Little wonder then, that his work acts as grist to the mill for numerous op-eds of a, shall we say, more considered sceptical viewpoint. That is, opinion pieces that try to marshal credible scientific evidence for arguing against decisive climate change action, rather than just mouthing off some inane contrarian talking points (it's a giant communist conspiracy, etc). Bjørn Lomborg and Matt Ridley, for example, are two writers that have cited Richard's research in arguing forcibly against the tide of mainstream climate opinion. I want to focus on the latter's efforts today, since it ties in rather nicely with an older post of mine: "Nope, Nordhaus is still (mostly) right."
I won't regurgitate the whole post, but rather single out one aspect: the net benefits that climate change may or may not bring at moderate temperature increases. The idea is encapsulated in the following figure of Tol (2009), which shows estimates of economic damages due to temperature increases relative to the present day.
Note: Dots represent individual studies. The thick centre line is the best fit stemming from an OLS regression: D = 2.46T - 1.11T^2, with an R-squared value of 0.51. The outer lines are 95% confidence intervals derived according to different methods. Source: Tol (2009)
Now, there are various points to made about the implications of Fig. 1. People like Matt Ridley and Bob Murphy -- who you may recall was the subject of my previous post -- are keen to point out that it demonstrates how climate change will bring benefits to us long before it imposes any costs. Ergo, we should do little or nothing about reducing our emissions today. Of course, there are multiple responses to this position and I tried to lay out various reasons in my previous post as to why this is a very misleading take (sunk benefits and inertia in the climate system, uncertainty and risk aversion, unequal distribution of benefits and costs, tipping points, etc).
However, I have two broader points to make here, for which Ridley will prove a useful foil. For example, here he is in The Spectator last year, arguing "Why Climate Change Is Good For The World":
To be precise, Prof Tol calculated that climate change would be beneficial up to 2.2˚C of warming from 2009[... W]hat you cannot do is deny that this is the current consensus. If you wish to accept the consensus on temperature models, then you should accept the consensus on economic benefit.Bold in my emphasis. Now it should be pointed out that Ridley's articled elicited various responses, including one by Bob Ward that showed several typos in Richard's paper that were relatively minor yet nonetheless relevant to the above figure and an accompanying table. In fact, only two out of the 14 studies considered in Tol (2009) actually show positive benefits accruing due to climate change... And one of these was on the borderline at best.[*] This is all very well-trodden ground by now, but it underscores just how tenuous -- to put it mildly -- Matt Ridely's appeal to economic consensus is.
However, we are still left with a curve that purports to show positive benefits from climate change up until around 2˚C of warming, before turning negative. So here are my two comments:
Comment #1: Outlier and functional form
Given that only one study among the 14 surveyed in Tol (2009) showed large-ish benefits from climate change, you may be inclined to think that the initial benefits suggested by Fig. 1 are hinged on this "outlier"... And you would not be wrong: individual observations will always stand to impact the overall outcome in small samples like this. However, I would also claim that it is partially an artefact of functional form. What do I mean by this? I mean that predicting positive benefits at "moderate" levels of warming is in some sense inevitable if we are trying to fit a quadratic function[**] to the limited data available in Tol (2009). This is perhaps best illustrated by re-estimating the above figure -- corrected for the minor typos -- but now leaving out the most optimistic assessment of climate benefits (red dot) as an outlier. [I have zoomed in to make things clearer, so please note the change in y-axis range.]
Based on Figure 1 in Tol (2009), but corrected for typos and including an additional best-fit line that excludes the most optimistic estimate of benefits due to moderate climate change (i.e. Tol, 2002).
You can see that, even when we drop this relative outlier, the best-fit line still suggests that we will experience small net benefits for a further 1˚C of warming. (Following Ridley's lead, I'll ignore the confidence intervals here for the moment, although these obviously bring important implications of their own.) And this, despite the fact that our modified sample only includes estimates that suggest a negative, or at best neutral, effect on welfare due to climate change! Now, I don't wish to come across as overly pedantic or critical of the choice of a quadratic damage function... Indeed, it is hard to think of another simple function that would better lend itself to describing the effect of moderate temperature increases. (Albeit not for higher levels of warming.) I am merely trying to expand on the way in which the interplay of limited data and choice of functional form can combine to give a misleading impression of the risks associated with climate change.
Comment #2: New data points
There have been several new estimates of the economic effects of climate change since Tol (2009). As it happens, Richard has updated his Fig. 1 accordingly and included it in the latest IPCC WG2 report. (Although -- surprise! -- even this is not without controversy.) You can find it on pg. 84 here, with an accompanying table on the preceding two pages. However, I note that this updated version does not include a best-fit line. That is perhaps a wise choice given the issues discussed above. Nevertheless, like me, you may still be curious to see what it looks like now that we have a few additional data points. Here I have re-plotted the data, alongside a best-fit line and 95% confidence interval.
Based on Figure 10 in IPCC WG2 (2014). As before, the best-fit line is computed according a quadratic function using OLS. This yields D = 0.01T - 0.27T^2, with an R-squared value of 0.49.
Whoops. Looks like those initial benefits have pretty much vanished!
So... What odds on Matt Ridley reporting the updated economic "consensus"?
UPDATE: On Twitter, Richard points me towards a recent working paper of his that uses non-parametric methods to fit a curve to the data.[***] This is all well and good, and I commend his efforts in trying to overcome some of the issues discussed above... Except for one overwhelming problem: Non-parametric methods -- by their very nature -- are singularly ill-suited to small samples! Even Wikipedia manages to throw up a red flag in its opening paragraph on the topic: "Nonparametric regression requires larger sample sizes than regression based on parametric models because the data must supply the model structure as well as the model estimates." Perhaps even worse, non-parametric estimations are particularly misleading in the tails. Such an approach is simply not able to produce meaningful results in this instance, since we are dealing with a rather pitiful 20-odd observations.
Ultimately, it is not so much a question of parametric versus non-parametric. The real problem is a paucity of data.
UPDATE 2: An errata to Tol (2009) has finally been published. Barring differences in how the confidence intervals were calculated, the updated figure is, of course,
UPDATE 3: Ouch! And double ouch! Statistician Andrew Gelman takes Richard out to the woodshed (making many of the same points that I have here). The result isn't pretty. Make sure to read the comments thread too.
[*] Specifically, Mendelsohn et al. (2000) suggest that 2.5˚C of warming will yield a net global benefit that is equivalent to 0.1% of GDP. Importantly, they do not account for non-market impacts -- typically things like ecosystems, biodiversity, etc -- which would almost certainly pull their estimate into negative territory. That leaves one of Richard's own papers, Tol (2002), which suggests that 1˚C of warming will yield a 2.3% gain in GDP.
[**] Tol (2009) uses a simple regression equation of D = b1*T - b2*T^2 to fit the data. He finds b1 = 2.46 and b1 = 1.11, which is where the thick, central grey line in Fig. 1 comes from.
[***] He uses what is known as kernel regression. This stands in contrast to the normal regression methods (e.g. OLS) that rely on predefined parametric specifications regarding the shape of the best-fit line, distribution of errors, etc.