Which is asymptotically distributed as chi-square with degrees of freedom equal to the number of variables in Z. , e n 2), i equals an n ×1 column of ones, and, then Koenkar andīassett's (1982) robust variance estimator The Breusch-Pagan test is a Lagrange multiplier test of the hypothesis that the independent variables have no explanatory This statistic is asymptoticallyĭistributed as chi-square with k-1 degrees of freedom, where k is the number of regressors, excluding the constant term. The White test is computed by finding nR 2 from a regression of e i 2 on all of the distinct variables in, where X is the vector of dependent variables including a constant. Tests are White's General test (White 1980) and the Breusch-Pagan test (Breusch and Pagan 1979). This test involves looking for patterns in a plot of the residuals from a regression. The most commonly used is the Time-Honored Method There are several methods of testing for the presence of heteroscedasticity. Thus, inferences from the standard errors are likely to be misleading. Income by state and its square is computed, the parameter estimates are still consistent but they are no longer efficient. If heteroscedasticity is present and a regression of spending on per capita Greater variation in expenditure than others. For example, in analyzing public school spending, certain states may have Often arises in the analysis of cross-sectional data. If this assumption is violated, the errors are said to be "heteroscedastic." Heteroscedasticity One of the classical assumptions of the ordinary regression model is that the disturbance variance is constant, or homogeneous,Īcross observations. 817-818.A Simple Regression Model with Correction of Heteroscedasticity White (1980), “A heteroscedasticity Consistent Covariance Matrix Estimator and a Direct Test of Heteroscedasticity”, Econometrica, Vol. If the cross-product is introduced in the model, then it is a test of both heteroscedasticity and specification bias. If no cross-product terms are introduced in the White test procedure, then this is a pure test of pure heteroscedasticity. In other words, “The white test can be a test of heteroscedasticity or specification error or both. In cases where the White test statistics are statistically significant, heteroscedasticity may not necessarily be the cause, but specification errors. If the calculated chi-square value obtained in (3) is greater than the critical chi-square value at the chosen level of significance, reject the hypothesis of homoscedasticity in favor of heteroscedasticity.įor several independent variables (regressors) model, introducing all the regressors, their square or higher terms and their cross products, consume degrees of freedom.\ under the null hypothesis of homoscedasticity or no heteroscedasticity, where df is the number of regressors in equation (2) Step by step procedure or perform the White test for Heteroskedasticity is as follows:Ĭonsider the following Linear Regression Model (assume there are two independent variable) To test the assumption of homoscedasticity, one can use auxiliary regression analysis by regressing the squared residuals from the original model on the set of original regressors, the cross-products of the regressors, and the squared regressors. Both White’s test and the Breusch-Pagan test are based on the residuals of the fitted model. Because of the generality of White’s test, it may identify the specification bias too. White test for Heteroskedasticity is general because it does not rely on the normality assumptions and it is also easy to implement. White test (Halbert White, 1980) proposed a test that is very similar to that by Breusch-Pagen. Typically, to assess the assumption of homoscedasticity, residuals are plotted.
In the case of heteroscedastic errors (non-constant variance), the standard estimation methods become inefficient. If the error has a constant variance, then the errors are called homoscedastic, otherwise heteroscedastic. One important assumption of Regression is that the variance of the Error Term is constant across observations.
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