I is the observed logged output thus our regression

i
is the observed logged output. Thus, our regression equation is
y
i
= c + °k
i
+ ±l
i
+ ²
i
+ "
i
:
2

(a) (5 points) First, take log of Y; K; L; and ° . Report summary statistics for Y; K; L; ° ; and w .
(b) (6 points) Regress y
i
on constant, k
i
; l
i
; and ²
i
: Test if this function exhibits constant returns to
scale.
(c) (6 points) In reality, we do not observe ²
i
: Typically a °rm with high productivity shock will use
more input. For the sake of argument, assume that capital is °xed, and therefore k
i
and ²
i
are not
correlated. However, l
i
and ²
i
are most likely correlated. Under this circumstance, what would
happen if we regress y
i
on constant, k
i
; and l
i
? Would the parameters be consistently estimated?
What would you expect those parameter estimates to be, compared to ones obtained in (b)?
(d) (6 points) Regress y
i
on constant, k
i
; and l
i
: Interpret your result.
(e) (5 points) Now consider wage w
i
that di/ers across locations of °rms. State conditions under which
variable w works as an instrument for l: Do you expect those conditions to be satis°ed? Explain.
(f) (6 points) Assume those conditions you identi°ed in (e) are satis°ed. Run the IV regression to
estimate ° and ±: Compare your result with the ones obtained in (b) and (d).
3