Viscount Ridley, a self-proclaimed ‘lukewarmer’, has again suffered the embarrassment of promoting a study that concludes global warming is having an overall positive economic impact, only to discover that it is fundamentally misleading and contains several apparent mistakes.

On 5 February, I published a commentary pointing out that Viscount Ridley, who is a Conservative hereditary peer, had misled the House of Lords on 30 January by making the inaccurate and misleading statement that “the consensus among climate economists and, indeed, in the Intergovernmental Panel on Climate Change, is that the economic impacts will be positive for the next 40 or 50 years”.

Unable to defend his false claims and apparently offended by my effrontery in challenging his propaganda, Viscount Ridley predictably resorted to abuse, calling me as a “paid climate attack dog”﻿ .

However, he also cited a new study by Professor Richard Tol which he indicated was the source of his statement in the House of Lords.

Professor Tol is based at the University of Sussex and until recently was, like Viscount Ridley, a member of the “Academic Advisory Council”﻿ of the Global Warming Policy Foundation, which was set up by Lord Lawson to lobby against policies to reduce greenhouse gas emissions.

Viscount Ridley is a keen follower of Professor Tol’s work. In October 2013, ‘The Spectator’ magazine published a front-page story by Viscount Ridley, under the headline ‘Why climate change is good for the world’. The article relied heavily on a paper by Professor Tol, ‘The economic effects of climate change’﻿ , which was published in 2009 in the ‘Journal of Economic Perspectives’.

After being cited by Viscount Ridley, I examined in detail Professor Tol’s paper, which described the results of a survey of academic studies estimating the economic impacts of climate change. I found numerous mistakes, including examples in which Professor Tol had claimed some previous studies had found net economic gains from warming, when they actually reported net losses.

I contacted the ‘Journal of Economic Perspectives’ about my findings and a remarkable series of corrections followed. Professor Tol made an initial set of amendments to the paper, blaming “gremlins” for the mistakes in the original paper. But it still contained errors so he provided a second correction﻿ in 2014, and updated his findings. A subsequent analysis by William Nordhaus and Andrew Moffat in July 2017, called ‘A survey of global impacts of climate change: replication, survey methods, and a statistical analysis’﻿ , concluded that “of 21 estimates [in Tol’s paper], 10 were found to be inaccurate or not replicable”.

The editors of the journal were also still not satisfied with Professor Tol’s second round of corrections, and published their own note﻿ . They substituted in the survey presented in Chapter 10 (Figure 10-1﻿ and Table SM10.2 in the ‘Supplementary Material’﻿ ) of the contribution of working group II of the Intergovernmental Panel on Climate Change to the Fifth Assessment Report in 2014, on which Professor Tol was a Coordinating Lead Author. The Editorial Note presented the survey data as a scatter plot, as in the IPCC report, and was particularly critical of Professor Tol’s attempts to estimate a best-fit line: “The original figure in the 2009 JEP article estimated a best-fit line passing through the points on this kind of figure, along with confidence intervals for that estimate. Given the differences across the studies as mentioned in the IPCC report, several outside reviewers involved in our editorial process expressed a concern that such estimates were not meaningful.”

Professor Tol also made partial corrections to a similar paper he had published in the ‘Journal of Economic Dynamics and Control’﻿ in 2013, but another paper in ‘Environmental and Resource Economics’﻿ in 2012 remains uncorrected.

Professor Tol’s new paper, ‘The economic impacts of climate change’﻿ , was published on 12 January 2018 by the ‘Review of Environmental Economics and Policy’. It provides an update to the survey of estimates that were published in the IPCC report, which are presented in Table 1 and Figure 1 along with explanatory text. Based on the 27 estimates from 22 studies listed in Table 1, Tol (2018) concludes that “the welfare impacts of initial warming are positive”. But a close examination of Tol (2018) reveals that this finding is unsound and based on overweighting of a single outlier study that is more than 15 years old. And the analysis contains some apparent sloppy errors, like previous papers by Professor Tol.

Of the 22 studies listed in Tol (2018), only 10 were published within the last 15 years. Just two studies, both more than 15 years old, report net positive impacts from climate change. One of the studies, a paper by Robert Mendelsohn, Michael Schlesinger and Larry Williams on ‘Comparing impacts across climate models’﻿ , was published in ‘Integrated Assessment’ in 2000. It contributes two positive values, both less than 0.1 per cent, to Table 1 in Tol (2018). The authors noted that they only measured “market effects” and so did not take into account the effects of climate change on ecosystems or health, or impacts from changes in extreme events or catastrophes. It is unsurprising that the authors reported net positive economic impacts given these omissions.

The other study that provides a net positive estimate is a paper by Professor Tol on ‘Estimates of the damage costs of climate change. Part 1: benchmark estimates’﻿ , published in ‘Environmental and Resource Economics’ in 2002. The results presented in Tol (2002) reflect assumptions of large agricultural gains from the effects of ‘carbon dioxide fertilisation’ and mild warming, but as others, such as Frank Ackerman and co-authors (2009)﻿ , have pointed out, more recent research results have indicated strong offsetting of these benefits by other factors, including increases in levels of ground-level ozone which can hinder crop growth. In addition, Tol (2002) acknowledges that “the list of omitted impacts is long”, including amenity, recreation, tourism, extreme weather, fisheries, construction, transport, energy supply and morbidity. Hence, it seems that Tol (2002) is based on assumptions that could exaggerate positive impacts, such as agricultural gains, while excluding many negative impacts, such as extreme weather.

Figure 1 of Tol (2018) shows the data along with a best-fit piecewise line, suggesting that the net economic impacts should be positive up to about 1.6°C of warming. However, this method of line-fitting is weighted towards the single data point from Tol (2002), which seems to be an outlier because it lies outside the 95 per cent confidence interval on Figure 1. It should be noted that this confidence interval around the best-fit line appears to have been misplotted as the values have been copied and pasted from the calculation of a quadratic line fit, rather than determined independently as part of the piecewise linear fit calculation.

The impact of the outlier data point is exacerbated by the omission of a number of other relevant studies which estimated negative economic impacts from climate change. The survey by Nordhaus and Moffat (2017) identified six studies that had been left out by Tol (2018), including two that investigated temperature rises of 1°C or less. For instance, a study by Claudia Kemfert on ‘An integrated assessment model of economy-energy-climate – The Model Wiagem’﻿ , which was published in ‘Integrated Assessment’ in 2002, found that a warming of 0.25°C between 2000 and 2050 would cause a loss in GDP of 0.17 per cent. Tol (2018) also ignored more recent studies, such as a paper by Marshall Burke, Solomon Hsiang and Edward Miguel on ‘Global non-linear effect of temperature on economic production’﻿ , published in ‘Nature’ in 2015, which found that the direct effect of a rise in global average temperature of 4.3°C between 2010 and 2100 would reduce global economic output by 23 per cent.

Hence it is clear that the conclusion by Tol (2018) that “the welfare impacts of initial warming are positive on net” is based on a single outlier data point, drawn from a study by Professor Tol that was published more than 15 years ago and which is given undue weight because of the omission of other studies that have found net negative impacts for moderate warming.

While the shortcomings of the method used by Tol (2018) may be overlooked by Viscount Ridley because the conclusions match his ‘lukewarmer’ narrative, others should be far more sceptical of its value.

In addition Tol (2018) undermines Professor Tol’s contribution to the IPCC report because there are multiple discrepancies compared with Table SM10.2﻿ and the accompanying Figure 10-1﻿ .

Tol (2018) states that there are three differences between his Table 1 and the corresponding Table SM10-2 presented in the IPCC report. First, Tol (2018) includes an estimate of the impact of 1.0°C of cooling from a study by d’Arge that was published in 1979. Second, two estimates attributed to a paper by Robert Mendelsohn and co-authors are listed for a warming of 2.5°C, whereas the IPCC report listed the temperature rise as 2.2°C. Third, Tol (2018) changes an estimate attributed to a study by David Maddison and Katrin Rehdanz in 2011 to a loss of 5.1 per cent, compared with a loss of 12.4 per cent in the IPCC report, as a result of using market exchange rate dollars instead of purchasing power parity.

However, there are apparent problems with these claims by Tol (2018).

First, the IPCC report listed 21 estimates from 18 studies published since 1994, whereas Tol (2018) lists 27 estimates from 22 studies published since 1979. In addition to the study by d’Arge (1979), Tol (2018) also includes papers by Nordhaus (1982), Nordhaus (1991), Berz (forthcoming), and Nordhaus (2013). For Nordhaus (1994a), Tol (2018) includes two estimates, one of which is different from the IPCC report, and for Rehdanz and Maddison (2005), Tol 2018 includes two estimates instead of the one listed in the IPCC report. Hence, there is more than one additional study included in Tol (2018).

Second, the explanation provided by Tol (2018) for changing the temperature values of the two estimates attributed to the paper by Robert Mendehlson and co-authors – namely that they are “the area average temperature change rather than population average” – is unconvincing. The paper by Robert Mendelsohn, Michael Schlesinger and Larry Williams on ‘Comparing impacts across climate models’﻿ , was published in ‘Integrated Assessment’ in 2000. According to Tol (2018), Mendelsohn et al. (2000) made two estimates of the impacts of a rise in temperature of 2.5°C: 0.0 and an increase of 0.1 per cent of GDP. However, the paper by Mendelsohn and co-authors states: “First, we assume that carbon emissions are on a global path consistent with reaching a maximum of 750 ppmv. Second, we examine the impacts in 2100. Given the IPCC path specified above, carbon dioxide will reach 612 ppmv by 2100. Third, we specify a global temperature sensitivity of 2.5°C. The model predicts a global-average temperature of 2.21°C by 2100.”

It should also be noted that the Mendelsohn et al. (2000) paper (‘Comparing impacts across climate models’﻿ , by Robert Mendelsohn, Michael Schlesinger and Larry Williams, published in ‘Integrated Assessment’) listed by Tol (2018) is different from the Mendelsohn et al. (2000) paper (‘Country-specific market impacts of climate change’﻿ , by Robert Mendelsohn, Wendy Morrison, Michael Schlesinger and Natalia Andronova, published in ‘Climatic Change’) listed in the IPCC report.

There are many other discrepancies between Table 1 of Tol (2018) and Table SM10.2 of the IPCC report. Overall, only 17 of the 22 studies listed in Table 1 of Tol (2018) also appear in Table SM10.2 of the IPCC report. For nine of the studies, the estimates presented in Table 1 of Tol (2018) are not the same as in SM10.2. In most cases, the discrepancy arises where Professor Tol has calculated estimates based on the original authors’ papers. Nonetheless, it means that either Tol (2018) contains many more errors, or Professor Tol’s chapter of the IPCC report is inaccurate. Details of these discrepancies follow.

Table 1 of Tol (2018) lists a paper by William Nordhaus and Zili Yang on ‘A regional dynamic general-equilibrium model of alternative climate-change strategies’﻿ , which was published in the ‘American Economic Review’ in 1996. According to Tol (2018), Nordhaus and Yang (1996) found that a rise in global temperature of 2.5°C would lead to a loss in GDP of 1.4 per cent. In fact, Nordhaus and Yang (1996) does not include an estimate of the global impact of climate change but does provide figures for different regions. It is not clear how Tol (2018) derived the global figure, but the IPCC report lists Nordhaus and Yang (1996) as finding a larger loss in GDP of 1.7 per cent from a warming of 2.5°C, so either Tol (2018) is wrong or Professor Tol’s chapter of the IPCC report is wrong.

Table 1 of Tol (2018) lists a paper by Erica Plambeck and Chris Hope on ‘PAGE95: An updated valuation of the impacts of global warming’﻿ , which was published in ‘Energy Policy’ in 1996. Tol (2018) suggests that Plambeck and Hope (1996) calculated that a warming of 2.5°C would lead to a loss in GDP of 2.9 per cent, with a “low” value of 0.5 per cent and a “high” figure of 21 per cent. But Plambeck and Hope (1996) does not contain such figures. Instead it estimates the impacts on the European Union of a warming of 2.5°C, and calculates impacts in other regions as ratios relative to the impacts in the European Union. It is not clear how Tol (2018) derived an estimate of global impacts from Plambeck and Hope (1996). However, the IPCC reported that Plambeck and Hope (1996) found a loss in global GDP of 2.5 per cent, not 2.9 per cent, so either Tol (2018) is wrong or Professor Tol’s chapter of the IPCC report is wrong. Nordhaus and Moffat (2017) indicated that they were unable to replicate this result from one of Professor Tol’s previous papers.

Table 1 of Tol (2018) includes a paper by David Maddison on ‘The amenity value of the climate: the household production function approach’﻿ , which was published in ‘Resource and Energy Economics’ in 2003. Tol (2018) indicates that Maddison (2003) had calculated zero impact on GDP from a warming of 2.5°C. In fact, Maddison (2003) includes no estimate of the global impact of climate change. Instead, he determined the change in the cost of living for 88 countries due to an increase in global mean temperature of 2.5°C. It is not clear how Tol (2018) obtained a global impact on GDP for Maddison (2003). The IPCC report claimed that Maddison (2003) found a loss in GDP of 0.1 per cent from a warming of 2.5°C. Either Tol (2018) is wrong or Professor Tol’s chapter of the IPCC report is wrong.

Table 1 of Tol (2018) cites a paper by Katrin Rehdanz and David Maddison on ‘Climate and happiness’﻿ , which was published in ‘Ecological Economics’ in 2005. Tol (2018) claims that Rehdanz and Maddison (2005) found that a warming of 0.6°C would result in a loss of GDP of 0.2 per cent, while a warming of 1.0°C would mean a decrease in GDP of 0.3 per cent. In fact, Rehdanz and Maddison (2005) calculated “the change in real GDP per capita necessary to hold happiness at its current levels in the face of predicted changes in climate for two different time slices: 2010–2039 and 2040–2069”, for 65 countries. The changes in climate are expressed in terms of maximum and minimum temperatures and maximum and minimum precipitation in each country. There is no figure in Rehdanz and Maddison (2005) for either the change in global mean temperature or the impact on global GDP, so it is unclear how Tol (2018) determined it. However the IPCC report claimed that Rehdanz and Maddison (2005) found that a warming of 1.0°C would lead to a loss in global GDP of 0.4 per cent, so either Tol (2018) is wrong or Professor Tol’s chapter of the IPCC report is wrong.

Table 1 of Tol (2018) includes a paper by Chris Hope on ‘The marginal impact of CO 2 from PAGE2002: An integrated assessment model incorporating the IPCC’s five reasons for concern’, which was published in ‘Integrated Assessment’ in 2006. Tol (2018) indicates that Hope (2006) projected a loss in global GDP of 1.0 per cent due to a rise in global temperature of 2.5°C, with a “low” estimate of a loss of 3.0 per cent and a “high” estimate of zero impact on GDP. However, Hope (2006) actually calculated the economic and non-economic impacts that would occur in various sectors of the European Union from a rise in local temperature above a “tolerable level” of warming. He also provided “multipliers” relative to the European Union for some other regions. Hope (2006) does not cite a figure for the impact on global GDP. It is not clear how Tol (2018) calculated the global figure, and the IPCC report claimed that Hope (2006) had found that a rise in global temperature of 2.5°C would result in a loss in global GDP of 0.9 per cent. Either Tol (2018) is wrong or Professor Tol’s chapter of the IPCC report is wrong.

Bob Ward is policy and communications director at the Grantham Research Institute on Climate Change and the Environment at the London School of Economics and Political Science.