Please I Need Clear and Sure Answer Short answers: a - Define heteroskedasticity
ID: 3250156 • Letter: P
Question
Please I Need Clear and Sure Answer
Short answers:
a - Define heteroskedasticity. Your answer should include the circumstances under which you would expect to find heteroskedasticity.
b - Are ordinary least squares estimators unbiased in the presence of heteroskedasticity? Explain
c - Are ordinary least squares estimators efficient in the presence of heteroskedasticity? Explain.
d - What are the undesirable consequences for ordinary least squares estimators, given the presence of heteroskedasticity? Your answer should include reference to the variance of least squares estimators, given the presence of heteroskedasticity.
e - Explain one method for testing for heteroskedasticity.
Explanation / Answer
a) heteroskedasticity:
heteroscedasticity is any set of data that isn’t homoscedastic. More technically, it refers to data with unequal variability (scatter) across a set of second, predictor variables.
->heteroscedasticity (also spelled heteroskedasticity) refers to the circumstance in which the variability of a variable is unequal across the range of values of a second variable that predicts it.
For example: annual income might be a heteroscedastic variable when predicted by age, because most teens aren't flying around in G6 jets that they bought from their own income. More commonly, teen workers earn close to the minimum wage, so there isn't a lot of variability during the teen years. However, as teens turn into 20-somethings, and 20-somethings into 30-somethings, some will tend to shoot-up the tax brackets, while others will increase more gradually (or perhaps not at all, unfortunately). Put simply, the gap between the "haves" and the "have-nots" is likely to widen with age.
b) heteroscedasticity is the absence of homoscedasticity. ... For instance, while the ordinary least squares estimator is still unbiased in the presence of heteroscedasticity, it is inefficient because the true variance and covariance are underestimated.
c)In the presence of heteroscedasticity, OLS estimates are unbiased, but ... rect, ordinary least squares (OLS) provides efficient and unbiased estimates of the parameters.
e)Testing for Heteroskedasticity: Breusch-Pagan Test :
The Breusch-Pagan test is designed to detect any linear form of heteroskedasticity. You run a regression, and then give the estat hettest command (or, hettest alone will work). Using the reg01 data,
Breusch-Pagan / Cook-Weisberg tests the null hypothesis that the error variances are all equal versus the alternative that the error variances are a multiplicative function of one or more variables. For example, in the default form of the hettest command shown above, the alternative hypothesis states that the error variances increase (or decrease) as the predicted values of Y increase, e.g. the bigger the predicted value of Y, the bigger the error variance is. A large chi-square would indicate that heteroskedasticity was present. In this example, the chisquare value was small, indicating heteroskedasticity was probably not a problem (or at least that if it was a problem, it wasn’t a multiplicative function of the predicted values). Besides being relatively simple, hettest offers several additional ways of testing for heteroskedasticity; e.g. you could test for heteroskedasticity involving one variable in the model, several or all the variables, or even variables that are not in the current model