Glejser test

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 to be not 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, ei.

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

|e<sub>i</sub>|=γ0+γ1Xi+vi |e<sub>i</sub>|=γ0+γ1√Xi+vi |e<sub>i</sub>|=γ0+γ11/Xi+vi

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.
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