I have a situation where I have an instrument that seems very convincing and robust during 2sls, but is significant in wrong direction when checking a reduced form equation, i.e. regression the dependent variables on the exogenous variables and the instrument itself without the endogenous variable. Is there anything to do but conclude that the instrument is invalid?
Does your model correct for the outcome or for something closely correlated with it? If so, that may be the problem.
For example, if your outcome is mortality and you correct for smoking status, but people only quit when they can't handle the side effects any more (i.e. are dying) current smoking may be associated with survival.
I have as far as possible; my idea was that trust may affect crime and so I instrumented for trust by using the ruggedness of terrain in Africa as this was shown to be a determinant of the slave trade which has been shown to affect contemporary trust. The strangest thing is that ruggedness and the slave trade had the wrong signs, despite giving consistent and intuitive IV estimates.
Not sure I understand your model, but I seriously doubt many of the assumptions. Most crimes, especially violent ones, are committed by acquaintances and thus a community which relies heavily on inter-individual trust rather than a centralized police force may have a higher crime rate. In turn, those communities may be more often found on rugged or otherwise impassable terrain (mountainous highlands, jungles, islands).
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