CEMLA Course: Introduction to Numerical Methods

Proficiency in numerical methods is essential due to recent advances in quantitative economic analysis. This course introduces key numerical techniques, including solvers for linear and nonlinear systems, bootstrapping, and structural estimation with macroeconomic applications. It is intended for analysts and researchers from CEMLA member central banks and collaborating institutions. This interactive course integrates theoretical discussions with computer-based applications. MATLAB scripts are provided to participants, enhancing both the delivery and the learning process.

This discussion is organized into three sections. The first section addresses the solution of linear and nonlinear systems of equations. In economics, non-linear, large-scale systems of equations are frequently encountered. Optimization techniques, widely applied in economics, can also be formulated as problems of solving nonlinear systems. The second section examines bootstrapping techniques. Rather than relying solely on large-sample properties of estimators, the sample can be treated as the population, enabling appropriate inference from the available data. Bootstrapping methods for both cross-sectional and time series data are considered. The third section covers structural estimation. In macroeconomics, it is often necessary to integrate theory and data to inform the values assigned to key structural parameters. The Generalized Method of Moments, the Efficient Method of Moments, and Indirect Inference are discussed.