True or False: (with explanation)

1) ______ The "exclusion restriction" imposed on the instrumental variable z implies that z belongs to the causal model of interest.

2) ______ Consider the model y=+x+u, where x is an endogenous covariate and z is a valid instrument for x. In this case we can write =C[y,z]/C[x,z].

3) _______ In the context of a 2SLS estimation, it is usually risky to use models that are non-linear in the parameters to produce first-stage estimates, since in this case we can no longer guarantee that the first-stage residuals will be uncorrelated with the regressors included in the second-stage.

4) ______ When all identifying assumptions are valid we can trust that the Instrumental variables (IV) estimator will be consistent.

5) ______ Consider the model y=+x+u, where x is an endogenous covariate and z is a candidate instrument for x. If there is correlation between z and u but it is smaller than the correlation between x and u it will be always better to use IV estimation than OLS estimation because IV should be less inconsistent.

6) ______ Weak instruments can cause coefficient standard errors produced by IV estimation to be much larger than those produced by OLS.