# **Technical Appendix: The Model and Numerical Analysis**

The results in this paper rely on the World Bank’s Environmental Impact and <u>Sustainability Applied General Equilibrium (ENVISAGE) Model.</u><sup>21</sup> The ENVISAGE model’s core is a relatively standard recursive dynamic global general equilibrium (CGE) model. Incorporated with the core CGE model is a greenhouse gas (GHG) emissions module that is connected to a simple climate module that converts emissions into atmospheric concentrations, radiative forcing and changes in mean global temperature. The climate module has feedback on the economic model through so-called damage functions—currently limited to productivity shocks in agriculture. The combination of the socio-economic CGE model with the climate module is commonly referred to an integrated assessment model (IAM).

ENVISAGE is calibrated to Release 7 of the GTAP dataset with a 2004 base year.<sup>22</sup> It has been used to simulate dynamic scenarios through 2100. For the purposes of this study, 2020 is the terminal year. The 113 countries/regions of GTAP are aggregated to 15 countries/regions for this study and the 57 sectors are aggregated to 21 sectors. Full detail on the aggregation is provided in Appendix Table 1. The GTAP data is supplemented with satellite accounts that include emissions of the so-called Kyoto gases—carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O) and hydrofluorocarbons (F-gases), different electricity production activities (coal, oil and gas, hydro, nuclear and other), and potential land and hydro supplies.

Within each time period a full equilibrium is achieved given the fixed regional endowments, technology and consumer preferences. Production is modeled as a series of nested constant-elasticity-of-substitution (CES) functions that are designed to reflect the substitution and complementarity of inputs. Unlike many standard models, energy plays a key role as an input and is modeled as a complement to capital in the short-run but a substitute to capital in the long run. This reflects the putty/clay specification of production that incorporates vintage capital. The key assumption is that there is greater substitution across inputs in the long run (i.e. with _new_ capital) than in the short run (with _old_ or installed) capital. One consequence of this specification is that countries that have higher growth and higher rates of investment typically have a more flexible economy in the aggregate. Thus, all else equal, the same tax on carbon has a lower cost. There is a single representative household that consumes goods and services and saves.<sup>23</sup> The savings rate is partially a function of the demographic structure of the region. Savings rise as either the elderly or youth dependency ratios fall. The government sector is relatively passive. Aggregate expenditures are fixed as a share of total GDP and revenues adjust to maintain fiscal balance (through a lump sum tax on households). Investment is savings driven.

> 21 See van der Mensbrugghe 2008 for full details of the model.

> 22 See www.gtap.org.

> 23 The model is designed with several different consumer demand specifications including the CDE (see Hertel 1997), the LES/ELES (see van der Mensbrugghe 2006) and the AIDADS (see Rimmer and Powell 1992 and van der Mensbrugghe 2006). For this paper we have used the AIDADS.

30