G-Cubed G-Cubed models
Table of contents
G-Cubed is a framework for working with multi-region/multi-sector models. Depending upon the purpose of a specific model version, the regions differ, the sectors differ, and the model is extended in various ways, for example including greenhouse gas emissions.
Model versions
Some of the currently documented G-Cubed model versions are summarised below. See the model version index for the same list as a standalone page.
Two sector / two region models
The 2 sectors differentiate between an energy sector (electricity and fossil fuels) and a second sector that aggregates all other sectors.
Model 2R is the symmetric teaching model of the USA and the Rest of the World. The Rest of the World data and parameters are adjusted to match the USA, making it useful for demonstrations and experiments where regional asymmetry is not the focus.
Six sector models
The 6 sector models aggregate production into energy, mining, agriculture, durable manufacturing, non-durable manufacturing, and services. They provide lighter-weight model versions for experiments where the full 12 or 22 sector structure is not required.
Model 6M focuses on providing more regional detail for Asia.
Model 6N is developed for users with a specific interest in the New Zealand economy. It was forked from 6M and splits the advanced economies region into New Zealand and Canada.
Model 6W extends the 6M regional structure by adding Pakistan, Bangladesh, and Sri Lanka as explicit regions.
Model 6T uses the 6 sector structure with Taiwan separated as an explicit region.
Model 6G provides a broader major-economy regional structure, including more detail within Europe and several G20 economies.
Seven sector models
The 7 sector models extend the 6 sector structure by splitting one sector into a more detailed sector that is useful for targeted experiments.
Model 7N is split from 6N to include a high-tech manufacturing sector.
Model 7W is forked from 6W and splits health services from other services.
Twelve sector models
The 12 sector models add transportation and construction sectors, and split the single energy sector in the 6 sector models into electricity distribution, gas extraction and utilities, petroleum refining, coal mining, and crude oil extraction.
Model 12N extends 6N to have 12 sectors while retaining the New Zealand-focused regional structure.
Model 12T uses the 12 sector structure with Taiwan separated as an explicit region.
Model 12U uses a compact 12-region aggregation with the United Kingdom, Vietnam, and oil-exporting economies represented explicitly.
Model 12W combines the regions of 6W with the 12 GTAP sectors used in the larger sectoral models, without the electricity generation sectors.
Twenty-two sector models
The 22 sector models track all greenhouse gas emissions (CO2, Methane, Nitrogen Dioxide, and CFCs). To do so, they split the agriculture sector into 3 sectors: crops, livestock, and other agriculture. The emission intensity parameters are calibrated using GTAP data.
Model 22U has 12 regions and 22 sectors. It adds crops and livestock sectors and includes all greenhouse gases.
Model 22W uses the regions of 6W and the sectors of 22U, combining the wider Asian regional detail with the greenhouse-gas sector structure.
Common features of G-Cubed models
The G-Cubed model is a global, multi-sector model. 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.
The most sectorally detailed G-Cubed models have 22 sectors provide detailed understanding of energy dependencies for each region while also differentiating the regions in terms of economic specialisation.
Households
Households are forward-looking representative agents in each region that maximise their intertemporal utility, through their labor, consumption and investment decisions. For additional details, review the specifics of their treatment in G-Cubed.
Production
Each sector has its own production function, described by a nested system of Constant Elasticity of Substitution functions.
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
Governments in each region raise tax revenue and engage in government expenditure. The difference flows through to government debt in the region in the form of government surpluses or deficits. The implementation of this system can be adapted to suit the simulation experiments being performed by switching between modules in the system of SYM files describing the model. Detailed documentation of the modular representation of government is available.
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).
Long bond rates
Long bond rates are available for all regions and are endogenously determined from their respective one-year bond rates.
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.
Catch-up model of growth
The default technology progress assumption in the G-Cubed baseline are derived from a catch-up growth model
Parameter calibration
G-Cubed models include a number of parameters. Details of their calibration are included for select parameters.
International transfers
Optionally, G-Cubed models can be extended to include international transfers of wealth, either permanently, through private remittances or sales of permits, or temporarily, through official loans between the governments of different regions. See the documentation for international transfer extensions for full implementation details.
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.
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.
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.