• Course Overview: This course is the first course in the core econometrics sequence. The main purpose is to introduce you to basic statistical inference and identification topics that you will find helpful as you pursue a graduate education in Economics. At the end of this course, you should be familiar with basic concepts in probability theory, commonly used univariate and multivariate distributions, basic strategies of econometric identifications, different types of estimation methods and inference procedures.

• Syllabus

• Notes

• Table of Contents

  1. Review of Probability and Distribution Theory
     • Probability space
     • Distributions
     • Markowitz's modern portfolio theory
     • Multiple choice model

  2. Large Sample Theory: Elementary
     • Notions of convergence
     • WLLN and CLT
     • Delta-method

  3. Large Sample Theory: Empirical Process
     • Symmetrization
     • ε-cover
     • Dudley's inequality
     • Peeling device
     • P-Donsker
     • Functional delta-method

  4. Mathematical Statistic Theory
     • Identification and Completeness
     • MLE and Efficiency

  5. Computations
     • Newton Raphson
     • Coordinate descent
     • Gradient descent
     • The Lasso as an example

  6. Statistical Inference
     • Trinity tests and Hausman's test
     • Neyman-Pearson lemma
     • Confidence regions
     • Partial identification

  7. Minimaxity
     • Shannon's information theory
     • Fano's inequality
     • Minimax risk
     • Packing
     • Normal models