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|
* 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.
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.
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.