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, June 17, 2026

Switzerland (1960-2100) Population Forecasts

 



June 14, 2026 Switzerland Rejects Measure to Cap Its Population at 10 Million from the NY Times. The referendum was about limiting migration after the number of residents rose by more than a quarter since 2000, but it was framed around affordability and sustainability.

The Population Cap (solid red line in the graphic above) proposed for Switzerland will not automatically be reached by any of my forecasting models, although the stable Business-as-Usual (BAU) model (see below) might eventually reach a steady state at a level lower than 10 Million after 2100. 

The best forecast (using the Akaike Information Criterion) is the CH_LM (Late Modern) model driven by Western Europe (WE, the dashed red line in the graphic above, state-space model presented below). However, linking to the EU (see below) breaks the Population cap around 2030. Notice that linking to the US leads to Population collapse.

For more information about Switzerland, view the Blog Roll: Switzerland. The video at the beginning of the Blog Roll explains why, even though the Population Cap referendum failed, it will keep coming up in the future and will probably pass at some point.

The forecasts at the beginning of this post show the Geopolitical cross-pressures Switzerland is under. Germany (WE, Western Europe) and the US are Switzerland's largest trading partners (see the DE_LM model below, which also leads to Population collapse). On the other hand, Switzerland is "highly developed free-market economy, ranked first in the world since 2015 on the Global Innovation Index (Wikipedia, see below)". To limit Population (without the cap) it could well chose to "go it alone" with the BAU model. 

It is also interesting that the Population cap, pushed by the right-wing Swiss People's Party, serves Environmental goals. 


Using the Kaya Identity, Population Stability (N) would stabilize CO2 Emissions and, ultimately, Global Temperature (T). Eventually, these two forces may come together and create a Steady-state Economy in Switzerland.


For more information about Switzerland, view the Blog Roll: Switzerland.

Notes

Wikipedia Links

AIC Statistics


All of the Akaike Information Criterion (AIC) Statistics have values in the 800 range except for the RW Model (Random Walk), which is best in the short-term (year-to-year).


CH_LM Western Europe Input


The CH_LM Model (WE, Western Europe Input) is stable and  provides the best Attractor Path, but it breaks the 10 million Population cap around 2030. From ChatGPT:


Switzerland, since it is not an EU member, is not obliged to accept migration from other EU members or link it's population to the EU




CH_LM BAU Model


The BAU model is stable and reaches a steady state after 2100 below the 10 million Population Cap.

CH_LM US Input




The CH_LM US Input model is stable but leads to population collapse with strong negative forces from the US Feedback components, US2 and US3.

CH_LM_N Model with DE_LM input


The CH_LM_M DE Input model is unstable and leads to population collapse in Switzerland.




Friday, May 15, 2026

East-Asia Pacific: Alternate Futures

 


May 15, 2026 Trump-Xi summit ends on cordial note but no breakthroughs ... - CNN

President Trump seems attracted to the old idea of Spheres of Influence when pursing Geopolitical Alignments. Critics argue that the idea is useless, at least for the US and China in the 21st Century. But President Trump presses ahead, leaving Europe and NATO while focusing more directly on Latin America. The idea seems to be that China's Sphere of Influence would naturally be the East-Asia Pacific Region (EAP). In this post, I use the EAP_L20 Model to ask what type of Geopolitical Alignment (if any) would be best for the people of the Indo-Pacific.

All of the Geopolitical Alignments for the EAP Region are unstable (except with China) while alignment with China (CN) produces rapid growth-and-collapse out to 2100.


In other words, allowing CN to assert it's Sphere of Influence over EAP would produce growth and stability benefits for the Indo-Pacific. China, however, does not seem to be interested.



Notes

Measurement Model



AIC Statistics



EAP_L20 Model CN Input



Sunday, March 22, 2026

Alternate Geopolitical Alignments for Israel

 



What is the "best" Geopolitial Alignment for Israel? In this post, I look at some options: (1) None (Business-as-Usual, BAU, or Muddling Along, Random Walk, RW), (2) Alignment with the Region (Middle East North Africa, MEA), (3) Alignment with the World System (W) or (4) Alignment with the US. Google AI reports the Conventional Wisdom:


However, the first question is "what do we mean by best?"

In terms of Systems Theory, the question is whether a Steady State Economy in Israel (and the Middle East) would be best or whether the Neoclassical Economic Dream of unstable, endless exponential growth is best. I cannot answer the question for policy makers even though endless economic growth is not possible on a finite planet. We just have to keep the question in the back of our minds as we are evaluating Geopolitical futures for Israel.

Another more specific question is whether we are interested in the short- or long-term? In the short-term, Israel is at War with Iran and currently aligned with the United States. So, the Long-term Attractor Path is of more interest since the path is unknown.

Using various IL_L20 Models, I ran five alternatives plotted in the graphic at the start of this post.  The best long-term model, which provides short-term exponential growth and long-term stability, is the IL_L20 MEA Input model (see the Notes below).

The second-best option is the IL_L20 BAU Model, but it is unstable. As a policy counterfactual, consider stabilizing the BAU model (see the Notes--stability involves reducing growth rates). Under a stable BAU regime, the IL_L20 Model reaches a Steady State around 2150 and provides over a century of continued growth for Israel.

Interestingly enough, alignment with US input is not best because the model is quite cyclical (see the Phase Diagram of the IL_L20 US-Input Model here). The prediction from US-Input model is that, after the War with Iran, the US will direct strategic attention elsewhere (back to Asia?) as happened after past Peace Agreements.






Notes

More readings:
You can run the IL_L20 model, written in R-codehere. Instructions in the code show how to stabilize the system. Other models for the Middle East and North Africa are available here.

IL_L20 Measurement Model


Three Component State Variables explain over 98% of the variation in the indicators: IL1 = (Overall Growth), IL2 = (LU - KOF - EF) Unemployment Controller and IL3 = (EF + L  - KOF - HDI) Environmental-Labor Controller.



IL1 AIC Statistics


The AIC Statistics are all closely grouped meaning that there is not one, dominant Geopolitical model.

IL_L20 BAU Model


The IL_L20 BAU Model is unstable and cyclical.

IL_L20 BAU Model Controlled


The IL20 BAU Controlled Model is stable and cyclical.




The historical time plot for the IL_L20 BAU Model is presented above.


The historical time plot for the stabilized IL_L20 BAU model is presented above.


IL_L20 MEA-Input Model


The IL_L20 MEA-Input Model provides the best attractor path. However, it seems quite unlikely that a stable Middle East will happen anytime in the foreseeable future.









Wednesday, March 11, 2026

Future Scenarios for Iran




In an Opinion piece for the NY Times How Does This End? Four Scenarios for What Comes Next With Iran, Bret Stephens argues that there are four likely future scenarios for the War in Iran: (1) Regime Change, (2) Regime Modification, (3) Both sides declare 
victory and (4) the Realistic Path, US seizes Kharg Island (see the video above which argues that the "Realistic Path" is a trap). These scenarios are all relatively short-term.

My interests are in more long-term Geopolitical Alignments that might benefit Iran. It seems that most of the World-System has abandoned Iran. Russia, China, and the EU are all sitting on the sidelines while the US and Israel continue an Air War. And, my simulations with the IR_LM model show that leaving Iran to "go it alone" (the Business-as-Usual or BAU model) produces the best future prospects (see the simulations here). The US and Israel seem intent on not letting the BAU Scenario go forward.

I asked ChatGPT about the Geopolitical Consequences of the current US-Israel-Iran War:


I can investigate the effects of a Global Oil Shock by using the WL203 Model.



The third component state variable (see Notes below) is dominated by Oil Prices. A large one standard deviation shock to the W3 component (an Oil Price Shock and associated effects: Wheat Prices, Oil Production and Ecological Footprint) produces the shock decomposition above. Overall growth in the World System (W1)  takes a negative shock that is never fully recovered. The same is true for the W2 state variable (an Environmental Controller); the negative shock is never recovered. Eventually, however, Oil Price Controller (W3) returns to the attractor path.


Notes

Friday, February 27, 2026

Is The Green Transition Over?

 


Feb 27, 2026  The New York Times (today) published an article titled Don’t Look Now, but the GreenTransition Is Still Happening in spite of retreats from Sustainable Development Goals  across the entire World-System. This would be good news if it was true, but it isn't. The NYT Article cherry-picks some positive examples but the aggregate data (graphic above) show that the Green Transition is basically stagnant.

This post will explain how the Green Transition Index (GREEN) is created and how the future forecast was constructed.

The GREEN index was created from seven indicator variables: Oil production (OIL), Oil Prices (P.OIL.), Global Temperature (TEMP), Carbon Dioxide Emissions (CO2), Carbon Emissions (Carbon) and the Ecological Footprint (TotalFootprint) and the number of Earths needed to support the current population (Earths). Data Sources are listed in the Boiler Plate. The, Principal Components Analysis (PCA) was used to construct three independent indexes that explain over 99% of the variation in the indicators (see the Measurement Model below)

The three components are: GREEN1 = (overall Growth in the Indicators), GREEN2 = OilMarket-Global Temperature controller and GREEN3 = Temperature-Oil Price Controller. The two historical controllers, GREEN2 and GREEN3, are of primary interest since they control overall growth.

The State Space model of GREEN index dynamics (see below) is stable with strong negative feedback. However, the behavior of the Green Transition over time is essentially at equilibrium and not changing. 

Shocks to the system (see below) are heavily damped. Oil Price shocks and Global Temperature shocks eventually return the system to equilibrium.


Notes


Green Transition Index Measurement Model






Green Transition model



Green Transition Shock Decomposition





Green Transition Model Full Forecast




Green Transition Full BAU Model







Thursday, February 19, 2026

Sub-Saharan Africa Forecasts, World System (1960-2100)

 


According to the World Bank 2024 Pathways Out of Poverty Report  "Two-thirds of the world’s extreme poor live in Sub-Saharan Africa, rising to three-quarters when including all fragile and conflict-affected countries". From the report:

To have the maximum impact on poverty reduction, that growth must be inclusive by creating employment opportunities while ensuring that the poor can take advantage of opportunities (for example, through quality education). Promoting economic growth, basic investments, and insurance are fundamental to sustainably improve the lives of the poor. Those actions reduce multidimensional poverty and enhance resilience against extreme weather and other shocks.

What does my SSA L20 model predict for future growth in Sub-Saharan Africa? The graphic above shows forecasts from five models. The forecasts are all positive:

  • Random Walk (RW) The Random Walk model presents the "Muddling-Through" baseline.
  • Business as Usual (BAU) The Business-as-Usual model assumes no Geopolitical Input from other countries.
  • World Input (W) The World Input Model (WL20) assumes input from the World System.
  • US Input The US Input model assumes input from the US Economy.
  • TECH The two Technology Models assume emphasis on Technical Productivity (TECHP) and Technical Efficiency (TECHE). They produce essentially the same forecasts.
Using the Akaike Information Criterion (AIC) the best short term model is a Random Walk (RW) while the best attractor path is presented by input from the USL20 model.

You can run the full USL20R SSA Regional Model (here), the USL20 model (here) and the WL20 model (here). The SSA1 component is an equal weighting of all the state-space indicators.

Notes

SSA L201 AIC Statistics