Question

True or False:

( ) Consider the model y=α1+β1x+u, where x is an endogenous covariate and z is a valid instrument for x. The model x=α2+β2z+u2 can be said to be a reduced-form equation for x.

( ) Valid instrumental variables are usually very difficult to find.

( ) 2SLS is (under certain assumptions) the most efficient IV estimator.

( ) The normal distribution of the error term is a crucial assumption for making inferences using the 2SLS estimator.

Answer 1

1: It is True because in reduced form equation , corelation between exogenous(independent ) variable and disturbance turm(u2) is zero, that is they are uncorrelated.

2: It is True because you need to show that it is correlated with the endogenous independent variable but not with the residual , which is often not trival.

3: It is true because it is valid in both under exact identification and over identification.

4: it is not true  because assumption of normal distribution of error term is valid for testing not for inference. For inference its not necessary to assumptins of normalty of error term.