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.

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 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 Left-Wing governments 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 estimate** 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.

Wednesday, November 19, 2025

World-System (1960-2100) CO2 Emission Forecast

 



November 12, 2025. The New York Times is reporting 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 the 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 or use R-code here).

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 employment 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.

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, change the System matrix from F[1,1]=1.07917 to F[1,1]=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. 

Since the World System is cyclical, emissions start to grow again around 2100. I would expect that if Carbon emissions hit zero before the 22nd Century, the World System itself  would be subject to changes that are only wildly speculative in 2025.





According to the NY Times article (here), China, the US, India and Europe are the Major CO2 emitters. I have produced a forecast for US CO2 Emissions (here). I will do the same for China, India and Europe in Future Posts.

Notes

More posts on the World System:

WL20W Measurement Model


CO2 Model

Kay Coefficient Model







WL20 Carbon Model