Term
| Define "heteroskedasticity" |
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Definition
| when a collection of random variables has sub-populations. These sub-populations have different variabilities. In other words, the relationships between regressant and regressors are not the same throughout sample |
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Term
| Define "homoskedasticity" |
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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 |
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Term
| State the Gauss-Markov theorem |
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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 off-diagonal terms
-E(X'ε) = 0
–The rank of X is K and K ≤ N) |
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Term
| What does "E(εi) = 0" mean? |
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Definition
| The residuals have a mean of 0 |
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Term
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Definition
| the difference between the sample and the estimated function value (from the regression) |
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Term
| What does "E(εi2) = σ" mean? |
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Definition
| The residuals are homoskedastic. |
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Term
| What does "E(εi*εj ) = 0 (i≠ j)" mean? |
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Definition
| There is no autocorrelation. |
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Term
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Definition
| "When an analysis is correlated with itself" (**fix**) |
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Term
| What does "X's are nonstochastic with values fixed in repeated samples" mean? |
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Definition
| X's are deterministic, non-random; outcomes are consistent |
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Term
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Definition
| no randomness is involved in the system; the same initial conditions always produces the same output |
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Term
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Definition
| a system/process that is intrinsically non-deterministic. Randomness is involved! |
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Term
| What does "xi and εi are uncorrelated" mean? |
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Definition
| X and the residuals are uncorrelated to each other |
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Term
| What does "The number of observations is greater than the number of parameters estimated" mean? |
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Definition
| There are more data points than unknown variables. |
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Term
| What does "No exact linear relationship exists between any of the explanatory variables" mean? |
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Definition
| There is no multicollinearity |
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Term
| Define "multicollinearity" |
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Definition
| when two or more predictor variables in a multiple regression model are highly correlated |
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Term
| What happens when εi are not identical for all i=(0,1,...,N)? |
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Definition
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Term
| What happens if εi and εj are correlated for i /= j? |
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Definition
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Term
| What effect does heteroskedasticity have on the OLS estimator? |
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Definition
| It remains unbiased and consistent, but coefficients are not efficient. Also standard errors are biased and inconsistent (effect: t statistics incorrect). |
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Term
| What is pure heteroskedasticity? |
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Definition
| Occurs due to the nature of the data. |
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Term
| What is impure heteroskedasticity? |
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Definition
| Occurs due to incorrect regression (ex: omitted variables) |
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Term
| Do heteroskedasticity tests distinguish between pure and impure types? |
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Definition
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Term
Is this heteroskedastic or homoskedastic?
[image] |
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Definition
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Term
Is this heteroskedastic or homoskedastic?
[image] |
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Definition
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Term
Is this heteroskedastic or homoskedastic?
[image] |
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Definition
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Term
| How do you detect heteroskedasticity via plots? |
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Definition
| Estimate model, calculate the residuals, then plot the residuals against each variable separately. |
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Term
| Name four tests for homoskedasticity. |
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Definition
| Park test White test Breusch-Pagen test Goldfeld-Quandt test |
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Term
| Which three tests for heteroskedasticity use residual plots? |
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Definition
| White test* Breusch-Pagen test* Goldfeld-Quandt test *More commonly used |
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Term
| Which three tests for heteroskedasticity use residual plots? |
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Definition
| White test* Breusch-Pagen test* Goldfeld-Quandt test *More commonly used |
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Term
| Which three tests for heteroskedasticity use residual plots? |
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Definition
| White test* Breusch-Pagen test* Goldfeld-Quandt test *More commonly used |
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Term
| When can you use the Park test? |
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Definition
| When you know something about Σ (the error term) |
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Term
Is this heteroskedastic or homoskedastic?
[image] |
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Definition
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Term
Is this heteroskedastic or homoskedastic?
[image] |
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Definition
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Term
Is this heteroskedastic or homoskedastic?
[image] |
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Definition
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Term
Is this heteroskedastic or homoskedastic?
[image] |
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Definition
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Term
| What are the steps of the Park test? |
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Definition
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Term
| When should you run a test for heteroskedasticity using a plot? |
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Definition
| When you do not have information about the error term (Σ is unknown) |
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Term
| What are the steps for the White test for heteroskedasticity? |
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Definition
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Term
| What is the modified version of the White test, and when/why would you use it? |
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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!) |
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Term
| What are two remedies for heteroskedasticity (after omitted variables has been ruled out)? |
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Definition
-Corrected Standard errors
-Generalized least squares (GLS) |
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Term
| How do you perform "Corrected Standard Errors" to correct for heteroskedasticity? |
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Definition
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