How does the White test detect heteroskedasticity without assuming its form?

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AcadiFi · Accepted Answer

Heteroskedasticity means the variance of regression errors varies across observations. It does not bias coefficient estimates but it invalidates standard errors, making hypothesis tests unreliable. The White test is a general diagnostic that does not presuppose any functional form for the variance. The procedure: after estimating the main regression, compute squared residuals e_t^2. Run an auxiliary regression of e_t^2 on the original regressors, their squares, and all pairwise cross-products. Compute nR^2 from this auxiliary regression. Under the null of homoskedasticity, nR^2 follows a chi-squared distribution with degrees of freedom equal to the number of regressors in the auxiliary regression excluding the constant. Imagine portfolio manager Elowen Pritchard regressing Stromwald Capital fund returns on three factor loadings. She runs the White test and gets nR^2 = 28.3 with 9 degrees of freedom. The critical value at 5% is 16.92, so she rejects homoskedasticity. ```mermaid flowchart TD A[Run main
regression] --> B[Get squared
residuals] B --> C[Auxiliary
regression] C --> D[Compute nR^2] D --> E[Compare to
chi-squared] ``` Remedies include White's heteroskedasticity-robust standard errors, weighted least squares if you can model the variance structure, or variable transformations like logging. The test's weakness is low power in small samples and inflated degrees of freedom when the regressor list is long. Heteroskedasticity is almost ubiquitous in cross-sectional financial data, so robust standard errors are good default practice.

How does the White test detect heteroskedasticity without assuming its form?

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