* Reference: Chapter 8 of * Jeffrey M. Wooldridge, Introductory Econometrics: A Modern Approach, * South-Western College Publishing, 2000. SAMPLE 1 100 READ (SAVING.shd) sav inc size educ age black cons * Example 8.6, pp. 264-265. * Table 8.1, Column (1) OLS sav inc * Test for heteroskedasticity (see Question 8.3, p. 265) DIAGNOS / HET * The DIAGNOS / HET command reports the LM test for * heteroskedasiticity given in Equation (8.16), p. 257 of the * text. The SHAZAM output reports the test statistic as LM=0.923 * and the p-value is 0.34. This suggests NO evidence to reject * the null hypothesis of homoskedasticity. * Note that the Breusch-Pagan form of the test statistic that * assumes that the errors are normally distributed yields * a test statistic of 14.22 with a p-value of 0.00016. * This appears to give the conflicting conclusion of heteroskedasticity. * However, it can be noted that the assumption of normality * may not describe this data set. Further illustration about this * point is given below. * Table 8.1, Column (2) * Weighted Least Squares - assume that the error variance is * proportional to income. * SHAZAM assumes that the error variance is inversely proportional * to the variable specified with the WEIGHT= option. GENR W=1/inc OLS sav inc / WEIGHT=W * Note that the R-square calculation that is reported with weighted * least squares is derived from an analysis of variance decomposition * based on weighted descriptive statistics. * Table 8.1, Column (3) * The ANOVA option reports an F-test for the overall significance of * regression. OLS sav inc size educ age black / ANOVA * Test of significance TEST TEST size=0 TEST educ=0 TEST age=0 TEST black=0 END * Table 8.1, Column (4) OLS sav inc size educ age black / WEIGHT=W ANOVA TEST TEST size=0 TEST educ=0 TEST age=0 TEST black=0 END * Additional Notes - A scatterplot of the data shows the * presence of some possible outlier observations. GRAPH sav inc * The GF option on the OLS command reports some tests for * normality of the residuals. OLS sav inc / GF * On the SHAZAM output, the Jarque-Bera test statistic reveals * strong evidence for non-normality. STOP