CEA Quantitative Analysis and Econometrics 3 — Questions and Answers
Question 1: A time series exhibits a unit root if its autoregressive parameter equals 1. What is the primary econometric concern with unit root processes?
- They always have zero mean and constant variance
- Regressions may produce spurious results even when variables are unrelated (Correct answer)
- They require larger sample sizes for OLS to work correctly
- Standard errors are systematically understated in cross-sectional data
Correct answer: Regressions may produce spurious results even when variables are unrelated
Non-stationary unit root series can produce spurious regressions with high R-squared and significant t-statistics even when the variables have no true relationship.
Question 2: The Augmented Dickey-Fuller (ADF) test adds lagged difference terms to the basic Dickey-Fuller test primarily to:
- Increase statistical power against the unit root null
- Account for serial correlation in the residuals (Correct answer)
- Remove the trend component from the series
- Test for cointegration between two variables
Correct answer: Account for serial correlation in the residuals
Augmenting with lagged differences corrects for autocorrelation in the error term, ensuring the test statistic has the correct distribution.
Question 3: If two non-stationary I(1) series are cointegrated, which modeling approach is most appropriate?
- First-difference both series and run OLS
- Apply a Vector Error Correction Model (VECM) (Correct answer)
- Use a seasonal ARIMA model on the levels
- Apply principal component analysis to remove trends
Correct answer: Apply a Vector Error Correction Model (VECM)
Cointegrated series share a long-run equilibrium, so a VECM captures both the short-run dynamics and the long-run error correction mechanism.
Question 4: In panel data analysis, the Hausman test is used to choose between:
- OLS and GLS estimators
- Fixed effects and random effects models (Correct answer)
- Pooled OLS and first-difference estimators
- Static and dynamic panel models
Correct answer: Fixed effects and random effects models
The Hausman test checks whether individual-specific effects are correlated with regressors; if they are, fixed effects is consistent but random effects is not.
Question 5: An ARMA(2,1) model contains which components?
- Two moving average terms and one autoregressive term
- Two autoregressive terms and one moving average term (Correct answer)
- Two seasonal lags and one differencing term
- Two trend terms and one intercept
Correct answer: Two autoregressive terms and one moving average term
ARMA(p,q) notation means p autoregressive lags and q moving average terms, so ARMA(2,1) has AR order 2 and MA order 1.
Question 6: Which condition must hold for an MA(q) process to be invertible?
- All autoregressive roots must lie outside the unit circle
- All moving average roots must lie outside the unit circle (Correct answer)
- The process must be stationary with zero mean
- The variance of innovations must equal one
Correct answer: All moving average roots must lie outside the unit circle
Invertibility of an MA process requires that the roots of the MA polynomial lie outside the unit circle, allowing the process to be expressed as a convergent AR representation.
Question 7: In a probit model, the estimated coefficient on a predictor represents:
- The change in probability for a one-unit change in the predictor
- The change in the standard normal z-score (index) for a one-unit change in the predictor (Correct answer)
- The log-odds ratio associated with the predictor
- The marginal rate of substitution between predictors
Correct answer: The change in the standard normal z-score (index) for a one-unit change in the predictor
Probit coefficients measure the change in the latent index (z-score) per unit change in X; marginal effects on probabilities require additional calculation using the normal PDF.
CEA Quantitative Analysis and Econometrics 3
A time series exhibits a unit root if its autoregressive parameter equals 1.
What is the primary econometric concern with unit root processes?