Actually, in social science you really can't test a hypothesis with data. What's true under one set of conditions won't be true under another and conditions change all the time. Famously, there's the Lucas critique - the idea that a relationship (or the lack thereof) between variables may break, if a policy that exploits the relationship is implemented.

Or take the matter of immigration and international conditions that many others noted in this thread. If every rich country depends on immigration and every poor country strives to become rich, at some point you are going to start running out of places to source immigrants from and there will be a relationship between birth rates and economic performance.