State Space Models

All state space models are written and estimated in the R programming language. The models are available here with instructions and R procedures for manipulating the models here here.

Wednesday, November 19, 2025

World-System (1960-2100) CO2 Emission Forecast

 



November 12, 2025. The New York Times is report that Carbon Dioxide Emissions Head for Another Record in 2025. The time plot above (with Bootstrap 98% Prediction Intervals) makes the same forecast from my WL20 model. Nothing has changed since 2008, the end of my historical data in this model. How are we to understand this projection?


The IPCC has accumulated a mountain of scientific results around CO2 Emission forecasts and produced a number of alternative Emission Scenarios for the future (see the Boiler Plate). Climate Change Deniers can pick at the underlying models and the Emission Scenarios, but the underlying Kaya Identity (directed graph above) is true by definition. An increase in population (N) or any of the other extensive variables (L=Labor Q=Production and E=Energy Use) will increase CO2 Emissions unless the intensive variables (coefficients n=N/L, q=Q/L, e=E/Q, and c=CO2/E) are reduced (you can calculate the coefficients yourself from available historical data).

It can also be argued that the Kaya Identity has no feedback effects. As conditions in the World System deteriorate due to increasing Global Temperature (T), it should feedback to reduce all the extensive variables. For example, population growth should be reduced by heat waves, crop failures, sea level rise, famines, production and unemployment declines etc. This is where state space DCM models (see the Boiler Plate) directly estimate feedback effects in the World System (see the WL20 model here and the Measurement Matrix in the Notes below). The feedback effects are from Environmental Controllers (W2=0.7705 LP - 0.235 T) and World Markets (W3 = 0.712 P.Oil. - 0.241 OIL - EF 0.293) on Overall Growth, W1.

Unfortunately, the feedback effects are not strong enough to limit the Kaya Dynamic, that is, change the intensive coefficients. The forecast graphic at the beginning of this post, whether CO2 is driven by Carbon Emissions or driven by the World System, predicts continued exponential growth.


One way to change the Kaya Dynamic is to reduce the growth rate of Carbon Emissions in the Kaya Coefficient model (see the notes below) is to reduce the Growth Coefficient in the System's matrix from 1.07917 to 1.07916  (a very small change that produces the graphic above). In other words, very small changes in Carbon growth rates, when linked to the World System, produce large reductions in Emissions. 

Unfortunately, since the World System is cyclical, emissions start to growth again around 2100. I would expect that if Carbon emissions hit zero before the 21st Century, the World System itself  would be subject to changes that are only speculative in 2025.

Notes

WL20W Measurement Model


CO2 Model

Kay Coefficient Model







WL20 Carbon Model





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