Weekly Homework 9: Detection of Heteroskedasticity
1. Heteroskedasticity (1 point each)
1) Carefully explain the difference between pure and impure heteroskedasticity and their consequences in OLS. Answer:
-Pure heteroskedasticity is caused by the error term of the correctly specified equation. Impure heteroskedasticity is caused by a specification error such as an omitted variable.
-Pure heteroskedasticity does not cause bias in the coefficient estimates. However, it typically causes OLS to no longer be the minimum-variance estimator. The error term causes the independent variable to fluctuate more, increasing their variance. Moreover, the OLS estimates of the standard errors become biased, leading to unreliable hypothesis testing. Heteroskedasticity increases the variance of the estimated coefficients variance, but OLS underestimates the variance.
-impure heteroskedasticity caused by an omitted variable will have possible specification bias. Impure heteroskedasticity causes bias in the coefficient and the variance of error is no longer minimum variance and no longer efficient. The variances of OLS estimators are biased.
2) Find any examples of heteroskedasticity in a time series, and explain why the heteroskedasticity exits. Answer:
-Heteroskedasticity can occur in time series models with a significant amount of change in the dependent variable. For example, DVD player sales from 1980 to 2005 would be a good example of this because there is larger disparity between the sizes of observations of DVD player sales during this time frame.
-The variance of sales of automobiles in US over past decades is correlated with time periods. As the economics growth, the variance would increase over time. Thus the square of error term is not constant but correlated with time, and there is heteroskedasticity. When stock market crashed, the market experienced very high variance while the variance is constant in normal periods.
3) Find any examples of...
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