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I try to grasp the concept of instruments in 2SLS regressions.

I have a variable that is correlated with an endogenous regressor (informative). I also believe that it is uncorrelated with the error term, however, it may be correlated with the error term by another variable in the model. I wonder if this is a valid instrument.

I give an example. Let's regress violent conflict on political stability and democracy.

For democracy I use as an instrument 'inflation'. Now inflation, let us suppose, is unrelated with any potentially omitted variable in my regression, such as, for example religion, military strength etc.

However, inflation is related with political stability as it may cause it and political stability predicts violence. So my instrument is indirectly related with the variation in the error term. Would that be still a valid instrument?

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