Introduction to econometrics II eco 356 faculty of social sciences course guide course Developers: Dr. Adesina-Uthman
Download 1.75 Mb. View original pdf
|
- Navigate this page:
- 3.1.3.6 The Glejser Test
| INTRODUCTION TO ECONOMETRICS II ECO 306 NOUN 107 sub-regressions. Representing these by RSS1 and RSS2 for the sub-regressions with the first n' and the last n' observations, respectively.The ratio RSS2/RSS1 will be distributed as an Fstatistic with (n' – k) and (n' – k) degrees of freedom, where kis the number of parameters in the equation, under the null hypothesis of homoscedasticity. The power of the test depends on the choice of n'about n. As a result of some experiments undertaken by Goldfeld and Quandt, they recommend that in general, n' should be about 11 when nis 30 and about 22 when nis 60. Which clearly shows that n' should be about 3 of n. If there is more than one explanatory variable in the model, the observations should be ordered by that which is hypothesized to be associated with the null hypothesis for the testis that RSS2 is not significantly greater than RSS1, and the alternative hypothesis is that it is significantly greater. If RSS2 turns out to be smaller than RSS1, the null hypothesis should not be rejected it only means that there would not be any point in computing the test statisticRSS2/RSS1. However, the Goldfeld–Quandt test can also be used for the case where the standard deviation of the disturbance term is hypothesized to be inversely proportional to X i . The procedure is the same as before, but the test statistic is now RSS1/RSS2, and it will again be distributed as anF-statistic within k) and (n' – k) degrees of freedom under the null hypothesis of homoscedasticity. 3.1.3.6 The Glejser Test This test permits you to search the nature of the heteroscedasticity a little more closely. Here, the assumption that i u is a relative quantity to X i is relaxed,and you can then investigate whether some other efficient form maybe more suitable, for example i u …[3.03] To use the procedure, you regress Yon Xusing OLS and then fit the absolute values of the residuals, | | to the function fora given value of . You may fit several such functions, varying the choice of . In each case the null hypothesis of homoscedasticity will be rejected if the estimate of is significantly different from 0. |