TOTAL LEAST SQUARES BIAS WHEN EXPLANATORY VARIABLES ARE CORRELATED
Continuing my exploration of the statistical elements of the IPCC climate attribution methodology I have a couple of papers under review at journals in which I use Monte Carlo simulations to analyse the properties of Total Least Squares (TLS, the preferred regression method) under conditions typical in a signal detection regression. There is very little underlying theory about when TLS yields consistent or unbiased results. In a single-variable model with a random explanatory variable TLS corrects a downward bias in Ordinary Least Squares (OLS, the standard regression method). But in many other cases it over-corrects or introduces new biases, and consistency results are not available without imposing unrealistic and untestable assumptions. In one paper I examine the consequences of omitted variables bias, and I will disseminate that paper separately. In this paper I look at what happens if the explanatory variables are allowed to be correlated (as they are in signal detection regressions). The results are, frankly, bizarre. I have posted a draft of the paper on the Earth and Space Science pre-print archive here:
I don't know what to make of the results and I would welcome comments. Unfortunately the table formatting in the archived version is wonky so here is a better version. The turn-key R code is in the Supplement provided, and is also here.
MARCH 25, 2022
SOMETHING WEIRD ABOUT TOTAL LEAST SQUARES IN OPTIMAL FINGERPRINTING-TYPE REGRESSIONS
Newspaper Columns, Commentary and Other
CLIMATE POLICY: WHEN EMOTION MEETS REALITY
I have done a few talks recently on the theme of why CO2 emissions, unlike other types of air pollution, have proven so hard to reduce. One such presentation was for the Irish Climate Science Forum and is available online:
My talk covers some of the main reasons why, after 30 years of concerted public policy effort, there has been so little achieved on climate policy, and why I think this will continue to be the case going forward. Governments do a disservice to the public when they keep promising more than they can deliver and when they try to rally support for climate policy by claiming not only will it not cost anything but will make us wealthier. Marcel Crok wrote an article about the presentation for Clintel here.
CLIMATEGATE: UNTANGLING MYTH AND REALITY 10 YEARS LATER
Steve McIntyre and I have written a retrospective and evaluation of the issues raised by Climategate and the inquiries that followed from it:
It's hard to believe that a decade later the controversies are still resonating, even to the point of having bearing on a decision of the US Supreme Court last week (via a point made by Justice Alito in his dissent), as well as a decision this past summer in a BC court pertaining to the dismissal of a defamation case. We discuss these things and many many more. We had hoped to write a short summary of a few key items, but ended up going deep into some topics that are still pertinent and subject to widespread misunderstanding and misinformation.
TEMPERATURE TRENDS IN CANADA SINCE 1888
We hear a lot about climate change. Would someone who lived in, say, 1918 notice much change in the average weather conditions compared to today? Once you delve into temperature data you will see that it's very hard to offer a simple answer to such a question. Patterns vary over time, by season and by place. For those Canadians who are curious about how the climate might have changed near where they live, I have written a rather lengthy report on the subject.
Or rather, I wrote an R program that generated a lengthy report. I analyze long term records on monthly average daytime highs in Canada, in various segments based on collections of stations available back 40, 60, 80, 100 and 130 years. There are also some nice graphs. If you think you know what "climate change" looks like in Canada, now you can test your perceptions against the data. The R program is here.
The idea of this site is very simple: to build the complete environmental record of every community across Canada. The site currently shows air emissions by source (back to 1990), air contaminant levels (back to 1974), monthly average high temperatures (back to 1900) for hundreds of places across the country, and water pollution records for several provinces.
The layout is self-explanatory and it's very easy to use. The data are all from government agencies, but most of it has not hitherto been disseminated in a usable form to the public. All my sources are linked and the data I use are easily-downloadable.
So the next time you find yourself in a conversation about some aspect of the environment and you wonder what is actually going on, look at yourenvironment.ca to find out.
Recent Journal Articles and Discussion Papers
CHECKING FOR MODEL CONSISTENCY IN OPTIMAL FINGERPRINTING: A COMMENT
I have several papers underway assessing the statistical methods used by IPCC authors over the past 20 years for attributing climate changes to greenhouse gas emissions. The first is a critique of the seminal paper in the field, published in 1999 in Climate Dynamics. My paper has likewise been published in Climate Dynamics.
UPDATE II (October 18): I have published through the Global Warming Policy Foundation a non-technical explanation of my paper. At the accompanying website the GWPF has reproduced comments Myles Allen provided to earlier media inquiries, to which I have added a reply, and Richard Tol has supplied a commentary on the exchange.
UPDATE: Here is a non-technical Backgrounder to try and make the material more accessible.
I have published a (somewhat) non-technical summary at Judith Curry's blog (PDF here). Optimal Fingerprinting has long been the dominant tool in climatology for attributing climate changes to greenhouse gases. It is a matrix-weighted generalized least squares (GLS) regression model, and as such is based on tools familiar to economists, although changed in non-standard ways. In my article I show that those changes destroy the properties of consistency and unbiasedness associated with regular GLS methods. Unfortunately the problems have been concealed by exclusive reliance on a test statistic introduced by Allen and Tett that is meaningless for checking specification errors. As a result, none of the applications of this method over the past 20 years can be considered to have yielded reliable results.
THE ECONOMICS LITERATURE DOES NOT SUPPORT THE 1.5C TARGET
Robert Murphy and I have published a study for the Fraser Institute arguing that standard mainstream economic analysis does not endorse the 1.5C target.
We don't conduct a cost-benefit analysis ourselves. And we point out that the IPCC SR1.5 likewise didn't do a cost-benefit analysis (they even admit as much early in the report). Instead we show that the economists who have done CBA's have found that the costs of trying to keep to a 1.5C warming target vastly exceed the benefits. Nordhaus' analysis, for instance, shows that it would be better to do nothing at all than to try to get warming down to 1.5C. And he got a Nobel Prize.
PRESENTATION TO THE HOUSE OF COMMONS COMMITTEE ON NATURAL RESOURCES
The Government's NR Committee is studying the potential for biofuels and renewable fuels to play a role in reducing greenhouse gas emissions in Canada. I was invited to speak to the Committee on rather short notice. In my presentation I summarize work I have done on this issue in the past as well as some basic principles that guide my thinking about climate policy.
IMPACTS OF A $170/TONNE CARBON TAX ON THE CANADIAN ECONOMY
Elmira Aliakbari and I have completed a study for the Fraser Institute modeling the effects of imposing a high carbon tax on the Canadian economy. The federal government has said it won't have any effect on GDP and most people will end up better off, but this is nonsense.
We project a GDP decline of about 1.8% and a loss of 184000 jobs nationally [Updated]. And we show that these estimates are right in line with numbers computed for policies at the time of Kyoto. The underlying model I developed is a hybrid CGE/Input-Output model with considerable provincial and sectoral detail. I developed my first CGE model (as part of my Ph.D. dissertation) which I used to model carbon taxes back before most people had ever heard of them. The data availability and computing power have improved a lot since then. Unfortunately what has not improved is government policy analysis: it's all but vanished. One of the themes in our report is the contrast between the extent of analysis and disclosure 20 years ago regarding the costs of implementing Kyoto versus the total absence today. Some of the modeling groups and capabilities are simply gone, but more generally the government has decided it doesn't want to know the answer.
PERVASIVE WARM BIAS IN CMIP6 TROPOSPHERIC LAYERS
John Christy and I have published a paper in Earth and Space Science comparing tropospheric warming rates in the new generation CMIP6 climate models to observations from satellites, weather balloons and reanalysis systems.
Every single model overpredicts warming. It has long been known that climate models on average overstate warming in the troposphere over the tropics. This was flagged as a serious inconsistency in 2005 in the first US Climate Change Science Program report and has been mentioned in every IPCC report since. But instead of the problem being corrected, it's gotten worse over time, and the bias is now global. We examined runs over the post-1979 interval in the first 38 climate models made available in the CMIP6 archive, looking at the lower- and mid-troposphere in the tropics and globally. Every model over-predicted warming in both layers, both globally and in the tropics. In most individual cases the bias is statistically significant and on average it is highly significant. We also show that the bias is larger in high-ECS models, but even the models with lower average ECS predict too much warming. If a group of models were to appear that had a realistic representation of global tropospheric warming, it would likely have to have a lower ECS than even the low-ECS members of the CMIP6 ensemble. Data and code here.