Econometrics 4: Classical Assumption Violations Flashcards
(14 cards)
Explain the implications of violating classical assumptions in regression analysis.
Classical assumptions (CLRA1–CLRA6) ensure OLS is BLUE (Best Linear Unbiased Estimator).
In practice, these assumptions are often violated:
Time-series models: errors may be autocorrelated → violates CLRA4.
Cross-sectional models: errors may be heteroscedastic → violates CLRA5.
Consequences:
OLS remains unbiased.
But standard errors are incorrect → invalid hypothesis tests.
OLS is no longer efficient → better estimators exist (e.g. GLS, WLS).
What is autocorrelation in regression errors?
Option B: Define autocorrelation and explain its relevance in
What are the consequences of autocorrelated errors for OLS estimation?
Unbiasedness: OLS remains unbiased even with autocorrelated errors.
Variance: OLS variance formulas are incorrect → standard errors are biased.
Inference: t-tests and F-tests may be invalid due to incorrect standard errors.
Efficiency: OLS is no longer BLUE — it is inefficient.
Better alternative: Generalised Least Squares (GLS) provides lower-variance estimates when autocorrelation is present.
Describe formal and informal methods for detecting autocorrelated errors.
Also, for DW, inconclusive evidence at 4-dU and 4-dL
Summarise the methods for dealing with autocorrelation in regression errors.
Explain the process for GLS
Explain the Cochrane-Orcutt Iterative Procedure
The procedure is said to be iterative, because we repeat the steps until convergence. Once
convergence has occurred, these are the final estimates of our model parameters. One additional
step that is often included is an attempt to remedy the fact that the procedure creates a loss of
observations due to the use of the first differences in the data. The Prais-Winsten technique adds
these back in to the dataset using 𝑌1star = 𝑌1√(1 − 𝜌^2) and 𝑋1star = 𝑋1√(1 − 𝜌^2).
What are the consequences of heteroscedastic errors in regression?
Unbiasedness: OLS remains unbiased even if errors are heteroscedastic.
Variance: OLS variance formulas are incorrect → standard errors are biased.
Inference: Hypothesis tests (t, F) may be invalid due to incorrect standard errors.
Efficiency: OLS is no longer BLUE — it is inefficient.
New equation for slope of bivariate model: picture
Better alternative: Weighted Least Squares (WLS) provides lower-variance estimates when heteroscedasticity is present.
Describe formal and informal methods for detecting heteroscedasticity.
Describe & explain ‘White’s test’
Describe & explain ‘Breusch-Pagan Test’
Describe & explain ‘Goldfeld-Quandt test’
What are robust standard errors and when should they be used?
Robust standard errors adjust the estimated standard errors of OLS coefficients to remain valid when classical assumptions (like homoscedasticity or no autocorrelation) are violated.
Key idea: OLS estimates remain unbiased even with heteroscedasticity or autocorrelation, but their standard errors are incorrect → inference is unreliable.
Newey-West standard errors:
Also called HAC (Heteroscedasticity and Autocorrelation Consistent).
Adjusts for both heteroscedasticity and autocorrelation.
Widely used in time-series econometrics.
Why use them:
Easier and safer than transforming the model (as in GLS or WLS).
Avoids risk of incorrect model specification.
Supported in most econometric software.
When to use:
When tests (e.g. White, BG, DW) indicate assumption violations.
When you want valid inference without changing the model structure.
Describe & explain ‘Weighted Least Squares’
