World Impact Forecasts

In the 3F blog, I have been primarily using state space models to make macro forecasts for the world system and countries within that system. The approach is a dynamic realization of ImPACT models developed by the Human Environment Program at Rockefeller University (here) in an article by Waggoner and Ausubel (2002). ImPACT models include the Kaya Identity used by the IPCC and the EIA and the I=PAT identity used for studying population growth impacts (here). Included in the class of ImPACT models is the neoclassical economic growth model (see note below) which has been used by William Nordhaus and Resources for the Future (here) to make climate change forecasts.

Whether or not state space models provide better forecasts than ImPACT models is an open question. The advantage of ImPACT models is that they can be calculated by hand. The disadvantage is that, as explained below, ImPACT models do not include feedback effects.

The directed graph above describes the causality underlying ImPACT models. Under long-run, full employment conditions, population growth (N) leads to greater aggregate production (Q)--more people mean more workers and, as long as the workers are fully employed, more workers mean more output and more demand. Output creates greater energy consumption (E). Energy consumption leads to greater CO2 emissions. And finally, great CO2 emissions leader to increases in global temperature (T).

The extent of these changes depends on the values of the lower case letters, called coefficients or intensive variables (the upper case letters are the extensive variables). In equation form:

T = N*(Q/N)*(E/Q)*(CO2/E)*(T/E) = N*q*e*c*t

where T is global temperature, N is global population, Q is world GDP, E is primary energy consumption, CO2 is global CO2 emissions, q = Q/N per-capita output, e = E/Q energy intensity of production, c = CO2/E carbon intensity of energy and t = T/CO2 is the climate sensitivity to radiative forcing.

The ImPACT formulation is very general. For example, if you think that CO2 emissions have no impact on global temperature, you can set t=0. In other words, if you can provide values for [N,q,e,c,t] then you can make global climate change forecasts using a hand calculator.

There are two problems with such forecasts: (1) you need to come up with reasonable values for population growth and for the other intensive variables (discussed below) and (2) you have to assume that there are no system feedbacks (for example from environmental degradation to population growth or to agricultural production). Said another way, will the intensive variables change over time?

Discussions of energy emissions or global temperature change all seem to rely on the assumption that population growth, energy intensity, and emissions intensity will all decrease over time and decrease enough to make up for increases in per capita GDP (improving standards of living). Generally, the climate sensitivity parameter is assumed to be constant.

Coming up with values for intensive variables in ImPACT models is thus yet another forecasting problem. Below I provide business-as-usual (BAU) forecast for each intensive variable using the WL20 model (data definitions are available in Appendix F). World population forecasts from the United Nations can be found here.

The BAU forecast for real per capita GWP (Gross World Product) is displayed above. Values in 2100 (the usual end-point of long-run forecasts) range anywhere from about 0.02 to 0.09 with a mid-range value of about 0.05 - 0.06.
The BAU forecast for energy intensity in millions of tons of oil equivalent is more difficult to forecast. Energy intensity will not go to zero as predicted by the model so values between 50 and 150 for e = E/Q would seem reasonable.
The BAU forecast for emission intensity (atmospheric CO2 concentrations in ppmv) is displayed above. Values seem to be stabilizing around 0.05.
Finally, BAU forecasts for climate sensitivity (degrees C) provide another surprise. Rather than being a constant as assumed by the IPCC, there would appear to be an observable time trend where climate sensitivity is decreasing. The decrease over time is possibly the result of feedback mechanisms. It is certainly not zero as assumed by global warming skeptics.

The observed trends in energy intensity and climate sensitivity might suggest that using ImPACT models to make long-run projections is an uncertain business. Since imPACT models are identities (true by definition), my suggestion would be to use ImPACT models to make the following types of assertions: (1) if other things remain equal, an increase in population growth would have the following impacts on production, carbon emissions and global temperature or (2) changes in intensive variables necessary to limit global warming to 2 degrees C would involve limiting per capita income growth or reducing energy intensity or decreasing carbon intensity.

NOTE: Neoclassical Economic Growth Models are a form of ImPACT model, which can be demonstrated using directed graphs.

In the standard neoclassical growth model, full employment and growth in autonomous technical change (A) drive growth in output. The Capital Stock, K, is an endogenous variable based on saving from output, K(t) = K(t-w) + ( sQ - d K ) where d is depreciation and s is saving.
Using graph theoretic rules, endogenous variables can be eliminated from the model. Technological change can also be endogenized assuming learning by doing. These two assumptions result in the graph above.

The neoclassical growth model is thus equivalent (nonparametrically) to a dynamic version of the ImPACT model displayed in the graph above.