Question

Answer the following questions as much detailed as you can.

1. Explain the difference between the Breusch-Pagan test and the White test of heterosckedascity.
2. What are the limitations of the Durbin-Watson test of a serial correlation?
3. Explain what the dummy variable trap is.

Answer 1

Difference between the Breusch-Pagan test and white test of heteroscedasticity:

1) The main difference between White’s test and the Breusch-Pagan is that its Auxillary regression doesn’t include cross-terms or the original squared variables.

2) If the data set has many explanatory variables, the white test may be challenging to calculate, vis-a-vis Breusch-Pagan test.

3) Breusch-Pagan test is a test for linear forms of heteroskedasticity, whereas, White test tests for nonlinear forms of heteroskedasticity.

----------------------------------------------------------------------------------------------------------------------------------------------------------

Limitation of the Durbin-Watson test of a serial correlation:

1) The critical values in the d test depend on the value of the Xs, which vary from one data to another. This means there is an indeterminate region.

2) Durbin Watson statistic is biased in the presence of a lagged dependent variable Yt-1 on the right-hand side.

3) There is a region of indecision - hence, can be inconclusive about the presence of positive or negative auto-correlation

4) Does not apply to AR(2+) or ARMA error terms.

----------------------------------------------------------------------------------------------------------------------------------------------------------

The Dummy Variable trap is a scenario in which the independent variables are multicollinear - a scenario in which two or more variables are highly correlated.

To demonstrate the Dummy Variable Trap, take the case of gender (male/female) as an example.

Including a dummy variable for each is redundant (of the male is 0, the female is 1, and vice-versa), however, doing so will result in the following linear model:

y ~ b + {0|1} male + {0|1} female

Represented in matrix form:

    | y1 |

    | y2 |

Y = | y3 |

    |... |

    | yn |

    | 1   m1   F1 |

    | 1   m2   f2 |

X = | 1   m3   f3 |

    |... ...  ... |

    | 1   mn   fn |

In the above model, the sum of all category dummy variables for each row is equal to the intercept value of that row - in other words, there is perfect multi-collinearity (one value can be predicted from the other values). Intuitively, there is a duplicate category.

If we dropped the male category it is inherently defined in the female category (zero female value indicate male, and vice-versa).