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.

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




Saturday, February 14, 2026

Hardship Forecasts for Venezuela (1960-2100)

 


According to Google AI (quote above) the Trump II Administration claims to be running Venezuela now after the Jan 3, 2026 invasion. Geopolitical Alignment with the US, however, is not the only option for the future and may (or may not) be the best option.

In this post, I will focus on what Geopolitical Alignment, if any, would be best for the Venezuela people.** The alignments range from none (RW, TECHE, TECHP, and BAU) to alignment with the World System:

  • No Geopolitical Alignments One option, that no longer seems practical, is for Venezuela to be left alone to manage it's own economy. This would involve letting the country take a Random Walk (RW), simply focus on Business-as-Usual (BAU) or turning the country into a Neoclassical Economic State focusing on Technical Productivity (TECHP) and Technical Efficiency (TECHE). From the time plot above, none of these options is best. Only TECHP results in a reduction in Hardship (HARD1). In any event, in the Long Twentieth Century, Venezuela has shown little ability to manage their own economy.
  • Geopolitical Alignment with Latin America The LAC model shows very little reduction in Hardship (HARD1), probably because the Latin American Region (LAC) has it's own problems managing Hardship.
  • Geopolitical Alignment with the US If there is a charitable interpretation of the US Invasion it is to rid Venezuela of incompetent Left-Wing governments (Heather Cox Richardson in the video below argues that what is really going on here is the destruction of the Rules-Based World Order) and align the country permanently with the US. Using the USL20 model (US) as input would result in a large reduction in Hardship (HARD1) but would only last until 2080 when there would be a rebound to increasing Hardship.
  • Geopolitical Alignment with the World System After 2080, the best  Geopolitical Alignment would be with the WL20 Model (if Venezuela survives the period of US dominance, which is not likely to be peaceful).
No one knows the future, and the future for Venezuela seems quite uncertain. The Trump II Administration will probably loose interest in the country once all the Oil is extracted (if this is even a practical possibility given the country's political uncertainty and deteriorating infrastructure).

If you are interested in understanding more about the US Invasion of Venezuela, here is an explainer from Heather Cox Richardson:



For more of my posts on Venezuela, see the Blog Roll (here).

Notes

** One Geopolitical Alignment I have not presented in the graphic at the beginning of this post is alignment with China. The uncontrolled, exponential increase in Hardship as a result of alignment with China is so great that all the other options look no better than a Random Walk (RW).

Information about data sources and descriptions of how the State Space models were constructed can be found in the Boiler Plate.


VEL20 Hardship Measurement Model


Three components were extracted from the Hardship Indicators: HARD1 = (Overall Growth), HARD1 = (CPI-LU-GINI) and HARD3 = (POV-FAM.WRK-CPI). Definitions of the indicator codes are given below. 

VEL20 Hardship Indicator Codes



The construction of the HARD index involves sixteen indicators drawn from the World Development Indicators (WDI, see Shefner et. al., 2015).

VEL20 Hardship AIC Statistics


Seven Hardship models were estimated** and the Akaike Information Criterion (AIC) statistics are presented above (smaller the better). The best short-term model is a Random Walk (RW). The best Attractor Path model is the World System (WL20).








Saturday, February 7, 2026

What If Iran Dominated the Middle East? World-System (1960-2100)

 



Iran has currently reentered talks with the US over the Iranian nuclear program (here) after the US Bombed Iran's nuclear facilities on June 22, 2025. Iran and the US have had a long history of troubled and turbulent relations. Both the US and Israel seem to fear that one day a nuclear powered Iran could dominate the Middle East. 

The best model for the Middle East is to stabilize growth rates with no Geopolitical Alignments

Since I have models of the Iranian (IRLM), the Middle-Eastern Regional (MEA _BAU), the US (USL20) and the World (WL20) economies, I can predict different paths of overall growth under different Geopolitical Alignments.
  • The Best Model (in terms of growth) is the MEA BAU (Business as Usual) model, essentially the Middle East without a dominant regional hegemon.
  • The Next-Best Model is MEA driven by the Iranian Economy (IRL20)
  • The Also-Ran Models are MEA driven by the US Economy (USL20) and the World System (WL20) when compared to a Random Walk (RW, the Middle East struggling to find some Geopolitical Alignments that work).
The only one of these models that is stable (see the AIC Statistics below) is MEA linked to the World System (WL20), but that  model peaks after 2020 and then declines. In other words, stability for the Middle East would involve growth-and-collapse rather than a steady state (growth rates of the BAU model could easily be modified to produce a steady state, see the MEA_L20 code).

Notice in the MEA_L20 code, stabilizing the system is not enough to prevent collapse. Growth rate of the Malthusian Factor, MEA2= (N-CO2-EG-Q), must be reduced beyond simply stabilizing the system. 


A simple summary of the MEA Measurement Model above is that growth is controlled by a Malthusian factor, MEA2 (N-CO2-EG-Q), and Energy Use, MEA3 = (Q-E). The interactions between the Control Components and Growth (in the System Matrix):

are small. You could also experiment with strengthening feedback effects by modifying the off-diagonal elements of F.

For the future, ChatGPT reports:
 





Notes

For more of my posts on Iran, see the Blog Roll. For more information about data sources and about how the State Space Dynamic Component Models were constructed, see the Boiler Plate.

IR Measurement Model


The IR Measurement Model has three components: IR1 = (Growth), IR2 = (0.9091 LU - 0.335 KOF) and IR3 = (0.827 KOF - 0.3878 LU - 0.258 EF - 0.217 EG) where LU = Unemployment, KOF = Globalization, EF = Ecological Footprint. Notice the low weightings on HDI, the Human Development Index.

MEA Measurement Model


The MEA Measurement Model has three components that explain 99% of the variation in the indicators: MEA1 = (Overall Growth), MEA2 = (0.8746 LU - 0.361 EG - 0.2320 CO2), MEA3 = (0.708 Q - 0.604 EG) where LU = Unemployment, EG = Energy use, CO2 = Emissions and Q = GDP. Briefly, Growth is controlled by an Unemployment-Energy use controller and a GDP-Energy use controller.


IR_MEA Model


The MEA1 model is unstable.

MEA BAU Model

The MEA L20 System Matrix has three unstable diagonal coefficients (greater than 1.0).

IR_MEA AIC Statistics


The IR_MEA models (RW, BAU, World, US and IRL20) are all very close together with the RW actually being best.




Thursday, December 11, 2025

World-System (1950-2100) Latin America and the Donroe Doctrine

 


The 2025 National Security Strategy of the United States reinvoked the Monroe Doctrine to justify aggressive military actions against (if not outright invasions of) Latin America countries using a spheres of influence argument as justification. Moreover, previous Geopolitical Alignments (particularly Europe) that have been important to the US have been downplayed using dismissive language such as "...economic decline [of Europe] is eclipsed by the real and more stark prospect of civilizational erasure" as a result of uncontrolled immigration (p. 25).

A lot has been said already about the 2025 National Security Strategy of the United States and I will have more to say in future posts. My question in this post, however, is "what is in the best Geopolitical interests of Latin America?" I have used the LA20 model to make seven forecasts of Latin American growth based on different Geopolitical Alignments (see the graphic above):
  • BAU (Business-As-Usual), that is, no Geopolitical Alignments. In terms of growth, BAU is the best future for Latin America as it provides maximal exponential growth into the Future.***
  • TECH (Productivity) is a variant on BAU with no Geopolitical Alignments but focusing on doing everything to increase productivity.  It provides the next-best rate of Exponential growth.
  • W (World System Linkage) Geopolitical alignment to the World System (the WL20 model) provides the third-best rate of exponential growth.
  • CN (China Linkage) provides the fourth-best rate of exponential growth based on input from the WL20 China model.
  • US (United States Linkage) produces growth-and-collapse, peaking between 2050 and 2100 (based on input from the USL20 model).
  • RW (Random Walk) anything can happen including stagnation.
  • RU (Russia Linkage) produces immediate collapse based on input from the RUL20 model.
The negative forecast for Russian Linkage should give pause to leaders such as Nicolas Maduro of Venezuela. According to ChatGPT:


Also, the exponential performance of the BAU, TECH and W forecasts should be viewed from the perspective of World-Systems Theory where the relationship between Core (US) and and Peripheral (LA) countries is viewed as exploitative.

If US Linkage is not beneficial after 2055, one benefit in the short-term is if the US would clean up the Latin American Drug Cartels. Violence created by Cartel turf Wars and the need to employe drug mules (drug smuggling) is one factor in illegal immigration to the US.

American policy should focus on enlisting regional champions that can help create

tolerable stability in the region, even beyond those partners’ borders. These nations

would help us stop illegal and destabilizing migration, neutralize cartels, nearshore

manufacturing, and develop local private economies, among other things (p.16 of the 2025 National Security Strategy of the United States).


However, according to ChatGPT:

The six forecasts above leave Latin American in a difficult situation: The US and the new "Donroe Doctrine" are intent on maintaining Latin American Dependency. Part of the Doctrine is resisting inroads to Latin America from China. I cannot say I am very confident about Latin America's future.

Please see the Boiler Plate for a discussion of data sources and how the models were constructed.

Notes

** The exponential growth forecasts do not imply that they are the "best" forecasts and the environmental consequences might be quite negative (another possibility that the 2025 National Security Strategy of the United States rejects ("...We reject the disastrous “climate change” and “Net Zero” ideologies"...p.14 ).

Blog Roll



Wednesday, November 26, 2025

Technology Long Waves

  


The Kondratiev Wave is an important element of World-Systems Theory. The graphic above is taken from Andreas Goldschmidt and gives historical specifics for technological cycles. Goldschmidt's formulation allows for the idea to be tested (one of the models I always test), is partially consistent with economic Growth theory (particularly if we do not assume a functional form for exogenous disembodied technological change in the Solow-Swan Model) and I can present some examples.