Guest essay by James McCown
Oxford economists Felix Pretis and David Hendry (henceforth Pretis), published a critical paper, with a very patronizing and sanctimonious tone, in 2013 in Earth System Dynamics to comment on earlier research by Beenstock, Reingewertz, and Paldor (2012), (henceforth Beenstock) in the same journal. Amazingly, they didn’t bother to note that their criticisms, if accurate, also invalidate the results of previous researchers who support the AGW theory.
Beenstock’s research concerns the issue of whether or not there is a statistical relation between the radiative forcing of greenhouse gases (GHG), and atmospheric temperatures, using advanced statistical methods that were developed by economists. There have been a number of researchers who have previously used this methodology to discern a relation between the GHGs and temperature, including both climatologists and economists. The latter include James Stock at Harvard, one of the foremost experts at time series econometrics.
Beenstock’s paper was in response to earlier papers by pro-AGW researchers Stern and Kaufman (2000), Kaufman and Stern (2002), Kaufman, Kauppi and Stock (2006), and Liu and Rodriguez (2005), and several others, who claimed to have found an equilibrium relation between radiative forcing from GHGs and atmospheric temperatures. The main contribution of Beenstock was to show that there cannot be an equilibrium relation between temperatures that are integrated of order one, I(1), and GHGs integrated of order 2, I(2), unless they are polynomially cointegrated. And Beenstock show they are not polynomially cointegrated.
Beenstock’s conclusion (from their abstract) is:
…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.
Pretis criticize Beenstock’s use of spliced data for atmospheric CO2 and N2O, and criticize them for not stating that this data comes from a variety of different sources. However, they do not criticize the previously mentioned pro-AGW researchers who used the exact same data.
Pretis criticize Beenstock for finding the time series properties of the radiative forcing of the three human-emitted GHGs to be integrated of order 2, I(2), even though the pro-AGW researchers came to the same conclusion. And they don’t bother to mention that the pro-AGW researchers also found the GHGs to be I(2).
Pretis’ comment shows dismayingly flawed logic. To give an analogy to what they have done: Suppose that Kaufman claimed to have built a house, from the foundation to the roof. Beenstock claim that Kaufman could not have done so, by proving that they never shingled the roof. Pretis reply that Beenstock are in error, because Pretis prove that the foundation was never laid. Therefore Beenstock must be wrong and Kaufman is right! The more I think about it, the more ridiculous it sounds.
Pretis point out there is a structural break in the annual data for CO2 at 1957 (Hardly surprising since that is the point at which the data were spliced from the different sources), then they run Augmented Dickey-Fuller (ADF) unit root tests (Said and Dickey, 1984) on the first differences of the data for the two subperiods from 1850 – 1957 and 1958 – 2011 (See Table 1 of Pretis), and conclude that the CO2 radiative forcing series cannot be I(2). However, Pretis omitted tests of the levels of the series, which would enable the researcher to determine whether the GHGs are I(1), which could potentially be cointegrated with the I(1) temperature series, as the warmist researchers have claimed.
I tested the CO2 radiative forcing for the two subperiods in levels, first differences, and second differences. I used the ADF test, and also the test by Kwiatkowski, Phillips, Schmidt, and Shin (1992) (KPSS). For the latter 1958 – 2011 period, I conclude the series is I(1), as did Pretis. However, for the earlier 1850 – 1957 period, which uses CO2 data from ice core measurements by Etheridge et al (1996), I got the following results:
| ADF with Trend & Constant | ADF D-lag | KPSS with Trend & Constant | |
| Levels | -3.496* | 2 | 0.126 |
| 1st Difference | -3.807* | 0 | 0.078 |
| 2nd Difference | -13.288** | 0 | 0.039 |
* Rejects null hypothesis of a unit root at 95% confidence
** Rejects null hypothesis of a unit root at 99% confidence
The ADF D-lag is the number of lags included in the ADF test, selected using the Schwarz criterion.
The KPSS test has the null hypothesis of stationarity with a trend and constant, versus the alternate hypothesis of a unit root. The results fail to reject the null hypothesis of stationarity at 95% confidence or higher.
The results of both tests indicate that time series of the levels of CO2 radiative forcing from 1850 to 1957 is well-modeled by a trend stationary process with no unit root. That is, I(0). An ordinary least squares regression of the series on the year gives the following relation:
RFCO2 = -9.935203+0.005346 x YEAR
where RFCO2 is the radiative forcing from the concentration of carbon dioxide in the atmosphere, converted to radiative forcing using the method of Myhre et al (1998). This regression has an adjusted R-square of 0.988 and the slope coefficient has a t-statistic of 41.34.
The CO2 radiative forcing series is very close to a straight line. Since it does not have a unit root, it cannot be cointegrated with the nonstationary temperature data for the period from 1850 to 1957. See the following graph of the series:
Kaufman and Stern (2002) give their economic justification for the nonstationary time series of global average temperatures:
…changes in radiative forcing might introduce a stochastic trend in temperature if the radiative forcing variables have a stochastic trend. This is likely because the concentrations of trace gases and sulfate aerosols are driven by anthropogenic emissions, which are determined by the stochastic trends that characterize many macroeconomic time series.
But as can be seen in the graph above, and the tests of stationarity of CO2 I have conducted for the 1850 – 1957 period, the GHG that is widely viewed by the warmists as the primary culprit has a trend-stationary process. This leads me to believe that if the CO2 concentration is accurately measured by Etheridge et al (1996), then it is more likely the result of a natural process than from industrial sources.
The editors of Earth System Dynamics did not allow Beenstock to publish a response to Pretis’s comment. Beenstock made an informal response here: http://www.earth-syst-dynam-discuss.net/4/C118/2013/esdd-4-C118-2013-supplement.pdf.
The last two sentences of Beenstock’s response are telling:
The main difference between this [warmist] literature and our paper is that we do not think that greenhouse gas emissions have a long term effect on Earth’s climate. Perhaps this is why HP waited until 2013 to voice their criticisms rather than 1997 when this literature was pioneered by Stern and Kaufmann.
Pretis have opened up a can of worms through their comment, and have likely done more damage to the warmist cause than help.
Furthermore, as an economist who has done research on pre-World War II data, I am struck by something I don’t see in the above chart. If the increasing concentration of carbon dioxide in the atmosphere is caused by burning fossil fuels, which has increased significantly during the industrial era, then why don’t we see any decrease, or at least a deceleration, during the great depression of 1929 to 1933?
The great depression had severe effects on two of the largest industrial economies: the USA and Germany. Industrial production in the USA, from 1929 to 1932, dropped by 46%. Coal production in the USA dropped from 608 million short English tons in 1929 to 359 million in 1932. In Germany, industrial production dropped by 42% from 1929 to 1932. German coal production dropped from 163 million metric tons in 1929 to 104 million in 1932.
And yet, according to Etheridge et al (1996), the concentration of carbon dioxide in the atmosphere increased from 307.2 ppm in 1929 to 308.9 ppm in 1933. And the concentration kept increasing every year after that until 1942. There was no deceleration in the increases. Either the theory that burning fossil fuels adds to the atmospheric concentration of CO2 is flawed, or perhaps Etheridge’s estimates of the concentration of this GHG are inaccurate. I don’t know which is the case.
References
Beenstock, M., Y. Reingewertz, and N. Paldor (2012). Polynomial cointegration tests of anthropogenic impact on global warming. Earth Syst. Dynam., 3, 173–188.
Etheridge, D. M., Steele, L. P., Langenfelds, L. P., and Francey, R. J.: 1996, ‘Natural and anthropogenic changes in atmosphericCO2 over the last 1000 years from air in Antarctic ice and firn’, J. Geophys. Res. 101, 4115–4128.
Liu, H. and G. Rodriguez (2006), Human activities and global warming: a cointegration analysis. Environmental Modelling & Software 20: 761 – 773.
Kaufmann, A., Kauppi, H., and Stock, J. H.: Emissions, concentrations and temperature: a time series analysis, Climatic Change, 77, 248–278, 2006.
Kaufmann, R. K. and Stern, D. I.: 2002, ‘Cointegration analysis of hemispheric temperature relations’, J. Geophys. Res. 107, D210.1029, 2000JD000174.
Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., and Shin, Y.: Testing the null hypothesis of stationarity against the alternative of a unit root, J. Economet., 54, 159–178, 1992.
Myhre, G., Highwood, E. J., Shine, K. P., and Stordal, F.: New estimates of radiative forcing due to well mixed greenhouse gases, Geophys. Res. Lett., 25, 2715–2718, 1998.
Pretis, F. and D. F. Hendry (2013). Comment on “Polynomial cointegration tests of anthropogenic impact on global warming” by Beenstock et al. (2012) – some hazards in econometric modelling of climate change. Earth Syst. Dynam., 4, 375–384.
Said, S. and Dickey, D.: Testing for unit roots in autoregressive moving average model with unknown order, Biometrika, 71, 599–607, 1984.
Stern, D. I., and R. K. Kaufmann, Detecting a global warming signal in hemispheric temperature series: A structural time series analysis, Clim. Change, 47, 411 –438, 2000.
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James McCown an economist with Toltec Group, an economic consulting practice in Oklahoma and has a PhD in economics from Ohio State. You can see some of his research here: http://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=154208.
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I love a detailed report that treats me with the dignity of assuming I know what all those words mean. Now I shall have to learn some new words to understand this but in the meantime I “get” that the great depression ought to show up as a non-linearity of the CO2 graph. I also sense that CO2 doesn’t stay in the atmosphere for a thousand years by seeing that dip at 1940. That’s a pretty substantial dip at a time of intense industrial (war-making) activity.
“…then why don’t we see any decrease, or at least a deceleration (of CO2 levels), during the great depression of 1929 to 1933?”
That’s the first time I’ve heard of that question being asked and I’m looking forward to any answers.
AGW = All Gone Wrong!
It is amusing the contortions to perpetuate the alarmist agenda. They are basically stabbing each other in the back now. It will only get bloodier as the panic increases.
poor old MET,
http://notrickszone.com/2014/06/24/laughing-stock-met-office-2007-peer-reviewed-global-temperature-forecast-a-staggering-failure/
An outstanding analysis, my thanks. There is one missing equation that should appear between the following lines, viz:
I’ll need to re-read this, but very well done.
w.
REPLY: Yes that was a transfer error from MS-Word, fixing now. Thanks – Anthony
”Also, their criticisms apply to the existing literature […]”.
“First, Beenstock et al. (2013) inappropriately reference the existing literature claiming a “standard result” that is not standard (see section 1.2). Second, our criticisms of working with this data would then naturally extend to other papers making the same strong assumptions as Beenstock et al. (2012) make. This particular point raised by Beenstock et al. (2013) re-enforces the fact that our critique is relevant to their work. Most of the papers cited here do not make this strong claim of all anthropogenic series being I(2) and do not over-rely on this assumed property.”
http://www.earth-syst-dynam-discuss.net/4/C233/2013/esdd-4-C233-2013-supplement.pdf
“Also, their criticisms apply to the existing literature which we reviewed in our paper, including Kaufmann, Kauppi and Stock (2006, 2010). The main difference between this literature and our paper is that we do not think that greenhouse gas emissions have a long term effect on Earth’s climate. Perhaps this is why HP waited until 2013 to voice their criticisms rather than 1997 when this literature was pioneered by Stern and Kaufmann.”
Or, perhaps, just perhaps, the calender year 1997 is 15 years BEFORE the 2012 POS Beenstock paper. And, perhaps, just perhaps, 2013 is one year AFTER the 2012 POS Beenstock paper.
James McCown:
Thankyou for your very fine analysis. It concludes saying
There is a third possibility which you have not mentioned and we investigated in one of our 2005 papers
(ref. Rorsch A, Courtney RS & Thoenes D, ‘The Interaction of Climate Change and the Carbon Dioxide Cycle’ E&E v16no2 (2005) )
The possibility you do not mention is that the equilibrium of the carbon cycle system has been disturbed and the system is adjusting to the new equilibrium. Some processes of the carbon cycle have rate constants of years or decades and, therefore, the system takes decades to adjust to a new equilibrium.
Using that assumption we demonstrated it is possible to model the atmospheric CO2 rise indicated by the Mauna Loa data as being caused by any one of several mechanisms with either a natural or an anthropogenic cause. Each of our models matched the data to within reported measurement error for each year.
The assumption of anthropogenic CO2 overloading the carbon cycle induces the IPCC to use its Bern Model which requires unjustifiable 5-year smoothing to obtain agreement between that model’s output and the empirical data.
Also, the dynamics of the seasonal variation indicate that the carbon cycle can sequester all of the emitted CO2 (both natural and anthropogenic) of a year but it does not. This apparent paradox is explicable by the assumption that the equilibrium of the carbon cycle system has been disturbed and the system is adjusting to the new equilibrium.
If the assumption that the equilibrium of the carbon cycle system has been disturbed and the system is adjusting to the new equilibrium is correct, then the observed rise in atmospheric CO2 concentration is a result of whatever has caused the equilibrium to change. The most likely cause is the rise in global temperature which is observed as recovery from the Little Ice Age (LIA), but other causes are possible and the anthropogenic emission of CO2 is one of them.
Hence, it is possible (although unlikely) that the anthropogenic CO2 emission is causing the rise in atmospheric CO2 while it is also possible that Etheridge’s estimates are correct.
Richard
Either the theory that burning fossil fuels adds to the atmospheric concentration of CO2 is flawed, or perhaps Etheridge’s estimates of the concentration of this GHG are inaccurate. I don’t know which is the case.
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Yep….and I think the same every time I look at this
http://drtimball.com/wp-content/uploads/2012/05/Callendar-circle.gif
http://en.wikipedia.org/wiki/Keeling_Curve
Have a look at the details of the Keeling CO2 curve. There is a very odd SINGLE cycle to the rise and fall during the year. The peak is in late April, and the lowest level, in end September, beginning October. The annual rise is the difference between the rise and fall, of course, and attributed to power-plant, fossil fuel use. The cycle is attributed to “natural causes”. Yet what processes start net CO2 production in September and end net production in May? And why only one?
Planet Earth has a two-hemisphere biotic environment of plant growth and decay. The two hemispheres are opposite in time, though. As the Northern Hemisphere comes out of winter in March through June, the south is going into winter. There is a non-equal distribution of land, sea and rock to the two hemispheres, but one would expect a double peak and valley, not just the slight change in ONLY the rise (February).
What I see here is a regional dominance of the planetary C02 cycle. Does plant matter really rot DURING THE WINTER of the Northern Hemisphere. Or are we seeing degassing of the oceans based on both temperature and phytoplancton activity? And if it is the ocean, then are we witnessing the dominance of a particular patch of ocean that degasses from late September until May, and then absorbs CO2 from Jay until late September?
If we can’t pin down where this “natural” CO2 is coming from to give us this nice cyclicity, then how can we know that “most” of the rise is man-made, and now a function of natural (oceanic) processes at this time?
James
Succinctly stated.
Suggest explaining polycointegration of Ln(CO2) vs of CO2
where CO2 = Anthropogenic(t) + Natural(t) + Preindustrial
I find it suspicious that the plot above stops at 1960 .. right AFTER the 1945-1975 COOLING trend of land-based temperature anomalies was changing. Thus, he is plotting the rise in temperatures 1915 – 1945, the “static” temperatures 1940-1950, and the slight cooling 1945-1960. But ignoring the continued decrease 1960-1975, the “significant-> catastrophic” warming 0f 1975 – 1998, and the static temperatures 1996 – 2014. Those time-frames will show some significant trend differences in supposed warming “forcings” that will be instructive.
Also, but very difficult to extract from the yearly NH-SH heating/cooling trends, the significant change in “forcings” due to the monthly CO2 changes should be visible as well: If a change in CO2 from 1945 to 2014 is “significant” then the change in temperatures compared should also be visible when compared between years.
Doug Proctor: Yet what processes start net CO2 production in September and end net production in May?
No natural processes come to mind, but there is the matter of all those Northern Hemisphere residents who respond to cold weather by firing up their furnaces, or otherwise burning stuff to keep warm.
Hi David L. Hagen:
All of the researchers mentioned use the methodology of Myhre et al (1998) to convert the GHG concentrations to radiative forcing. And they are logarithmic functions. But actually it shouldn’t make any difference for cointegration tests, so long as the function is a monotonic transformation.
In a phone conversation Hu McCulloch raised questions about Myrhe’s conversion functions. He said they should be something more like Rf(x) = 1 – e^(-x), since the radiative forcing will cease when the GHG is absorbing 100% of the radiation in some band of the infrared spectrum. If we used that for the conversion, and then did unit root and cointegration tests, they would likely yield different results.
Doug Proctor says:
June 24, 2014 at 11:15 am
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Plant matter does indeed continue to rot during northern hemisphere fall and winter.
Even in the coldest days of winter, most of the southern tier of states in the US are still above freezing, sometimes well above. This should be true for Europe and Asia as well, though I don’t know by personal experience. Even as you get up towards the Canadian border, the land isn’t frozen all of the time. In fall there are a number of weeks after plants go dormant but before the first frost.. Similar in spring, snows have melted weeks before the first buds appear.
CO2 is rising for 98% natural reason. See: http://wattsupwiththat.com/2013/06/04/an-engineers-take-on-major-climate-change/
Richardscourtney:
Thanks, I shall read your paper.
Why don’t we see comensurate acceleration of levels now?
John Slayton says:
June 24, 2014 at 11:38 am
Doug Proctor: Yet what processes start net CO2 production in September and end net production in May?
No natural processes come to mind, but there is the matter of all those Northern Hemisphere residents who respond to cold weather by firing up their furnaces, or otherwise burning stuff to keep warm.
And there is the small matter of all those Northern Hemisphere residents who respond to warm weather by firing up their air conditioners to keep cool. In the South the most expensive season of the year for electricity is summer.
Yet what processes start net CO2 production in September and end net production in May?
A much better way to ask the same question is: What CO2 sequestering process slows beginning in September and doesn’t recover till May?
And the answer would be photosynthetic sequestering of vegetation in the NH.
Ron Voisin”;
The CO2 sequestering in that period for the SH slows because temperature starts to rise and the SH is mainly ocean. This might be an explanation.
Learned lunatics all, or should that be solatics? Get a life gentlemen, your education and skills not to mention the benefactors purse are be wasted.
I credit the denizens of this site (and at CA) that I now have a fairly decent working understanding of statistics and can comprehend the important parts of Mr McCown’s essay — even some of the more esoteric stuff! If you would have told me 15 years ago that I would one day be able to even loosely understand a conversation between statisticians, I would have laughed out loud.
An edifying read, thanks.
The global carbon emission estimates according to the U.S. Department of Energy show a vast increase post WW2:
http://cdiac.ornl.gov/trends/emis/graphics/global.total.jpg
ICU: http://www.earth-syst-dynam-discuss.net/4/C233/2013/esdd-4-C233-2013-supplement.pdf
thank you for the link. That should definitely be read by anyone interested in McCown’s essay.
The Beenstock et al paper is worth reading for anyone interested in these attempts to use advanced vector autoregressive models in causal analyses of what are probably nonstionary data (in any differences — differencing adds problems along with solving problems.) ESDD seems to have put up a vigorous and informed debate over the Beenstock paper and the criticism of it. That looks like something that we should encourage.