The ‘curse of dimensionality’ resolved: The effects of climate change and trade barriers in large dimensional modelling

Abstract

Solving large scale optimisation problems over space and time quickly generates a computational impasse, termed the ‘curse of dimensionality’. This severely limits the practical use of economic models, especially for determining the effects of climate change and protectionist trade policies. In this paper, we employ an innovative approach to solving (otherwise unsolvable) large scale systems through the use of parallel processing methods and a proper ordering of variables and equations in a ‘Nested Doubly Bordered Block Diagonal’ form. We illustrate how the approach can be used to solve an intertemporal CGE model with more than 500 million equations. Using existing damage functions, the framework allows us to determine the impact of climate change on long-run economic growth for 112 countries as a result of the effect of sea-level rise on land endowments, variation in crop yields and productivity and shifts in the demand for energy and transportation. We also compare our solution to more common (and smaller dimensional) recursive methods, in terms of both the economic effects of climate change and potential increases in trade barriers, showing the power and efficiency of our computational approach and parallel processing routine.