Tests that should be retired from empirical work:
Durbin-Watson statistic.
Jarque-Bera test for normality.
Breusch-Pagan test for heteroskedasticity.
B-P test for random effects.
Nonrobust Hausman tests.
I feel uncomfortable using names, but this is #metricstotheface.
Durbin-Watson statistic.
Jarque-Bera test for normality.
Breusch-Pagan test for heteroskedasticity.
B-P test for random effects.
Nonrobust Hausman tests.
I feel uncomfortable using names, but this is #metricstotheface.
D-W test only gives bounds. More importantly, it maintains the classical linear model assumptions.
J-B is an asymptotic test. If we can use asymptotics then normality isn't necessary.
B-P test for heteroskedasticity: maintains normality and constant conditional 4th moment.
J-B is an asymptotic test. If we can use asymptotics then normality isn't necessary.
B-P test for heteroskedasticity: maintains normality and constant conditional 4th moment.
B-P test for RE: maintains normality and homoskedasticity but, more importantly, detects any kind of positive serial correlation.
Nonrobust Hausman: maintains unnecessary assumptions under the null that conflict with using robust inference. Has no power to test those assumps.
Nonrobust Hausman: maintains unnecessary assumptions under the null that conflict with using robust inference. Has no power to test those assumps.
The D-W test is easily replaced by regressing OLS residuals on one or more lags; including the covariates makes the test valid when the x(t) are not strictly exogenous. It's easy to make that test robust to heteroskedasticity, too.
If you reject the null that your errors are normally distributed, what would you do? Model the distribution as something else and use MLE? OLS has good properties without normality provided second moments are not infinite. To improve over it requires extra assumptions.
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