As of 2024-08-25.

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 probability and statistics.

Participation in the Methods Camp is voluntary, but all PhD students at the Economics Department are expected to sit a 90 minutes exam on the probability/statistics part 2024-08-26, in Karl Borch Auditorium, 1030-1200 in order to evaluate if some further tutoring is necessary. One A4 sheet of paper with notes is allowed.

If you plan to take part in this course, please fill out this brief survey such that we know a bit about how many students there will be and something about your background. Looking forward to see you in August!

# Math (week 1)

**Preliminary, all of the Math section is subject to later update.**

- Instructor: Fred Schroyen
- email: fred.schroyen@nhh.no
- office: D230
- lectures: Week 33 (Aug 12–16). 0915-1100 and 1315-1500 (Aud I).

## Outline

The mathematics camp consists of two parts. The first part reviews a number of concepts and results from mathematics that can be regarded as the foundation for the mathematics that economists use. For this part, a handout will be made available. You are expected to read through the handout and to solve the exercises at the end. We will not go through the handout in the lectures but refer to it regularly.

The handout covers the following topics:

- Vectors in Rn;
- Supremum, infimum, maximum and minimum of a set of real numbers;
- Functions in one and several variables;
- Norm and metric in Rn;
- Sequences in Rn ;
- Open and closed sets;
- Limit of a function;
- Continuity of a function;
- Compact sets;
- Convex sets;
- Matrices;
- Linear dependency of vectors;
- Determinant of a matrix;
- Inverse of a matrix;
- Derivatives and implicit derivatives;
- Gradient, Jacobian and Hessian;
- Inverse function and inverse function theorem;
- Implicit function theorem.

The second part, which the lectures are about, will cover the theory and techniques of optimization under side constraints, and related issues. This part consists of the following topics:

- A “no-arbitrage”" argument of optimality;
- Lagrange’s multiplier method;
- Extensions of Lagrange’s theorem: the Kuhn-Tucker theorem;
- Taylor expansions, approximations, and quadratic forms;
- Concave and quasi-concave functions;
- Second order conditions and comparative statics.

The mathematics refresher course has a Canvas page where the handouts for the first and second part will be posted. If you intend to take the course, send an email to fred.schroyen@nhh.no to get access to this Canvas page.

Good textbooks for the mathematics that economists make use of are:

- Carl Simon and Lawrence Blume (1994) Mathematics for Economists (New York: Norton)
- Avinash Dixit (1990) Optimization in Economic Theory (Oxford: Oxford University Press).

# Probability and Statistics (week 2)

- Instructor: Erik Ø. Sørensen
- email: erik.sorensen@nhh.no
- office E228
- lectures: Week 34 (Aug 19–23), two daily sessions: 1015-1200 and 1415-1400 in:
- Monday 2024-08-19 in LAB2.
- Tuesday 2024-08-20 in Aud I.
- Wednesday 2024-08-21 in Aud I.
- Thursday 2024-08-22 in Aud J.
- Friday 2024-08-23 in Aud I.

## 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**: There is no required textbook, but a suggestion of a book that covers everything is Oliver Linton’s Probability, Statistics and Econometrics.
A set of compact notes and a few additional readings will be made available.

## List of topics:

- Probability on sets
- probability spaces
- Conditional probability and Bayes' law

- Random variables in one dimension
- distributions
- Expectations, including moment generating functions
- Transformations

- Random vectors
- Generalizations to more dimensions (for the general case, mostly two dimensions)
- Independence and random n-samples.

- Estimation
- The analog principle
- Method of moments
- Maximum likelihood

- Asymptotics
- Convergence in probability and distribution
- A central limit theorem
- The delta-rule

- Inference
- Null hypothesis testing
- Statistical power
- Some statistical properties of common statistical practices