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.

Monday, July 7, 2025

World-System (1950-2100+) Global Temperature Projections


A Recent Paper in Nature Communications: Earth and Environment was titled Warming of +1.5 °C is too high for polar ice sheets. I terms of projections from my models (above), this would mean that if we reach the 15.5 temperature level, it will be too late for the Polar Ice Caps to maintain their integrity and sea level rise will inundate most countries around the World (to include Mar-a-Lago, President Trumps Empire). Does this mean catastrophe for the World-System

The first project to point out is the Random Walk (RW). If Global Temperature were a  Random Walk it would mean that it cannot be forecast, a result that would please Climate Change Deniers. Given the high variability of the Global Temperature data, it should be no surprise that, in the short-run year-to-year, Global Temperature is a RW given the Akaike Information Criterion [-77.33, AIC=-65.15,-55.0]. However, in the long-run there is a clear trend. The issue is how far into the future can the trend be carried.

In the Stokes (2025) Global Sea Level article the conclusion is that, to prevent destabilizing the Arctic Ice Caps, Global Temperature should return to the levels somewhere around the 1980's. The graphic above plots a forecast of the Temperature BAU model that has no inputs (no forcings). Without forcings from human systems (anthropogenic forcings) the model would say within the "safe" zones. Unfortunately, isolating Global Temperature from human systems seems impossible.



The next one of my models to consider simply uses CO2 emissions to predict global temperature, something similar to the Kaya Impact Model (graphed above) used by the IPCC.





You can experiment with the stable WL203 model (here) or the unstable WL20W model (here).


Notes



Sunday, June 22, 2025

World-System (2000-2150) Seven Futures for Iran


The Trump II Administration in the US has just attacked Iran and claims to have seriously damaged Iran's Nuclear Sites (here). Iran claims it will retaliate, but the future after the unprecedented attack using B2 Stealth Bombers and Bunker Buster Bombs remains unclear both for Iran, the US and Israel (who started the attacks on Iran). The future is unknowable and there is a lot of current speculation. I can use the IR_LM (Iran, Late Modern) model to project seven possible future scenarios for Iran (graphic above).

The Business-as-Usual (BAU) model is clearly the best and it forecasts unending exponential growth for the Iranian Economic System. The worst scenario is Geopolitical Alignment with China (CN) which leads to collapse. The scenario for alignment with Russia (RU), (light-blue dashed line) is quite cyclical and unstable. Alignment with the US produces stable growth out to 2100. The World System (W) and the EU Alignment models are not much better than a Random Walk (RW).

These seven scenarios suggest that Iran would prefer to be left alone to pursue its own future, but that seems unlikely to happen. Geopolitical Alignment with the US  would also produce a desirable future, but that also seems unlikely to happen. Russia (RU) might be attractive in the very short run but that alignment will prove to be unstable. This leaves Iran with no desirable futures within the IR_LM BAU model.

You can experiment yourself with the IR_LM BAU model here. The period prior to the Iranian Revolution of 1979 sowed possibilities of alignment with the West, but after the Revolution the economy was converted into strong central planning aimed at Autarky (see the Economic History of Iran). In these circumstances, the IR_LM BAU model could be stabilized at any time by reducing growth rates (a counterfactual you can run here). Notice in the IR_LM BAU Model that the feedback controllers are dominated by Globalization, Unemployment, Ecological Footprint and Energy Use.

ChatGPT reports the following:


For more information about how the statistical models were constructed and estimated see the Boiler Plate.

The Axis of Evil

Friday, June 13, 2025

World-System (2000-2150) China and the Global South

 


In a prior post (here), I looked at China's possible Geopolitical Alignments, first with the World-System and then with Russia. In this post, I look at China's possible Geopolitical Alignments with the Global South. In the long-run, alignment with Latin America (LA) would clearly be in LA's interest; Africa (AF), not so much.

Thursday, June 12, 2025

World-System (2000-2100) Six Futures for China, One Scary

 


Most Geopolitical Alignments are mildly beneficial, except for alignment with the World System which is not. The order of benefits (in terms of comparison to a Random Walk, RW) are Asia Region (AXJ), Business as Usual (BAU, no alignment) and United States (US). 



One forecast missing from my standard forecasts (and the most concerning) is the one involving Geopolitical Alignment between Russia and China. Although the alignment has been publicly proclaimed by each country, there is increasing concern about CN intelligence activities in Russia (here). For more information about China-Russia relations, see the Wikipedia page (here).

I will investigate Global South alignments for China in a another post here. For more information about how the statistical models were constructed and estimated see the Boiler Plate.

Notes

Excerpts from ChatGPT:

Wednesday, June 11, 2025

World-System (1950-2150) India as a Small Regional Country

 


A recent article in the New York Times (here) about the evident decline of US Hegemonic Power suggests that India (IN) might be one of the countries competing for world leadership once US dominance has passed. India might well try to resurrect the "... Indosphere, a zone of Indian cultural and linguistic influence that stretched far beyond the subcontinent in the period roughly between 250 B.C. and A.D. 1200..." The question not being asked here is what would be the best Geopolitical Alignment for a country such as India and does that alignment involve Hegemonic domination of the World-System. This post investigates the question by estimating a state space model for India in the period (1950-2000) and then testing various Geopolitical Inputs to see the effect on the Indian Economy.

The graphic above shows the two state variables, IN1=(Growth) and IN2=(Q-N), with forecasts out to 2150. The best model (in terms of the AIC statistic, AIC=-6272.714 when compared to the BAU model AIC=-385.2805, smaller is better) to produce those forecasts (see the Boiler Plate for a description of the state space model and the data sources used) is the IN_LM_SC model (a Small Open Country) model. It shows that India would be approaching a steady state around 2150 when part of the Asia Region.

In another post (here), I look at alternative forecasts for World-System Hegemonic Dominance. India is one of the also-ran countries (in fact, the worst performer), not providing large growth stimulus to the World-System. In the upcoming period of Environmental Crisis and Hegemonic Chaos, maximum growth might not be the best choice for the World-System but it will be a Dynamic Attractor.

Notes

In term of Systems Theory, a Small Open Country is one that has no state variables. The state of the system is driven by the dominant Input Economy (the Asia Region in this case).  Here are the System Matrix (F) and the Input Matrix (G) for the IN_LM_SC model:


The small values for the coefficients in the System Matrix (e.g., -2.605049e-23) are effectively zero to within machine precision.

You can run the IN_LM_SC model yourself at the following Google Sites (here).


Monday, June 9, 2025

World-System (1950-2150) Hegemonic Dominance Forecasts


A few new books have been written and reviewed in the New York Times (here) about the evident decline of US Hegemonic Power in the Trump II Administration. From what I can tell, all of the discussions are  qualitative and speculative. Since the Future is unknown, there is plenty of space for conjecture.

What has not seemed to have been done is to make multi-model forecasts for the World System given inputs for different countries that are competing for Hegemonic Dominance. Since I have state space models for the World System and all of the Hegemonic contenders (you can inspect and run the models here), I might as well see what the forecasts say.

The graphic at the beginning of this post shows seven alternative forecasts for overall growth in the World System.








 here

Friday, June 6, 2025

World-System (1980-2080) Alternative Forecasts for US CG Debt


The US Congress is currently debating a Spending Bill being advanced by the Trump II Administration that will add $2.4 Trillion to the Deficit. In a prior post (here), my model for the US Economy forecasts that Central Government (CG) Debt will decline (the forecast was made after the Trump I Administration). I have also suggested that the outcomes of the Trump Administrations cannot be forecast because they are essentially a random walk (here).

In the graphic above I give four forecasts for US CG Debt (data taken from the World Development Indicators, see the Boiler Plate). The Random Walk (RW) line is meant to show that Debt Shocks (see the Trump I Administration) can happen at anytime in the future and are unpredictable. The prediction driven by the USL20 Model (US, dashed green line) shows the decreasing path of US CB Debt. The prediction driven by the WL20 Model (W, dashed blue line) shows debt peaking around 2050. The Business as Usual Line (BAU) shows debt growing linearly (it actually levels off in 2500).

One point to make is that all these models are stable (largest eigenvalue < 1.0)**. This means that none of my models predict that US CG DEBT is out of control or will grow forever (uncontrolled exponential growth). However, other Econometric models (for example, the Penn-Wharton Budget Model, PWBM) forecast that the US has about 20 years before Debt levels become unsustainable.

My best guess? Given that my forecasting models are stable and that the Trump Shocks will eventually be history, it seems reasonable to project that US CG Debt will keep pace with growth in the US Economy and will eventually stabilize when economic growth is over (see my forecasts for US  Economic growth here).

NOTES

** All my models are estimated from historical data and are not assumed, prior to estimation, as either stable or unstable (as are most Economic Models). For more information about the models I use and data sources, see the Boiler Plate.

I analyze the causes of the US CG Debt Bubble in another post.

Friday, May 23, 2025

About

 


This blog takes it's title from a book by Nelson Goodman Fact, Fiction and Forecast. The blog documents and explains World-System state pace models and forecasts the results out into the future. No one can know the future and forecasting, at first glance, might seem foolish. Forecasting may or may mot help us understand the future but it does help us understand our quantitative models. So, we keep doing it.

Code for my state space models is available in Google Sites. A list of my blogs is available here. More information about the statistical state space models is available here.

Tuesday, May 6, 2025

World-System (1950-2050): A Range of Forecasts for US Growth

 




Economic Forecasting during and after the Great Recession took a devastating hit (here and here). Some of the criticism was deserved, others was not. The work of the IPCC provides a way forward. Let me apply the IPCC approach to forecasting the future of the US Economy.

First, when faced with the problem of predicting the future of Climate Change for the World-System, the IPCC acknowledges that the future is unknowable. If something is done to address Climate Change, the future must be different than we can envision it right now. Policy must be able to change the future, but it well might fail. So, instead of making "best" forecasts, the IPCC constructed Emission Scenarios. Each of the scenarios is considered equal likely depending on what policy options are pursued (see the Boiler Plate for examples and links).

My approach to forecasting is a little different but conducted in the same spirit. I have a number of different models of the US Economy with different variables and covering different time periods (here). The models are based on Systems Theory (as are the IPCC Emission Scenarios--again covered in the Boiler Plate). The models produce many different output paths (forecasts) when different assumptions about input variables and estimated model coefficients are made.

For this post, I'm just going to group a few of these outputs into three categories: Steady State, Growth-and-Collapse and Collapse. The time paths for these Business-as-Usual (BAU) models is presented in the graphic above. 


None of the forecasts from my models would be considered acceptable by economic commentators. However, some forecasting models (for example the Atlanta Fed GDPNow model, which is based on an approach similar to mine), are starting to forecast collapsing growth rates (quarterly percentage change in GDP) for the US Economy. 

My models begin forecasting in the year 2000 while the GDPNow models are as current as possible. Predicting collapse scenarios before the Subprime Mortgage Crisis should not be taken as predictions of Economic Crises. The Crises are largely unpredictable shocks to the system that should be presented along with any forecast using shock decomposition diagrams. The shocks are external to the model and cannot be predicted but the effects can be explored (I'll do that in a future post).

I don't know what information economic decision makers actually have or use. But, some of the current extreme policy measures being pursued by the Trump II Administration may (charitably) be interpreted as desperate measures taken in anticipation of growth-and-collapse scenarios for the US Economy.

Notes


If you would like to experiment with my models, the computer code is available here and can be run in a web browser presented with each code Snippet. Explanations about model construction are available in the Boiler Plate.


Friday, May 2, 2025

World-System (1950-2040) Power Outage in Spain and Portugal


 




A European Power Outage this week in Spain and Portugal (here) suggests it might be an interesting time to compare the economy of Spain (ES), the economy of Portugal (PT) and the economy of Western Europe (WE) and ask what the effects of shocks to these economies might be.

First, let's look at my Business-as-Usual (BAU) forecast for growth in each economy (graphic above) the models run from 1900-2000, forecast until 2040 and do not include the many shocks after 2000 (see below): Portugal (PT) has the best overall growth forecast; Spain (ES) seems to be reaching a steady state and WE is somewhere in between. Things are different after 2040 (see below).





Negative shocks to each country model show that the economies would respond differently. Spain (ES1) has the best recovery but it takes a few years. Portugal (PT1)  and the WE1 react very poorly to negative shocks and essentially do not recover the same level of growth. Shocks to these countries include Great Recession 2020 pandemic1997-2007 real estate bubblethe 2008 financial crisis burst Spain's property bubble, 2008–2014 Spanish financial crisisthe Spanish Real Estate boom and rocketing oil prices,  Spanish property bubble2008–2014, Spanish real estate crisis (the bubble imploded in 2008), record oil prices by the mid-2000s financial crisis of 2007–2008, April 2007 The Economist described Portugal as "a new sick man of Europe", European sovereign debt crisisformation of the European Union (EU) in 1999, the September 11 Attacks in the United States in 2001,  and the Eurozone debt crisis.  ES, PT and WE have all had many shocks to deal with after the turn of the century. 

How do you think the results from my models compare to the conventional analysis of each country (follow the links in the first paragraph for more information)?

Notes

ES1, PT1, and WE1 are the dominant state variables for each model, computed by Principal Components Analysis. Each state variable explains over 80% of the variation in the indicator variables.

Each of the models (ES_M, PT_M and WE_M) are unstable. In the long run, they are all growth-and-collapse models (except for WE_M). You can experiment with each model here. You will notice that economic performance is different after 2040. See if you can find coefficients that will stabilize the economies and produce a steady state at some time in the future. Spain will be the easiest economy to stabilize and I have some hints about how to achieve stability in the code for each model (it essentially involves reducing growth rates as called for by the Limits to Growth report).

Portugal (PT_M) is an interesting case. The economy can be stabilize by setting the growth component (f[1,1] <- 1.0) to a Random Walk (History is just One damned thing after another).

Aside from Portugal, some of the coefficients used to stabilize the model are improbable (exceed either the LCI or the UCI of the bootstrap confidence intervals). To me, this suggests that reaching a steady state economy will take more than Business-As-Usual. One hypothesis is that a steady state economy is better able to handle shocks (you can experiment with with the effects of stabilization here) .


Sunday, March 30, 2025

Boiler Plate

 

Notes

The first six indicators in standard scores are taken from the World Development Indicators (WDI). KOF = KOF Index of Globalization, EF = Ecological Footprint, HDI = Human Development Index

State Space Model Estimation

The Measurement Matrix for the state space models was constructed using Principal Components Analysis with standardized data from the World Development Indicators. The statistical analysis was conducted in an extension of the dse package. The package is currently supported by an online portal (here) and can be downloaded, with the R-programming language, for any personal computer hereCode for the state space Dynamic Component models (DCMs) is available on my Google drive (here) and referenced in each post.


Atlanta Fed Economy Now

My approach to forecasting is similar to the EconomyNow model used by the Atlanta Federal Reserve. Since the new Republican Administration is signaling that they would like to eliminate the Federal Reserve, the app might well not be available in the future.


While the app is still available, there have been some interesting developments. In earlier forecasts, the Atlanta Fed was showing GDP growth predictions outside the Blue Chip Consensus. Right now, after unorthodox economic policies from the Trump II Administration, the EconomyNow model is predicting a drastic drop in GDP (the Financial Forecast Center is only predicting a slight drop here).

Another comparison for what I have presented above are the IPCC Emission Scenarios. These scenarios are for the World System. Needless to say, (1) the new Right-Wing Republican administration plans on withdrawing the US from all attempts to study or ameliorate Climate Change and (2) the IPCC does not produce any RW modes for the World System (but seem my forecasts here).

Climate Change

Another comparison for what I have presented above are the IPCC Emission Scenarios. These scenarios are for the World System. Needless to say, (1) the new Right-Wing Republican administration plans on withdrawing the US from all attempts to study or ameliorate Climate Change and (2) the IPCC does not produce any RW modes for the World System (but seem my forecasts here).


World System

The longest running set of data we have for the World-System is the Maddison Project based on the work of Angus Maddison (more information is available here). Data on production (Q) and population (N) for most countries and regions runs from years 0-2000. More data becomes available as we near the year 2000. 


Available data were entered in a spreadsheet (see Population above, double click to enlarge). Missing data were interpolated with nonlinear spline smoothing using the R programming Language.


In cases where initial values were not available (see GDP above), the E-M Algorithm was used to estimate initial conditions.

From the graph of GDP above (W_Q) for the World System, it can be seen that economic growth from the year 0-1500 was basically flat. The period of British Capitalism (after 1500) had a small plateau of growth. Takeoff does not happen until the Nineteenth Century.



From a system's perspective, the only model that can be tested for the entire period is Kenneth Boulding's Malthusian Systems Model [Q,N] = f[Q,N].



When developed as a State Space model (measurement matrix above) there are two components: W1=Growth and W2=(Q-N), the Malthusian Controller. When more data is available, the Malthusian Controller can be generalized to other SocioEconomic theories.

What the Malthusian Controller shows (plotted as Q-N above) is that a long-developing Malthusian Crisis (Q<N) started in the Late Middle Ages and accelerated through the period of British Capitalism (Dark Satanic Mills) and was reversed spectacularly during the Nineteenth Century.  Takeoff in response to a deepening Malthusian Crisis would not be an unreasonable way to view Modern Economic Growth.

Hurricane Forecasting

My vision for SocioEconomic system forecasting is to follow the US National Oceanic and Atmospheric Administration's (NOAA) approach to hurricane (Economic Crisis?) forecasting using Spaghetti Models (see below).


Currently, Economic forecasting does not use Multimodel Inference but it is getting there! The best state space model for the US SocioEconomic System in the graphic at the beginning of this post is the World System (W) model based on the AIC Criterion.


Climate Change

Another comparison for what I have presented above are the IPCC Emission Scenarios. These scenarios are for the World System. Needless to say, the new Right-Wing Republican administration plans on withdrawing the US from all attempts to study or ameliorate Climate Change.


Error Correcting Controllers (ECC)


In another post (here), I presented Leibenstein's Malthusian Error Correcting Controller (ECC). It can be generalized to the dominant ECCs in most theoretical economic models (above). These controllers can be further generalized. For example, (X-U) and (L-U) can be generalized to (N-U), a more general Urbanization Controller which describes market expansion for economic growth. In countries and periods with limited data, (N-U) might subsume all these processes. ECCs describe important feedback processes in SocioTechnical System that are typically not recognized as such in academic literature.

Kaya Identity


The basic theoretical model underlying all the World-System models I crate is the Kaya Identity. There are a number of advantages to starting theoretical development with the Kaya Identity: (1) An "identity" is true by definition Adding other variables to the model ensure that theory construction is on a solid footing. (2) The Kaya Identity is also used as the foundation for the IPCC Emissions Scenarios allowing a linkage between World-Systems Theory and the work of the IPCC.


World Development Indicators (WDI)



After WWII, extensive data sets on all countries in the World-System became available from the World Bank (here). The indicators above where chose to construct the state space for each WDI-based model. Addition indicators can be added for specific forecasts and analyses.


Monday, March 17, 2025

World-System (1960-2006) Seven Futures for Argentina

 


At the 2025 Conservative Political Acton Conference (CPAC, here) meeting in Washington, DC, Argentinian President Javier Milei gifted Elon Musk the "chainsaw for bureaucracy," a symbol of the deep cuts they both want to make in both the US and Argentina's bureaucracy. Elon Musk waved the chainsaw around on stage at CPAC. Milei has been president of Argentina since 2023 and is considered a right-wing libertarian as is Musk (currently). Milei considers himself aligned with the United States although prior Argentinian governments have sought closer ties with China and Russia (according to chatGPT). This post explores which of those Geopolitical Alignments might be best for Argentina. Another post (here), looks at the Economy of Argentina and whether bureaucracy is the problem.

From the time plot above, the BAU model (no input from other countries) exhibits unstable exponential growth, probably what most economists (including Javier Milei) would want. Alignment with China (CN), on the other hand, would produce unstable collapse. How Argentina would isolate itself from the World Economy is unclear but the country does have geopolitical options with China.

The more moderate alignments (the World-System, W, the US and the Latin American Regional economy LAC) all produce stable economic growth and a resulting steady state economy at some time in the future. Although a steady state economy might be preferred for environmental reasons, it is probably not an end-result embraced by current Argentinian elites. You can run the Argentinian state space model (AR20) under these various geopolitical influences here.



Geopolitical Alignment with Russia (RU) produces the strongest unstable exponential growth. Finally, alignment with Mexico (MX) is not much better than a Random Walk (RW).


Since the Random Walk is similar to the political strategy of the current Trump II Administration in the US (here), it is worth simulating the same future path for Argentina in the time plot above.  The result for Argentina is not the same as the US. Under a Random Walk there are neither growth nor collapse scenarios for Argentina.


Notes

The Akaike Information Criterion (AIC) statistics for all the Argentinian models are presented below.

In the Measurement Matrix below, the first six indicators in standard scores are taken from the World Development Indicators (WDI). KOF = KOF Index of Globalization, EF = Ecological Footprint, HDI = Human Development Index


The Error Correcting Controllers (ECC) are (Growth-EF), (LU+EF+KOF-Q), (EF+CO2-KOF-LU). It is interesting and somewhat unusual that, in Argentina, growth is controlled by the Ecological Footprint (EF) and the EF is important in the other two ECCs.

State Space Model Estimation

The Measurement Matrix for the state space models was constructed using Principal Components Analysis with standardized data from the World Development Indicators. The statistical analysis was conducted in an extension of the dse package. The package is currently supported by an online portal (here) and can be downloaded, with the R-programming language, for any personal computer hereCode for the state space models is available on my Google drive (here) and referenced in each post.


Atlanta Fed Economy Now

My approach to forecasting is similar to the EconomyNow model used by the Atlanta Federal Reserve. Since the new Republican Administration is signaling that they would like to eliminate the Federal Reserve, the app might well not be available in the future.


While the app is still available, there have been some interesting developments. In earlier forecasts, the Atlanta Fed was showing GDP growth predictions outside the Blue Chip Consensus. Right now, after unorthodox economic policies from the Trump II Administration, the EconomyNow model is predicting a drastic drop in GDP (the Financial Forecast Center is only predicting a slight drop here).

Climate Change

Another comparison for what I have presented above are the IPCC Emission Scenarios. These scenarios are for the World System. Needless to say, (2) the new Right-Wing Republican administration plans on withdrawing the US from all attempts to study or ameliorate Climate Change and (2) the IPCC does not produce any RW modes for the World System (but seem my forecasts here).