ANNEX

DETAILS OF THE STATISTICAL ANALYSIS

The data set is made up of 162 simulations derived from 16 models. From each simulation, the percentage change in CO₂ emissions and the percentage change in GDP, both relative to the baseline projections for the terminal year of the simulation, were recorded. In addition, a set of descriptive variables was recorded for each model simulation, representing basic structural assumptions and policy assumptions embedded in the model. These were represented either as binary dummy variables or as discrete numerical variables. All the variables considered in the analysis are presented in Table A.1 and include the following:

GDP	percentage change in real GDP relative to projected baseline, in terminal year
CO2	percentage reduction in CO2 emissions relative to projected baseline, in terminal year
MACRO	1 if a macro model, 0 if a CGE model
NCBACK	1 if there is a constant cost, non-carbon backstop
RECYCLING	1 if revenues from policy instrument are used to reduce existing distorting taxes
CLIMATE	1 if averted climate change damages are modeled
NON-CLIMATE	1 if averted air pollution damages are modeled
JI	1 if joint implementation or global emissions trading is modeled
PRODUCTION	1 if the model allows for product substitution
FUELS	the number of primary fuel types recognized for possible inter-fuel substitution
YEARS	the number of years available to meet the abatement target

Using the data, multiple regression analysis was performed to show how these modeling assumptions affected the predicted relationship between the change in GDP and the change in CO₂ emissions. The regression equation, with GDP as the dependent variable, was specified as a quadratic (through the origin) in the extent of CO₂ abatement from the projected baseline. The variables listed above were assumed to shift the coefficient of the linear term in CO₂, except that the variable for the non-carbon backstop was specified to affect the coefficient of the quadratic term in CO₂ because the presence of a backstop fuel source mainly affects the curvature of the abatement cost curve at high levels of abatement.

FORM OF REGRESSION:

REGRESSION RESULTS

No. of observations: 162
R²: 0.83

	Coefficient	Standard Error
CO2	-0.02319	0.00907
(CO2)2	-0.00079	0.00011
MACRO	-0.05548	0.01395
NCBACK	0.00051	0.00005
RECYCLING	0.04427	0.00652
CLIMATE	0.00943	0.00399
NON-CLIMATE	0.03823	0.00778
JI	0.02337	0.00327
PRODUCTION	0.00378	0.00365
FUELS	0.00018	0.00116
YEARS	0.00005	0.00006

Notes

1. Including an intercept term in the regression adds little to the regression's overall explanatory power. Moreover the assumption that the regression passes through the origin is consistent with the models' definition of a baseline projection

2. The inclusion of dummy variables to represent the individual models adds little to the explanatory power of the regression beyond that provided by variables representing underlying modeling assumptions

3. The R² for a regression of GDP against CO₂ and (CO₂)² terms alone was 0.35.

4. Typically, the number of primary fuel types differs substantially from the number of energy sectors and energy technologies included in the models

TABLE A 1 - SUMMARY OF DATA

Notes

1. '1 or 0' signifies that different runs from the same model incorporate alternative assumptions

2. The number of observations from each model varies with the number of alternative assumptions and end dates considered by the model

3. Despite its name, the Markal-Macro model has optimizing characteristics and is not a macro model according to the distinction made in Box 1

4. Because the Boyd et al model is a comparative static model, the terminal years have been interpolated

5. The results from the IIAM model come from the model's Single Open Economy Section of the model which does not include the effects of JI that appear in the Multi-Regional Trade (MRT) section

6 The IIAM model is characterized as having no backstop because the backstop does not affect the time frame for which results were available

7. Although the Edmonds-Reilly-Barns model has several non-carbon fuel sources all are subject to increasing marginal costs, inconsistent with the definition of a backstop energy source adopted here (see Section 3 D for discussion)