Econ 302.
Econometrics
Bilkent University
Department of Economics
Taskin
Sample Questions
1.
In the following system which describes the equilibrium in a macro model:
Ct   1   2YDt   3 Ct 1  u1t
I t  1   2 rt 1   3Yt  u 2t
YDt  Yt  Tt
Yt  Ct  I t  Gt  NX t
a) Distinguish between the exogenous and endogenous variables of the system.
b) (*2) If you are going to use 2SLS in the estimation of the consumption and investment
equations, what are the equation that you will estimate in the first stage. How will you use
these estimation in the second stage?
c) If the following regressions are the results of the 2SLS and OLS estimation of the
consumption function:
Cˆ t  209.06  0.37YDˆ t  0.66Ct 1
seˆ.....................(0.13).......(0.14)
2SLS
t  stat..............2.73...........4.84
Cˆ t  266.65  0.46YDt  0.56Ct 1
seˆ.....................(0.10).......(0.10)
OLS
t  stat..............4.70...........5.66
What is the difference between the YDˆ t and YDt variables?
d) What are the properties of the 2SLS and OLS estimators? Why?
2. Consider the following model:
Yt   1   2Wt   3 X t  et
Wt   1   2Yt  u t
where et and u t are random errors with mean zero and constant variance.
a)
b)
c)
d)
Indicate the exogenous and endogenous variables of the model.
If you estimate the first equation by least square method, what would be the properties of the least square?
Solve for the reduced form equations of the model.
A researcher estimates the reduced from equation that you find in (c) and obtain
Yˆt  4  8 X t
Wˆ t  2  12 X t
Which structural coefficient, if any, can be estimated from the reduced form coefficients? Demonstrate your
calculations.
e) How does your answer to (d) change if it is known a priori that  2  0 ,? (Find the
structural form parameters if  2  0 )
3. In the following simultaneous equation model: The first equation is a demand relationship where quantity
demanded ( q t ) is a function of price (
p t ) , and the second equation is the supply relation where supply price (
p t ) is a function of wage ( wt ) and quantity ( qt ) produced , the structural equations are:
q t   0   1 p t  u1t
p t   0   1 wt   2 q t  u 2t
a.
Indicate the exogenous and endogenous variables of the model.
b.
Derive the reduced form equations. Using the reduced form equations, express the structural parameters
 ' s, and  ' s in terms of the reduced-form coefficients.
c.
If the reduced form equations are estimated as:
q t  25  12wt
p t  11  24wt
Compute the identified structural parameters. Are there other structural parameters that are not
identified? Explain.
d.
4.
(Extra Credit) How will you modify the system to make both of the equations identifiable.
The following system of equations is given:
Y1  a0  a1Y2  a 2 X 2  u
Y2  b0  b1Y1  b2Y3  b3 X 2  b4 X 3  v
Y3  c0  c1Y2  c 2 X 4  w
[All time subscripts are dropped from the variables for the ease of computation]
a.
b.
c.
Determine the endogenous and exogenous variables.
(Using order conditions determine the identification condition of each equation.)
Explain how you will use 2SLS method of estimation for equation 2 of the system.