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. After it was found not to be asymptotically valid under asymmetric disturbances, similar improvements have been independently suggested by Im, and Machado and Santos Silva.

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.

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

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.

Software Implementation

Glejser's Test can be implemented in R software using the glejser function of the skedastic package. It can also be implemented in SHAZAM econometrics software.