Jukina Hatakeyama

Lecture Notes / Econometrics I — TA Sessions (2024)

Course materials

Econometrics I — TA Sessions (2024)

Supplementary notes for Econometrics I, progressing from matrix methods and asymptotic theory to instrumental variables and large-sample testing.

  • Academic year: 2024
  • Term: Spring & Summer
  • University: Osaka University, Graduate School of Economics
DateSessionTopicsMaterials
1
Course orientation and matrix foundations
  • Course aims and objectives
  • Matrix notation and basic operations
  • Matrix differentiation
Session 1 handout
2
Functions, optimisation, and convergence
  • Mappings and functions
  • Optimisation review
  • Big-O and little-o notation
  • Basic modes of convergence
Session 2 handout
3
Multivariate normality and ordinary least squares
  • Multivariate normal distribution
  • Ordinary least squares
  • R exercises
Session 3 handout
4
Probability inequalities and limit theory
  • Lebesgue-Stieltjes representation
  • Markov and Chebyshev inequalities
  • Law of large numbers
  • Moment-generating and characteristic functions
  • Central limit theorem
Session 4 handout
5
Asymptotic properties of OLS and test statistics
  • Consistency and asymptotic normality of the OLS estimator
  • Construction and interpretation of test statistics
Session 5 handout
6
Multiple regression and the Gauss-Markov theorem
  • Multivariate normal distribution: selected results
  • Multiple regression model
  • Gauss-Markov theorem
  • Asymptotic normality of the OLS estimator
Session 6 handoutExercise sheet
7
F tests and constrained least squares
  • Review of the F test
  • Constrained OLS
  • R exercises
Session 7 handout
8
Generalised least squares
  • Matrix transformations
  • GLS estimator
  • Gauss-Markov theorem for GLS
  • Comparison of OLS and GLS
  • Asymptotic normality of GLS
Session 8 handout
9
GLS, M-estimation, and an introduction to maximum likelihood
  • Further results for GLS
  • M-estimation
  • Introductory maximum-likelihood methods
  • R exercises
Session 9 handout
10
Large-sample theory for maximum likelihood
  • M-estimation
  • Consistency and asymptotic normality of the MLE
  • Non-linear optimisation procedures
Session 10 handout
11
Maximum likelihood in regression and serial correlation
  • MLE for simple and multiple regression
  • Properties and estimation of an AR(1) process
  • Regression with autocorrelated errors
Session 11 handout
12
M-estimation in the linear regression model
  • Review of asymptotic theory
  • Asymptotic normality of M-estimators
  • M-estimation for linear regression
  • R exercises
Session 12 handout
13
Endogeneity, identification, and instrumental variables
  • Measurement error and endogeneity
  • Instrumental variables
  • Identification problems
  • Instrumental-variable estimation
  • Partial identification
Session 13 handout
14
Two-stage least squares
  • Derivation of the 2SLS estimator
  • Properties of the 2SLS estimator
  • R exercises
Session 14 handoutExercise sheet
15
Large-sample hypothesis tests
  • Wald test
  • Score (Lagrange multiplier) test
  • Likelihood-ratio test
  • Comparison of the three tests
Session 15 handout