HOMEWORK #3 - DUE NO LATER THAN 11:10 AM, THURSDAY, DECEMBER 3, 1998
(LATE PAPERS WILL NOT BE ACCEPTED)
First study Section 7.5 on Estimating Seasonal Effects and Exercise 7.2
with answers in Appendix B.
The file data9-7 has quarterly data for the U.S. on the following
variables for the 64 quarters 1975.1 through 1990.4.
YEARS = 1975.1 - 1990.4
QNC = Number of new car sales, in thousands
PRICE = New car price index in real terms
INCOME = Disposable personal income per capita, in thousands of
1982 dollars
PRIME = Prime interest rate charged by banks (%)
POP = Population, in millions
UNEMP = Unemployment rate (%)
STOCK = Total number of cars on the road, in thousands
(ignore this variable from your models)
WINTER = 1 for the winter quarters, 0 otherwise
(ignore this also from the analysis)
SPRING = 1 for the spring quarters, 0 otherwise
SUMMER = 1 for the summer quarters, 0 otherwise
FALL = 1 for the fall quarters, 0 otherwise
For a clear understanding of Chapter 9, I have broken down this homework
into easy to implement parts. You should turn in the relevant computer
outputs with answers to each parts written on the margins or import to
a word processor and insert comments. If you study the assignment
carefully, the entire empirical work can be done in one session.
A.
You need to generate the following transformations of the data.
genr Y = QNC/POP
logs Y PRICE INCOME PRIME ;
genr SPPRICE = SPRING * l_PRICE [l_ is "el" underscore]
genr SMPRICE = SUMMER * l_PRICE
genr FPRICE = FALL * l_PRICE
genr SPINCOME = SPRING * l_INCOME
genr SMINCOME = SUMMER * l_INCOME
genr FINCOME = FALL * l_INCOME
genr SPPRIME = SPRING * l_PRIME
genr SMPRIME = SUMMER * l_PRIME
genr FPRIME = FALL * l_PRIME
list
First download this web page into the folder c:\esl\user (or
c:\workarea in the Econ 100 lab) and save it as inpa.txt.
Next use NOTEPAD, select File, Open, go to the esl\user or \workarea
folder, load the file inpa.txt, delete all the lines except the above
statements, and save the file. Delete also the comment part [...].
Use ESLWIN, either at home or in Econ 100, select interactive,
text-book data set data9-7, and give different names for input and
output files in each session.
When the ? prompt appears, type the following command.
run inpa.txt
If ESL cannot find this file, give the full path as
run \esl\user\inpa.txt (or run \workarea\inpa.txt)
ESL will load the data and perform all the above operations.
B.
First use the OLS procedure to estimate the following model (you can use
variable numbers listed in the list command).
l_Y = b0 + b1 SPRING + b2 SUMMER + b3 FALL + b4 l_PRICE + b5 SPPRICE
+ b6 SMPRICE + b7 FPRICE + .... + u
Note that b1, b2, b3 are the seasonal adjustments for b0, b5 is the
spring shift for the coefficient of l_PRICE, and similarly for the others.
You must have the logs of the income, price, and prime rate variables
and all the above interactions with the three seasonal dummies. WINTER
is omitted to avoid the "dummy variable trap." DO NOT INCLUDE THE
ORIGINAL VARIABLES PRICE, ETC.
CAUTION: SINCE THIS IS A TAKE-HOME, YOU WILL NOT GET ANY CREDIT FOR
WHAT FOLLOWS UNLESS YOU GET THE ABOVE MODEL CORRECT. DISCUSS AMONG YOUR
TEAM MEMBERS AND CLASSMATES AND MAKE SURE THAT YOUR MODEL SPECIFICATION
IS CORRECT.
If you like, you can use Notepad or MSWord to open the file inpa.txt,
add the lines for the above ols command as well as the commands listed
below, save the new file as the text file inpb, and then run ESLWIN,
select batch mode, inpb.txt as the input file and data9-7 as the data
file. All the commands in inpb.txt will be run as a batch in the
background and you will get a screen output at the end.
C.
Because the data are quarterly, we can suspect fourth-order autocorre-
lation. Test the above model for fourth-order serial correlation, at
the 1 percent level. [First study the Breusch-Godfrey LM test in
Section 9.5]. The commands for this part are:
genr ut = uhat [this saves uhat as ut]
lags ut ; [this generates lagged ut's]
smpl 1976.1 1990.4 [to suppress the first 4 obs.]
[the following is the auxiliary regression where
numbers may be used, but proceed carefully]
ols ut const ut_1 ut_2 ut_3 ut_4 SPRING SUMMER FALL
l_PRICE SPPRICE etc. for the remaining variables in the
Model in B, followed by a semicolon.
genr LM = $nrsq [compute LM value]
pvalue
3 [choose chi-square]
df [type the correct value for df here]
LM
D.
Reset the sample range back to 1975.1 using the command,
smpl 1975.1 1990.4
and then use the ar command as (note: two ; are required here)
ar 1 2 3 4 ; l_Y 0 SPRING SUMMER FALL l_PRICE SPPRICE etc. ;
using the original model in (B) above. AGAIN EXERCISE CAUTION HERE.
If any of the rho values is insignificant, reestimate the ar model
after the omitting the lag that is least significant. For example, if
the coefficient for ut_3 is least significant, then your new
specification will be
ar 1 2 4 ; l_Y 0 SPRING SUMMER FALL l_PRICE SPPRICE etc. ;
Note that , at this time, you should keep all the right-hand side
variables in the model in B. If all the coefficients for ut_i are
significant, then use the omit command to delete the variable with
the least significant regression coefficient. Proceed until you find
a model with all variables (ignore the constant terms) having
significant coefficients (at the 10 % level). Then choose the "best"
model.
E.
Using the final best model, write down the estimated relation separately
for each of the four seasons. For each season, look at the numerical
values for the elasticities with respect to income, price, and prime
rate, and indicate whether they are elastic or inelastic (you should
ignore the sign and answer the question). Note that you are not asked to
do a test here, just to look at the values and answer the question.