# White test

In statistics, the White test is a statistical test that establishes whether the residual variance of a variable in a regression model is constant: that is for homoscedasticity.

This test, and an estimator for heteroscedasticity-consistent standard errors, were proposed by Halbert White in 1980.[1] These methods have become extremely widely used, making this paper one of the most cited articles in economics.[2]

In cases where the White test statistics is statistically significant, heteroscedasticity may not necessarily be the cause, but specification errors. In other words, “The white test can be a test of heteroscedasticity or specification error or both. If no cross product terms are introduced in the White test procedure, then this is a pure test of pure heteroscedasticity. If cross product are introduced in model, then it is a test of both heteroscedasticity and specification bias.[3]

## Testing constant variance

To test for constant variance one undertakes an auxiliary regression analysis: this regresses the squared residuals from the original regression model onto a set of regressors that contain the original regressors, the cross-products of the regressors and the squared regressors. One then inspects the $R^{2}$. The Lagrange multiplier (LM) test statistic is the product of the R2 value and sample size:

$\ LM = n \cdot R^2 .$

This follows a chi-squared distribution, with degrees of freedom equal to the number of estimated parameters (in the auxiliary regression).

An alternative to the White test is the Breusch–Pagan test.

If homoscedasticity is rejected one can use heteroscedasticity-consistent standard errors.