Proving causal relationships using observational data
We describe a means of rejecting a null hypothesis concerning observed, but not deliberately manipulated, variables of the form H0: A -/-> B in favor of an alternative hypothesis HA: A --> B, even given the possibility of causally related unobserved variables. Rejection of such an H0 relies on the availability of two observed and appropriately related instrumental variables. While the researcher will have limited control over the confidence level in this test, simulation results suggest that type I errors occur with a probability of less than 0.15 (often substantially less) across a wide range of circumstances. The power of the test is limited if there are but few observations available and the strength of correspondence among the variables is weak. We demonstrate the method by testing a hypothesis with critically important policy implications relating to a possible cause of childhood malnourishment.
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