Question

Consider the linear model to explain monthly beer consumption: beer = Bo + B, inc + B2 price + B3 educ + 34 female + u where E(ulinc, price, educ, female) = 0 and Var(uinc, price, educ, female) = o-inc. Answer the following questions. 1. What is heteroskedasticity? Explain. 2. Write the transformed model that has an homoskedastic error term. 3. Outline the intuition behind the BP and White tests for heteroskedasticity. 4. If we have dummy variables in our model (e.g., female), we will get an error when using the White test. Why does this happen? How can we get around this problem?

Answer 1

1. Heteroscedasticity is the phenomenon of the non-constant variance of the error term across independent variables. it means the part of the dependent variable which is not explained by the change in independent variables is not distributed equally across all the independent variables.

2. given Var(u|inc,price,educ,female)=sigma.inc^2

the transformed model will be beer/inc=beta(0)/inc+beta1+beta2 (price/inc)+beta3(educ/inc)+beta4(female/inc)+u/inc

3. in both the tests the linear relationship/correlations between the estimated error terms and the indepedndent variables if there is a significant relation between the error and independent variables then we can say that there is a problem of heterscadiscity in the model.

4. when applying white test we regress the estimated errors on the independent variables as well as their interaction(multiplication with each other ) and their square terms. when the dummy is zero we won't be able to get correct interaction terms even if there are any. hence white test will have an error.

we have to take the different test for heteroscedasticity when this is a problem is there. such as Levene's test.

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