Spearman’s rank correlation test for heteroscedasticity. The following steps are involved in this test, which can be explained with the wage regression (9.3):
a. From the regression (9.3), obtain the residuals ei.
b. Obtain the absolute value of the residuals | ei |.
c. Rank both education (Xi) and | ei| in either descending (highest to lowest) or ascending (lowest to highest) order.
d. Take the difference between the two ranks for each observation, call it di.
e. Compute the Spearman’s rank correlation coefficient rs, defined as
where n = the number of observations in the sample.
If there is a systematic relationship between ei and Xi, the rank correlation coefficient between the two should be statistically significant, in which case heteroscedasticity can be suspected.
Given the null hypothesis that the true population rank correlation coefficient is zero and that n > 8, it can be shown that
follows Student’s t distribution with (n – 2) d.f.
Therefore, if in an application the rank correlation coefficient is significant on the basis of the t test, we do not reject the hypothesis that there is heteroscedasticity in the problem. Apply this method to the wage data given in the text to find out if there is evidence of heteroscedasticity in the data.