Building a Baseline of the G-Cubed Model

There are two different concepts of a baseyear used in the model. The first is the baseyear to which the model is calibrated. This is currently 2011. The database with 2011 as the baseyear is in file called GGGDATv[model version].CSV. where model version refers to the letter summarizing the country coverage of the model (e.g. E for the standard 8 country G-Cubed model)

The other concept of a baseyear is the baseyear from which projections are made. For example the projection baseyear is currently 2018. Note that this does not have to be the same as the calibration baseyear. There is also a database for the projection baseyear since the price base must be consistent with the baseyear of projection. This file is called GGGDATv[model version]N.CSV where there is an "N" added to the database year. In the case where the baseyear of calibration equals the baseyear of the baseline projection both databases will be identical.

Because G-Cubed is an intertemporal model, it is necessary to calculate a baseline, or “business as usual”, solution before the model can be used for policy simulations. In order to do so we begin by making assumptions about the future course of key exogenous variables. We take the underlying long-run rate of world population growth plus productivity growth to be 1.4 percent per annum, and take the long-run real interest rate to be 4 percent. We also assume that tax rates and the shares of government spending devoted to each commodity remain unchanged.

Growth in the G-Cubed model depends on the growth of inputs. There are two key inputs into the growth rate of each sector. The first is the economy wide population projection. The second is the sectoral productivity growth rate. The productivity growth is calculated exogenously to the mode but within a programs provided within the model software. We assume that each sector in the US will have a particular rate of productivity growth over the next century. We then assume that each equivalent sector in each country is some proportion of the level of productivity of the equivalent sector in the US. We also assume that each sector in each country will catch up to the US sector in terms of productivity growth closing the gap by x% per year (usually x=2 for complete convergence but this is a user selected rate). The initial productivity gaps are critical for the subsequent sectoral productivity growth rate. We then overlay this productivity growth model with exogenous assumptions about population growth for each country.

Given these exogenous inputs for sectoral productivity growth and population growth, we then solve the model with the other drivers of growth, capital accumulation, sectoral demand for other inputs of energy and materials all endogenously determined. Critical to the nature and scale of growth across countries are these assumption plus the underlying assumptions that financial capital flows to where the return in highest, physical capital is sector specific in the short run, labor can flow freely across sectors within a country but not between countries and that international trade in goods and financial capital is possible subject to existing tax structures and trade restrictions.
Thus growth of any particular country is not completely determined by the exogenous inputs in that country since all countries are linked through goods and asset markets.
Carbon emissions are determined by the amount of fossil fuels (coal, oil, natural gas) that are consumed within each country in each period. These primary factors are endowed within countries but can also be traded internationally subject to transportation costs (captured implicitly through the elasticities of substitution between each good in the model). Thus economic growth can occur within a country without any particular pattern on energy use since it will be dependent on the underlying inputs into the growth process.

The exogenous inputs are one part of the solution requirements. We also face anoth problem of benchmarking the base year of the projection to the actaul data we observe in the database. If we solve the model from the baseyear (i.e. 2018) to 2100 it is unlikely theat the model will reproduce that year’s historical data exactly in 2018. In particular, it is unlikely that the costate variables based on current and expected future paths of the exogenous variables in the model will equal the actual values of those variables in 2018. This problem arises in all intertemporal models and is not unique to G-Cubed. Most intertemporal models eiather assume that the model starts in steady state and so modifying the actual data to be a solution of the model. We assume that the model is not in steady state and thereoe modify the model so that the baseyear is a solution of the model non in steady state but along teh stable manifold transitionaing towards a steady state. The idea is indicated in the following figure where 2150 is a stylized steady state year of teh model and 2018 is the benchmark year for teh baseline proejction.

To address the problem we add a set of constants, one for each costate variable, to the model's costate equations. For example, the constants for Tobin's q for each sector in each country are added to the arbitrage equation for each sector’s q. Similarly, constants for each real exchange rate are added to the interest arbitrage equation for each country, and a constant for human wealth is added to the equation for human wealth. To calculate the constants we use Newton's Method to find a set of values that will make the model's costate variables in 2018 exactly equal their 2018 historical values. After the constants have been determined, the model will reproduce the base year exactly given the state variables inherited from 2018 and the assumed future paths of all exogenous variables.

One additional problem is to solve for both real and nominal interest rates consistently since the real interest rate is the nominal interest rate from the money market equilibrium less the ex ante expected inflation rate. To produce the expected inflation rate implicit in historical data for 2018 we add a constant to the equation for nominal wages in each country.

Finally, we are then able to construct the baseline trajectory by solving the model for each period after 2018 given any shocks to variables, shocks to information sets (announcements about future policies), or changes in initial conditions.

As well as assumptions about the future growth of the world economy was also need to benchmark the model solution to a particular baseyear. This baseyear is currently 2018. The database used for the baseline benchmark is contained in a data file GGGDAT[model version]N.CSV. This may be teh same database as the model calibration database but it can also be a different year since the model calibration is best undertaken on data that is well established whereas baseline projections are usually undertaken on more recent data.

See the flowchart on the sequence of steps in generating a baseline and the key input filenames for this process.