# Climate DICE [Dynamic Integrated Climate-Economy (DICE)](https://en.wikipedia.org/wiki/DICE_model) model by [William Nordhaus](http://www.econ.yale.edu/~nordhaus/homepage/homepage.htm) is one of the mainstream Integrated Assessment Models (IAMs) for evaluation of *optimal* climate policy under certain assumptions. Despite its simplicity, DICE is broadly used and cited in climate change economics discussions. The model is a very helpful starting point to understand relations between climate change, economy, and policy with very long run effects. </div>

</center>

Fig.1 Dice players (Pompeii, wall-painting).</figcaption> </a> ## Motivation Original DICE model is written in [**GAMS**](https://www.gams.com/), an efficient and powerful language and software for formulating and solving a broad set of optimization problems. DICE model is quite simple and can be translated and solved in various alternative programming languages. This project provides such alternative formulations of DICE model in [**R**](https://www.r-project.org/), [**Julia**](https://julialang.org/), and [**Python**](https://www.python.org/). All of them are free, open source software, which also provide a vast of tools for data analysis and graphical representation. ## Disclosure The aim of this project is not to endorse nor oppose DICE model, but rather educational, to lower barriers of access to IAMs by translating them into alternative, preferably free and open source software; to draw attention of broader research community to economy-climate models (and hopefully, make our chances for fortune higher than the dice-players on the Fig.1 had). ## Original versions of DICE model in GAMS Several versions of DICE, starting from **DICE123** (1991) to **DICE2016**, are openly available from William Nordhaus' websites (see http://www.econ.yale.edu/~nordhaus/homepage/homepage.htm and https://sites.google.com/site/williamdnordhaus/dice-rice). All of them are formulated in GAMS (there are some simplified Excel versions which do not offer optimization). The original GAMS source codes of the models are also stored in the "GAMS/" folder of this project for reference. The most recent version (*DICE2016*) has been translated to **R** and **Julia**. Earlier versions of DICE in R, as well as Python interpretation, are forthcoming. ## DICE in R R ([The R Project for Statistical Computing](https://www.r-project.org/)) provides broad set of features for computing and graphics. This project aims to provide two R versions of the model. The first one is a "direct translation", standalone version with a step-by-step conversion of original GAMS code to R. This script could be helpful to those who are familiar with GAMS code of the model and/or want to understand the translation strategy, solver options, and the model itself more deeply. All variables and parameters are stored in R global environment, i.e. fully accessible for review and analysis, though this feature doesn't allow simultaneous work with several versions of DICE model family, thus models should be run sequentially to generate results for following analysis and comparison. The model can be solved with several alternative solvers, or as without a solver, with provided simple stochastic search algorithm. The second version of R code (*forthcoming*) is an R-package-style with all mechanics of optimization hidden under the hood of one function __solveDICE__(*forthcoming*). It is more suitable for comparative analysis of scenarios and results from different DICE versions. All parameters to the model are supplied as parameters to the function and can be manipulated by users. ## DICE in Julia [Julia](https://julialang.org/) is a modern high-level programming language for numerical computing with the main focus on performance, and offers ergonomic, compact coding style. With [JuMP](https://github.com/JuliaOpt/JuMP.jl) package and [IPOPT](https://projects.coin-or.org/Ipopt) open-source solver (embedded in [Ipopt](https://github.com/JuliaOpt/Ipopt.jl) package for *Julia*), the translation from GAMS is pretty straightforward. This version of DICE2016 in Julia is tested with [JuliaPro v06.2.1 Personal](https://juliacomputing.com/products/juliapro.html) assembly, and produces identical results with GAMS version for baseline scenario (others are not tested). ## DICE in Python A Python version of DICE2016 (by Hazem Krichene, who followed the [R-version](https://github.com/olugovoy/climatedice/blob/master/R/DICE2016inR_standalone.Rmd) strategy to solve the model), is available here: https://github.com/hazem2410/PyDICE. ## DICE in BUGS language The problem of maximization of a welfare can be seen as a maximization of statistical likelihood function subject to unknown parameters (the savings and emissions control rate in DICE). Therefore, the model can be rewritten and solved with standard Bayesian statistics packages like BUGS, WinBUGS, OpenBUGS, JAGS, and others. Per my testing, the convergence of the optimal DICE scenario takes from one to several minutes in JAGS (http://mcmc-jags.sourceforge.net/), running it from R with and provides identical to other solvers solution. The code of the translated DICE2016 model in BUGS language is saved in "BUGS" folder. ## DICE in C++ and Fortran The benefits of translating the model to lower level C++ and Fortran is potential improvement of time-performance. Luckily both languages are easy integrate with R, and manage input-output from R. (forthcoming) ## DICE-OLG Overlapping generation (OLG) version of growth model provide several features vs. infinitly lived agent (ILA) framework. The solusion strategy differs, and it is harder to solve such model in GAMS then ad-hoc solution. The OLG version is implemented in R and will be published soon. ## Comparative runs of different software versions of DICE model (forthcoming)