Agricultural productivity change

It has been known for decades that increasing the atmospheric concentration of carbon dioxide enhances plant growth (Idso and Idso 1994; Cuniff et al. 2008) both by raising the rate of net photosynthesis and increasing water use efficiency within the plant. For numerous crop types around the world, CO 2 fertilization more than offsets negative effects of climate change on crop water productivity, with some of the largest gains likely in arid and tropical regions (Derying et al. 2016). An additional benefit of climate warming arises from lengthening the growing season—the time between the last killing frost of the spring and the first one in the fall. Studies of US maize that take into account farmer adaptation to changing growing conditions confirm the potential for net yield gains under climate change (Butler et al. 2018).

FUND attempts to capture these changes in a simple form. The FUND model estimates agricultural output as a fraction of total output, where the fraction declines over time at a rate consistent with historical data. Specifically, the output share of agriculture at year t is the product of the 1990 agricultural output share and \(\left( {y_{1990,r} /y_{t,r} } \right)^{0.31}\) where \(y_{t,r}\) is GDP per capita in year t for region r. From 1990 to 2050, this expression declined steadily from 1.0 to about 0.7, so if 5.0% of an economy’s output is agricultural as of 1990, by 2050 that would decline to about 3.5%. This equation determines the potential welfare associated with regional agricultural output, and actual welfare is then determined by a parameterized function that depends on the temperature level, speed of climate change, and atmospheric CO 2 . Changes in each of these affect welfare by changing regional agricultural yields, which in turn affect prices and trade patterns. Consequently, the function parameters vary among regions. A reduction in the yield of a particular crop, for example, will tend to harm import-dependent regions but might benefit exporting regions.

The temperature-level effect is represented by a quadratic equation with an implicit peak that a region may either be approaching or diverging from as it warms. The temperature change effect penalizes productivity in intervals when temperature changes rapidly from one year to the next. We take the parameter distributions associated with these effects as given.

The CO 2 fertilization effect \(A_{\text{r}}\) for region r is determined by a logarithmic function:

$$A_{\text{r}} = \gamma_{\text{r}} \ln \left( {\frac{{{\text{CO}}_{2} \left( t \right)}}{275}} \right),$$

where CO 2 (t) is the current atmospheric CO 2 concentration with 275 parts per million assumed to be the preindustrial level and \(\gamma_{\text{r}}\) is a region-specific constant derived by calibration to the results of a number of studies done using computable general equilibrium models, chiefly Tsigas et al. (1997) who separated out the CO 2 fertilization effect. An earlier global general equilibrium study, Kane et al. (1992), reported potential yield decline due to temperature increase based on simulations that did not include CO 2 fertilization, but added that based on the limited amount of information then available, doubling the amount of CO 2 in the atmosphere could increase yield by about 15%. By the time of Tsigas et al. (1997) more information was available and they incorporated global yield gains averaging between 20 and 30% for CO 2 doubling. The effects were large enough effectively to negate the losses from moderate climate changes and generate some regional net gains. The authors thus emphasized in their conclusions the importance of including CO 2 fertilization effects in future studies so as not to overstate the net damages of climate change in agriculture.

The parameterizations in FUND are consistent with this early evidence. Of particular note, while the categories wheat and other crops experience net gains from the combination of warming and CO 2 fertilization, rice does not, based on the limited studies then available that suggested CO 2 fertilization would insufficiently offset damages due to warming. Because of the importance of rice in China and Asia, this assumption is influential on overall climate damages (Tsigas et al. 1997, Table 11.2).

Three forms of evidence gained since then indicates that the CO 2 fertilization effects in FUND may be too low. First, rice yields have been shown to exhibit strong positive responses to enhanced ambient CO 2 levels. Kimball (2016) surveyed results from free-air CO 2 enrichment (FACE) experiments, and drew particular attention to the large yield responses (about 34%) of hybrid rice in CO 2 doubling experiments, describing these as “the most exciting and important advances” in the field. FACE experiments in both Japan and China showed that available cultivars respond very favorably to elevated ambient CO 2 . Furthermore, Challinor et al (2014), Zhu et al. (2015) and Wu et al. (2018) all report evidence that hybrid rice varietals exist that are more heat-tolerant and therefore able to take advantage of CO 2 enrichment even under warming conditions (2013). Collectively, this research thus indicates that the rice parameterization in FUND is overly pessimistic.

Second, satellite-based studies have yielded compelling evidence of stronger general growth effects than were anticipated in the 1990s. Zhu et al (2016) published a comprehensive study on greening and human activity from 1982 to 2009. The ratio of land areas that became greener, as opposed to browner, was approximately 9 to 1. The increase in atmospheric CO 2 was just under 15% over the interval but was found to be responsible for approximately 70% of the observed greening, followed by the deposition of airborne nitrogen compounds (9%) from the combustion of coal and deflation of nitrate-containing agricultural fertilizers, lengthening growing seasons (8%) and land cover changes (4%), mainly reforestation of regions such as southeastern North America.

Zhu et al. used satellite-sensed leaf area index (LAI), which does not directly translate into grain yields—rather it is a measure of direct fertilization and the production of dry matter. However, for grassland, the most common agricultural land use, LAI in fact does relate directly to yield since grassland vegetation is consumed by grazing animals, and it is harvested for hay to feed livestock in the nongrowing season as well as to feed livestock removed from pasture. Also, in a new analysis of satellite LAI data, Gao et al. (2018) reported that agriculture-related trends were more than double those of natural vegetation, indicating that trends in LAI are likely indicators of increased agricultural productivity.

Munier et al. (2018) likewise found a remarkable increase in the yield of grasslands. In a 17-year (1999–2015) analysis of satellite-sensed LAI, during which time the atmospheric CO 2 level rose by about 10%, there was an average LAI increase of 85%. A full 31% of earth’s continental land outside of Antarctica is covered by grassland, the largest of the three agricultural land types they classified. Also, for summer crops, such as maize (corn) and soybeans, greening increased by an average of 52%, while for winter crops, whose area is relatively small compared to those for summer, the increase was 31%. If 70% of the yield gain is attributable to increased CO 2 , the results from Zhu et al (2016) imply gains of 60%, 36% and 22% over the 17-year period for, respectively, grasslands, summer crops and winter crops, associated with only a 10% increase in CO 2 , compared to parameterized yield gains in the range of 20–30% for CO 2 doubling in FUND.

Third, there has been an extensive amount of research since Tsingas et al. (1997) on adaptive agricultural practices under simultaneous warming and CO 2 enrichment. Challinor et al. (2014) surveyed a large number of studies that examined responses to combinations of increased temperature, CO 2 and precipitation, with and without adaptation. In their metanalysis, average yield gains increased 0.06% per ppm increase in CO 2 and 0.5% per percentage point increase in precipitation, and adaptation added a further 7.2% yield gain, but warming decreased it by 4.9% per °C. In FUND, 3 °C warming negates the yield gains due to CO 2 enrichment, but this is not what the Challinor et al. results imply. Suppose that over the next 100 years, CO 2 doubles from 400 to 800 pm while temperatures rise by 3 °C and precipitation increases on average by 2%, Challinor et al.’s regression coefficients would imply an average yield increase of 2.2% in the tropics without adaptation versus 9.3% with; and 5.0% outside the tropics without adaptation versus 12.1% with, indicating the productivity increase in FUND is likely too small.

Figure 1 provides further evidence based on the recent historical record. It shows total global output of maize, rice, soybeans and wheat per year from 1980 to 2017. Over this interval, the global average land surface was estimated to have warmed by 1.0 °C,Footnote 3 the CO 2 concentration rose by 68 ppmFootnote 4 and crop output doubled. Hence, the record since 1980 provides prima facie evidence that the combined effects of warming, CO 2 fertilization and adaptation can have positive net growth results at the global level, and the meta-analysis results indicate the direction of this balance is likely to persist.

Fig. 1 Source: authors’ calculation using data from https://www.fao.org/faostat/en/#data/QC/visualize. Fitted line is a quadratic trend Global crop production shown as sum of maize, rice, soybean and wheat grown during 1980–2017. Full size image

In light of these issues, we examine the effects of increasing the \(\gamma_{\text{r}}\) parameters in FUND by 15% and 30%, namely multiplying them by 1.15 and 1.30. These changes are conservative in view of the evidence on CO 2 -driven growth enhancement; however, they provide guidance on the sensitivity of the SCC to the emergent information on agricultural productivity.

Climate sensitivity

ECS is the most basic measure within an IAM of CO 2 impacts on climate. Secondary impacts, such as sea-level rise, changes in storm intensity, depth and frequency of droughts and floods, etc., all depend on a reliable ECS.

The mean ECS of the climate models used in the most recent Assessment Report of the United Nations’ Intergovernmental Panel on Climate Change (IPCC 2013) was 3.2 °C by the IPCC and 3.4 °C in the peer-reviewed literature describing those models (Andrews et al. 2012). The IWG applied Monte Carlo analysis to the ECS parameter using a distribution published in Roe and Baker (2007), based on climate models, which has a median value of 3.0 °C, a 90% confidence interval range from 1.91 to 5.86 °C, and is truncated at an upper limit of 10 degrees Celsius (IWG 2010). Roe and Bauman (2013) criticized the application of the Roe and Baker (2007) distribution in IAMs, because the higher climate sensitivities imply time spans to equilibrium which are inconsistent with the assumed speed of adjustment (via ocean heat uptake efficiency) in IAMs. The time to equilibrium in simple climate models goes up with the square of ECS, and the fat upper tail of ECS values implies such long adjustment times that realization of such warming takes over a 1000 years (Roe and Bauman 2013, p. 653). IAMs apply these high-sensitivity estimates on much shorter time scales, which Roe and Bauman argue involves physically impossible outcomes.

More fundamentally, the climate model-based ECS distributions have been challenged within the climate literature as potentially being arbitrary. There are numerous tunable parameters in climate models (Hourdin et al. 2017), and a range of sensitivity values can be made to fit the historical record equally well as long as tunings that increase climate sensitivity are accompanied by compensating adjustments elsewhere, which appears to be the case (Kiehl 2007).

A valid ECS estimate for use in IAMs must therefore be based on empirical constraints. Use of climate model-based metrics to construct Bayesian models may not get around the problem of arbitrariness. Lewis (2013) criticized the use of informative priors in Bayesian ECS derivations similar to that used in Olsen et al. (2012), in which likelihoods are derived from diagnostics of model-observational discrepancies, which are in turn functions of the model parameters. Because of parameter interdependence in the models, the diagnostics do not strongly constrain the ECS distribution and the posterior density is typically very close to the subjective prior. As an example, he reproduced an earlier Bayesian ECS estimation that had yielded a distribution similar to that in Roe and Baker. He found that under an informative prior, large sections of the posterior ECS distribution were unresponsive to the observations. Application of an objective Bayesian method on the same data set, however, yielded a lower and more tightly constrained distribution with a mode of 1.6 °C and a 90% credible interval of 1.2–2.2 °C.

Lewis (2013) noted that this mode was identical to that found in two contemporaneous empirical studies (Aldrin et al. 2012; Ring et al. 2012) that had estimated relatively simple energy balance models on observational data. This latter approach has subsequently been widely applied yielding modal ECS values consistently below 2.0 °C and much narrower confidence or credible intervals (Otto et al. 2013; Masters 2014; Lewis and Curry 2015; Skeie et al 2014 Lewis and Curry 2018). Of particular interest is the distribution in Lewis and Curry (2018) since it is conditioned on a joint estimation with ocean heat uptake efficiency, uses up-to-date estimates of aerosol forcing from the IPCC and explicitly addresses concerns about spatial variation in effective forcing and other potential deficiencies of empirical energy balance model methods. Based on the post-1850 Hadley Centre surface temperature data set their best estimate of ECS is 1.50 with a 5–95% range of 1.05–2.45 °C.Footnote 5 By conditioning the estimate on ocean heat uptake efficiency the method yields an ECS distribution consistent with the main observed constraint on time to equilibrium, addressing the concern in Roe and Baumann (2013).

Beyond energy balance models, there are other even more strictly empirical methods. One approach is to estimate transient climate sensitivity (TCS, the estimated warming from doubling greenhouse gas levels over a 70-year span without allowing the oceans fully to adjust) then scaling it up to an ECS estimate based on an estimated ratio of the two. Christy and McNider (2017) used satellite bulk atmospheric temperature data from 1979–2016 and estimated a TCR of 1.1 \(\pm\) 0.26 °C which is similar to the Lewis and Curry (2018) estimate of 1.2 °C (5–95% 0.9–1.7 °C). Using the estimated ECS/TCR ratio of 1.3 in Lewis and Curry (2018) implies a corresponding ECS mode of 1.4 °C in Christy and McNider (2017).

These are very different ECS ranges from the ones used by the IWG and unsurprisingly they yield much lower SCC estimates. We will review arguments in the final section why the lower estimates are relevant for IAM studies.

In our implementation herein, the Christy and McNider (2017) and Lewis and Curry (2018) distributions were sampled using inverse transform sampling. We had the full ECS distribution from Lewis and Curry (2018) from which to sample. For the Christy and McNider (2017) distribution, we fit a generalized gamma distribution to 5th, 50th, and 95th percentiles of the associated distributions via the method of least squares. Figure 2 shows plots of these probability density functions, as well as the Roe–Baker (2007) distribution used in this study.

Fig. 2 Probability density functions of equilibrium climate sensitivity distributions used to estimate the social cost of carbon Full size image

Discount rate

The long-running debate about appropriate discount rates for climate change policy analysis will not be reviewed here. Considerations of uncertainty and the ethical argument against time preference lead to a preference for a low discount rate, whereas viewing the discount rate as an opportunity cost of capital leads to a preference for a higher discount rate. We will present results using 2.5%, 3%, 5% and 7%.

Economic intuition

Simulations of the economic impacts of CO 2 emissions differ from those of conventional pollution in a few important ways, which taken together give rise to the possibility that the SCC can be negative as well as positive. First, whereas air contaminants like particulates and nitrogen oxides are directly injurious to human health, CO 2 is not. Because exhaled breath has a very high CO 2 concentration, when people travel in cars or spend time in crowded buildings (such as office towers) they routinely experience CO 2 exposure at levels far higher than outdoors, without noticeable effects. Second, CO 2 is a principal food source for plants, and if the only environmental effect of CO 2 were its aerial fertilization of plant life then emissions would almost certainly be a net benefit. But (third) its other main environmental effect is its infrared absorption property, which gives rise to projected atmospheric warming as outdoor CO 2 levels increase. Here again the effects on plants, animals and people are complex and may involve gains as well as losses. A longer growing season and less harsh winters may be a net benefit in some regions, whereas more drought and heat stress would reduce agricultural productivity. Also, if changing temperatures increase (decrease) the risk of extreme weather events, economic damages will in consequence increase (decrease).