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Eonomics 835
Spring 1995
D. Maki
                     Final Examination

There are three parts to this examination, each with two
questions.  Answer one question from each part (a total of
three questions).  All Parts are weighted equally.  Total
time allowed = four hours.  This is a closed book
examination - no books or notes are allowed.

Part I.  Answer question 1 or question 2.

1.  A.  Explain the meaning of the following terms:
     a.  DFFITS
     b.  bounds for parameters (regarding errors in         
         variables in simple regression)
     c.  structural equations versus reduced-form equations
     d.  measuring multicollinearity
     e.  Ramsey's test for homoskedasticity

    B.  Explain how you would fit a piecewise linear
regression function with two "knots" (at Xm and Xn) for a
simple regression model:  Y = f(X).  (Some people would call
this a "three-piece linear spline function.)  How would you
test whether each of the "kinks" actually exists?

2.  Assume there are four models explaining Y:

(A)  Yt = b0+b1Yt-1+b2Xt+b3Xt-1  +b4Zt+b5Zt-1  +uA
(B)  Yt = b0+b1Yt-1+b2Xt         +b4Zt         +uB
(C)  Yt = b0+b1Yt-1+b2Xt-b1b2Xt-1+b4Zt-b1b4Zt-1+uC
(D)  Yt = b0       +b2Xt         +b4Zt         +uD

Explain how you would test each of these models pairwise
against all the others in an attempt to determine which
model is "correct".  Be explicit about how you would
interpret the results of tests applied.

Part II.  Answer question 3 or question 4.

3.  A.  Explain the meaning of the following terms:
     a.  cross validation
     b.  grouping methods (regarding errors in variables)
     c.  normalization (in simultaneous systems)
     d.  Ridge regression
     e.  Goldfeld and Quandt's test for homoskedasticity

    B.  Assume you have micro data on a number of
individuals, giving:  Yi = annual expenditure on clothing,
Xi = annual income; and you know which individuals are
female, and which individuals are college graduates.  How
would you test the following using regression analysis:

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(a)  females spend more on clothing than do males, given
income.
(b)  female college graduates spend more on clothing than do
other females, given income.
(c)  the marginal propensity to spend income on clothing
differs for females versus males.
(d)  the marginal propensity to spend income on clothing
differs for female college graduates versus other females.

Be explicit about how you would do the tests, given your
specification.

4.  Using quarterly data for the period 1950-1960, F.
Brechling obtained the following demand function for labour
for the British economy (standard errors in parentheses):

(Et-Et-1) = 14.22 + 0.172Qt - 0.028t - 0.0007t2 - 0.297Et-1
            (2.61)  (0.014)   (0.015)  (0.0002)   (0.033)

               Corrected R2 = 0.76, DW = 1.37

where E is employment, Q is output and t is time.
The equation is based on the assumption that desired
employment, E* is a function of Q, t and t2, and that
(Et-Et-1) = k(Et*-Et-1), where k is the coefficient of
adjustment.
(a)  interpret the equation in economic terms
(b)  what is the estimated value of k?
(c)  what is the long-run demand for labour function?
(d)  how would you test for serial correlation in the model?
(e)  how would you estimate the model if serial correlation
     were found to be present?

Part III.  Answer either question 5 or question 6.

5.  A.  Explain the meaning of the following terms:
     a.  Plosser-Schwert-White differencing test
     b.  errors in variables bias
     c.  indirect least squares
     d.  principal component regression
     e.  Breusch and Pagan's test for homoskedasticity

    B.  M. Nerlove used cross-sectional data for 1955 on 145
privately owned utilities in the U.S. to regress the
logarithm of total cost on the logarithms of output, wage
rate, price of capital and price of fuel.  The estimated
residuals produced a low Durbin-Watson statistic.  The
stylized graph of the residuals looks like:







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                                        log(output)





What econometric problem is present, and how would you
correct it?

6.  G. Menges developed the following model of the West
German economy:

     Yt = b0 + b1Yt-1 + b2It + u1t
     It = b3 + b4Yt + b5Qt + u2t
     Ct = b6 + b7Yt + b8Ct-1 + b9Pt + u3t
     Qt = b10 + b11Qt-1 + b12Rt + u4t

where Y = national income, I = net capital formation, C =
personal consumption, Q = profits, P = cost of living index,
and R = industrial productivity.

(a)  which equations are under, just or over-identified by
the order conditions?  by the rank conditions?
(b)  is there any equation in the system where the
coefficients can be consistently estimated by OLS?  Explain.
(c)  is there an "economic reason" for including the
variable P in the consumption function?  Is there a
"statistical reason" for doing so?
(d)  explain in detail how you would estimate the
coefficients of the model.