Regression Part-7 Heteroskedasticity Flashcards
What is homoskedasticity?
Random errors appearing in the PRF have equal variance
Why does hetero come into picture?
- Error learning models (num of errors decrease) 2. outliers 3. Model misspecification 4. Skewness 5. Incorrect transformation 6. data collection improvement
What is pure hetero?
When error term is a function of error term. Eg. of comparing spending changes in CA vs RI is affected by population size which acts as the proportionality factor
What is impure hetero?
Caused by model misspecification - omitted variable
WHat is a BLUE?
Best - min variance; Linear function of observed variable; Unbiased Estimatorβ> Expected value of OLS estimator is equal to the true value of parameters
What does the gauss markov theorem say?
If linear model satisfies the CLRM assumptions then OLS estimators are BLUE. Expected value of disturbance is zero, Expected value of disturbance squared is a constant equal to varinace.
If hetero exists then do we have BLUE for our model?
No, since they wont have minimum variance. We need to find BLUE
Why cant we use OLS estimators in case of hetero?
Since OLS gives equal weights to all observations despite the difference in variability in populations we cant use the estimators. It becomes LUE since its not efficient for small and large samples. GLS will give BLUE
Why use GLS?
GLS is OLS on the transformed variables that satisfy the standard least-squares assumptions. In GLS the weight assigned to each observation is inversely proportional to its ππππ - i.e., the observations coming
from a population with larger ππππ will get relatively smaller weight and those from a population with smaller ππππ
will get relatively larger weight in minimizing sum of error squares.
What assumption are we making on residuals?
although residuals squared (sample) are not the same thing as the square of random error (population), they can be used as proxies, especially if the sample size is sufficiently large.
What are informal tests?
Plot residual squared with predicted Y and X to see if theres a pattern
What is the limitation of park test?
The error term introduced using the equation could bring heteroskedasticity
What is the Park Test?
Park formalizes the graphical method by suggesting that ππ
2 is some function of the explanatory variable ππ
What is the glejser test?
We regress the absolute value of π’π (estimated sample residual) on the π variable related to the heteroscedastic variance πi squared.
Heteroscedasticity is likely to be more seen in cross sectional or time series data?
cross-sectional data
