Lagged variables with multicollinearity

[Chris_Banana]

Hey everybody

I am trying to find out the influence of macroeconomic factors on premium payments in mergers & acquisitions for UK. I have 10 regressors (GDP; interest rate, consumer sentiment, foreign direct investment etc...). The premiums I use are average and median for quarters and later on to check results also average and median for months. I use the percentage change between the quarter/months of premiums. I have done unit roots tests and to get stationarity of may variables had to take the dlog of all my regressors. In addtion, this step allows me that I actually compare apples with apples (for both sides the precentage changes).

My question:

It is common that there is a strong multiocollinearity between the macroeconomic factors. But I do not know the real lag length of my regressors (I expect that some of them myigh be lagged up to about 18 months or 6 Quarters). How can I then check for collinearity and multicollinearity in this case - I mean do I have to make pariwise correlation Cheng et al. suggested that if variables are highly correlated in a pairwise check, they most likely are also multicollinear) with all lagged values or how would the process look like?. Would „orthogonalization of the independent variables“ be a solution.

If I have received the ideal lag-lenght of all my regressor, what would be the ideal model to be used in Eviews? Or would it be a alternative to just run a Polynomial Distributed Lag Regression model, because influence of my macroeconomic factors mitght be distributed over several periods. How can I determine this? What about VAR and factor model?

Many thanks in advance for your support. My main problem is really how I can achieve a "clean" process working with my many potentially lagged variables ...

Best,