Suppose I start out with the following regression: Wage = Bo + | Education + 2Ag

Question

Suppose I start out with the following regression: Wage = Bo + | Education + 2Age + 3Agee 1. If I added a dummy variable for female to the regression, how would do you think that would affect the standard errors on and A? 5 2. If I added a variable for parental income and parental education to the regression. How do you think that would affect the standard error on ? How would it affect the standard errors on 2 and 3? You will be graded as much on the quality of your explanation as on the correctness of your answer. 3. You are not sure whether to assume homoskedasticity for this regression or not. What should you do to decide? Be explicit and detailed about what you plan to do.

Explanation / Answer

1. Here the question is whether there will be any multicolinearity in the model or not. If a female gender dummy is included in the model then this will mean there is a chance of correlation with age. If this happens then this will increase the standard errors of the age variables and so make the t statistics insignificant. This depends completely on the correlation of the female dummy with the age variable. If the correlation is high then this mean standard errors will be high and insgnificant t stats.

2. Now we are adding variables on parental income and education to the regression. This will surely have a high correlation with the education variable which is the B1 variable. This will mean that multicolinearity will be high between the variables and so the standard errors of B1 will be high. This will also mean the t stat for B1 will be insignificant. Age is also likely to be correlated with education as well and so this will deflate the standard errors here as well. These are questions in mullicolinearity and so any addition of correlated variables will increase the standard errors.

3. The best way to assess homoscedasticity for this regression is again to look at the standard errors and also to conduct tests like the Goldfeld Quandt Test and also the White Test to try and find out if the variance of the errors is non constant.

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