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. Documentation is available for all of the model versions that are currently maintained.

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

Central banks in G-Cubed set short-term nominal interest rates using Henderson–McKibbin–Taylor (HMT) monetary policy rules. The rules can respond to inflation, potential-output growth, and exchange-rate targets, with different parameters used to represent different regional monetary regimes.

The monetary policy documentation explains the HMT rule, its adaptation to G-Cubed, how it anchors inflation, and how the nominal policy rate is connected to equilibrium real interest rates through asset markets and the Fisher relation. Long bond rates are derived from the projected path of short-term rates.

Exchange rates

Exchange rates in G-Cubed are determined jointly with interest rates and prices through uncovered interest parity (UIP). Model versions can represent floating exchange rates, exact pegs to the US dollar or another model region, and managed pegs implemented through the monetary-policy rule.

The exchange-rate documentation explains how exchange rates are determined and how alternative exchange-rate regimes can be implemented in a G-Cubed model.

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.

The demographic contribution to effective labor growth combines population projections with labor-income weights by age. The labor-force growth documentation explains the sources, age-composition effects, country proxies, missing data, smoothing and long-run continuation used to construct the model’s growth-rate inputs.

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.