G-Cubed model description

Table of contents

The G-Cubed model is a global, multi-sector model, which has been designed to evaluate climate policy. It has been used extensively to estimate the impact of various environmental and economic shocks and policies (see McKibbin and Wilcoxen 2013 and McKibbin et al. 2018 and 2020, IMF 2020, 2021).

While the teaching version of the model has just 2 regions (The USA and the rest of the world) and 2 sectors (energy and non-energy), there are eleven regions and 20 sectors in the most recent version of the fully articulated model.

Regions

In the version of G-Cubed that is used for analysis of environmental issues, the regions are listed below:

  • United States
  • Japan
  • Australia
  • Europe
  • Canada
  • China
  • India
  • Rest of the OECD
  • Oil-Exporting developing countries
  • Russian Federation
  • Rest of World

Sectors

Each region aggregates production into the same 20 sectors. These sectors are aggregations of the 65 sectors defined in the GTAP database. See See Aguiar et al. (2019) for more details. All 20 sectors are listed below:

  1. Electricity distribution
  2. Gas extraction and utilities
  3. Petroleum refining
  4. Coal mining
  5. Crude oil extraction
  6. Construction
  7. Other mining
  8. Agriculture and forestry
  9. Durable goods
  10. Nondurable goods
  11. Transportation
  12. Services
  13. Coal generation of electricity
  14. Natural gas generation of electricity
  15. Petroleum generation of electricity
  16. Nuclear generation of electricity
  17. Wind generation of electricity
  18. Solar generation of electricity
  19. Hydroelectric generation of electricity
  20. Other generation of electricity

13 of the 20 sectors articulate the production and distribution of the energy required to drive economic activity and the resulting greenhouse gas emissions.

Sector 1 captures the distribution of electricity. Sectors 13 to 20 split electricity generation by type of energy source, enabling detailed analysis of shifts in fossil-fuel dependency. Sectors 2 to 5 captures fossil-fuel extraction and processing for coal, gas, and oil. The 7 non-energy sectors capture all other types of production.

The full set of 20 sectors provide detailed understanding of energy dependencies for each region while also differentiating the regions in terms of economic specialisation.

Sectoral production

As outlined in Jaumotte et al. (2021), there is a production structure for each sector within each region. This production structure is shown in Figure 1.

Figure 1. Production and consumption structure for each sector

Figure 1. Production and consumption structure for each sector

Note that the elasticities of substitution between capital, labor, energy, and materials and between the sub nests within each sector are estimated using US data. These elasticities are assumed to be the same across countries but different across sectors. In other words, the degree of substitution across input in production is a sector are different across sectors but are the same for the same sector in different countries.

The parameters for input shares in the CES production function are taken from the input-output tables in the GTAP database.

Carbon emissions

CO2 emissions are measured through the burning of fossil fuels in energy generation.

Stocks and flows

The model completely accounts for stocks and flows of both physical and financial assets. For example, budget deficits accumulate into government debt, and current account deficits accumulate into foreign debt. The model imposes an intertemporal budget constraint on all households, firms, governments, and countries. Thus, a long-run stock equilibrium obtains by adjusting asset prices, such as the interest rate for government fiscal positions or the real exchange rates for the balance of payments. However, the adjustment towards the long-run equilibrium of each economy can be very slow.

The model incorporates heterogeneous households and firms. Firms are modeled separately within each sector. The model distinguishes between consumers and firms that base their decisions on forward-looking expectations and those that follow more straightforward rules of thumb, which are optimal in the long run but not necessarily in the short run.

Fiscal policy

The fiscal rule varies across model versions. For example, G-Cubed can incorporate an endogenous budget deficit with lump-sum taxes on households adjusted gradually over time to cover any incremental interest payments to ensure fiscal sustainability. Thus, the level of government debt can permanently change in the long run with the change in debt to GDP equal to the ratio of the long-run fiscal deficit to the long-run real growth rate of the economy. Based on the extensive literature, including previous studies with the G-Cubed model, we know that the assumption of how carbon tax revenue is used can have significant macroeconomic implications. See McKibbin W. J., Morris, A., Wilcoxen P. J., and Y. Cai (2015) and McKibbin W. J., Morris, A., Wilcoxen P. J. and L. Liu (2018). We assume that the tax revenue is used to reduce the fiscal deficit across all central bank monetary regimes.

Monetary policy

Households and firms in G-Cubed must use money issued by central banks for all transactions. Thus, central banks set short-term nominal interest rates to target macroeconomic outcomes (such as inflation, unemployment, exchange rates, etc.) based on Henderson-McKibbin-Taylor monetary rules. See Henderson and McKibbin (1993), Taylor (1993), Orphanides (2003). These monetary rules approximate actual monetary regimes in each country or region in the model. They tie down the long-run inflation rates in each country and allow short-term adjustment of policy to smooth fluctuations in the real economy. The parameters and equations of the model can be adjusted to represent a broad range of alternative monetary policy regimes, across regions in a model or across different models.

The central bank sets the nominal policy rate INTN (it is either the preferred policy rate from an HMT rule INPN or a partial adjustment towards that desired rate INPN). The risk free real interest rate (INTF) is the INTN adjusted by expected inflation.

There is a risk premium (RISR) in the equation linking the risk-free real interest rate (INTF) to the real interest rate that agents used to discount future income streams (INTR). You can think of RISR as a term premium. RISR is exogenous to simulations but can be changed as part of a simulation design.

The real interest rates on 2, 5, and 10-year bonds (RB02, RB05, RB10) are calculated using the geometric average of the short rate over time. i.e., the two-year bond rate in period t is the geometric average of the 1-year rate in period t and period t+1. Even though we calculate these bond rates at different durations, what actually goes into the model is the real interest rates expected at every period in the future (INTR).

Labor

Nominal wages are sticky, adjusting over time based on country-specific labor contracting assumptions. Firms hire labor in each sector up to the point where the marginal product of labor equals the real wage, defined in terms of the output price level of that sector. Any excess labor enters the unemployed pool of workers. Unemployment or the presence of excess demand for labor causes the nominal wage to adjust to clear the labor market in the long run. In the short run, unemployment can arise due to structural supply shocks or changes in aggregate demand.

Rigidities

Rigidities prevent the economy from moving quickly from one equilibrium to another. These rigidities include wage rigidities, lack of complete foresight in the formation of expectations, cost of adjustment for investment by firms. With these rigidities and monetary and fiscal authorities following monetary and fiscal rules, short-term adjustment to economic shocks can be very different from the long-run equilibrium outcomes.

Capital and investment

Note that each sector, in each region, has a capital stock that is based on putty-clay technology. It is costly to move installed physical capital between sectors. These costs are important to capture when decarbonizing economies, given current energy systems and technologies for using energy.

References

Aguiar, A., Chepeliev, M., Corong, E., McDougall, R., & van der Mensbrugghe, D. (2019). The GTAP Data Base: Version 10. Journal of Global Economic Analysis, 4(1), 1-27.

Bang, E., Barrett, P., Banerjee, S., Bogmans, C., Brand, T., Carton, B., Eugstger, J., Fernandez, D. R., Jaumotte, F., Kim, J., Liu, W., McKibbin, W. J., Mohammad, A., Pugacheva, E., Tavares, M. M. & Voights, S. (2020), “Mitigating Climate Change”, World Economic Outlook, International Monetary Fund.

Bems R., Juvenal, L. Liu, W. and W.J. McKibbin (2022) “Climate Policies and External Adjustment” Chapter 2 on International Monetary Fund External Sector Report: Pandemic, War and Global Imbalances, August 2022. IMF Washington DC.

Henderson, D. W. & McKibbin, W. J. (1993), “A Comparison of Some Basic Monetary Policy Regimes for Open Economies: Implications of Different Degrees of Instrument Adjustment and Wage Persistence”, Carnegie-Rochester Conference Series on Public Policy, 39, 221-318.

Jaumotte, F., Liu, W. & McKibbin, W. J. (2021), “Mitigating Climate Change: Growth-friendly Policies to Achieve Net Zero Emissions by 2050”, IMF Working paper wp2021195. Washington DC. CAMA Paper 75/2021.

Liu, W., McKibbin, W. J., Morris, A. & Wilcoxen, P. J. (2020), “Global Economic and Environmental Outcomes of the Paris Agreement”, Energy Economics, 90, pp 1-17.

McKibbin, W. J. & Wilcoxen, P. J. (2013), “A Global Approach to Energy and the Environment: The G-cubed Model”, Handbook of CGE Modeling, Chapter 17, North Holland, pp 995-1068.

McKibbin, W. J., Morris, A. C., Wilcoxen, P. J. & Cai, Y. (2012), “The Potential Role of a Carbon Tax in US Fiscal Reform”, The Brookings Institution.

McKibbin, W. J., Morris, A., Wilcoxen P. J. & Liu, L. (2018), “The Role of Border Adjustments in a US Carbon Tax”, Climate Change Economics vol 9, no 1, 1-42.

McKibbin, W. J., Morris, A., Wilcoxen P. J. & Panton, A. (2020), “Climate change and monetary policy: Issues for policy design and modelling”, Oxford Review of Economic Policy, 36(3), 579–603.

Orphanides, A. (2003), “Historical Monetary Policy Analysis and the Taylor Rule”, Board of Governors of the US Federal Reserve, Working Paper No. 2003-36.

Taylor, J.B. (1993), “Discretion Versus Policy Rules in Practice”, Carnegie-Rochester Conference Series on Public Policy, 39(1), North Holland, December, pp. 195-214.