* 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