Practice Problems

Serial Correlation

Practice Problem 9.1

The Durbin-Watson test results can be obtained from the following SHAZAM program: 
READ (DATA4-3) T HOUSING POP GNP UNEMP INTRATE
OLS HOUSING INTRATE POP /DWPVALUE
OLS HOUSING INTRATE GNP /DWPVALUE
OLS HOUSING INTRATE POP GNP /DWPVALUE
The equation for the disturbances is ut =  ut-1 + t .The null hypothesis is  = 0 and the alternative hypothesis is  > 0. The test would accept the null hypothesis if d > dL, and reject the null hypothesis if d < dU  (See Appendix Table A.5). Where the exact p-value is available, as is the case here, we accept (reject) the null hypothesis if the p-value is greater than (less than) the designated significance level. In this case, the p-values are all less than 0.003. We conclude that the null hypothesis is false, and that the OLS estimates are inefficient, although unbiased and consistent.
 
 

Practice Problem 9.2

The following SHAZAM commands will obtain the necessary test statistics for Model A. The other two models can be tested similarly. 
READ(data4-3) T HOUSING POP GNP UNEMP INTRATE
OLS HOUSING INTRATE POP  / RESID=U
*
* Perform a Breusch-Godfrey LM test of an AR(1) process.
* Regress U on Y and U lagged.
GENR ULAG = LAG(U)
* set ULAG=0 for first observation
IF (T.EQ.1963) ULAG=0
* Run auxiliary regression. 
?OLS U ULAG INTRATE POP 
* One version of the test is an ordinary t-test on ULAG.
TEST ULAG
* Another is an LM test on NR2, which is asymptotically chi-square.
GEN1 LM = $N*$R2
DISTRIB LM /TYPE=CHI DF=1
All tests are highly significant, with p-values less than 0.01, leading to rejection of the null hypothesis and confirming the conclusions of Practice Problem 9.1.

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Updated March 5, 2001.
noelroy@morgan.ucs.mun.ca