* The Multiplicative Heteroskedastic Error Model
* Reference: George G. Judge, R. Carter Hill, William E. Griffiths,  
*            Helmut Lutkepohl and Tsoung-Chao Lee,
*            Introduction to the Theory and Practice of Econometrics,
*            Second Edition, 1988, Wiley.
* Section 12.3.3, page 538.
SAMPLE 1 20
* Read Table 9.1, page 374.
READ Y X2 X3 SIG2 E
41.65077 14.53 16.74   3.8923   2.6964
40.99370 15.30 16.81   4.9037   3.1250
39.78592 15.92 19.50   5.9062  -2.0071
50.31161 17.41 22.12   9.2350   2.4802
56.97006 18.37 22.34  12.3172    .8845
52.41802 18.83 17.47  14.1399   2.8034
51.74554 18.84 20.24  14.1824   4.0700
59.74142 19.71 20.37  18.4120  -3.8105
40.64725 20.01 12.71  20.1459    .5304
46.96075 20.26 22.98  21.7149  -4.8352
51.27611 20.77 19.33  25.3049  -8.5556
49.41824 21.17 17.04  28.5313   2.3973
51.52437 21.34 16.74  30.0241  -2.3593
54.41408 22.91 19.81  48.0864 -11.9732
60.90808 22.96 31.92  48.8132  -7.1302
66.65003 23.69 26.31  60.7642   4.5329
81.31264 24.82 25.93  82.2851   8.0104
58.26339 25.54 21.96 105.8476  -1.4822
54.18337 25.63 24.05 108.7444  12.9430
77.73936 28.73 25.66 275.6136  -2.2802

* Estimate the model using the HET command
HET Y X2 X3 (X2) / MODEL=MULT

* As an alternative method use the NL command.
* Set up the likelihood function corresponding to Equation 12.3.48
* Use the LOGDEN option on NL to tell SHAZAM you are giving it
* the log-density for an observation rather than an equation
GENR CONST=LOG(2*$PI)
NL 1 / NCOEF=5 LOGDEN 
EQ -.5*(CONST+(A1+A2*X2))-.5*((Y-B1-B2*X2-B3*X3)/EXP((A1+A2*X2)/2))**2
COEF B1 1.01 B2 1.657 B3 .896 A1 -4.376 A2 .366
END
* Do the Wald test that A2=0 as a replacement for Equation 12.3.93
* Note that SHAZAM has a somewhat different result (although same conclusion)
* because of differences in computing the standard error of A2
TEST A2
GEN1 LLFU=$LLF
* Section 12.3.4b
* Get the LLF for the restricted model (OLS)
OLS Y X2 X3
GEN1 LLFR=$LLF
* Compute the likelihood ratio test statistic
* Compare the chi-square with 1 d.f. (1 restriction A2=0)
* Compute the LR test statistic based on Equation 12.3.102
GEN1 LRT=2*(LLFU-LLFR)
PRINT LRT
STOP