Name___________________________________________________________________
Qume 436 – Problem Set 9: Due on December 1 by 2:30 pm
INSTRUCTIONS: Answer all questions in the spaces provided (or indicate clearly where you have
continued your answer). Reduce all computations to the simplest form so that anyone with a
calculator could attain the answer easily. Show your work and reasoning to the fullest extent
possible so that part marks can be assigned as warranted. NOTE: these data are fictitious. All
hypotheses testing is at the 5% level. All questions are worth 5 points unless otherwise stated.
Q.1
The following questions refer to the computer output in EXHIBIT A. These are hypothetical
demand data concerning a cross-sectional sample of 100 individuals and their annual
consumption of frozen waffles (y). Available explanatory variables include the income of the
individual in thousands of dollars per year (x) and the cost of electricity to prepare waffles in
cents per dozen waffles (z). Assume that all individuals face the same price of waffles, but
marginal costs of electricity vary across individuals (according to how much electricity their
household consumes in total each month).
a.
Consider Regression A1 and Regression A2. If these specifications satisfied the
maintained hypotheses for ordinary least squares regression, would you conclude that
frozen waffles were a normal good, an inferior good, or both, depending upon the level
of income. Explain your reasoning.
b.
Regression A2 is followed by a diagnos command. What do the results of this command
suggest, and what are the implications for your interpretation of Regression A2?
c.
Consider Regression A3, Regression A4, and Regression A5. What do these regressions
reveal about the nature of any systematic variations in the magnitude of s i2? If you had
to choose just one variable that was strongly correlated with the magnitude of si2, what
would it be, and why?
d.
Just prior to Regression A6, a number of potential weighting variables are generated.
Which of these weights is more appropriate, and hence, which of Regression A6,
Regression A7, or Regression A8 is preferred as a "correction" for the problems
besetting the naive model in Regression A2? Explain.
e.
Are the standard errors for the estimated parameters in your preferred model smaller
than those for the naive model in Regression A2? _______ For a single sample, is it
necessary that the weighted least squares estimator always produce smaller parameter
standard errors than the ordinary least squares estimator? Explain.
Q2. (Serial Correlation)
The following questions pertain to EXHIBIT B. These are real data, and we will explore a
preliminary model to explain the observed quarterly time-series variation in automobile loans
at commercial banks. The variables read by the program are defined as follows: (All regression
commands are EVIEWS commands)
DATE = year and quarter in decimal form (e.g. 1960.25=1960:1)
AUTOCRED = consumer installment credit outstanding: automobiles, commercial banks
(million $, end of month, not seasonally adjusted) [CITIBASE variable CCIUAC; monthly
data averaged for each quarter (1960:1-1996:4)]
YP = gross national product, total [CITIBASE variable GNP; quarterly (1960:1-1996:4)].
R = nominal interest rate, measured as the rate on commercial paper, 6-mo (% per
annum, not seasonally adjusted) [CITIBASE variable FYCP; monthly data averaged for
each quarter (1960:1-1996:4)].
AUTOINV = inventories, business, retail durables, motor vehicle dealers; billions
[CITIBASE variable GLRDA; quarterly (1960:1-1996:4)]
QTR1, QTR2, QTR3, QTR4 = set of quarterly dummy variables, equal to one during each
respective quarter, zero otherwise.
(QTR1 = Jan – Mar, QTR2 = April – June, QTR3 = July – Sept QTR4 = Oct – Dec)
a.
Is there evidence of systematic "seasonal" variations in the level of AUTOCRED,
according to REGRESSION B1? Explain. (hint: are the quarterly dummies jointly
significant?)
b.
What is the purpose of REGRESSION B2? What does it imply about the results obtained
from REGRESSION B1?
c.
Is REGRESSION B3 likely to be adequate to correct the problems revealed by
REGRESSION B2? Why or why not? Explain.
d.
Suppose that REGRESSION B4 was your preferred model. Which months tend to have
the highest amount of outstanding car loans?
Which months tend to have the lowest amount of outstanding car loans?
.
e.
Why would you prefer REGRESSION B4 to REGRESSION B3 ? Explain
Q.3
For pure serial correlation, the appropriate remedy is to apply Generalized Least Squares
estimators to improve on the properties of OLS estimators in the face of such ‘incorrect’
stochastic error terms.
Starting from the given specifications below, generate a step by step transformation used by
GLS to transform an equation that does not meet the classical assumption into one that meets
those assumptions. Show every step of the transformation for full credit
𝑌𝑡 = 𝛽0 + 𝛽1 𝑋𝑡 + 𝜖𝑡
(1)
𝜖𝑡 = 𝜌𝜖𝑡−1 + 𝑢𝑡
(2)
Where ε is a serially correlated error term, ρ is the coefficient of serial correlation and u is a
classical white noise error term.