Glejser test

In statistics, the Glejser test for heteroscedasticity, developed by Herbert Glejser, regresses the residuals on the explanatory variable that is thought to be related to the heteroscedastic variance.^[1] After it was found not to be asymptotically valid under asymmetric disturbances,^[2] similar improvements have been independently suggested by Im,^[3] and Machado and Santos Silva.^[4]

Steps for using the Glejser method

Step 1: Estimate original regression with ordinary least squares and find the sample residuals e_i.

Step 2: Regress the absolute value |e_i| on the explanatory variable that is associated with the heteroscedasticity.

${\displaystyle {\begin{aligned}|e_{i}|&=\gamma _{0}+\gamma _{1}X_{i}+v_{i}\\[8pt]|e_{i}|&=\gamma _{0}+\gamma _{1}{\sqrt {X_{i}}}+v_{i}\\[8pt]|e_{i}|&=\gamma _{0}+\gamma _{1}{\frac {1}{X_{i}}}+v_{i}\end{aligned}}}$

Step 3: Select the equation with the highest R² and lowest standard errors to represent heteroscedasticity.

Step 4: Perform a t-test on the equation selected from step 3 on γ₁. If γ₁ is statistically significant, reject the null hypothesis of homoscedasticity.

References

1. Glejser, H. (1969). "A New Test for Heteroskedasticity". Journal of the American Statistical Association. 64 (235): 315–323. doi:10.1080/01621459.1969.10500976. JSTOR 2283741.
2. Godfrey, L. G. (1996). "Some results on the Glejser and Koenker tests for heteroskedasticity". Journal of Econometrics. 72: 275. doi:10.1016/0304-4076(94)01723-9.
3. Im, K. S. (2000). "Robustifying Glejser test of heteroskedasticity". Journal of Econometrics. 97: 179. doi:10.1016/S0304-4076(99)00061-5.
4. Machado, José A. F.; Silva, J. M. C. Santos (2000). "Glejser's test revisited". Journal of Econometrics. 97 (1): 189–202. doi:10.1016/S0304-4076(00)00016-6.