Usually its best to understand what specific question you are trying to answer along with the nature of the data you have and its context in order to give useful advice.
Can you elaborate on some of these?
Currently i have the following multivariate model Y = a + bX +bZ, where Y is the dependent variable and X and Z are independent variables. I have ran a Granger Causality test, and have found that variables Y causes X and X Causes Y). The Z variable causes Y, but Y does not causes Z. I believe multivariate regression may be the wrong technique to apply in this situation, but i am not sure though. Do you guys have any suggestions?
Any help would be much appreciated!
the dependent variable Y, is a measure of economic activity (I.e. log-difference induatrial production). The independent variable X is a measure of monetary stance (I.e. term spread) and the Z variable is a default risk indicator (baa aaa spread). The X variable is granger causal of Y, and Y is granger causal of X. Z is grandual causal od Y, not the other way round.
If you are going to use regression, then one thing you should be asking is how much variation the regression model explains given the response and predictor variables (and any assumptions used).
The correlation/causation issue is something that you will need to evaluate on top of this and it will require expertise, domain knowledge, and some kind of judgement on your part that I can't help you with.
The amount of variation explained in a model can be found by running regression algorithms in normal statistics packages.
You will want to look at things like the AIC and Likelihood Ratio Statistics to see how well a regression explains the relationship between variables.
If the relationship is good, then these statistics will reflect that.