Exercises
Problem sets for the course, as PDFs. Each set is meant to be worked after the corresponding block of lectures; justify every answer. Solutions are distributed separately.
1 Problem Set 1 — Foundations
The data-generating process, the conditional expectation and the linear projection, and the algebra and geometry of least squares.
2 Problem Set 2 — Finite and Large Samples
Unbiasedness and omitted-variable bias, the sandwich variance and Gauss–Markov, the exact and asymptotic distributions of OLS, consistency, and a shrinkage estimator.
3 Problem Set 3 — Hypothesis Testing, GLS, and Clustering
Hypothesis-testing methodology, the \(t\)-test and confidence intervals, restricted least squares and the \(F\)-test, and the Wald–LR–LM trinity; the generalized regression model and GLS; heteroskedasticity and weighting; and clustered dependence with the Moulton factor.
4 Problem Set 4 — Instrumental Variables and Resampling
Endogeneity and identification, the IV and 2SLS estimators, the asymptotic distribution of 2SLS, weak instruments, and the Monte Carlo and bootstrap resampling methods.