High Speed Heteroskedasticity Review

2 Review: Heteroskedasticity Heteroskedasticity leads to two problems: –OLS computes standard errors on slopes incorrectly (also  biased t-, F-stats) OLS assumes errors are homoskedastic –OLS is no longer efficient (“BLUE”) Estimates could be more precise if done differently Solutions –First problem: fix OLS standard errors using “robust” Important: STILL ESTIMATING BY OLS, but fixing standard errors

3 Addressing Heteroskedasticity Solution to second problem: –Estimate by weighted least squares (WLS) Efficient estimator and correct standard errors Two ways of thinking of WLS: –Downweighting “noisier” observations (ones with larger error variance) –“Transforming” data to create a model with a homoskedastic error, so OLS is efficient E.g., if var(u) =  2 /N c, then…. …with -- homoskedastic!

4 Not a fan of WLS Problem: if you don’t know the form of var(u), you have to estimate the weights: –“Feasible” GLS – you’re not responsible for this –There is no discipline on feasible GLS: nothing stops you from searching for weights that give you the results you want So my view: don’t use WLS unless you know the form of the heteroskedasticity –For example, like above, Y data are averages from samples of different sizes (say, cities)