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Social Science
Economics
Econometrics
Heteroskedasticity
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Terms in this set (17)
Pure Heteroskedasticity cause
Is caused by the error term of the correctly specified equation
Impure heteroskedasticity cause
Is caused by a specification error such as an omitted variable
Heteroskedasticity
The violation of classical assumption V- the observations of the error term are drawn from a distribution that has a constant variance, OLS when applied to heteroskedastic models is no longer the minimum variance estimator
Homoskedasticity
The assumption of constant variances for different observations of the error term
Heteroskedasticity often occurs
In data sets that have a wide disparity between the largest and smallest observed value of the dependent variable
Consequences of heteroskedasticity
Pure heteroskedasticity does not cause bias in the coefficient estimates; heteroskedasticity typically causes OLS to no longer be the minimum variance estimator; heteroskedasticity causes the OLS estimates of the SE(B)s to be biased, leading to unreliable hypothesis testing and confidence testing
Questions to ask before testing for heteroskedasticity
Are there obvious specification errors? Are there early warning signs of heteroskedasticity? Does a graph of the residuals show any evidence of heteroskedasticity
Breusch-Pagan test
A method of testing hetero skedasticity in the error term by investigating whether the squared residuals can be explained by possible proportionality factors
How to Breusch-Pagan test works
Obtain the residuals from the estimates regression equation; use the squared residuals as the dependent variable in an auxiliary equation; test the overall significance of the auxiliary equation with a chi-square test
Strengths of Breusch-Pagan test
It's easy to use and it's powerful if heteroskedasticity is related to one or more linear proportionality factors
Weaknesses of Breusch-Pagan test
If it fails to find heteroskedasticity, it only means there is no evidence of heteroskedasticity related to the Zs you've chosen
White test for heteroskedasticity
Investigates the possibility of heteroskedasticity in an equation by seeing if the squared residuals can be explained by the equation's independent variables, their squares, and their cross-products
To run the White test
Obtain the residuals of the estimated regression equation; estimate an auxiliary equation, using the squared residuals as the dependent variable, with each X from the original equation, the square of each X, and the product of each X times every other X as the explanatory variables; test the overall significance of the auxiliary equation with a chi-square test
Strengths of White test
Including all the variables from the original model allows the White test to check to see if any or all of them are Z proportionality factors. Including all squared terms and cross products allows us to test for more exotic and complex types of heteroskedasticity
Weaknesses of White test
The White test contains more right hand side variables than the original regression. If the number of right hand variables in the auxiliary regression exceeds the number of observations, you can't run the White test because you would have negative degrees of freedom in the auxiliary equation.
Heteroskedasticity-corrected standard errors
SE(B)s that have been calculated specifically to avoid the consequences of heteroskedasticity. The HC procedure yields an estimator of the standard error that, while they are biased, are generally more accurate than uncorrected standard errors for large samples in the face of heteroskedasticity. Thus the HC SE(B)s can be used in t-tests that and other hypothesis tests in most samples without the errors of interference potentially caused by heteroskedasticity
Redefining the variables
Another approach to ridding an equation of heteroskedasticity is to go back to the basic underlying theory of the equation and redefine the variables in a way that avoids heteroskedasticity
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