Previous midterms

Midterm Formula Sheet

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2022  
2022  
2020  
2019 Mid 2  
2019 Mid 1 Answers
2016 Mid 2 Answers
  Final question
2016 Mid 1 Answers
2015 Mid 2 Answers
2015 Mid 1 Answers
2014 Mid 2 Answers
2014 Mid 1 Answers
2013 Answers

Previous finals

Final Formula Sheet

Year Answer Key
2023  
2022 Answers
2022 Winter  
2020 Answers
2019  
2016 Answers
2015 Answers
2014 Answers
2013 Answers

Proofs that we skipped. References are to the lecture slides.

  • Distribution of the t-test statistic: slides 8, pg. 18
  • Khinchin’s theorem, weak law of large numbers for proving the consistency of $s^2$: slides 9, pg. 14
  • Deriving the RLS estimator: slides 11, pg. 21-22
  • RLS estimator has smaller variance than LS estimator: slides 11, pg. 26-28
  • Joining the spline at the knots: slides 12, pg. 10
  • Deriving the Newton-Raphson by Taylor series approximation: slides 12, pg. 16-17

Course overview (post midterm)

Chapter 7: Asymptotics

  • Why consider asymptotic properties of estimators?
  • What is consistency? (two versions)
  • The plim() operator and the consistency of various estimators ($b$, $\hat{\sigma}^2$, $s^2$)
  • Asymptotic efficiency, and why the $\sqrt{n}$ is needed to avoid a “spike”

Chapter 8: IV

  • The missing variable problem, and the resulting inconsistency of LS
  • Two properties to make an instrument “valid”
  • Some intuition behind how the instrument is used
  • The over- and just-identified IV estimator
  • 2SLS procedure
  • Testing (Hausman, exogeneity, weak instruments)
  • Returns to education example

Chapter 9: Multiple hypotheses

  • What a multiple hypothesis is
  • Why t-tests can’t be used
  • $R$ and $q$ matrices
  • Wald test, then the F-test (and which one to use)
  • The RLS estimator and what it tells us about “imposing restrictions” on a model
  • Conducting an F-test using $R^2$ from a restricted and an unrestricted model
  • Testing for differences

Chapter 10: Non-linear effects and NLS

  • Avoiding NLS and keeping LS: linearizing and polynomial approximation
  • Reasons to estimate non-linear model directly (for example gravity model)
  • Definition of NLS estimator
  • Why a numerical algorithm is typically needed
  • How the Newton algorithm works
  • Convergence, iterations, tolerance
  • Issues in estimation (singularity, cycling, etc.)

Chapter 11: Heteroskedasticity

  • Define het.
  • Consequences of het. (inconsistent s.e., LS is inefficient)
  • Testing for het.
  • Fixing het.
  • The GLS estimator
  • Clustering (group sizes determine $P$ matrix, apply GLS directly)

Chapter 12: Time series

  • AR process
  • variance of an AR(1) error term
  • $\lvert \rho \rvert < 1$ and $\lvert \rho \rvert = 1$
  • random walks and spurious regressions