Economics 835                                               1
Spring 1998
D. Maki
                     Final Examination

Instructions:  There are three parts to this examination,
each with two questions.  Answer one question from each part
(a total of three questions)  Questions are equally
weighted.  Total time allowed = three hours.  This is a
closed book examination.  Throughout the examination, I am
not looking for SHAZAM commands as answers.

Part I:  Answer one of the following two questions.

1. The results of estimating several equations designed to
estimate the effect of interest rates (INT) on housing
starts (HS), using population (POP) and gross national
product (GNP) as additional variables are presented below.
The data are annual times series for the U.S., 1963-1985.
Equation 6 is ridge regression, k=0.2, and equation 7 is
estimated in first differences (drop first observation).
(Student's t-values in parentheses)

1.  HS = -1315.8 - 184.8 INT + 14.9 POP + 0.5 GNP
          (-0.27)  (-3.18)     (0.41)     (0.54)

2.  HS = -3812.9 - 198.4 INT + 33.8 POP
          (-2.40)  (-3.87)     (3.61)

3.  HS = 687.9 - 169.66 INT + 0.9 GNP
         (1.80)  (-3.87)      (3.64)

4.  HS = -2705.7 - 184.1 INT + 21.5 POP + 110.2 (GNP/POP)
          (-1.08)  (-3.19)     (0.92)     (0.58)

5.  (HS/POP) = 2.1 - 0.7 INT + 0.9 (GNP/POP)
              (0.62) (-3.75)   (2.55)

6.  HS = 652.1 - 74.9 INT + 4.5 POP + 0.2 GNP
         (1.07)  (-3.28)    (1.91)    (2.60)

7.  DHS = -375.8 - 228.2 DINT + 165.9 DPOP + 0.8 DGNP
           (-0.63) (-3.67)      (0.64)       (0.95)

The (R2, Sigma2) values for these equations are:  Eq 1
(0.44, 77801), Eq 2 (0.43, 75029), Eq 3 (0.43, 74557), Eq 4
(0.44, 77627), Eq. 5 (0.43, 1.719), Eq 6 (0.28, 98948), Eq 7
(0.51, 63789).

a.  If equation 1 is the basic model, what econometric
problem is being solved by equations 2-7?  Comment on the
appropriateness of each solution, and how well it worked.
b.  Which equation would you use to provide the estimate of
interest?  Explain.
c.  Can the above results be used to perform a Hausman test
of model adequacy?  Explain.
d.  Is there anything in the above output which must be a
typo (impossible result)?  Explain.


2.  a.  Explain how the following tests for                 2
heteroscedasticity may be performed:  Park test, Glejser
tests, Goldfeld-Quandt test, Breusch-Pagan-Godfrey test,
White's general heteroscedasticity test.
b.  In a case where Y=f(X1, X2) explain in detail how you
would correct heteroscedasticity using WLS, including how
you would test to see if WLS actually "cured" the problem.
c.  For the matrix model Y=XB+u, where E(uut)=V, show what V
looks like if there is heteroscedasticity.  Since GLS is
equivalent to OLS on a transformed system TY=TXB+Tu, show
what the T matrix looks like in this case.

Part II.  Answer one of the following two questions.

3.  Shirley Almon estimated the following model using
quarterly data for the period 1953-1961 (U.S.
manufacturing). E is capital expenditures, the Sit are
seasonal dummies and the A terms are capital appropriations,
(standard errors in parentheses).

Et = -283St1 + 13St2 - 50St3 + 320St4 + 0.048At  +0.099At-1
                                        (0.023)   (0.016)

+ 0.141At-2 + 0.165At-3 + 0.167At-4 + 0.146At-5 + 0.105At-6
  (0.013)     (0.023)     (0.023)     (0.013)     (0.016)

+ 0.053At-7         Rbar**2 = 0.922,  DW = 0.890
  (0.024)

a.  Explain carefully how you would test whether the data
exhibit seasonality.
b.  What degree of Almon lag do you think was used?
Explain.
c.  Do you suspect that any end-point restrictions were
applied?  Explain.
d.  Do you consider this a good estimation?  If not (or if
you are uncertain on the basis of the information given)
what tests and/or additional estimations would you perform?

4.  a.  Derive the estimating equation for an application
where Yt = f(X1t, X2t, X3t) + ut, and a Koyck lag is desired
for X1 but no lag distribution is desired for X2 or X3.
b.  If ut (case 1) satisfies the CLR assumptions, or (case
2) is AR(1), what are the properties of the estimators
derived by OLS estimation of your equation in part a?
Explain.
c.  If in either of the two cases in part (b) OLS produces
inconsistent estimators, how might you obtain consistent
estimators?  Explain.

Part III.  Answer one of the following two questions.

5.  Using cross-section data for the 58 counties in
California, data on the following variables were obtained
for 1980 and 1990 (116 observations in total):  MINC=median
income, FS=persons per household, HS=percentage of
population (25 years and over) that had only high school
education, COLL=percentage of population (25 years and over)
that completed four years or more of college, URB=percentage
of population in urban areas, D90=1 for the 1990 data, zero

for 1980 data.  Information for four estimated models is    3
available (p-values in parentheses):

Variable   Model A     Model B       Model C      Model D
CONSTANT  -16.9(.22)   98.4(<.01)   -17.0(.21)   -40.2(<.01)

FS          4.9(.12)  -20.2(<.01)     4.9(.10)    10.0(<.01)

HS          0.2(.02)   -0.4(<.01)     0.2(.02)     0.3(<.01)

COLL        0.3(<.01)   0.5(<.01)     0.3(<.01)    0.4(<.01)

URB         0.1(<.01)   0.1(.53)      0.1(<.01)    0.4(<.01)

D90       -36.2(.05)                -35.8(.04)

D90xFS      9.9(.01)                  9.8(<.01)    2.1(<.01)

D90xHS      0.2(.12)                  0.2(.12)

D90xCOLL    0.9(<.01)                 0.8(<.01)    0.8(<.01)

D90xURB    -0.1(.94)
____________________________________________________________
RSS         763.029     5172.56       763.069      796.560

a.  Calculate the test statistic, and note its distribution,
for testing the hypothesis that the coefficients are the
same in 1980 as in 1990.
b.  Using Model C, calculate the marginal effect on MINC of
FS, HS and COLL for both 1980 and 1990.
c.  Discuss the good points and bad points of each model.
Which one do you prefer?  Explain.

6.  Answer both unrelated parts of this question.
a.  In a four equation model with 3 exogenous variables: X1,
X2 and X3, the matrix of coefficients is:

Dep.Var.  Y1   Y2   Y3   Y4   X1   X2   X3
Y1        X    0    X    X    X    0    0
Y2        X    X    X    0    0    X    X
Y3        0    0    X    0    X    0    0
Y4        X    0    X    X    0    X    0

Which of the equations are identified by (i) the order
conditions and (ii) the rank conditions?  Explain in detail
how you would get consistent estimators of the coefficients
of the identified equations.

b.  In the case of autocorrelation of form AR(1), explain
how the (i) Cochrane-Orcutt and (ii) Hildreth-Lu approaches
estimate rho.  Explain how the equivalent of EGLS is
performed using OLS on a transformed system, once rho has
been estimated.  Include an explanation of the calculation
of the residuals of the equation.