CEA Quantitative Analysis and Econometrics 4 — Questions and Answers
Question 1: The Gauss-Markov theorem guarantees that OLS estimators are BLUE. What does BLUE stand for?
- Bounded, Linear, Unbiased, and Efficient
- Best (minimum variance) Linear Unbiased Estimators (Correct answer)
- Bayesian, Likelihood-based, Unbiased, and Exact
- Balanced, Least-squares, Unbiased, and Exponential
Correct answer: Best (minimum variance) Linear Unbiased Estimators
Under the Gauss-Markov assumptions, OLS produces the Best (minimum variance) Linear Unbiased Estimator among all linear unbiased estimators.
Question 2: When the White test for heteroscedasticity is significant, the recommended correction is typically:
- Remove the heteroscedastic observations from the sample
- Use heteroscedasticity-robust (White) standard errors (Correct answer)
- Switch from OLS to maximum likelihood estimation
- Add a quadratic term to the regression model
Correct answer: Use heteroscedasticity-robust (White) standard errors
White's heteroscedasticity-consistent standard errors correct inference without requiring knowledge of the specific form of heteroscedasticity.
Question 3: In a difference-in-differences (DiD) design, the key identifying assumption is:
- Treatment and control groups have identical pre-treatment outcomes
- Treatment assignment is random across all time periods
- Treatment and control groups would have followed parallel trends absent treatment (Correct answer)
- The treatment effect is constant across all subgroups
Correct answer: Treatment and control groups would have followed parallel trends absent treatment
The parallel trends assumption states that without the intervention, the treated and control groups would have changed by the same amount over time.
Question 4: A regression F-statistic for joint significance has a p-value of 0.32. The correct interpretation is:
- At least one predictor is statistically significant at the 5% level
- The model explains 32% of the variation in the dependent variable
- The predictors jointly fail to explain significant variation in the outcome (Correct answer)
- The model is misspecified due to omitted variable bias
Correct answer: The predictors jointly fail to explain significant variation in the outcome
A p-value of 0.32 exceeds conventional significance levels, so we fail to reject the null hypothesis that all slope coefficients are simultaneously zero.
Question 5: Which forecasting error measure is most appropriate for comparing models applied to variables with different scales or units?
- Mean Absolute Error (MAE)
- Root Mean Squared Error (RMSE)
- Mean Absolute Percentage Error (MAPE) (Correct answer)
- Sum of Squared Residuals (SSR)
Correct answer: Mean Absolute Percentage Error (MAPE)
MAPE expresses errors as a percentage of actual values, making it scale-independent and suitable for comparing forecast accuracy across differently-scaled variables.
Question 6: In principal component analysis (PCA) applied to economic data, the first principal component is defined as:
- The variable with the highest variance in the dataset
- The linear combination of original variables that maximizes explained variance (Correct answer)
- The eigenvector with the smallest eigenvalue of the covariance matrix
- The standardized average of all input variables
Correct answer: The linear combination of original variables that maximizes explained variance
The first principal component is the linear combination of original variables with weights chosen to maximize the variance of the resulting scores.
Question 7: The Akaike Information Criterion (AIC) penalizes model complexity primarily to:
- Ensure coefficients remain statistically significant
- Prevent overfitting by trading off goodness-of-fit against number of parameters (Correct answer)
- Guarantee normally distributed residuals
- Maximize the in-sample R-squared value
Correct answer: Prevent overfitting by trading off goodness-of-fit against number of parameters
AIC = 2k - 2ln(L), where k is the number of parameters; the penalty term 2k discourages adding parameters that only marginally improve fit.
CEA Quantitative Analysis and Econometrics 4
The Gauss-Markov theorem guarantees that OLS estimators are BLUE.
What does BLUE stand for?