HOMEWORK #3  - DUE NO LATER THAN 9:35 AM, THURSDAY, JUNE 4, 1998
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              (LATE PAPERS WILL NOT BE ACCEPTED)


The file  data9-9  has quarterly data for the U.S. on the following 
variables for the 60 quarters 1976.1 through 1990.4:

  period   =  1976.1 - 1990.4
  nocars   =  number of new car sales, in thousands
  pop      =  population, in millions
  Y        =  disposable personal income per capita, in thousands of
              1982 dollars
  price    =  New car price index, 1982 base year.
  primert  =  Prime interest rate charged by banks (%)
  unemp    =  unemployment rate (%)

For a clear understanding of Chapter 9, I have broken down this problem
set 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.  ONLY ORIGINAL COMPUTER
PRINTOUTS WILL BE ACCEPTED (NO XEROX COPIES).

FIRST READ THE FOLLOWING AND WRITE DOWN THE NECESSARY ESL COMMANDS ON A 
PIECE OF PAPER TO ANSWER THE RELEVANT QUESTIONS.  ONLY THEN SHOULD YOU 
ACTUALLY RUN ESL.

First exit temporarily to DOS and change directory to \ESL (\PGMS\ESL
in Econ 100).

Then type:    esl  data9-9

to load the above data set.  Appendix D, Page D-32 describes this data.

When the ? prompt appears type each of the following commands (watch
the program's response carefully.  If you get any error message, retype
the command.  (only logs needs the ;)

     genr pccar = nocars/pop
     logs pccar price Y primert unemp ;
     genr dummy 

A.
Estimate the following model by OLS, using the variables created above. 
[Caution: use the correct variable numbers in all cases.  Otherwise, as
the cliche goes, "garbage in, garbage out."]

    ln(pccar)  =  a0 + a1 ln(income) + a2 ln(price) + a3 ln(primert)
                     + a4 ln(unemp) + ut

Perform a Durbin-Watson test for first order serial correlation
(Section 9.3).  Next perform an LM test for the same (at 10%).  To get
uhat(t) and uhat(t-1), use the commands genr ut = uhat and genr ut1 =
ut(-1) immediately after the ols command.  Before running the auxiliary
regression you should reset the sample range because of the ut(-1)
term.  The command is

     smpl 1976.2 ;

 which suppresses the first observation.  Otherwise you will get a
 "missing data -999" error.

B.
Reset the sample range back to smpl 1976.1 ; and then estimate the
following model by OLS.  It allows the intercept to vary across the
seasons (dummy_1 is omitted to avoid the dummy variable trap).

    ln(pccar)  =  b0 + b1 ln(income) + b2 ln(price) + b3 ln(primert)
                     + b4 ln(unemp) + b5 dummy_2 + b6 dummy_3
                     + b7 dummy_4 + vt

Using the LM Test, check for first order serial correlation.  [You
cannot do the D-W test because the table doesn't give the critical
values.  Here also you should smpl 1976.2 ; ]

C.
Reset the sample range back to smpl 1976.1 ; and then estimate the
model in B by the Cochrane-Orcutt iterative procedure (Page 445).  The
command is

   corc  dependentvariable independent variables  ;

One by one, omit the variable with the least significant regression
coefficient (use the omit command) until you have the "best" model. 
Explain how you arrived at this model.

D.
Estimate the "best" model in C by the Hildreth-Lu procedure (Page 447). 
The command is

   hilu dependentvariable independent variables ;

Compare the results with those for the CORC procedure.

E.
Because the data are quarterly, we can suspect fourth-order
autocorrelation.  Test your "best" model for fourth-order serial
correlation, again at 10 percent level.  [First study the 
Breusch-Godfrey LM test in Section 9.5].

F.
Reset the sample range back to smpl 1976.1 ; and then use the ar
command as

      ar 1 2 3 4 ; dependentvarible independent variables ;

and estimate the best model by generalized CORC.  If any of the rho
values is insignificant, reestimate the ar model (e.g.  ar 1 2 4 ;
.....  ; ).  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) have significant 
coefficients (at 10 % level).

G.
Which model is now the "best"? Justify your answers.  In this model,
test whether each of the elasticities is NUMERICALLY equal to 1 (that 
is, ignore the sign and test whether or not beta = 1).  [Note: you are
not testing that the coefficient is zero but equal to 1.] Is demand for
cars elastic or inelastic with respect to each variable (except the
dummy variables)? Do the numerical values appear reasonable? What is
the interpretation of the coefficient for the dummy variable?