Instead of removing multicollinearity, you can choose the regression methods that take multicollinearity into consideration. (For example ridge regression).

Muawya - 

You are talking about collinearity between independent variables, correct?  That was not clear.  Each independent variable needs to correlate with the dependent variable.

This is not something with which i had to deal with very much, but there are some possibilities.  Yes, as noted by Mehmet, ridge regression may help, at the expense of bias, and principle components might help, at the expense of interpretability.  Perhaps you might also want to consider a combined estimator, analogous to the case of forecasts shown in Bates, J.M., and C.W.J. Granger (1969), "The Combination of

Forecasts," Oper. Res. Q 20, 451-468. 

Cheers - Jim

PS - I think that anytime you are looking at relationships between continuous variables, which is what I assume you are doing, it may be informative to look at some scatterplot graphs. 

Leave FDI out, as this is part of exports. So what sense makes the additional FDI variable? Conditional ob exports, the "effect" of FDI on GDP is zero. The other way round, conditional on FDI, the "effect" of exports on GDP is one.

What are you trying to explain anyway? You are estimating an identity: GDP = C+I+G+Ex-Im. Controlling for all of them would yield exact ones on all variables. Leaving out one yields omitted variable bias, and you measure the relationship between the dependent variables.

Sometimes it is not a severe problem. If, anyway, you have to do it, think about more accurate modelling, first of all, of the updated list of the explanatory variables. Also, as it was mentioned in one of the previous answers, try to use more advances regression models that know how to take care of multicollinearity.

... As I understand your project, you view the stock market evolution and its influence on growth. I would first define variables describing stock market evolution (e.g. including FDI and exports) and then condense those within a factor analysis (PCA) to rule-out multicollinearity among the predictors.

I know that it’s not easy to decide which dependent variable you need to remove but you can use data reduction method and put summary scores into the model and put all variables adjusted for the effects of competing variables.

There isn't really enough information to suggest a solution, but some issues you can consider may be: can you just let it be - multicollinearity is not necessarily a show stopper? Can you drop one of the variables? Can you grow the data period by adding more years? do you have multiple dummy variables that cause a dummy variable trap? Or as suggested before, can you use ridge regression or partial least squares?

Since I study similar problem for Brazil, here some consideration:

Well, from you project, and the problem you are facing, I can give some opinions. First, I need to make very clear the fact that I do not know what methodology Omar uses to build it's national countability.

(1) First, you need to learn if FDI is considered on Export (in Brazil it is not). If it is not, then there is no reason to assume that there is multicollinearity. You should test it to see if there is;

(2) If there is multicollinearity, that by itself is a finding, and you should explain, rather then discard. Economy is the science of thing how they are, not how they should be... (in my opinion...);

(3) I suggest you to test different models and see how the R-square and Durbin-Watson fit. That should give more indication how Omar's growth work. I would test: (a) a model with export only, (b) a model with FDI only, (c) a model with both, (d) a model with public debt and FDI; (e) so on...., Also, I would test both GDP and Capital Formation. You could, theoretically, find that Export explains better GDP growth, but FDI explain better Capital Formation.... That have to be tested. In Brazil, for the time series I study, for instance, I found that FDI is a better predictor on both Capital Formation and GDP then Export alone. Internal debt was a better predictor then both, but import was a even better predictor (what is actually already very clear on Brazil's literature). That led me to a tsls model, that I'm still working on considering GDP, investments, consumption, exports, imports, FDI and national debt.

(4) And finally, in my opinion, for the method of analyses I use, i think you should never start from complex econometric models. I usually start from X-Y dispersion and correlation chart. Then try to understand the nature of the variables on that time series, then I look on the literature if anyone already worked with that kind of relation. Then I build sq models for every 2 variables I have, and only then I try to build a theoretical consistent and econometric verifiable model with more complex regressions.

Again: I do not know the country you are studying, and I do not know what theoretical school you prefer, so fell free to ignore all my considerations.

Regarding the comment of Alfred Garloff: FDI is not part of exports, What is true is that FDI is a capital flow that is part of the balance on capital and financial accounts in the balance of payments. That balance equals the current account balance, which in turn includes exports. Of course, this is just accounting, but tells us that any relationship between exports and FDI is not an identity and not likely to be 0 or 1. You need a model to help drive whatever effect you are speculating about.

David is right and I was wrong. FDi is not part of exports (i mixed FDI with the Export of capital goods which is generally not the same). Thus, in fact, it is not an identity that is being estimated and it might be worthwile thinking about a model that relates FDi and GDP.

On the Problem of multicollinearity, when using time series data, common trends might be a reason that drive collinearity. If there is no trend, and you cannot collect more data, there is probably no other way, than to Interpret the joint significance of both. (If your model suggests that you should use FDI and exports as explanatory variables, omitting  is not an Option) 

Multi is problem of independent variables, according to my best of knowledge. if you are asking in this respect then merge variable in to new one, like PCA

take log of variables

Use Principal Component analysis of the multicollinear variables to get an instrumental variable to use in your analysis

I agree with David  O Cushman answer.