How to make sure explaining variable actually explains explained variable, and not vice versa? I'm somehow stuck about the way I should verify regression models.
For instance, an extremely over-simplified version of the Solow Growth Model might look like this:
$$ growthrate = \beta_0 + \beta_1 savingsrate + u $$
So how can I make sure now that there is not only correlation, but causation in exactly that direction?
How can I make sure that the real relation is not
$$ savingsrate = \beta_0 + \beta_1 growthrate + u $$
I understand that endogoneity deals with the case where u is related to the explaining variable; simultanity deals with the case when explaining and explained variable are determined at the same time; but how about cases where explained variable is determined before explaining variable?
I somehow feel that I miss a very basic point here, but cannot figure out where exactly. 
 A: You could rewrite the bottom equation as growthrate = -b0/b1 + (1/b1) savingsrate - u/b1
In other words each expression is just a re-parameterization of the other.
What I think you're really getting at is a question of causality, which generally only enters into statistical analysis in terms of how the model is specified (at which point the direction of causality is either assumed or implied, as in your case, or the investigators limit the scope of the interpretation to being a correlation-based prediction). 
It is possible to see whether data is consistent with a particular specification, or use some model selection statistics to choose between specifications. With some time series data, you could check which direction of causality is more consistent with the data, but you would need more than those two equations, you'd need to incorporate the time dependence into the model.
In general, determining the certainty of whether one has the correct specification is outside statistical analysis and is in fact, unknowable (hence the "all models are wrong" aphorism). 
