MEcon Master of Economics Econometrics and Research Methods 1 — Questions and Answers
Question 1: In ordinary least squares (OLS) regression, the estimator minimizes the sum of:
- Absolute residuals
- Squared residuals (Correct answer)
- Residuals divided by fitted values
- Cubed residuals
Correct answer: Squared residuals
OLS finds the regression coefficients that minimize the total squared vertical distance between observed data points and the fitted regression line.
Question 2: The Gauss-Markov theorem states that, under its classical assumptions, the OLS estimator is:
- Consistent but not unbiased
- BLUE — Best Linear Unbiased Estimator (Correct answer)
- The maximum likelihood estimator always
- Efficient only with large samples
Correct answer: BLUE — Best Linear Unbiased Estimator
Given linearity, exogeneity, homoskedasticity, no autocorrelation, and no perfect multicollinearity, OLS produces the estimator with the smallest variance among all linear unbiased estimators.
Question 3: Omitted variable bias occurs when a relevant variable is excluded from a regression and that variable is:
- Correlated with the error term and uncorrelated with the included regressors
- Correlated with the error term and correlated with included regressors (Correct answer)
- Uncorrelated with the error term regardless
- A dummy variable
Correct answer: Correlated with the error term and correlated with included regressors
When an omitted variable affects the dependent variable AND correlates with an included regressor, the OLS coefficient on that regressor absorbs the omitted effect and is biased.
Question 4: Heteroskedasticity in regression means that the variance of the error term:
- Is constant across all observations
- Varies across observations (Correct answer)
- Is correlated with lagged residuals
- Is exactly zero
Correct answer: Varies across observations
Heteroskedasticity violates the classical assumption of constant error variance, making standard OLS standard errors incorrect even though coefficients remain unbiased.
Question 5: Instrumental variable (IV) estimation is used to address:
- Multicollinearity between regressors
- Endogeneity caused by reverse causality or omitted variables (Correct answer)
- Heteroskedasticity in error terms
- Serial correlation in time-series data
Correct answer: Endogeneity caused by reverse causality or omitted variables
IV estimation uses an instrument — a variable correlated with the endogenous regressor but uncorrelated with the error — to isolate exogenous variation and obtain consistent estimates.
Question 6: In a difference-in-differences (DiD) estimator, the key identifying assumption is:
- No selection into treatment
- Parallel pre-treatment trends between treatment and control groups (Correct answer)
- Random assignment to treatment
- No heteroskedasticity in the error term
Correct answer: Parallel pre-treatment trends between treatment and control groups
DiD requires that absent the treatment, the treated and control groups would have followed the same trend — the 'parallel trends' assumption.
MEcon Master of Economics Econometrics and Research Methods 1
In ordinary least squares (OLS) regression, the estimator minimizes the sum of: