CEA Quantitative Analysis and Econometrics 2 — Questions and Answers
Question 1: In a multiple regression model, what does heteroscedasticity specifically refer to?
- Non-constant variance of the error term across observations (Correct answer)
- Correlation between two or more independent variables
- Serial correlation in the residuals over time
- Non-normality of the dependent variable
Correct answer: Non-constant variance of the error term across observations
Heteroscedasticity means the variance of the regression error term is not constant across all levels of the independent variables.
Question 2: A researcher finds that the Durbin-Watson statistic is approximately 0.5. This most likely indicates:
- No autocorrelation in residuals
- Positive serial correlation in residuals (Correct answer)
- Negative serial correlation in residuals
- Perfect multicollinearity
Correct answer: Positive serial correlation in residuals
A Durbin-Watson value close to 0 indicates strong positive autocorrelation, while values near 4 suggest negative autocorrelation, and values near 2 suggest no autocorrelation.
Question 3: Which transformation is most commonly used to linearize an exponential relationship of the form Y = ae^(bX)?
- Square root transformation of Y
- Natural log transformation of Y (Correct answer)
- Reciprocal transformation of Y
- Box-Cox transformation with lambda=2
Correct answer: Natural log transformation of Y
Taking the natural log of both sides converts ln(Y) = ln(a) + bX, which is a linear relationship suitable for OLS estimation.
Question 4: In instrumental variable (IV) regression, a valid instrument must satisfy which two conditions?
- Exogeneity and homoscedasticity
- Relevance and exogeneity (Correct answer)
- Stationarity and invertibility
- Identification and normality
Correct answer: Relevance and exogeneity
A valid instrument must be correlated with the endogenous regressor (relevance) and uncorrelated with the error term (exogeneity).
Question 5: The Variance Inflation Factor (VIF) of 10 for a predictor variable suggests:
- The variable explains 10% of variance in the dependent variable
- Severe multicollinearity affecting that predictor's coefficient estimate (Correct answer)
- The predictor has 10 times more variance than the outcome
- Acceptable levels of correlation with other predictors
Correct answer: Severe multicollinearity affecting that predictor's coefficient estimate
A VIF of 10 indicates that 90% of the variance of that predictor is explained by other predictors, signaling severe multicollinearity.
Question 6: When performing a Chow test in econometrics, the null hypothesis states that:
- All regression coefficients are jointly zero
- The error variance is constant across groups
- The regression coefficients are equal across two subgroups (Correct answer)
- The residuals are normally distributed
Correct answer: The regression coefficients are equal across two subgroups
The Chow test examines structural stability by testing whether the same regression coefficients apply to two different data subsets or time periods.
Question 7: In logistic regression, a log-odds coefficient of 0.693 for a binary predictor implies an odds ratio of approximately:
- 0.50
- 1.00
- 2.00 (Correct answer)
- 6.93
Correct answer: 2.00
The odds ratio equals e^(coefficient) = e^(0.693) = 2.00, meaning the event is twice as likely when the predictor equals 1 versus 0.
CEA Quantitative Analysis and Econometrics 2
In a multiple regression model, what does heteroscedasticity specifically refer to?