Climate Damage on Production or on Growth: What Impact on the Social Cost of Carbon?

Abstract

Recent articles have investigated with integrated assessment models the possibility that climate damage bears on productivity (TFP) growth and not on production. Here, we compare the impact of these alternative representations of damage on the social cost of carbon (SCC). We ask whether damage on TFP growth leads to higher SCC than damage on production ceteris paribus. To make possible a controlled comparison, we introduce a measure of aggregate damage, or damage strength, based on welfare variations. With a simple climate-economy model, we compare three damage structures: quadratic damage on production, linear damage on growth and quadratic damage on growth. We show that when damage strength is the same, the ranking of SCC between a model with damage on production and a model with damage on TFP growth is not unequivocal. It depends on welfare parameters such as the utility discount rate or the elasticity of marginal social utility of consumption.

Appendices

Appendix 1

Moyer et al. [30] and [12] rely on the same representation of the impact of climate change on productivity growth. They start from damage bearing only on production, with a damage function D _t that depends quadratically on the temperature T _t : D _t = 1 − Ω(T _t ). Net production (that is including climate damage) Q _t is reduced by a factor 1 − D _t from Y _t , the production that would have occurred given factors on production (technology, capital, labor), had climate change not existed: Q _t = Y _t (1 − D _t ).

From this standard case, the current damage D _t are then “allocated” between damage on production and damage on TFP growth, a procedure that originates, to our knowledge, from [22]. The TFP growth rate is reduced by f.D _t , when the production, instead of being reduced by 1 − D _t is reduced by (1 − D _t )/(1 − f D _t ), where f is the “share” of damage that impact growth. Speaking of an “allocation” of damage conveys the impression that there is the same “amount” of damage.

However, the damage apply on very different quantities. Damage on TFP growth have a (first-order) cumulative effect on the whole output path, whereas damage on production does not.⁷ Far from keeping aggregate damage constant across the scenarios studied, the allocation introduces more damage when f increases. Thus, it is not surprising that these studies find that the SCC increases when more damage are allocated to damage on growth. To illustrate this, we consider two possible ways to measure aggregate damage: the real production loss and the damage strength used in the main text.

Figure 5 plots the real production loss at 3 ^∘C (the percentage of production loss between the baseline and the idealine when the temperature increase reaches 3 ^∘C) against the theoretical loss (the value of D _t when the temperature increase is 3 ^∘C), for several “shares” of damage on growth: 0, 2.5, 5, 10, 15, and 20 (percents). Because temperature increase feedbacks on the economic dynamic and thus on emissions, the date at which 3 ^∘C is reached changes slightly when the theoretical loss and the “share” vary.

Fig. 5

Real production losses as a function of theoretical production losses, for different “shares” of damage on growth f increasing from 0 to 20 percents

When damage bear only on production, real losses are already higher than the theoretical damage from the damage function (equal theoretical and real damage is represented by the dotted line in Fig. 5). This is due to feedbacks through reduced accumulation of capital. But the difference between real and theoretical losses remains quite small. When the “share” of damage on TFP growth increases, the wedge between the real loss and the theoretical loss increases rapidly. This is of course no surprise, because the damage that reduces long-term growth rates has long-lasting effects. However it has the consequence that damage is much higher at 3 ^∘C than what is commonly assumed. This means that the value of reduction of output at 3 ^∘C is not kept constant.

Figure 6 plots the damage strength against the theoretical production loss. We can see that theoretical loss and damage strength goes in the same direction. Therefore, when the “share” of damage on TFP growth is kept constant, theoretical loss can be used as a proxy for damage strength. However, when the “share” of damage on TFP growth is changed, the same theoretical loss can lead to highly different damage strengths.

Fig. 6

Damage strength as a function of theoretical production losses, for different “shares” of damage on growth f increasing from 0 to 20 percents

Appendix 2

The model is resolved over a 600 years time horizon, by 5 years time steps. It is calibrated in 2005. Table 2 gives the parameters values.

Table 2 Values of model parameters

In addition, four variables follow exogenous trends, as defined below:

g _t = g ₀ e ^−χt (exogenous trend of TFP growth)

L _t = L ₀ e ^−γt + L _∞ (1 − e ^−γt) (population)

$\sigma _{t}=\sigma _{0} e^{-g_{\sigma } t e^{-d_{\sigma } t}} \frac {1+e^{-s_{peak} d_{peak}}}{1+e^{s_{peak} (t-d_{peak})}}$ (exogenous evolution in carbon content of production)

$\theta _{1}(t)=\sigma _{t} \frac {p_{backstop}}{\theta _{2}} \frac {r_{backstop}-1+e^{-g_{backstop}t}}{r_{backstop}}$ (exogenous decrease of abatement costs)

Table 3 gives the values of the parameters used in these four exogenous trends.

Table 3 Values of parameters defining exogenous trends