# **1. Introduction**

Understanding how the ongoing climate change could ultimately affect our society and the well-being of current and future generations requires an evaluation of the complex interplay between human and natural systems.

The human or anthropogenic influence on the earth climate is mainly associated with the emissions of greenhouse gases in the atmosphere, which is in turn related to the level of several economic activities. To forecast the future climate, physical scientists need to know the expected level of GHG emissions, which depend on scenarios of economic growth as well as on the possible implementation of climate mitigation policies. On the other hand, economic growth itself is influenced by the climate change, through its manifold impacts. As Tol (2015) puts it: “There are so many and so different effects: crops hit by worsening drought, crops growing faster because of carbon dioxide fertilization, heat stress increasing, cold stress decreasing, sea levels rising, cooling energy demand going up, heating energy demand going down, infectious disease spreading, and species going extinct. It is hard to make sense of this. Therefore, aggregate indicators are needed to assess whether climate change is, on balance, a good thing or a bad thing and whether the climate problem is small or large relative to the many other problems that we have.”.

Damage functions have been introduced to this purpose, that is to “translate” physical impacts in terms of economic variables inside CGE, IAM and other numerical economic models. Therefore, damage functions are one or more relationships between climate variables (typically average temperature, but sometimes also humidity or “heating days”) and economic variables (potential income, productivity, resource endowments, etc.). It is generally acknowledged that damage functions constitute a weak link in the economics of climate change (Weitzman, 2010).

Various methodologies have been employed for the estimation of their parameters, from subjective expert assessment (Nordhaus, 1994) to panel methods (Dell, Jones and Olken, 2014) to meta-analyses of non-economic literature (Tol, 2002). Also, the functions may be built by summing up different effects into a single aggregate, or they may retain some sectoral detail. The first approach is typical of earlier models like RICE (Nordhaus and Yang, 1996, Nordhaus and Boyer, 1999), MERGE (Manne, Mendelsohn and Richels, 1995) and CETA (Peck and Teisberg, 1992), where a relationship is posited between loss of potential income (GDP) and temperature. More recent contributions, based on multisectoral models like DART (Deke et al., 2001), GTEM (Pant, 2002), ICES (Eboli, Parrado and Roson, 2010) and ENVISAGE (Roson and van der Mensbrugghe, 2012) keep the sectoral detail and attribute the various impacts to different variables and parameters in a disaggregated macroeconomic model, which typically has a general equilibrium structure.

The main advantage of holding distinct the different economic effects of climate change, despite the cost of higher computational complexity, is that it is possible to trace the various mechanisms through which the climate can affect the economic system. Furthermore, in a general equilibrium formulation, it is possible to account for second-order effects linked to variations in relative prices, which are often very relevant.

This document illustrates the methodology and presents some results for the estimation of damage functions parameters, for all 140 countries and regions in the GTAP9 dataset, and for six climate impacts: sea level rise, variation in crop yields, heat effects on labor productivity, human health, tourism and household energy demand. Effects from 1°C up to 5°C average temperature increments are separately considered, as most impacts are non-linear.

The GTAP social accounting matrix has become a de-facto standard for the calibration and implementation of computable general equilibrium models, or integrated assessment models with a CGE core, so our set of estimates can be seen as a “ready-to-use” information source for the realization of climate-related numerical experiments with a general equilibrium structure.

Our parameters are obtained by processing information coming from many diverse studies, based on different approaches and methodologies, as we are undertaking an interdisciplinary assessment of 2