How to test heteroskedasticity using eviews
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Muhammad saeed aas khan Meo from superior university Lahore Pakistan
FOR MORE VIDESO AND Research TIPS AND TRICS PLEASE VISIT MY ECONOMETRIC Blog
http://saeedmeo.blogspot.com/
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Pakistanimeo
What is heteroskedasticity?
Heteroskedasticity. One of the key assumptions of regression is that the variance of the errors is constant across observations. If the errors have constant variance, the errors are called homoscedastic. Typically, residuals are plotted to assess this assumption.
Or
That is, the variance of the error term is constant. (Homoskedasticity). If the error terms do not have constant variance, they are said to be heteroskedastic. [Tidbit from Wikipedia: The term means “differing variance” and comes from the Greek “hetero” ('different') and “skedasis” ('dispersion').]
What are its consequences?
Consequences of heteroskedasticity
Note that heteroskedasticity is often a by-product of other violations of assumptions. These violations have their own consequences which we will deal with elsewhere. For now, we’ll assume that other assumptions except heteroskedasticity have been met. Then,
• Ols no longer blue
• Heteroskedasticity does not result in biased parameter estimates.
• In addition, the standard errors are biased when heteroskedasticity is present. This in turn leads to bias in test statistics and confidence intervals.
• Inconsistency in covariance so test of hypostasis no longer valid (f-test- test)
Causes of Heteroskedasticity
• Due to outliers
• Violation assumptions of CLRM, that the model is not correctly specified.
• Heteroskedasticity arises also when one uses grouped data rather than individual data.
• Due to skewness in one or more repressors in model
• Incorrect data transformation ,incorrect function form, linear or log linear model
• Errors may increase as the value of an IV increases. For example, consider a model in which annual family income is the IV and annual family expenditures on vacations is the DV. Families with low incomes will spend relatively little on vacations, and the variations in expenditures across such families will be small. But for families with large incomes, the amount of discretionary income will be higher. The mean amount spent on vacations will be higher, and there will also be greater variability among such families, resulting in heteroskedasticity
• Errors may also increase as the values of an IV become more extreme in either direction, e.g. with attitudes that range from extremely negative to extremely positive. This will produce something that looks like an hourglass shape:
• Measurement error can cause heteroskedasticity. Some respondents might provide more accurate responses than others. (Note that this problem arises from the violation of another assumption, that variables are measured without error.)
• Heteroskedasticity can also occur if there are subpopulation differences or other interaction effects (e.g. the effect of income on expenditures differs for whites and blacks). (Again, the problem arises from violation of the assumption that no such differences exist or have already been incorporated into the model.)
• Other model misspecifications can produce heteroskedasticity. For example, it may be that instead of using Y, you should be using the log of Y. Instead of using X, maybe you should be using X2 , or both X and X2 . Important variables may be omitted from the model. If the model were correctly specified, you might find that the patterns of heteroskedasticity disappeared.
Heteroskedasticity occur more in cross sectional data as compare to time series
Remedies for Heteroskedasticity
If the standard deviation of the error is known, we can use ‘Weighted Least Squares’ to overcome the problem, which simply involves dividing equation 1 through by the standard deviation. However it is unlikely that we will know this value, in which case we have to suggest a relationship, such as a non linear one as below:
Next we need to divide equation (1) through by xt.
We can show the error term is no longer suffering from heteroskedasticity, by showing its variance is now constant.
As the final term is a constant we can conclude that this has removed the heteroskedasticity. This process is often not required, as simply taking logarithms of the data can remove the heteroskedasticity.
Muhammad saeed aas khan Meo from superior university Lahore Pakistan
FOR MORE VIDESO AND Research TIPS AND TRICS PLEASE VISIT MY ECONOMETRIC Blog
http://saeedmeo.blogspot.com/
Join my Facebook econometric group
Facebook: saeedk8khan
Email me for any query
[email protected]
Join me on Facebook
Facebook: saeedaaskhanmeo
Join me on Skype
Pakistanimeo
What is heteroskedasticity?
Heteroskedasticity. One of the key assumptions of regression is that the variance of the errors is constant across observations. If the errors have constant variance, the errors are called homoscedastic. Typically, residuals are plotted to assess this assumption.
Or
That is, the variance of the error term is constant. (Homoskedasticity). If the error terms do not have constant variance, they are said to be heteroskedastic. [Tidbit from Wikipedia: The term means “differing variance” and comes from the Greek “hetero” ('different') and “skedasis” ('dispersion').]
What are its consequences?
Consequences of heteroskedasticity
Note that heteroskedasticity is often a by-product of other violations of assumptions. These violations have their own consequences which we will deal with elsewhere. For now, we’ll assume that other assumptions except heteroskedasticity have been met. Then,
• Ols no longer blue
• Heteroskedasticity does not result in biased parameter estimates.
• In addition, the standard errors are biased when heteroskedasticity is present. This in turn leads to bias in test statistics and confidence intervals.
• Inconsistency in covariance so test of hypostasis no longer valid (f-test- test)
Causes of Heteroskedasticity
• Due to outliers
• Violation assumptions of CLRM, that the model is not correctly specified.
• Heteroskedasticity arises also when one uses grouped data rather than individual data.
• Due to skewness in one or more repressors in model
• Incorrect data transformation ,incorrect function form, linear or log linear model
• Errors may increase as the value of an IV increases. For example, consider a model in which annual family income is the IV and annual family expenditures on vacations is the DV. Families with low incomes will spend relatively little on vacations, and the variations in expenditures across such families will be small. But for families with large incomes, the amount of discretionary income will be higher. The mean amount spent on vacations will be higher, and there will also be greater variability among such families, resulting in heteroskedasticity
• Errors may also increase as the values of an IV become more extreme in either direction, e.g. with attitudes that range from extremely negative to extremely positive. This will produce something that looks like an hourglass shape:
• Measurement error can cause heteroskedasticity. Some respondents might provide more accurate responses than others. (Note that this problem arises from the violation of another assumption, that variables are measured without error.)
• Heteroskedasticity can also occur if there are subpopulation differences or other interaction effects (e.g. the effect of income on expenditures differs for whites and blacks). (Again, the problem arises from violation of the assumption that no such differences exist or have already been incorporated into the model.)
• Other model misspecifications can produce heteroskedasticity. For example, it may be that instead of using Y, you should be using the log of Y. Instead of using X, maybe you should be using X2 , or both X and X2 . Important variables may be omitted from the model. If the model were correctly specified, you might find that the patterns of heteroskedasticity disappeared.
Heteroskedasticity occur more in cross sectional data as compare to time series
Remedies for Heteroskedasticity
If the standard deviation of the error is known, we can use ‘Weighted Least Squares’ to overcome the problem, which simply involves dividing equation 1 through by the standard deviation. However it is unlikely that we will know this value, in which case we have to suggest a relationship, such as a non linear one as below:
Next we need to divide equation (1) through by xt.
We can show the error term is no longer suffering from heteroskedasticity, by showing its variance is now constant.
As the final term is a constant we can conclude that this has removed the heteroskedasticity. This process is often not required, as simply taking logarithms of the data can remove the heteroskedasticity.
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