OLS Violations: Consequences & Fixes

Vocabulary flashcards describing OLS violations and their fixes.

Error variance is not constant across observations.

Heteroskedasticity

Fix for Heteroskedasticity

Use robust standard errors (White's) or GLS.

Error terms are correlated across time (usually time series).

Autocorrelation

Fix for Autocorrelation

Use Newey-West SEs or transform model using GLS.

Fix for Measurement Error in X

Use instrumental variables to correct.

Regressors are highly correlated.

Multicollinearity

Fix for Multicollinearity

Drop one of the correlated variables or collect more data.

A relevant variable is left out and it's correlated with included regressors.

Omitted Variable Bias (Endogeneity)

Fix for Omitted Variable Bias

Include the variable or use IV estimation.

Instruments are weakly correlated with endogenous regressors, low f stat

Weak Instruments

Fix for Weak Instruments

Use stronger instruments; check F-stat in first stage (>10).

Consequences of Heteroskedasticity

Inefficient, Standard errors are incorrect, t-tests and confidence intervals may be invalid, Inference is unreliable (you might think something is significant when it’s not)

Consequences of Autocorrelation

Ineffecient, Standard errors are incorrect, t & f test may be overstated, Leads to false positives in hypothesis testing, especially a problem in time series regressions

Consequences of Multicollinearity

Standard errors are inflated. Coefficients become unstable and sensitive to small data changes, making it hard to determine which variables are significant

Consequences of Omitted Variable Bias (Endogeneity)

Coefficients are biased and inconsistent. Inference about causal relationships is invalid Standard errors may be misleading

Consequences of Weak Instruments

IV estimates become biased and inconsistent. Standard errors are inflated. Hypothesis testing becomes unreliable. May be worse than just using OLS