You can't estimate the effect until you know the causal structure: $Edu \to GDP$ or $Edu \leftarrow GDP$, $Edu \leftrightarrow GDP$, $Edu_{\leftarrow}^{\to} GDP$, $Edu_{\to}^{\leftrightarrow} GDP$, etc.
Learning the causal graph between two variables is an active area of research. There are currently two main classes of techniques available:
Methods based on non-Gaussianity of the error terms (e.g. LiNGAM) and
Methods based on non-linear relationships between the variables (e.g. Additive Noise Models).
However, these two classes of methods generally assume that there are no unobserved confounders and no feedback cycles. People are working on allowing unobserved confounders (see, e.g., (1), (2)). Furthermore, both methods require IID data and a pretty large sample size.
You might want to look at the solutions used by the winners of the 2013 Cause-Effect Pairs Challenge (solutions were presented at the 2013 NIPS workshop on causation, and the slides and code are all up on the website).
Adding more variables to the model could help a lot, because then the conditional independence relations become informative, and allow the use of causal inference algorithms that can handle cycles (e.g. CCD). Frederick Eberhardt is working on a SAT-solver based method that can handle cycles AND unobserved confounders (it's still in development).