Question

Consider the following equations:
y1 = a1y2 +a2y3 +x1 +x2 +e1 (1) y2 = by1+2x3+x1+e2 (2) y3 =cy1+e3 (3)
Here a1, a2, b, c are unknown parameters of interest, which are all posi- tive. x1, x2, x3 are exogenous variables (uncorrelated with y1, y2 or y3). e1, e2, e3 are error terms.
(a) In equation (1), why y2,y3 are endogenous?
(b) what is (are) the instrumental variable(s) for y2, y3 in equation (1)?
(no need to explain why)
(c) In equation (1), are (a1,a2) over-, exact-, or under-identified? (no need to explain why)
(d) In equation (3), why y1 is endogenous?
(e) what is (are) the instrumental variable(s) for y1 in equation (3)?
(no need to explain why)
(f) In equation (3), is c over-, exact-, or under-identified? (no need to explain why)

Answer 1

a) y2,y3 is Endogenous variables because y2,y3 have values that are determined by other variables in the system (these “other” variables are called exogenous variables). and y2,y3 are endeogenous as they are explained by model.

b) z1 is instrumental variables.

c) a1,a2 exact identified.

d) y1 is Endogenous variables because y1 have values that are determined by other variables in the system (these “other” variables are called exogenous variables). and y1 are endeogenous as they are explained by model.

e) z2 instrumental variables.

f) c over-identified.