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Methods Camp for new PhD students (August 2020)

Methods Camp is a two-week intensive course to get all incoming PhD students in economics to ensure that everyone are familiar with some technical tools before the main courses start. There are two week-long and separate parts: The first deals with general mathematical tools: Calculus, Analysis, and Linear Algebra. The second part is more specific and deals with with probability and statistics.

Participation in the Methods Camp is voluntary, but all economics students are expected to sit a 3 hour exam immediately after the camp in order to evaluate if some further tutoring is necessary.

Math part

  • Instructor: Justin Valasek
  • email: justin.valasek@nhh.no
  • office: D222
  • lectures: Week 33 (Aug 10–14), 1015-1200 and 1415-1600 in Karl Borch (all days).

Outline

For some of you this will be a review (again, the course is not mandatory), and some of you will be seeing this material for the first time. My main goal with the class is to make everyone comfortable with: (1) the basic mathematical tools we use in economic theory, and (2) constructing simple proofs. I am assuming everyone is familiar with basic calculus (derivatives and integrals), and this course will focus on giving you “deeper” conceptual insight into math.

Textbook: The main textbook is Carl P. Simon and Lawrence Blume, “Mathematics for Economists”, Norton 1994. However, this book is more of a reference than a pedagogical text, so I will also be providing handouts and notes. Again, if something is new to you, the best way to learn is by doing problems!

Some other standard textbooks in Mathematical Economics: Alpha C. Chiang, “Fundamental Methods of Mathematical Economics”, McGraw Hill, 1983. Walter Rudin, “Principles of Mathematical Analysis”, McGraw Hill. A. MasCollel, M.D. Whinston, and J.R. Green, “Microeconomic Theory” (math appendix). A more advanced books: Rakesh V. Vohra, “Advanced mathematical economics”, Routledge, 2005. A.N. Kolmogorov, “Introductory Real Analysis”, Courier Dover Publications, 1975. A more dense, dictionary like book: Knut Sydsæter, Arne Strøm, Peter Berck, “Economists’ Mathematical Manual”, Springer 1999.

List of topics

  1. Elementary Analysis: Sets, numbers and proofs
    • Proofs and logical arguments, Set theory: functions, relations, Numbers, Countability, Sequences, Convergence, Boundedness
    • Limit, Continuity
  2. Linear Algebra
    • Linear mappings and matrices, Vectors: addition, subtraction, inner product, rotation, Linear independence, Rank of a matrix, Determinant, Eigenvalues and eigenvectors, Diagonalization, Solving linear difference equations.
  3. Multivariate Calculus
    • Open ball, Limit point, Continuity, Partial derivative, Total derivative, Gradient, Hessian, Differentiability and continuous differentiability, Implicit Function theorem, Introduction to Ordinary Differential equations
    • Concavity and optimization
      • Quadratic form, Definiteness of matrix, Lagrangean, Kuhn-Tucker theorem, Bordered Hessian, Quasi-concavity

Probability and Statistics

  • Instructor: Erik Ø. Sørensen
  • email: erik.sorensen@nhh.no
  • office E228
  • lectures: Week 34 (Aug 17–21), 1015-1200 and 1415-1600 in Karl Borch (all days).

Outline

The plan is to go through all of the basics of probability and statistics - not to introduce topics that are unfamiliar to most new PhD students, but introduce a bit more of the formal notation than new students traditionally have been familiar with.

Textbook: A very compact book that covers everything is Oliver Linton’s Probability, Statistics and Econometrics. A few additional readings will be made available.

List of topics:

  1. Probability on sets
    • probability spaces
    • Conditional probability and Bayes’ law
  2. Random variables in one dimension
    • distributions
    • Expectations, including moment generating functions
    • Transformations
  3. Random vectors
    • Generalizations to more dimensions (for the general case, mostly two dimensions)
    • Independence and random n-samples.
  4. Estimation
    • The analog principle
    • Method of moments
    • Maximum likelihood
  5. Asymptotics
    • Convergence in probability and distribution
    • A central limit theorem
    • The delta-rule
  6. Inference
    • Null hypothesis testing
    • Statistical power
    • Some statistical properties of common statistical practices