Take the linear instrumental variables equation Y1 Z1 Y22 e with E[e j Z] 0 where both X and Z are

Take the linear instrumental variables equation Y1 Æ Z¯1 Å Y2¯2 Å e with E[e j Z] Æ 0 where both X and Z are scalar 1£1.

(a) Can the coefficients (¯1,¯2) be estimated by 2SLS using Z as an instrument for Y2?

Why or why not?

(b) Can the coefficients (¯1,¯2) be estimated by 2SLS using Z and Z2 as instruments?

(c) For the 2SLS estimator suggested in (b), what is the implicit exclusion restriction?

(d) In

(b) what is the implicit assumption about instrument relevance?
[Hint: Write down the implied reduced formequation for Y2.]

(e) In a generic application would you be comfortable with the assumptions in

(c) and (d)?