CEMLA Course: Introduction to Numerical Methods

Recent developments in the numerical approach to economic problems require some proficiency in the basics of numerical methods as a preliminary step toward understanding more complex methods and applications in the field of macroeconomics.

Since the Membership brings together a group of professionals dedicated to the proposal and solution of economic problems, focused on the formulation and conduct of monetary policy, the Course aims to offer a basic treatment of numerical aspects of economic problems for the benefit of analysts and researchers who are less than familiar to the following topics: solution of linear and non-linear systems of equations, bootstrapping techniques, and structural estimation. This Course is thus a combination of numerical methods and econometrics from a macroeconomic perspective.

The Course is interactive, combining theoretical discussions about each tool and its application on the computer, for which MATLAB execution codes will be shared. Applications of interest in the field of macroeconomics will be developed, taking advantage of the flexibility of the codes so that the user can use them for their own benefit and allow them to answer their own research questions.

The discussion is organized in three sections. The first one deals with solving linear and non-linear systems of equations. In economics, we regularly encounter non-linear, large-scale systems of equations. Optimization techniques, which are amply used in economics, can also be seen as a problem in solving a system of non-linear equations, so this topic has broad implications. The second section focuses on bootstrapping techniques. Instead of relying on large-sample properties of estimators, we can treat the sample as if it were the population, making inferences appropriately. We will discuss the basics of bootstrapping and its applications to time series. The third section will discuss structural estimation. In macroeconomics, we often want to combine theory and data to discipline the values attached to key structural parameters. We will discuss the Generalized Methods of Moments, the Efficient Methods of Moments, and Indirect Inference.