variables into your regression, you may want to start with a more theoretical approach to try an determine the underlying supply side and demand side factors that drive industrial output.
It seems to me that the regressors you have included can be broken down in this way:
- Supply Side: producer price index and interest rates
- Demand Side: population, inflation, interest rates, unemployment, and seasonal adjustment
- Other: auto and truck sales and PMI
While I am sure that the "Other" regressors are correlated with your dependent variable, do you really think they are determinants?
That said, if you were to include a lagged term for auto sales you could make the argument that the more cars/trucks bought in the last period would influence the demand for gas and electric in the current period. Additionally, you may have an argument for the PMI, but my point is that you should try and think of the underlying variables driving the supply and demand for industrial production.
Given the above comments, I would say you could add these potential variables:
- Supply Side: Government investment in infrastructure, gross fixed capital formation (for the relevant industries), oil prices
- Demand Side: Per capita income, manufacturing exports, oil prices
I am sure there have also been many studies like this in the past, and the previous literature is always a good place too look for additional ideas in the modeling process.
