CEMLA Course: Introduction to Numerical Methods

The Introduction to Numerical Methods course, taught by Gustavo Leyva (CEMLA) in a virtual format from June 15 to June 19, 2026, offered an introductory look at numerical methods and their applications to macroeconomic problems. Recent developments in the numerical approach to economic analysis require some proficiency in the basics of these methods as a preliminary step toward understanding more complex techniques and applications in the field of macroeconomics.

Given that the Membership brings together professionals dedicated to the proposal and solution of economic problems, focused on the formulation and conduct of monetary policy, the course provided a basic treatment of the numerical aspects of such problems, aimed at analysts and researchers with incipient familiarity with three topics: the solution of linear and non-linear systems of equations, bootstrapping techniques, and structural estimation. In this sense, the course combined numerical methods and econometrics from a macroeconomic perspective. It was interactive in nature, pairing theoretical discussions of each tool with its application on the computer through MATLAB execution codes, designed with the flexibility needed for participants to adapt them to their own research questions.

The content was organized in three sections. The first addressed the solution of linear and non-linear systems of equations, which are commonly encountered in economics in their non-linear, large-scale form; since optimization techniques, widely used in the discipline, can also be framed as the solution of a non-linear system of equations, this topic has broad implications. The second focused on bootstrapping techniques, which allow the sample to be treated as if it were the population in order to make inferences appropriately, without relying on the large-sample properties of estimators, with particular attention to their applications to time series. The third covered structural estimation, which in macroeconomics seeks to combine theory and data to discipline the values of key structural parameters; it discussed the Generalized Method of Moments (GMM), the Efficient Method of Moments, and Indirect Inference.