Econometrics and Data Analysis
Econometrics and Data Analysis tests whether you can specify, estimate, and interpret regressions, and whether you recognize when an estimate is credible. The exam combines OLS mechanics, inference, omitted-variable reasoning, instrumental variables, panel data, and basic time-series properties.
Core rules and concepts
- OLS minimizes the sum of squared residuals. In a simple regression, the slope is Cov(X,Y)/Var(X), and the intercept is ȳ − b·x̄.
- Gauss–Markov: under linearity, exogeneity, homoskedasticity, and no autocorrelation, OLS is the best linear unbiased estimator. Exogeneity fails with omitted variables, simultaneity, or measurement error.
- R² measures the share of sample variation in Y explained by the regressors. Adjusted R² penalizes additional regressors; R² itself cannot fall when a variable is added.
- Inference: use t-tests for single coefficients and F-tests for joint restrictions. Heteroskedasticity does not bias OLS but invalidates default standard errors; use robust standard errors.
- Instrumental variables require relevance, Cov(Z,X) ≠ 0, and exogeneity, Cov(Z,u) = 0. A weak instrument produces biased and imprecise IV estimates.
- Panel fixed effects remove time-invariant unobserved heterogeneity; time-series work requires attention to stationarity and autocorrelation.
Worked example
Suppose Cov(X,Y) = 12, Var(X) = 16, x̄ = 8, and ȳ = 10. The slope is 12/16 = 0.75. The intercept is 10 − 0.75 × 8 = 4. The fitted value at X = 12 is 4 + 0.75 × 12 = 13. If instead the model is ln(wage) = 2.5 + 0.08·educ, one additional year of education is associated with approximately 8% higher wages; the exact percentage is 100 × (e^0.08 − 1) = 8.33%. Omitted ability would likely bias the education coefficient upward, so the estimate should not be read as causal without further identification.
Traps that cost marks
Do not treat a high R² as proof of causality. Adding regressors cannot reduce R², so compare adjusted R² or use theory. Interpret log-level coefficients as approximate percentage changes, not absolute units. Avoid the dummy-variable trap. Heteroskedasticity biases conventional standard errors, not the OLS slope, and a weak instrument can be worse than OLS.