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This question is about finding valid instrumental variables.

Variables are:

  • the response variable for the structural equation, $y$
  • the jointly endogenous RHS variable in the structural equation, $m$
  • two control variables ($x_1$ and $x_2$) that will always appear on the RHS of the structural equation
  • four potential instrumental variables, denoted by ($z_1$, $z_2$, $z_3$, $z_4$)

The problem of course, is that you have no idea if the potentional IVs are admissible. Your mission in life is to identifity those Instrumental Variables for which the exclusion restrictions are valid, and to estimate the casual effect of $m$ on $y$ in a linear regression on the form:

$$y=x_1\alpha_1+x_2\alpha_2+m\beta+u$$

I dont have any background in these area; is that question trivial or not ?

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Take a look at Austin Nichols' causal inference with observational data notes for a nice outline of endogeneity testing for IV. The handout is aimed at Stata users, but most of the tests should be available in other packages. Christopher Baum's IV notes are pretty good as well. They cover weak instruments and testing when you have more instruments than endogenous variables (over-identified case).

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Try this one: http://en.wikipedia.org/wiki/Sargan_test there is no way to conclusively determine the exogeneity of a given instrument, but it might provide some information.

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