Download ECON 6313-001

ECON 6313-001
Fall Semester, 2012
Exam 2
Professor C. Brown
The data (in Excel format) you will need to complete this examination can be found at
http://myweb.astate.edu/crbrown/6313.html
Answer all questions. The Exam is due on Wednesday, October 24.
1. This question is worth 35 points—3 points each, except for subparts (a) and (j),
which are worth 5 ½ points each. You will need to download data for question 1
from the course web page (see URL above) to complete this question. This file
contains 188 monthly observations (January 1997 to August 2012) on the
following variables:
Appliances: Sales of new major appliances in the U.S.(seasonally-adjusted, in
millions of dollars).
HS: Monthly Housing Starts (seasonally-adjusted, in thousands of units).
RCO: Revolving consumer credit outstanding (end of the month, seasonallyadjusted, in billions of dollars)
UR: Unemployment rate, civilian labor force, in the U.S. (in percent).
a) Use regression to estimate the following model specification. Report the
results of the regression—that is, report your estimates of β0 , β1 , β2, and β3.
Appliances t   0  1 HS t 4   2 RCOt   3URt 1
b) Are the signs of the (estimated) coefficients consistent with your (prior)
expectations? Explain.
c) Monthly housing starts (HS) fell from a peak of 111,400 in March 2007 to
22,700 in January 2009. What was the effect on appliance sales (Appliances),
other things being equal, according to your estimates?
d) Recent reports indicate that credit card issuers are applying tougher credit
standards on the issue of credit card (revolving) accounts. Is this a welcome
development from the point of view of appliance manufacturers and retailers?
Explain.
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HS t – 4 means a 4-month lag of housing starts.
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e) Report the t-statistic for the estimate of the UR ( ̂ 3 ) parameter. Set up a null
and alternative hypothesis for this coefficient. Can you reject the null
hypothesis at the .01 (1 percent) significance level? Briefly Explain.
f) Use the equation you estimated above to obtain a fitted value of Appliances
for September 2001. Is the actual value of Appliances for this month within
one standard error of its fitted value for this month? Explain.
g) Prepare a chart illustrating actual and fitted values of Appliances for the
period May 1997 to August 2012.
h) Report the value of R2 and provide a (precise) interpretation.
i) Set up an F-test. Can you reject null hypothesis at the 1 percent (.01)
significance level?
j) Use the data contained in “sheet 2” of your spreadsheet to forecast the value
of appliance sales November and December 2012. Report your results.
2. This question is worth 35 points—3 points for each part except for subparts (e)
and (j), which are worth 5 ½ points each. You will need to download data for
question 2 from the website (see URL above) to complete this question. You have
140 monthly values of retail sales of books (Books) in the U.S. beginning in
January 2001 and running through August 2012 (in millions of dollars, not
seasonally adjusted).
a) Forecast retail book sales for October 2012 using a 4-month prior moving
average technique.
b) Compute root mean square error ( MSE ) for the in-sample forecast using
the same technique as in part (a) above.
c) Find the 3-decimal point smoothing constant (  ) which gives the best fit for
(based on the MSE criterion) for the in-sample forecast using the
exponential smoothing technique. (Note: the “damping factor” in Excel is
equal to 1   ).
d) How does MSE for the exponential smoothing technique compare to its
value for the 4-period moving average technique?
e) Forecast retail book sales in September 2012 using the exponential smoothing
technique (using the smoothing constant you found in part (c)).
f) Estimate and report a linear trend component for the Books time series using
the ordinary least squares (OLS) technique.
g) Compare the trend value of your series for August 2007 with its actual value
in that month. What factors might account for the difference between the trend
value and the actual value of Books for February 2007?
h) Compute a seasonal index using a 12 month centered moving average of the
Books series. What are the best months in the book retailing industry? What
are the worst months?
i) Do an in-sample forecast on Books sales using the multiplicative time series
technique (assume the cyclical component is equal to 1 for every month).
j) Use the information contained in following table to perform a forecast of
Books for November and December 2012 using the multiplicative time series
technique (Note: you will need to compute a trend component for these
3
months using the equation you obtained in part (f)).
Month
Nov-12
Dec-12
Trend
Seasonal
Cyclical
Forecast
Component
Component
Component (in millions of US $)
?
Use Nov-11 value
0.997
?
Use Dec-11 value
1.006
3. Question 3 is based on the figure below. This question is worth 15 points.
P
20
Price (dollars)
15
10
5
D
Q
0
1,000
2,000
3,000
4,000
Q uantity
a) When price is $15 and quantity demanded is 1,000, what is the point
elasticity of demand?
b) What is the equation for marginal revenue?
c) When quantity demanded is 1,000, what is marginal revenue?
d) When price is $10 and quantity demanded is 2,000, what is the point
elasticity of demand?
e) When quantity demanded is 2,000, what is marginal revenue?
f) When price is $5 and quantity demanded is 3,000, what is the point
elasticity of demand?
g) When quantity demanded is 3,000, what is marginal revenue?
4. This question is worth 15 points. Henry Goot is the owner of Discount Books, a
bookseller housed in large warehouse. Sales have been growing rapidly since he
opened his shop (in much smaller quarters) 4 years ago. Goot has been tracking
sales and has observed that compound growth has been 25% a year since opening.
At year’s end, gross sales have totaled about $1,250,000.
a) Assuming that demand continues to grow at this rate, what will be gross sales in
the next three years?
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b)
Goot has observed that he needs to rent 1,000 square feet of warehouse space in
order to stock sufficiently to sell $100,000 gross sales in a year. He can sign a
long-term lease to rent space adjacent to his current space (of 17,000 square feet)
and wants to do so in order to prevent overcrowding of the store. When should he
arrange to have the space available for stocking books?
c) How reliable is the forecast for the next three years of sales? Explain. Do you
see any weaknesses in the forecast?