CEA Data Analysis & Statistical Methods 4 — Questions and Answers
Question 1: The Granger causality test in time-series econometrics determines whether:
- Two variables share a common long-run trend
- Past values of one variable improve the prediction of another variable (Correct answer)
- A variable has a unit root
- Residuals are autocorrelated
Correct answer: Past values of one variable improve the prediction of another variable
Granger causality tests whether lagged values of variable X provide statistically significant information for forecasting variable Y, beyond Y's own lags.
Question 2: In principal component analysis (PCA), the first principal component:
- Explains the least variance in the data
- Is the linear combination of variables that maximizes explained variance (Correct answer)
- Is always equal to the original first variable
- Minimizes the correlation among all variables
Correct answer: Is the linear combination of variables that maximizes explained variance
The first principal component is the direction in variable space along which the data exhibit maximum variance, capturing the most information.
Question 3: A confidence interval that is constructed using a higher confidence level (e.g., 99% vs. 95%) will, all else equal, be:
- Narrower
- The same width
- Wider (Correct answer)
- Unaffected by confidence level
Correct answer: Wider
Higher confidence requires a larger critical value (e.g., z = 2.576 for 99% vs. 1.96 for 95%), producing a wider interval that is less precise but more certain to contain the true parameter.
Question 4: The Augmented Dickey-Fuller (ADF) test is used to:
- Detect heteroskedasticity in residuals
- Test whether a time series has a unit root (is non-stationary) (Correct answer)
- Measure the strength of a linear relationship
- Test for structural breaks in a regression model
Correct answer: Test whether a time series has a unit root (is non-stationary)
The ADF test extends the original Dickey-Fuller test by including lagged differences to account for serial correlation when testing for a unit root.
Question 5: Which measure of central tendency is most affected by extreme outliers?
- Mode
- Median
- Geometric mean
- Arithmetic mean (Correct answer)
Correct answer: Arithmetic mean
The arithmetic mean incorporates every observation equally, so extreme values (outliers) can pull it substantially away from the center of the bulk of the data.
Question 6: In a two-way ANOVA, the interaction term tests whether:
- Each factor independently affects the outcome
- The effect of one factor on the outcome depends on the level of the other factor (Correct answer)
- Residuals are normally distributed within groups
- The variances across all groups are equal
Correct answer: The effect of one factor on the outcome depends on the level of the other factor
A significant interaction term indicates that the combined effect of the two factors is not simply additive—one factor modifies the effect of the other.
Question 7: When using a panel data model, fixed effects estimation controls for:
- Time-varying unobserved heterogeneity across units
- Endogeneity caused by measurement error
- Time-invariant unobserved individual characteristics (Correct answer)
- Serial correlation in the error term
Correct answer: Time-invariant unobserved individual characteristics
Fixed effects models remove time-invariant individual-specific unobserved factors by within-transformation (demeaning), eliminating their confounding influence.
CEA Data Analysis & Statistical Methods 4
The Granger causality test in time-series econometrics determines whether: