The assumption that the disturbances are normal allows exact inference about the estimates and standard errors of the estimated coefficients. When the normality assumption is not valid (and the other assumptions are) the estimates are still consistent and the central limit theorem allows one to make inferences that are valid in an asymptotic sense. Wooldridge, Introductory Econometrics, (Chapter 5 in 4th edition) contains a good introduction to this asymptotic theory.

I should perhaps not that your variables are likely to be non-stationary and OLS may give rise to spurious results. This probable failure of OLS assumptions is far more serious than the failure of normality  . 

The assumption that the disturbances are normal allows exact inference about the estimates and standard errors of the estimated coefficients. When the normality assumption is not valid (and the other assumptions are) the estimates are still consistent and the central limit theorem allows one to make inferences that are valid in an asymptotic sense. Wooldridge, Introductory Econometrics, (Chapter 5 in 4th edition) contains a good introduction to this asymptotic theory.

I should perhaps not that your variables are likely to be non-stationary and OLS may give rise to spurious results. This probable failure of OLS assumptions is far more serious than the failure of normality  . 

Dear friend

in expanding the 1st answer

If your data is monthly or quaterly => you should check the seasonal effects before going to check the stationary of your data

In other case, you should check the stationary by unit root test and then regress again and check your models with other problem such as autogression, heteroskedastilicy or endogeneity to chose the suitable model

Best

Canh

The consequence of the lack of normality is that the better the concepts based on the t-Student distribution. Models where random noise are modeled distribution Student give much better results.

The answer depends on the type of non-normality. Some non-normal distributions have infinite variance. Error terms with such distributions are an econometric situation explored early on by C. Granger and D. Orr and others. For example, stable non-Guassian distributions (mostly discovered by the French mathematician Paul Lévy in the early 20th century) have this interesting property, among others.  Also, t-distributions with low degrees of freedom have infinite variance. One key OLS assumption is that the distribution of the error terms has finite variance; this assumption will be stated among the equations of one’s time series model (sigma-squared > 0, etc). Some asymptotic properties of OLS estimates that apply in the “usual” non-normal case depend on the existence of higher-order moments. Check a rigorous statement of the theorem you are relying on in an advanced text. Also, properties of bootstraps are likely to be affected by non-normality in the distribution of the error terms, given that the non-normality is of an infinite-variance type.

Since you probably have a problem of non-constant variance, I would experiment with one of the ARCH family models (ARCH, GARCH, PARCH, TARCH, EGARCH, etc.)

Estimate your variables in real terms, that is real GDP, Real exports, Real consumption. Make use of standardized residual to identify the ith observation and dummy it. Nonnormality is not a problem if u data are stationary and exogenous-- see Hendry's work 

By standardized res, I mean your non-normal residuals divided by SEE of your estimated equation. ith observation implies to select the (in absolute value)  largest std residuals.