Regression interpretation question
I'm doing an OLS regression with an ending balance (econometrics class) as my dependent variable and the S&P 500 (among others) as my independent variable. The data is monthly. Now, I've discovered that the S&P 500 is not stationary, but it is in first differences. I'm keeping my dependent variable as is (level, not logged). Here's my question:
1. If I take the log of the first difference of the S&P 500 (dlog(S&P 500)), I would interpret its coefficient as, "a 1% increase in the S&P 500 will change the ending balance by (coefficient)/100."
2. Suppose I lag the variable so now I'm looking at dlog(S&P 500(-4)). I would interpret this as, "a 1% increase in the S&P 500 four months ago would increase this months ending balance by (coefficient)/100. Thus, it seems that it takes four months for S&P movements influence the ending balance."
What do you guys think?