A Latin Hypercube Sampling Utility: with an application to an Integrated Assessment Model

Abstract

This paper describes the use of a utility that creates a Latin Hypercube Sample (LHS). The LHS approach to sampling has had wide applicability as it represents a Monte Carlo strategy that limits sample size and therefore computer time to study the outcomes of simulations under uncertainty. Other approaches to deal with the ’size’ problem include Gaussian Quadrature (GQ) (Arndt, 1996), often used in the context of large models such as computable general equilibrium models. However, the GQ approach is most suitable for focusing on a small set of uncertain parameters as the number of model evaluations increases substantially with the number of uncertain parameters and/or the moments to track. The utility is a new version of the LHS utility that has been publicly available from Sandia National Labs since the early 2000s. Beyond the recoding from FORTRAN to C/C++, the new version of the utility has some additional features including new output options and additional statistical distributions. This paper demonstrates the use of the new utility by coupling it to an integrated assessment (IAM) model which is derived from the META 21 model developed by Dietz et al. (2021). The META 21 model has many components that can be readily integrated into global economic models that track greenhouse gas emissions—a simple climate module, economic impacts derived from sea-level and temperature rises and bio-physical tipping points such as the Amazon dieback. The IAM results suggest that the social cost of carbon increases by an average of around 26% when taking into account the tipping points and that the tipping points lead to an additional decline of 0-5% in per capita consumption in 2100 on top of the other damages related to climate change. The utility and the code to the IAM model are available as supplementary materials.