Question

Explain the difference between the Breusch-Pagan test and the White test of heterosckedascity

What are the limitations of the Durbin-Watson test of a serial correlation?

Explain what the dummy variable trap is.

Answer 1

1) Breusch - Pagan test and White's general heteroscedasticity test are widely used to detect the presence of heteroscedasticity in an econometric model. Let's look at the difference between these two tests.

* The Breusch- Pagan test assumes that, error variance is a function of the non stochastic Z variables; some of all of the X's can serve as Z's.

On the other hand, white's test isn't sensitive to the normality assumption.

* In Breusch- pagan test , maximum likelihood estimator of error variance is used. white's test, involves running an auxiliary regression.

* Breusch- pagan test is asymptotic or a large sample test.lt can be used even if there are a large number of regressors in the model.

If a model has several regressors, we should be extremely careful while implementing the white's test because regressors , their squared terms , and their cross products can quickly consume degrees of freedom.

* The white's test can be a test of ( pure) heteroscedasticity or specification error or both. Breusch- pagan test is mainly a test of heteroscedasticity.

* White's test is easier to implement compared to Breusch- pagan test.

2) Durbin Watson test is the most powerful test of serial correlation or autocorrelation. Following are the limitations of Durbin - Watson test.

* The test takes into account of only first order serial correlation

* Significance of the obtained test statistic may not necessarily indicate the presence of serial correlation.

* There are chances of the test being inconclusive.

* Durbin Watson test is inappropriate if a constant isn't included in the econometric model.

3) When dealing with dummy variables in the regression functions, we should be aware of some important facts. One of them is the awareness of dummy variable trap.

* lf an intercept is included in the model and if qualitative variable has m categories, then we should introduce only ( m-1) dummy variables.

For example, gender has only two categories- male and female. Therefore, we should introduce only one dummy variable.

If we fail to follow the above mentioned rule, we fail into dummy variable trap, the situation of perfect collinearity.

( Note : Number of dummy variables = number of categories-1.

When we don't follow this rule, we fall into dummy variable trap. )