Getting down to the stats on global warming

Verbal arguments about statistical issues always get messy. So rather than have another round of words with Ken Parish, I thought I’d copy in the data from Christy’s graphs, and run the stats. I started checking for trends. As expected, the upward trend in the surface data (0.02 degrees per year) is stronger than that in the satellite data (0.005). More importantly, the upward trend in the surface data is statistically significant. That is, we can reject, with high confidence (above 99 per cent) the hypothesis that there is no trend. For the satellite data, we cannot reject either
(a) the hypothesis that there is no trend
(b) the hypothesis that the trend is the same as for the surface data
That is, as I said, it’s impossible to draw strong inferences from short runs of inconclusive data.
I was struck by the similarity in movements between the two series, which seemed to contradict some of what Christy said about the lack of linkage, so I also regressed the satellite data against the surface data. The slope coefficient was 0.76, and was statistically significant. The meaning of the slope coefficient is that, on average, if surface temperature goes up 1 degree, satellite temperatures go up by 0.76 degrees. We cannot reject the hypothesis that the coefficient is 1, that is that the two temperature series move together in the way predicted by standard global warming theory.
Just for fun, I tried out my suggestion of dropping the first five years. The slope coefficient was 0.95, close enough to 1 to verify my claim that just by eyeballing the data you can see that the two series move together from 1985 onwards.
Of course, the statistical analysis I’ve presented here is very crude, and there are lots of better things you can do with more data and fancier time-series techniques. But it confirms my view that the NAS panel got the story pretty much right when they concluded that:
(i) surface temperatures are rising strongly
(ii) there is no conflict between the surface and satellite data.
When I get time, I’ll try to post a more formal version of this.

Efficiency and all that

Replying to Jason Soon, Tim Dunlop puts his finger on one of the more embarrassing secrets of economics. Although we use the term ‘efficiency’ all the time, we don’t really have a consistent and rigorous definition of what it means for an economic policy to improve efficiency. A typical welfare economics textbook will define an economic situation as Pareto-efficient if there is no other situation that would constitute a Pareto-improvement, that is, make some people better off and no-one worse off. This doesn’t just require technical efficiency in production. It’s also necessary that there be no unexploited gains from trade (often called allocative efficiency)
So a Pareto-improvement would be an improvement in efficiency. But policies that naturally produce Pareto-improvements are as scarce as hen’s teeth. So when economists talk about improvements in efficiency, they are usually talking about one of the following possibilities (neither of which is generally defined in a rigorous fashion)
(a) If the gainers from the policies felt like it, they could fully compensate the losers while remaining better off themselves
(b) If the government chose it could tax the gainers, still leaving them better off, and use the proceeds to fully compensate the losers
Cases like (a) are common, but, in the absence of an outbreak of altruism among the beneficiaries of efficiency-oriented policies, don’t tell us much about the impact of policy changes on the welfare of society as a whole. If a policy change makes all 20 million Australians (but one) $100 poorer and James Packer $2.1 billion richer, it’s not helpful to know he could pay us back and keep $100 000 for himself if he chose.
Cases like (b) are more relevant, but the required analysis to show that a policy satisfies this condition is generally difficult and rarely done.


Like other users of netcomments, I suddenly found that my comment facility wasn’t working and the site had vanished – you get a redirect to a hosting service. I guess this explains why businesses don’t want to trust their vital operations to Application Service Providers (for those who don’t follow fashion, these were the Next Big Thing in mid-2000). Following the lead of Tim Dunlop, I’ve moved to Haloscan – I hope they are better. Talking of Tim, check out his stoush with the Rittenhouse Review. I thought global warming was a hot topic, but I’ll make sure never to mention the Pope.

The Great Home Equity Fallacy

US Home Sales Surged in July, prompting statements like this:
“A continued solid gain in prices of existing homes — a proxy for housing wealth– suggests that rising home equity will continue to buffer any weakness in equity wealth and sustain household spending,” said Maury Harris, chief economist at UBS Warburg.”
Exactly, the same argument has been pushed by Alan Greenspan.
In economic terms this simply doesn’t stand up. As the name suggests, households live in houses. The services of the housing stock are consumed by households, and any increase in the value of housing for one household is a loss for others. The only way the household sector as a whole can gain from rising house prices is to sell to immigrants or for non-residential use.
It follows that a consumption boom based on rising home prices is, in the words of the Bible, a house built on sand.
(This argument needs to be qualified by the special features of the US mortgage market, discussed below. Arguably, it’s not households who are in trouble but the institutions who lend to them. But the boom is just as unsound either way).

Satellites and global warming II

Ken Parish responds to my post on satellites, making a small but important error in doing so. He attributes the view I quoted to the IPCC then makes the reasonable point that, just because you are one of the 2000 scientists who worked on the report doesn’t mean you endorse everything in it. In fact, the statement I quoted was from the report of a panel assembled by the US National of Academy of Sciences specifically to examine the issue of the apparent discrepancy between satellite and ground data. It had 15 members, one of whom was John Christy. Judging by Christy’s evidence to the US Senate, cited by Ken, Christy would not have written exactly the same report as that of the panel, but he signed his name to it nonetheless, and did not append any dissenting notes as he could have done if he wished. I don’t think it’s “fast and loose” to quote a joint report on a specific topic as evidence of one author’s views on that topic.
To illustrate my point about the fragility of arguments based on short time series take a look at the graph (Fig 1) in Christy’s evidence and drop out the first five years. Even eyeballing it, you can see that the discrepancy between the trends would just about disappear. (As drawn, the level of the satellite data is lower, but that’s a graph artifact).

Satellites and global warming

At the urging of Ken Parish, I’m returning to the topic of global warming, but I’ll do my best to keep things civilised. One issue raised by Ken is the discrepancy between ground level and satellite measurements of global warming. I have followed this one fairly closely and on one crucial aspect of debate, I have a fair bit of professional expertise.
The big expert on satellite measurements of climate is John R. Christy of the University of Alabama. His data, which started in 1979, initially appeared to show a cooling trend in the troposphere. Since satellite data seemed free of many of the errors that affect surface measurements, these results were seized on by global warming ‘sceptics”.
However, it was discovered in 1998 that the satellite data had problems of their own, arising from a failure to correct for the gradual decay in their orbits. Correcting for this, and adding more data, the satellite data now shows a slight warming trend, but not as much as the surface data. These facts were enough for an NAS panel, including Christy, to publish a report Reconciling Observations of Global Temperature Change which concluded that
“Despite differences in temperature data, strong evidence exists to show that the warming of the Earth’s surface is undoubtedly real, and surface temperatures in the past two decades have risen at a rate substantially greater than average for the past 100 years”

Of course, some sceptics could not bear to give up their best bit of evidence and have put a lot of weight in the remaining discrepancy. Speaking as someone who has taught and researched the statistical analysis of time series, I can say that putting this kind of weight on 20 years of inconclusive data is not justified, even if such events as the eruption of Mt Pinatubo in 1981 had not added to the usual background noise.

The satellite data does raise some issues – for example it shows that the link between tropospheric and surface level temperatures is not as tight as was once thought, but the idea that it represents serious evidence against the hypothesis of human-induced global warming has been thoroughly refuted.