Term
Define "heteroskedasticity" 

Definition
when a collection of random variables has subpopulations. These subpopulations have different variabilities. In other words, the relationships between regressant and regressors are not the same throughout sample 


Term
Define "homoskedasticity" 

Definition
when a collection of random variables has no subpopulations; the variance is constant across the sample. In other words, on average the relationships between regressant and regressors are the same throughout sample 


Term
State the GaussMarkov theorem 

Definition
β(ols) is the Best Linear Unbiased Estimator (BLUE) when: –ε~(0,σ^2*I(N)) E(ε) = 0, E(ε^2*I(N))is a symmetric matrix with constant diagonal terms and 0 for all offdiagonal terms E(X'ε) = 0 –The rank of X is K and K ≤ N) 


Term
What does "E(εi) = 0" mean? 

Definition
The residuals have a mean of 0 


Term

Definition
the difference between the sample and the estimated function value (from the regression) 


Term
What does "E(εi2) = σ" mean? 

Definition
The residuals are homoskedastic. 


Term
What does "E(εi*εj ) = 0 (i≠ j)" mean? 

Definition
There is no autocorrelation. 


Term

Definition
"When an analysis is correlated with itself" (**fix**) 


Term
What does "X's are nonstochastic with values fixed in repeated samples" mean? 

Definition
X's are deterministic, nonrandom; outcomes are consistent 


Term

Definition
no randomness is involved in the system; the same initial conditions always produces the same output 


Term

Definition
a system/process that is intrinsically nondeterministic. Randomness is involved! 


Term
What does "xi and εi are uncorrelated" mean? 

Definition
X and the residuals are uncorrelated to each other 


Term
What does "The number of observations is greater than the number of parameters estimated" mean? 

Definition
There are more data points than unknown variables. 


Term
What does "No exact linear relationship exists between any of the explanatory variables" mean? 

Definition
There is no multicollinearity 


Term
Define "multicollinearity" 

Definition
when two or more predictor variables in a multiple regression model are highly correlated 


Term
What happens when εi are not identical for all i=(0,1,...,N)? 

Definition


Term
What happens if εi and εj are correlated for i /= j? 

Definition


Term
What effect does heteroskedasticity have on the OLS estimator? 

Definition
It remains unbiased and consistent, but coefficients are not efficient. Also standard errors are biased and inconsistent (effect: t statistics incorrect). 


Term
What is pure heteroskedasticity? 

Definition
Occurs due to the nature of the data. 


Term
What is impure heteroskedasticity? 

Definition
Occurs due to incorrect regression (ex: omitted variables) 


Term
Do heteroskedasticity tests distinguish between pure and impure types? 

Definition


Term
Is this heteroskedastic or homoskedastic?
[image] 

Definition


Term
Is this heteroskedastic or homoskedastic?
[image] 

Definition


Term
Is this heteroskedastic or homoskedastic?
[image] 

Definition


Term
How do you detect heteroskedasticity via plots? 

Definition
Estimate model, calculate the residuals, then plot the residuals against each variable separately. 


Term
Name four tests for homoskedasticity. 

Definition
Park test White test BreuschPagen test GoldfeldQuandt test 


Term
Which three tests for heteroskedasticity use residual plots? 

Definition
White test* BreuschPagen test* GoldfeldQuandt test *More commonly used 


Term
Which three tests for heteroskedasticity use residual plots? 

Definition
White test* BreuschPagen test* GoldfeldQuandt test *More commonly used 


Term
Which three tests for heteroskedasticity use residual plots? 

Definition
White test* BreuschPagen test* GoldfeldQuandt test *More commonly used 


Term
When can you use the Park test? 

Definition
When you know something about Σ (the error term) 


Term
Is this heteroskedastic or homoskedastic?
[image] 

Definition


Term
Is this heteroskedastic or homoskedastic?
[image] 

Definition


Term
Is this heteroskedastic or homoskedastic?
[image] 

Definition


Term
Is this heteroskedastic or homoskedastic?
[image] 

Definition


Term
What are the steps of the Park test? 

Definition


Term
When should you run a test for heteroskedasticity using a plot? 

Definition
When you do not have information about the error term (Σ is unknown) 


Term
What are the steps for the White test for heteroskedasticity? 

Definition


Term
What is the modified version of the White test, and when/why would you use it? 

Definition
Same as standard White test except in the auxiliary regression, use only the x and x2 terms (no cross products). Use when you have many independent variables, as they make the White test much more complicated (example: 6 independent variables in regression > 27 variables in White test auxiliary regression!) 


Term
What are two remedies for heteroskedasticity (after omitted variables has been ruled out)? 

Definition
Corrected Standard errors Generalized least squares (GLS) 


Term
How do you perform "Corrected Standard Errors" to correct for heteroskedasticity? 

Definition

