CEA Quantitative Analysis and Econometrics 5 — Questions and Answers
Question 1: A regression discontinuity design (RDD) estimates causal effects by exploiting:
- Random assignment of treatment to units above a threshold
- A discontinuous jump in treatment probability at a known cutoff value (Correct answer)
- Instrumental variables derived from natural experiments
- Matched pairs of treated and untreated observations
Correct answer: A discontinuous jump in treatment probability at a known cutoff value
RDD compares outcomes just above and just below a cutoff where treatment assignment changes sharply, using the discontinuity as a source of quasi-random variation.
Question 2: In a GARCH(1,1) model used for financial econometrics, the conditional variance depends on:
- Only the previous period's squared error
- The previous squared error term and the previous period's conditional variance (Correct answer)
- The unconditional variance and the current observation only
- A moving average of squared returns over a fixed window
Correct answer: The previous squared error term and the previous period's conditional variance
GARCH(1,1) specifies conditional variance as a function of both the lagged squared shock (ARCH term) and the lagged conditional variance (GARCH term).
Question 3: The concept of identification in econometrics refers to:
- Assigning unique identifiers to each observation in the dataset
- The ability to consistently estimate model parameters from the available data (Correct answer)
- Verifying that instrumental variables are correlated with each other
- Confirming that the sample is representative of the population
Correct answer: The ability to consistently estimate model parameters from the available data
Identification means the model parameters can be uniquely determined from the data's population moments; without it, multiple parameter values fit equally well.
Question 4: When applying the Box-Jenkins methodology to build an ARIMA model, the correct sequence of steps is:
- Estimation → Identification → Diagnostic checking → Forecasting
- Identification → Estimation → Diagnostic checking → Forecasting (Correct answer)
- Diagnostic checking → Identification → Estimation → Forecasting
- Forecasting → Estimation → Identification → Diagnostic checking
Correct answer: Identification → Estimation → Diagnostic checking → Forecasting
Box-Jenkins follows: identify appropriate ARIMA orders using ACF/PACF, estimate parameters, check diagnostics with residual tests, then use the validated model to forecast.
Question 5: An economist uses two-stage least squares (2SLS) because OLS yields biased estimates. The bias in OLS arises from:
- Too few observations relative to the number of predictors
- Correlation between an explanatory variable and the error term (endogeneity) (Correct answer)
- Non-normality of the dependent variable's distribution
- Omission of irrelevant variables from the model
Correct answer: Correlation between an explanatory variable and the error term (endogeneity)
Endogeneity — when a regressor is correlated with the error term — causes OLS to be inconsistent; 2SLS uses instruments to purge the endogenous variation.
Question 6: In quantile regression, the median regression (tau = 0.5) differs from OLS in that it minimizes:
- The sum of squared residuals
- The sum of absolute deviations (Correct answer)
- The sum of squared percentage errors
- The maximum absolute deviation
Correct answer: The sum of absolute deviations
Quantile regression minimizes a weighted sum of absolute deviations; at the median, this reduces to the unweighted sum of absolute residuals (LAD regression).
Question 7: The Granger causality test is best described as determining whether:
- One variable structurally causes another through a mechanism pathway
- Past values of X improve the forecast of Y beyond Y's own past values (Correct answer)
- Two variables share a common stochastic trend
- A variable's effect on another is instantaneous versus lagged
Correct answer: Past values of X improve the forecast of Y beyond Y's own past values
Granger causality tests whether including lagged X significantly reduces forecast errors for Y compared to using only Y's own lags — it is a predictive, not structural, concept.
CEA Quantitative Analysis and Econometrics 5
A regression discontinuity design (RDD) estimates causal effects by exploiting: