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Economists have previously made little use of high-performance computers (HPC) in their research. This is despite the fact that the complex interactions and heterogeneity of their models can quickly cause them to reach hundreds of dimensions, which cannot be calculated using conventional methods. In the past, simplified models were therefore often formulated for answering complex questions. These models solved some problems, but they could also provide false predictions, explains Simon Scheidegger, Senior Assistant at the University of Zurich's Department of Banking and Finance. For example, quantitatively studying optimal monetary policy in the wake of a financial crisis cannot be properly achieved using the conventional methods. However, calculating high-dimensional models on a supercomputer is not easy either. Until recently, researchers lacked appropriate numerical analysis and highly efficient software.
Unlike in physics models, in which time is considered as a fourth dimension alongside the three spatial dimensions, economic models have to consider ten- or even a hundred-times more dimensions. Even a "simple" model of pension insurance in a single country, which aims to depict the prosperity of its society at each year of age, clearly shows how quickly a higher dimensionality is reached: "If we assume that people will live to 80 years old on average and will be earning from the age of 20, and want to determine prosperity for each year of age, we already have 60 dimensions," explains Scheidegger. What's more, people make their current decisions while taking into account future uncertainties. Ideally, a model should consider all these influences.
Points - Models - Functions - Iteration - Steps
There are two main sticking points in calculating such complex economic models. The first is recursively approximating the high-dimensional functions using many iteration steps. At the same time, systems of non-linear equations must be solved at millions of grid points that describe the model. Calculating such a model can take hours...
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