This study is leveraging a VAR model introduced in an earlier presentation to forecast global temperature out to 2100, and assess how likely are we to keep such temperatures at or under the + 1.5 degree Celsius threshold.

1. How likely are we to limit temperature increase to + 1.5
degree Celsius by the end of the Century?
This reflects agreement by the G20 summit in Rome on October 31, 2021
Gaetan Lion, November 5, 2021

2. Introduction
I will leverage the climate change models introduced within my presentation “Climate Change Models to
Estimate and Forecast Temperature”, September 2021.
You can find extensive background on these models at my original presentation at Slideshare.net
https://www.slideshare.net/gaetanlion/climate-change-model-250126342
You can also see a shorter overview of such models at my blog within the environment label category, post
dated October 30, 2021.
https://considerworthy.blogspot.com/search/label/environment
To forecast temperatures till the end of the century, I will use the VAR model with the LN(CO2 concentration)
as the causal variable and temperature anomaly level as the dependent or response variable. This same VAR
model was able to generate pretty accurate out-of-sample forecast of temperatures from 1982 to 2020 using
historical data until 1981 with no information whatsoever regarding the out-of-sample period (1982 to 2020).
On the next slide, I am just copying slide 50 of my original presentation. This slide outlines how surprisingly
successful this VAR model was in forecasting the 1982 to 2020 period with no information whatsoever. Given
this empirical success, it is going to be informative what this model temperature forecast looks like over the
2021 – 2100 period, using historical data out to 2020.
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3. A VAR model w/ 1 lag using LN(CO2) can predict with no info whatsoever!
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Temperature Anomaly. VAR w/ LN(CO2) forecast 1 lag, 1982 - 2020. P.I. 95%
Actual VAR fcst Lower Upper
Just using LN(CO2) instead of CO2 as
our second Z variable within a VAR
model with 1 lag generates a
surprisingly good forecast of the
temperature anomaly over the 1982
– 2020 period with no information
whatsoever regarding this period!
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This is rather astonishing.
As shown, the VAR forecast does
overestimate temperature by just
about 0.1 degree Celsius at the onset
in 1982 and in 2020. That’s a very
small error given the model is not fed
any information.

4. VAR model fits historical data really well
Well, frankly fitting the historical data very well
is the easy part. Just about any VAR model
using level variables will inevitably do that.
(Note that the variables are cointegrated. So
the mentioned variables having unit roots is not
a statistical issue).
Far more impressive and relevant, is that this
same VAR model was able to predict
temperatures pretty well over the 1982 – 2020
period using historical data up to 1981, as
shown on the previous slide.
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Temperature
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over
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VAR Model historical fit
using LN(CO2 concentration as causal variable) with 1-lag
Actual Est.
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5. So, what does the VAR model temperature forecast out to 2100 look like?
This VAR model forecasts out to 2100 is even more
severe than the most severe scenarios of the recent
IPCC assessment (SSP5-8.5) shown below. By 2100,
the VAR model forecasts a + 5.3 Celsius increase vs.
4.3 Celsius increase for the IPCC scenario SSP5-8.5.
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The temperature anomaly crosses the 1.5 Celsius in 2040.
It crosses 2.0 Celsius in 2053.
It crosses 2.5 Celsius in 2064.
It crosses 3.0 Celsius in 2072.
It crosses 4.0 Celsius in 2086.
It crosses 5.0 Celsius in 2098.

6. Can a model, that fit the historical data and predicted out-of-sample 1982 – 2020 very well, be
way off when predicting over the 2021 – 2100 period?
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Temperature
Anomaly
in
Degree
Celsius
over
1850
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1900
average
VAR Model historical fit
using LN(CO2 concentration as causal variable) with 1-lag
Actual Est.
… Yes, it can! See why on the next slide.

7. The VAR model forecasts extremely high CO2 concentration even when
compared with IPCC scenario SSP5-8.5.
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CO2
concentration
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VAR model CO2 forecast
IPCC most recent scenarios
By 2100, the IPCC scenario SSP5-8.5 forecasts that CO2 concentration will reach 1,120 ppm. Meanwhile, the VAR
model forecasts it will be 1,453 ppm. And, that is how the VAR model overshoots by forecasting a temperature
increase by 2100 that is about 1 degree Celsius higher than the most severe IPCC scenario (SSP5-8.5).
However, if we focus on shorter horizons out to 2050 the VAR forecast in CO2 concentration is quite reasonable
and in line with several of the IPCC scenarios. This is also the case for the temperature increase shown earlier.

8. Temperature forecast vs. CO2 Concentration
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Temperature
Anomaly.
Celsius
CO2 concentration in ppm
VAR vs. IPCC scenarios temperature anomaly
VAR IPCC
The table above measures the temperature increase sensitivity to
CO2 concentration. We note that the temperature anomaly
estimates generated by a simple OLS regression model
(temperature level ~ LN(CO2 concentration) introduced in our
earlier presentation generates nearly identical estimates vs. our VAR
model. In turn, those estimates are not far off from the ones
derived from the various IPCC scenarios.
Temperature anomaly estimates given CO2 concentration
CO2 ppm OLS VAR IPCC Scenario By
425 0.98 1.00 1.45 SSP-1-1.9 2100
470 1.33 1.33 1.75 SSP1-2.6 2100
500 1.54 1.57 2.00 SSP-3-7 2040
600 2.17 2.19 2.75 SSP2-4.5 2100
700 2.70 2.71 2.90 SSP-3-7 2080
875 3.46 3.48 3.70 SSP-3-7 2100
900 3.56 3.55 3.80 SSP5-8.5 2080
1000 3.92 3.93 4.03 SSP5-8.5 2090
1100 4.25 4.26 4.25 SSP5-8.5 2100
Temperature anomaly estimates IPCC scenario
The graph indicates that the VAR model underestimates a
bit temperature sensitivity to CO2 concentration at the
lower CO2 concentration levels. But, as such levels
increase, the VAR model temperature estimates and the
IPCC scenarios rapidly converge.

9. How likely are we to limit temperature increase to + 1.5 degree Celsius by the end of the
Century? …
Extremely unlikely because we have only + 0.4 degree Celsius to work with
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The most current data would indicate we are already at + 1.1 degree Celsius. So, we have only 0.4 degree Celsius as a
margin over the next 80 years or so. Meanwhile, over the past 40 years temperature has increased by 0.7 degrees.
This would suggest that over the next 23 years we would cross the + 1.5 degree Celsius threshold. Notice that this back
of the envelope estimate is fairly much in line with both the IPCC scenarios and the VAR model (which generates a
pretty reasonable forecast out to 2050 or so).

10. How likely are we to limit temperature increase to + 1.5 degree Celsius by the end of the
Century? …
Extremely unlikely because CO2 emissions are projected to rise fairly rapidly (EIA most recent
forecast)
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The U.S. Energy Information Administration (EIA) released its most recent
“International Energy Outlook 2021 (IEO2021)” on October 6, 2021. And,
they forecast that CO2 emissions (that gets cumulatively captured in CO2
concentration) will continue to rise fairly rapidly till the end of their forecast
period in 2050.
Quoting from their report’s conclusion:
“If current policy and technology trends continue, global energy consumption
and energy-related carbon dioxide emissions will increase through 2050 as a
result of population and economic growth.
Oil and natural gas production will continue to grow, mainly to support
increasing energy consumption in developing Asian economies.”

11. Considerations
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A model that fits the historical data and predicts out-of-sample over a long period of time may not necessarily
generate reasonable scenarios over an even longer prospective horizon. This is probably relevant to any models
that have autoregressive components such as VAR, ARIMAX, ARDLs, and other similar models.
However, while the VAR model did generate rather outlying forecasts by 2100; when looking at horizon out to
2050, its forecasts were pretty much in line with the IPCC scenarios.
Both a simple OLS regression and the VAR model generated temperature estimates in response to CO2
concentration scenarios that were pretty reasonable and in line with the IPCC scenarios. Thus, these models at
least got the economic carbon sensitivity right. Where the VAR model went off the road is in projecting CO2
concentrations that were too high during the second half or especially third quarter of this century.
This review suggests that attempting to maintain temperature increase at the 1.5 degree Celsius level by the end
of the century may turn out to be extremely challenging if not unlikely. Keep in mind that we are probably at the +
1.1 degree Celsius level as we speak. So, we have very little room to work with over the next 80 years or so.
Reaching this aggressive goal may entail drastic reduction in our historical demographic growth, economic growth,
and economic growth sensitivity to CO2 emissions. And, that is not what the most recent IEA forecast out to 2050
anticipates. Instead, the IEA anticipates ongoing reasonably robust economic growth and rising CO2 emissions
(resulting in rising CO2 concentration) driven by “increasing energy consumption in developing Asian economies.”