Burying the Lede

I suck at prioritizing things. It's a character flaw I've tried to work on, but I don't think I'll ever overcome it. This is a shame because it means I"ll often let myself get distracted by minor points when I ought to be focusing on much more significant points.

A perfect example of that is available in my criticism of Richard Tol's work on the economic effects of global warming. I recently wrote a post discussing that work and the controversy around it. The post mostly focused on misleading claims made by Tol in a recent article at the Huffington Post.

The article sought to defend Tol's position that moderate amounts of global warming will be beneficial. It contained a number of misleading, if not false, claims. The strangest of these claims is Tol criticized one of his critics, Bob Ward, saying:

Since 2009, however, more estimates of the economic impact of climate change have been published. These new results do affect the fitted trend, but not in the way suggested by Mr Ward. The new trend shows positive impacts for warming up to about two degrees global warming, just like the old trend did. The new trend, however, shows markedly less negative impacts for more profound warming than did the old trend. In other words, in the last five years, we have become less pessimistic about the impacts of climate change.

My post drew attention to the fact Ward's commentary was perfectly in line with what Tol himself had said. In a correction Tol was forced to publish because of Ward's criticisms, Tol said:

I nonetheless highlight two differences between the old and the new results. First, unlike the original curve (Tol 2009, Figure 1) in which there were net benefits of climate change associated with warming below about 2°C, in the corrected and updated curve (Figure 2), impacts are always negative, at least in expectation.

Which is perfectly in line with what Ward said. Tol's article offered no explanation as to why Ward should be criticized for saying the same thing Tol himself had said. I have some ideas as to what Tol's reasoning is, but that's not important. You see, my discussion buried the lede. This is a chart showing the data used for Tol's conclusions, as used by the IPCC:


As you can see, only one data point is notably positive. A second point is barely positive (at 0.1%), but nobody could seriously claim to draw conclusions based upon such a miniscule value. That means any attempt to claim moderate global warming will be beneficial is dependent upon a single data point.

If we look at the table for this figure, we see that single data point is from Tol 2002, a paper published by none other than Richard Tol. That is, his entire position is dependent upon a single paper he wrote. That's kind of shady. Tol "examined" some 20 papers. His conclusions should not depend upon only one of them, much less one of them that he wrote. This is especially true since his analysis of those papers originally said:

it is striking that the estimates are in broad agreement on a number of points—indeed, the uncertainty analysis displayed in Figure 1 reveals that no estimate is an obvious outlier

This claim was only true because of a number of mistakes Tol had made where he inverted the sign of the data he was using. Once those mistakes were corrected, the result was the figure seen above. In it, the one data point from Tol's work is a clear outlier.

I'm not the only one who has noticed this. Other people have noticed it as well. One individual, Andrew Gelman, wrote a good post about it. His analysis of Tol's data errors is particularly spot on:

Thus, there was possibly a cascading effect: Tol’s existing estimate of +2.3% made him receptive to the idea that other researchers could estimate large positive economic effects from global warming, and then once he made the mistake and flipped some signs from positive to negative, this made his own +2.3% estimate not stand out so much.

However he, like me, failed to point out a key problem with the figure in question. You see, neither Gelman nor I managed to comment on the fact this +2.3% value, the only value which ultimately supported Tol's conclusions, was cherry-picked. Here is a table from Tol 2002:


The +2.3% value is clearly shown in it. However, two other values are shown as well. One of these values is trivially positive (0.2%) while another is negative (-2.7%). Neither of these values are shown in the figure we've seen above. Tol never shows them. Tol never discusses them. Tol never does anything to alert readers of his work studying the economic effects of global warming to them. Instead, he just cherry-picks the one result which supports the idea moderate global warming will be beneficial, displays that and ignores the less favorable results.

Why does he do this? We can't know. Tol 2002 does not favor any one of those results. It highlights the positive estimate:

Table VIII displays the impact on the world as a whole. Simply aggregating estimated impacts across regions leads to a positive impact (i.e., a benefit) of about $448 billion per year, equal to 2.3% of total world income. The standard deviation is a little less than half of that, at $197 billion or 1.0% of income.

But it then suggests the other two estimates as alternatives:

One solution is to use globally averaged prices to value non-market goods and services. Table VIII displays the result. World impacts are estimated at a negative $522 billion, or 2.7% of income, with a standard deviation of $150 billion, or 0.8% of income. The sign switch is largely due to the impact of climate change on mortality. In numbers of deceased, the reduction in mortality in the OECD is smaller than the increase in mortality in developing countries. Using regionally differentiated values, the welfare gain in the OECD is higher than the welfare loss in developing countries. This is not the case with globally averaged values. The standard deviation of the world impact decreases because the difference between regions are smaller when using globally averaged values.

Another solution is advocated by Fankhauser et al. (1997). When added, different regions’ impact estimates should be given weights. These ‘equity weights’ reflect the regions’ risk aversion and the world inequality aversion. A mild version is to use the ratio of global to regional per capita income as an equity weight. Table VIII displays the result. World impact is again positive, at $40 billion or 0.2% of income. The standard deviation is substantially larger, at $257 billion or 1.3% of income. The difference with the simple summation is explained by the higher weight attached to the poorest regions, which are generally estimated to be negatively affected by climate. The increase in the standard deviation is due to the same reason, since impact estimates in developing rely more heavily on extrapolation and are therefore more uncertain.

And does nothing to suggest which, if any, of these three estimates is the "right" one. Tol could have used any, or all, of these three estimates in his later work seeking to study the economic effect of global warming. Instead, he chose the only one which supported his belief moderate global warming will be beneficial.

Having cherry-picked his own result to support his pre-conceived belief, Tol then mangled other people's data, inverting published results in a way which caused them to support his conclusions. After those errors were corrected, Tol continued to defend his belief based entirely upon the cherry-picked results from his 2002 paper.

Richard Tol used his position as an IPCC Coordinating Author to insert his work into the latest IPCC report absent any external review. Tol got a lot of media attention for his work. Self-proclaimed global warming skeptics supported him and promoted his work. Many articles were written about the supposed benefits of global warming.

And all this was based entirely upon Richard Tol simply cherry-picking results to reach the conclusions he wanted to reach.