Quantitative Economics

nieobowiązkowe

(tylko po angielsku) Linear algebra, mathematical analysis, probability calculus

This course studies quantitative approaches for solving dynamic economic models.

There is a heavy theoretical component: this course provides basic background in dynamic programming techniques (Bellman equation) frequently used in modern economics. We will also study economic theory related to consumption and savings decisions. There is also a heavy computational component: we will study numerical methods (value function iteration, endogenous grid, policy function iteration and similar) and learn to apply them in deterministic and stochastic settings.

We will use Julia, a modern, open source, high productivity language primarily used in technical and scientific computing. No prior knowledge of Julia is needed.

This course is a comprehensive introduction to quantitative methods used in modern economics. There are two main parts of the course. In the first part we discuss elementary topics in numerical analysis with applications to statistics, econometrics and economics. In the second part we will focus on recursive methods for solving sequential decision problems. The emphasis will be mostly on tools, techniques and theories used by macroeconomists. We will analyze consumption-savings problems, income dynamics and wealth inequality in partial and general equilibrium. To confront our models with the data we will solve them on a computer and compare their predictions with empirical regularities. Time permitting, we will also cover a range of other tools and techniques used in modern macroeconomics, primarily in models of business cycles.

We will make extensive use of mathematics, numerical methods and computer programming. There is a heavy theoretical component: this course provides basic background in dynamic programming techniques (Bellman equation) frequently used in modern economics. We will also study economic theory related to consumption, savings, wealth and income distributions. There is also a heavy computational component: we will study numerical methods and learn to apply them in various settings.

We will use Julia, a modern, open source, high productivity language primarily used in technical and scientific computing. No prior knowledge of Julia is needed as a brief introduction to this language and example code will be provided.

Students who do not find such a quantitative, computational approach to economics appealing, are strongly advised against taking this course.

We will discuss the following topics:

1. Programming in Julia.

2.Efficient and reproducible workflow: version control, debugging, benchmarking, modules, and packages.

3.Elementary concepts in scientific computing.

4. Linear and nonlinear (systems of) equations.

5. Optimization.

6. Function approximation and interpolation.

7. Numerical integration and Markov processes.

8. Introduction to dynamic programming.

9. Discrete Markov decision processes.

10. Continuous state models.

11. Heterogeneous agent models in macroeconomics.

12. Perturbation methods.

13. (Stochastic) difference equations and linear rational expectations models.

14. Projection methods.

Lecture notes.

The list of required readings will be posted on Moodle.

Students know basic computational techniques used to study dynamic economic models and know how to implement them in on a computer. Students are familiar with economic theories of consumption, savings, wealth and income distributions.

Grading will be based on:

• Problem sets (x3) 50%

• Final project 40%

• Class participation 10%