Is Multicollinearity important?

[ErikJosephine]

Hello!
I have a question. Im doing a double log regression to find a price-elasticity on which we are gonna base a lot of further calculations on. I found that my material suffers from multicollinearity so I tested for the VIF and it showed a value of 85(!) and R^2=98,9845 when I tested the price-elasticity variable on the other explanatory variables. Still I dont want to drop any explanatory variables since that would lead to less significance (p-value). What should I do, should I even care about the multicollinearity?

Thanks!

[trubador]

Multicollinearity only increases the parameter uncertainty. Unless they conceptually measure the same thing, then you do not have to drop your explanatory variables. You should be more afraid of the omitted variables problem. For instance, if you try to measure the impact of prices, then you can choose between consumer price index and deflator. However, if you have import unit value index (or oil prices) instead of deflator, then it would be wise to use both without worrying about the level of multicollinearity...

[ErikJosephine]

Thanks a lot for your answer!!
I want to interpret the parameter so that's an increase in parameter uncertainty I can't afford. Im using a consumer price index in this regression. Since it's elasticities I want to measure Im afraid I have to correct the Multicollinearity so I can know with certainty that my data at least is correct all the way, even if it now gives me sky high standard errors :?

[ErikJosephine]

Btw, there is one more thing I wonder about.
I found evidence of both trend-, and difference stationarity but when I adjust for trend stationarity (by adding a trend/time variable) I still get high correlation between my explanatory variables, as high as 0,9..! Should I still care about this since I adjusted with the @trend variable or does the multicollinearity problem still exist? I have looked through the literature but cant find a clear answer :S

[trubador]

Multicollinearity has nothing to do with the accuracy of the results, it just widens the confidence intervals. I am not sure if that much precision is really important for your study, but one way to decrease the parameter uncertainty is to increase the sample size, which might lead to other problems (e.g. parameter stability) within the context of time series analysis.

If the original forms of variables have to be nonstationary for the sake of analysis, I usually prefer to use the methods that can handle nonstationarity instead of transforming the variables to make them stationary. Anyway, you still get high correlation between explanatory variables since the trend variable itself is used as an additional explanatory variable that accounts for the nonstationarity only in the dependent variable (hence the very high standard errors). You should deal with the stationarity issue in the variables before you put them altogether to run a regression.

The results will depend on your choice of model structure, so I suggest you to spend more time at this model building stage and refer to the textbooks that you have access to...