Bryan Caplan  

Global Warming Econometrics Bleg

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What happens if you regress annual global temperature 1880-2011 on CO2, linear trend, and other stuff trending positively or negative over this era?  The list of regressors should ideally include not just other climatological variables, but placebo variables like church attendance per capita, the Dow Jones, televisions per capita, etc. 

Key question: Does CO2 really dominate in such a regression?

Nothing good popped up on Google Scholar.  If you know anywhere such regressions are published, or if you can easily run them yourself, please share. 

Comments and Sharing

COMMENTS (27 to date)
jstults writes:

Some of the things on the Niche Modeling site are worth a look. For example, some time series analysis: AGW Doesn’t Cointegrate

The community Lucia Liljegren has built around her site The Blackboard does and discusses all sorts of statistical analysis on global temperatures and other climate measures. You can even bet on what the global mean surface temperature will be next month. The readership there has enough people that can turn the crank with R or Matlab that the signal-to-noise is pretty good and any nonsense gets called pretty quickly.

[Comment edited with commenter's permission.--Econlib Ed.]

pj writes:

Why 1880-2011 rather than 1600-2011 or 1000-2011 or 1,000,000 BC - 2011?

In climate terms, that's like asking for a regression on GDP from 1929-1932. Whatever turns up, it's not going to be very good out of sample.

Kevin Dick writes:

It's also important to specify whether you want raw or "adjusted" temperatures. Most of the global land surface temperature datasets have been adjusted in various ways. Often, subsequent version of a data set will result in adjustments to temperatures decades or even centuries in the past. Moreover, these adjustments are not randomly distributed. The systematically adjust past temperatures cooler and recent temperatures warmer.

Kevin Dick writes:

Also, Google "McKitrick & Michaels". They found a fair amount of contribution to the temperature change from economic growth (from 79-00). But it's a big point of controversy

Grieve Chelwa writes:

The website Watts Up With That? is a useful repository for checking whether anyone has done this kind of work before and just reading up on climate change issues in general. This paper published in Earth Systems Dynamics uses time series regression techniques and seems to come close to answering your question. The paper's abstract is as follows:

We use statistical methods for nonstationary time series to test the anthropogenic interpretation of global warming (AGW), according to which an increase in atmospheric greenhouse gas concentrations raised global temperature in the 20th century. Specifically, the methodology of polynomial cointegration is used to test AGW since during the observation period (1880–2007)global temperature and solar irradiance are stationary in 1st differences, whereas greenhouse gas and aerosol forcings are stationary in 2nd differences. We show that although these anthropogenic forcings share a common stochastic trend, this trend is empirically independent of the stochastic trend in temperature and solar irradiance. Therefore, greenhouse gas forcing, aerosols, solar irradiance and global temperature are not polynomially cointegrated, and the perceived relationship between these variables is a spurious regression phenomenon. On the other hand, we find that greenhouse gas forcings might have had a temporary effect on global temperature.

Krishnan writes:

"Global Warming" is not about data - it is not even as "science" - but a philosophy - That man is evil because we dig things up from the ground, burn them as fuel and create CO2 - that the way to economic growth is through conservation of existing resources in the ground and not exploration and creation of new resources - and so on and so on ...

CO2 is the target because it can be directly linked to fuel usage/discovery - and in particular, the use of gasoline as fuel for vehicles, coal for power plants ...

But - to answer the question at hand - yes, is perhaps the best site to begin - is also a very good site - we have learned that papers from "Science" (a leading journal indeed) about "Global Warming" are useless - propaganda disguised as science (the paper by Marcott et all in 2013 is perhaps a good example)

Tobias writes:

@Grieve Chelwa: There's a comment on that paper that contests the main conclusions (

The Sheep Nazi writes:

What Kevin Dick says more or less. My understanding of the issue is that anything other than satellite or high-altitude balloon data must first be corrected using proxies of some kind. If you have confidence in data that old, could you explain why you do?

Steve writes:

Global temperatures are negatively correlated with pirates.

Dave Tufte writes:

1) Lots of people have done the time series, but few bothered to publish it. It's a negative result: there isn't much there. I can probably find some notes from when I had an (incredulous) environmental engineering Ph.D. class at Tulane do this in 2000. I first heard that the time series didn't support the AGW argument from John Seater in the fall of 1989.

2) On a slightly different note, I wrote 2 posts about the elasticity of carbon dioxide with respect to growth, and temperature with respect to carbon dioxide. You need both relationships to get AGW, and they both are more inelastic than the demand for cigarettes.

MingoV writes:

That timeline shows no significant increase in annual mean global temperatures. Atmospheric carbon dioxide concentrations were not measured until relatively recently. (Mediocre, inaccurate techniques were used to estimate past CO2 concentrations.) CO2 concentrations increased during the last half of the 20th century. There was no correlation between CO2 concentrations and mean global temperatures. That's hardly surprising, since our planet does not experience a greenhouse effect (see below).

Note: I was a scientist allowed to read and comment on the final draft of the 2004 report by the IPCC. It was the lowest quality "scientific" report or paper I had seen. Not surprisingly, my comments were ignored.

The greenhouse effect is based on two factors: molecules (such as water and CO2) in the air that absorb solar energy and a transparent enclosure of the right shape. In a greenhouse, much of the morning sunlight striking the east side of the roof and the east wall passes through the west wall. The reverse situation occurs in afternoons and evenings. By increasing the humidity and/or CO2 concentrations, more of sunlight that would pass through the greenhouse is captured by water and CO2 in the air, and the greenhouse gets warmer. (The greenhouse "steals" solar energy that would have warmed outside surfaces.)

Note that there is no greenhouse gas effect at noon, because with the sun overhead, the sunlight that isn't absorbed by the air is absorbed by the plants, racks, or floor (none would pass through a wall to the outside). Planet earth is ALWAYS like noontime in a greenhouse. Sunlight that isn't absorbed by the air is absorbed by something on the surface. If the air absorbs more solar energy, the surface gets less, and the overall temperature is the same (since air can transfer heat to the surface and vice versa). Climatologists either don't know these concepts or ignore them, and they believe (or pretend to believe) that solar energy absorption by a CO2 molecule is EXTRA and doesn't decrease solar energy absorption by the surface.

Vangel writes:

...annual global temperature 1880-2011...

What does this actually mean? How do you have a meaningful measure of the annual global temperature? Do you measure surface temperatures? Where would you take the measurements? How do you account for contamination of those temperatures? Do you measure the temperatures of the oceans? Where do you take those? At what time of day do you take the temperatures? Do things like changes in cloud cover while taking the temperature matter? And once you have all of your data how do you make sense of it all by coming up with the one number that you want to look at? Does this number have any meaning in the real sense?

I think that you are searching for some average of an aggregate and try to assign meaning to it without explaining how it is that the aggregate is valid, that averaging is meaningful, and that the final number makes sense. But I do not see how any rational person can take such a methodology seriously.

J Storrs Hall writes:

I did a little of this a couple of years ago and Watts kindly cross-posted it...
Check out the earlier post it refers to as well. At the time I didn't know what the 6-sigma excursion was, but it turns out it was measurement error in CRUTEM -- I could somewhat grandiosely claim that my 6 dof model predicted it.

The model is super simple: fit HADCRUT sea-surface temps to a sum of two sine waves, with degrees of freedom for amplitude, wavelength, and phase for each. It does a much better job predicting current temps than most major climate models.

Radford Neal writes:

I don't think you will get meaningful results from such a regression. Even aside from all the data quality issues mentioned in earlier comments, the nature of the problem just doesn't allow for discovering anything this way.

The theoretical basis for a CO2 -> temperature influence would imply that there is a variable lag from CO2 to temperature, so that a low-pass filtered version of the CO2 series is what is relevant. There is also lots of natural variability in temperature, which may be autocorrelated at high time lags. Together, these imply that there are only a few independent data points in the period where there is any data. When you also consider that CO2 has gone up monotonically at a not too variable rate, and lots of other things have also gone up monotonically over this period, providing alternate explanations (some such as land-use changes perhaps having some theoretical basis), demonstrating the effect of CO2 (or lack thereof) by this direct method is clearly hopeless.

warren writes:

I guess the answer to this is there is an absolute ton of stuff out there. Time delays are an issue. Cause and effect is an issue (does a warm PDO cause warming or does warming cause a warm PDO).

I suppose since you are asking this you know that the main historic data support (rather than theoretical or modelled support) is that scientists claim not to be able to explain the warming rate from 1950 to 2000 using only natural variables, ie without manmade CO2. Since there was no real warming from 1950 to 1978, this boils down to the argument that they believe that only manmade CO2 could explain the warming rate from 1978 to 1998.

1. There are folks who are dis-aggregating temperature history into a linear trend plus a cyclical factor. The reason for this is the conclusions about catastrophic man-made global warming are mostly formed by the temperature rise from 1978-1998. But that rise looks to be the combination of a linear trend and the rising part of a sine wave, meaning looking at rates in this period alone may overstate long term rates. Here is an example I did It also raises the issue that if there is a linear underlying trend since 1880, can we really attribute that to CO2?

2. Numerous people on the web have tried their hand. Here is an example

3. Here is one from academia. There are bajillions.

4. The field is rife with statistical mistakes. (read past beginning to comments at end). An economist might well be horrified at the analyses that get published in climate. Certainly statisticians frequently are.

Ben Haller writes:

The more crap you throw into the regression, the more it will be overfit and won't give you anything useful back. But it's worse than that. All of the random variables you suggest will probably be fairly correlated with CO2, for the simple reason that CO2 has been steadily rising, whereas (I would expect) church attendance has been slowly falling, the Dow Jones has been rising, and televisions per capita has probably been rising as well. Separating the effects of correlated variables in a regression is hard; the stronger the correlation, the bigger the dataset needed to do it. CO2 probably wouldn't dominate in such a regression, no. So what? We know from first principles that it shouldn't, even if it is causal. The point is that we have a mechanistic explanation for why CO2 would cause rising global temperatures. To conclude that it does not, in fact, have that effect, despite all of our understanding from basic physics why it should have that effect, we'd need overwhelmingly strong evidence. Whereas we have no mechanistic explanation for why church attendance, or the Dow Jones, or televisions per capita, ought to affect global temperatures – and thus no good reason to include them in a regression in the first place. Running the regressions you suggest would be an abuse of statistical methodology that any competent first-year stats student would call you out for. So... why exactly do you want to do it?

Luke Meehan writes:

Time series results from Trevor Breusch indicate that the last decade or so requires a warming trend to explain the outside-confidence high temperatures.

Doug writes:

"What happens if you regress annual global temperature 1880-2011 on CO2, linear trend, and other stuff trending positively or negative over this era? "

What you're suggesting would be regressing unit root time series against each other. You'd want to regress the annual changes in these values to be statistically meaningful.

Radford Neal writes:

Luke Meehan: Regarding the Breusch and Vahid paper, from a quick glance, it seems that it does not address the question of interest, which is whether or not the trend in temperature has changed since about 1950, which is when (it is generally accepted) the level of CO2 became high enough that one might expect it to have a noticeable effect on temperature. Instead, they test whether the values since 1960 are compatible with no trend, barely rejecting this hypothesis. But it is widely accepted that there has been a (non-anthropogenic) warming trend since the end of the "little ice age", around 1850, so this doesn't address anything that is in dispute.

David C writes:

This paper uses first Granger Causality, and then a combination of regression and a Monte Carlo simulation to estimate the relationship between CO2 and temperature. The data series is from 1959-2005.

I found several papers using regression analysis to get a better estimate of the warming trend, but I don't think that's what you wanted.

Tim Worstall writes:

"The list of regressors should ideally include not just other climatological variables, but placebo variables like church attendance per capita, the Dow Jones, televisions per capita, "

Reasonably famously the decline in the number of pirates correlates with the rise in CO2 concentration.

Grieve Chelwa writes:

@Vangel, you make a great point. Ross McKitrick of the University of Guelph, wrote an interesting paper in 2006 which argued that the concept of a global annual temperature, to put it mildly, is nonsensical. Abstract:

Physical, mathematical and observational grounds are employed to show that there is no physically meaningful global temperature for the Earth in the context of the issue of global warming. While it is always possible to construct statistics for any given set of local temperature data, an infinite range of such statistics is mathematically permissible if physical principles provide no explicit basis for choosing among them. Distinct and equally valid statistical rules can and do show opposite trends when applied to the results of computations from physical models and real data in the atmosphere. A given temperature field can be interpreted as both "warming" and "cooling" simultaneously, making the concept of warming in the context of the issue of global warming physically ill-posed.

[comment edited by commenter request--Econlib Ed.]

Glen S. McGhee writes:

Why would you want to regress non-linear events?

Chaotic phenomena are, well, chaotic. Climate is, if anything, complex, and simple regressions don't model anything that's complex (right?).

Roger Sweeny writes:


You are right that "Planet Earth is always like noon in a greenhouse" in that the average angle of the sun is always the same. However, the "greenhouse effect" of climate science and politics has little to do with the angle of solar radiation. It has to do with the frequency (wavelength) of solar radiation. (Yeah, "greenhouse effect" is a lousy term for it.)

Radiation from the sun comes in lots of different frequencies but it is concentrated in visible light. This light mostly travels through water vapor and carbon dioxide and methane and all the greenhouse gases. It is sometimes said that the greenhouse gases are "transparent" to visible light. Visible light from the sun largely reaches the earth and heats it.

The earth then radiates lots of this energy back. However, since the earth is much cooler than the sun, the radiation is much lower frequency (higher wavelength), largely infrared. Infrared does not easily pass through the greenhouse gases. Instead, much of it is absorbed and heats the air. Scientists sometimes say greenhouse gases are "opaque" to IR.

"Other things being equal," more CO2 in the atmosphere would mean a higher average global temperature. Of course, other things aren't equal--and we are remarkably ignorant about a lot of the "other things."

David Jinkins writes:

If you throw enough stuff into the regression, something is bound to be more correlated with temperature than CO2 levels. So what? Econometrics, unlike statistics more broadly, is about model testing. The reason many climate scientists are alarmed about CO2 levels is that they have a theory of why CO2 levels could be dangerous. If you have an alternative hypothesis about what is causing climate change, then we can test your hypothesis against the CO2 hypothesis.

Will writes:

@MingoV- you don't seem to understand how a greenhouse works. Glass is transparent in the visible, but not in the IR. The sun radiates very strongly in the visible, but plants and rocks radiate mostly in IR. So the sun pours energy in, in the form of radiation (what fraction of total potential output is taken in by the greenhouse WILL depend on the angle of incidence, but always some energy will be absorbed), but the re-radiated energy (which does not depend on the angle of the sun) gets trapped by the glass, and the greenhouse ends up hotter. IF the greenhouse has a minimal albedo, the maximum greenhouse effect is right at noon, contrary to your post.

Importantly, CO2, like glass, is transparent in the visible but not in the IR. No one should dispute that more CO2 = hotter, everything else held constant- the causal mechanism is measurable in a lab. The issue is whether there is anything to give negative feedback.

Vangel writes:

Ross McKitrick of the University of Guelph, wrote an interesting paper in 2006 which argued that the concept of a global annual temperature, to put it mildly, is nonsensical.

That is the point. If Bryan can't tell us what the global annual temperature really is and can't really figure out how it is calculated why is he so concerned about regressions?

This is a 'if you have a hammer' situation. Economists know a bit of math and are always trying to show off even when the application of the mathematical tools is very inappropriate. We see this every time they talk about some index that looks at aggregate price level changes, analysis of monetary velocity, etc. The fact is that the tools are inadequate to be applied to very complex systems in which sound methodology cannot be applied to come up with meaningful empirical data. But for some reason they keep trying and by doing so they pretend to know more than they actually do.

Bryan is a very smart fellow and seems to understand this but for some reason still implies that you can use mathematics even when it is inappropriate to do so. (And yes, I am fully aware that he is probably trying to show how inadequate the AGW methodology really is. If he wants to do that there is probably a much better way to show it as Ross McKitrick and Stephen McIntyre did when they discredited the hockey stick that was created by MBH98 and MBH99. What scares me is that Paul Samuelson made a full scholarship offer to McIntyre for a PhD in mathematical economics. Fortunately for the world McIntyre decided to become a mining engineer and had enough sense to discredit the AGW movement's attempt to use bad math to create hockey sticks out of random data.)

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