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.
G-Cubed models
Some of the more widely used G-Cubed model versions are summarised below.
Model 2R
Model 2R is publicly available to demonstrated G-Cubed usage and to support teaching. It is a regionally symmetric model. As in all G-Cubed models, the reference region is the USA. The other region is identical to the USA in terms of its data and parameters.
The 2 sectors differentiate between an energy sector (electricity and fossil fuels) and a second sector that aggregates all other sectors.
Model 20R
Model 20R is a 2 Region and 20 sector model, typically used for testing energy and emission experiments. This is a hybrid between the 2R model and the 20C model.
Model 20C
Model 20C is an 11 region and 20 sector model, typically used for energy and emission experiments.
Model 22C
Model 22C is an 11 Region and 22 sector model, extending the 20C model to include two extra agricultural sectors. It also includes all greenhouse gases.
Model 22P
Model 22P is a 10 Region and 22 sector model, similar to 22C but merging the Russia region into the region representing countries with heavy dependence on oil exports.
Model 6G
Model 6G extends the number of regions provide detailed representation of most major economies. The number of sectors is increased as well, splitting the other sector in the 2R model into sectors representing mining, agriculture, durable manufacturing, non-durable manufacturing and services.
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).
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.
Parameter calibration
G-Cubed models include a number of parameters. Details of their calibration are included for select parameters.
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.