Regression of Real GDP on Intellectual Property Products Problem

I have a question regarding regressing the log growth of Real GDP on the log growth of Intellectual Property production which contributes to GDP (through using the expenditure method of calculating GDP). My question is does this regression make sense? I used the dollar values initially and I had an absurdly high R^2. After refreshing my knowledge of Time Series regression I changed the model as well as adding a lag for the log growth of IP production. The values I get seem as if they are economically and statistically sound. However, I am not sure if my model makes sense as IP production is a component of calculating Expenditure based GDP.

My goal for this was to find out what effect IP production will have on economic growth in order to quantify some type of relation that I can add in a report regarding to a project which proposes an increase in IP production of a state.

I apologize if the question seems rather trivial. I'm possibly undertaking more then what is required for this project but I'd like to gain some knowledge through doing this. Thank you in advance.

It is never a good idea to regress something so complex as GDP on a single variate. There may be myriad confounding factors.

I can think of two suggestions here:

1) Lookup Barro's and Sala-i-Martin book on Growth, the empirical part, to get an idea of what kind of factors seem to appear to influence growth (or what kind of factors growth can be decomposed into). They can be used as control variables, in order to check whether in their presence IntProp remains a statistically significant variable, and even if it does, what is the magnitude of its effect (so that one can assess its economic significance also).

2) Consider detrending your variables, either linearly or non-linearly using for example the HP-filter, and regress the cycle components and perform the usual correlation analysis of real business cycle models, in order to see whether IntProp leads or lags the GDP cycle. If it leads, an argument could be made that in the short-run at least IntProp pushes the growth cycle out of its trough.

• Thank you for your suggestions, I shall research them accordingly. Just to add some more insight on my question, I was looking to utilize a range of coefficients using a positive and negative bias, preferably just a minimum as it will be a supplement to the main arguments made in the report. Also, I included a liner time trend in the regression, however, it is statistically insignificant, do you know why this is so? – Sam Jul 5 '17 at 15:08
• Edit: After further looking at my regression it seems as if after transforming the data to log difference's, the relationship between time and log growth of Real GDP is no longer linear. Would this be correct? – Sam Jul 5 '17 at 15:22
• @Sam Log-differences approximate the growth rate of GDP which has been found to be roughly constant and certainly without a linear time trend (but this means that log-GDP has a linear trend). The issues you pose in your first comment are foggy. You need to include then with enough detail in your question perhaps. Writing down the regression expression would help. – Alecos Papadopoulos Jul 5 '17 at 15:34
• This is my regression expression $\Delta \ln(GDP_t)=\beta_0+\beta_1t+\beta_2\Delta \ln(IP)_t+\beta_3\Delta \ln(IP)_{t-1}+\epsilon_t$ – Sam Jul 5 '17 at 16:30