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.

Tuesday, November 4, 2025

US (1960-2100) If Things are so Great, Why is Hardship in the US Increasing?

 


Measurable Hardship in the US (graphic above), is increasing and projected to increase until 2025. If US economic performance is so great, why is this happening? And, why does Hardship decrease after 2025 in the estimated model (see the Boiler Plate) above?

Quantitative Counterfactual Analysis indicates that impacts from growth in the World System are driving Hardship in the US. Decline in Hardship after 2025 is the effect of slowing growth in the World System. In other words, Growth in the World System has increased Hardship in the US even though the US is the Hegemonic leader of the World-System.

Part of the reason is that the current US Administration (Trump II) is cutting benefits for SNAP (Food Stamps) and other US Welfare programs. Why "millions of Americans" have to be on food assistance in the first place is a question that bothers me and the answer has to do with World-System forces.

The graphic at the beginning of this post is a forecast driven by outputs from the WL20 model. To determine the effect of World System forces, we can rerun the forecast with the BAU model (no input from the World System).

The BAU model shows Hardship reaching a high-level plateau after 2100. The Trump II Administration's actions to withdraw from the World-System and their attempts to cut US Welfare programs is an attempt to bring this Hardship Future into being. Increasing Hardship in the US was one of the prices of Hegemonic Leadership

The peak and decline of the World System would benefit the US if it still stays connected to the World-System. High levels of Hardship and World-System isolation are possibly a benefit to some elements of the US Right-Wing elite, but not most of the US Public. The Hardship Future will likely also be one of Conflict and Chaos--another potential benefit to the Right-Wing.

You can experiment yourself with the USL20 Hardship model here. For comparison, the System Matrices for the the USL20 Hardship model with World Input are presented in the Notes. Bootstrap 98% Confidence intervals for coefficients in the Systems Matrix (F) are provided in the code. Both models are stable.

Is there anything in the US Economy that controls Hardship or is it primarily driven by World System conditions? Economic theory doesn't have much (or anything) to say about Hardship. Controlling Hardship is essentially a Political Systems problem (among a lot of there things here), but current Neoliberal Ideology seems to rely on Economic growth to resolve all problems. In a future post, I'll investigate the topic of what (if anything) controls Hardship.



Notes

Hardship Index

The following indicators (from Shefner,  Roland and Pasdirtz, 2015) were used to construct the HARD (Hardship) Index. All data were taken from the World Development Indicators (WDI).
In addition to HARD1, two other indexes were constructed, HARD2 (dominated by Unemployment) and HARD3 (dominated by Inflation). Each index explained another 10% (0.841% and  0.933%, respectively) in the indicators. So, indeed, Unemployment and Inflation were important components of US Hardship, but the other indicators also played a role. Whether the US Electorate made a good choice in electing the TRUMP II administration to resolve their issues with hardship will have to wait and be seen over the next four years.


The Measurement Models for the WL20 Index and the US_HARD index are presented above. The time series forecast plots are presented below. The WL20 index first:




Growth in the World System (W1) peaks in 2040 and is forecast to decline after that. The Food-Market Index (W2=(LP+P.Wheat.-TEMP) declines throughout the period because Global Temperature is increasing and the Oil- Market-Environmental Index (W3=(P.OIL+P.WHEAT-OIL-EF-Earths) increases to a plateau in 2075.

And the the WL20 HARD index:
 
Overal Hardship (W1) increases through the period while W2 (Unemployment) and W3 (Poverty) are cyclical.







World-System (1970-2100) World Population Collapse


October 27, 2025. NPR ran a segment on how Populations are Shrinking and Altering the Global Economy. It is somewhat surprising that Population Decline has not been bigger news. It has been going on in many countries and for the entire World System (graphic above with 98% bootstrap prediction intervals).


The United Nations has essentially been making Population projections (graphic above) similar to my WL20 Model at the start of this post.


The basic theoretical model underlying the possible impact of Population Decline is the Kaya Identity (above) used by the IPCC to help understand Global Temperature Change. The 
Kaya Identity is true by definition (see the Boiler Plate) so any decrease in Population will not only decrease economic growth (Q) but also decrease CO2 emissions and moderate Global Temperature (T).

My models are also predicting that growth in the World System will peak before 2100 (here) as will Global Temperature (here). The reasons are that there are powerful negative feedback loops from environmental and market controllers that eventually limit growth of the World System. 

Exercises

You can experiment yourself with one of my World System models here. The models are written in the R programming language and can be run on line. Suggestions in the code, to include bootstrap confidence intervals for choosing reasonable counterfactuals, can be found in the code. The model is stable and cyclical.

Another one of my World Systems models is unstable and produces exponential growth forever (here). When it is stabilized (instructions in the code) the World System reaches a steady state after 2100.

The future could be any one of these models or something else entirely (see the Boiler Plate for IPCC Emission Scenarios). You have to ask yourself which one of the models (if any) seem reasonable.





Wednesday, October 15, 2025

World-System (1980-2100) Will Political Instability Hurt the French Economy?

 


Recently, the NY Times reported (here) that "...after three government upheavals in France since last summer, the damage to the French economy has already been done." In this post, I will take a look at the data. Recent data on French GDP comes from the World Bank and ends in 2024. The graphic above shows French Real GDP (GDP in constant 2015 US$) with a forecast and 98% confidence intervals out to 2100. 

French GDP is forecast to grow until about 2045 and then collapse after that. 

In terms of "damage to the French economy," the 2020 COVID-19 Pandemic was a major shock (outside the lower 98% confidence interval). In 2024, French GDP was a bit above the forecast attractor path (dashed red line). Political turmoil might reasonably be expected to bring the economy back to the attractor path but not create another COVID-style shock.

Possibly the most concerning aspect of the GDP forecast is the collapse starting around 2045. Why is the French Economy forecast to be in Growth-and-Collapse mode?

If you have been following my prior postings on the French Economy (here) you will see that France is approaching a Steady State Economy (maybe).*** French GDP, on the other hand, is best predicted by the World System (see the Notes below), which is in growth-and-collapse mode (see the WL203 Model). To avoid this future, some geopolitical re-orientation** will be needed.

Looking at the AIC statistics (below). One approach would be to reorient the French Economy to Business as Usual (BAU, [16.16 <  AIC =  21.38 < 25.79]) with no external geopolitical alignments, which produces the steady-state forecast above.  Compared to the World System model (W, [-97.78 < AIC =   -46.24 < -9.145]) which has the best AIC, this will require some geopolitical work. One path would be through the Random Walk (RW, [ -67.1 <   AIC =  -56.52 < -47.09]) which has a very good  AIC but is not predictive of the future.

One charitable analysis of current French Political Instability is that it is part of a Random Walk walk process to find a different Geopolitical Alignment. There is no guarantee that the process will end in a Steady State Economy.

You can experiment with the FRL20 BAU model here and explore alternative futures.

Notes

** The New York Times also reports (here) that France's ability as a geopolitical actor has been compromised by the current Political Instability.

*** The issue surrounding unending (exponential, unstable) Economic Growth, Limits to Growth, Steady State Economies,  and Growth-and-Collapse Modes have been uncovered (again--the debate has been ongoing since the 1970s) in the 2025 Nobel Prize for Economics. Joel Mokyr, a historian and one of the recipients, argues (here) that a Steady State Economy where growth has ended is unlikely. If history is any guide, new innovations will always break the Steady State and create more opportunities for growth. However, see my discussion of French Technology Cycles here and here. Also see Joseph Schumpeter's Creative Destruction model (here). I will review all these models in a future post, but as an obvious summary: no one knows the future. I can only report on forecasts from models and wait to see what happens to the actual French Economy.

AIC Statistics



Technology Models

The Nobel Price in Economics was recently award to Phillipe Aghion, Peter Howitt and Joel Mokyr for their work on How Technology Drives Economic Growth. Reviewers have claimed that their work has relevance for current Growth Policy. For this post, I can just point out that the two technology input models, TECHE (TECH Efficiency) and TECHP (Tech Productivity) are reasonable competitors but not the best models.

An interesting point is that the Aghion-Howitt model with Creative Destruction defaults to a Random Walk (RW) with drift.

I will investigate La French TECH in a future post (here).





Thursday, October 9, 2025

World-System (1970-2150) Six Futures for Colombian Growth

 


The Trump II Administration's Gunboat Diplomacy in the Caribbean  has brought Colombia into the supposed War on Narco-trafficers. The BBC Reports (here) that

Colombian President Gustavo Petro has said that a boat recently bombed by the US was "Colombian with Colombian citizens inside", an allegation the White House called "baseless".

To provide some background to Trump's legally questionable military actions in International Waters, it would seem useful to understand the Economy of Colombia and how it might be affected by possible US military action. Google AI provides the following overview:


Colombia also has an historical reputation as a Cocaine Trafficker, but the Cocaine trade has recently been disrupted as a result of domestic and global forces that are reshaping the drug industry.

My first question, in this post, is what Geopolitical Alliances would be best for Colombia and how might Trump's Drug War affect the alliances. The graphic at the beginning of this post shows six "reasonable" future alignments for Colombia (some "unreasonable" futures are discussed below). Alignment with the US is cyclical and unstable, as is alignment with Russia (RU) and just continuing Business as Usual (BAU). Focusing on Globalization (KOF) provides the most stable future and is the best model from the standpoint of the AIC (see the Notes below, [23.47 < AIC = 51.86 < 81.82). Linkage with the World System (W) generates collapse starting around 2025.


There are a number of the collapse scenarios for Colombian Geopolitical Alignment (graphic above): Emphasis on Technical Efficiency (TECHE) and linkage with China (CN), the differences being when the collapse is forecast to start.






Notes

Economy of Columbia

Columbia





Google AI on the Economy of Columbia:


ChatGPT on Columbia Globalization:

 AIC Statistics:




Tuesday, September 30, 2025

World-System (1960-2100) Eight Forecasts for Venezuelan Growth

 





Notes








A More Detailed Look at the Economy of Portugal

In a prior post (here), I reviewed an journalistic article from the Atlantic (here) that tried to understand the puzzle of Portugal's economy using a sampling of conventional wisdom from macroeconomic analysis. One of the articles mentioned in the piece was published by the prestigious Brookings Institution and written by Prof. Ricardo Reis of Columbia University (here). It provides a more in depth, academic, macro-economic analysis that is worth some careful reading. The graph above is taken from earlier post and annotated with various historical fictions about the economy of Portugal from A-E. I will refer to each fiction in the discussion below.





Notes


World-System (1960-2100) Venezuela Growth Forecast

Venezuela is in the news right now for a number of reasons.


Notes

Data taken from the World Development Indicators (WDI). All variables are in standard scores. The methodology used to create forecasts is similar to the one used by the Atlanta Federal Reserves GDPNow app. Prediction intervals are generated using a Bootstrap algorithm in the R programming language.

You can run the VE20 Model here.
 

World System (1940-2040) Inflation in Venezuela


Latin America has not appeared much in the US News lately given a continuing preoccupation with the Middle East. But yesterday, NPR ran a story (here) titled "As Inflation Soars, Venezuela's Leader Opts for Drastic Steps." Venezuela has had past historical episodes with inflation, particularly in the 1990's and the new outbreak caught my attention. Why the new outbreak? To provide some context for my explanation, here's some background.

The conventional explanation for problems in Venezuela's economy (here) invokes the petroleum and manufacturing sectors.


Thursday, September 25, 2025

World-System (1970-2100) Latin American Futures

 



The Trump II administration, which took office in January 2025, is threatening to impose tariffs on Latin American Countries , in turn, the Latin American Countries are threatening retaliation on the US (here). Rather than investigating whether this trade war is a good or bad thing, let me take a broader look at Latin America's future from the perspective of Geopolitical Alignment (I'll look at Mexico, Venezuela, Columbia, Panama, etc. in future posts).



Latin American faces a wide range of futures from unlimited exponential growth if aligned with China (CN, in the graphic at the beginning of the post) or collapse if aligned with the World System (W). But, let's take China out of the picture (assuming the US would resist such a future). The graphic above shows the "also ran" input models:
  • BAU The Business as Usual model (which you can run here) is cyclical but has the best growth out to 2100. 
  • TECHE The Technical Efficiency model is stable and a strong contender (AIC = -160.3, smaller is better). 
  • TECHP The Technical Productivity Model is also stable and has one of the best statistics (AIC = -264.3). This model is the Systems Theory analog of the Neoclassical Economic Growth Model with erogenous technological change.
  • US The model drive by the US is also stable, cyclical and an obvious contender given the history of Latin America (AIC = -85.96).
  • RW In the short run, the Random Walk is a strong contender (AIC = -108.1)
  • W The World System input model is stable, cyclical and also a strong contender (AIC = -71.53). Unfortunately, it leads to collapse starting in the very near future.
You can experiment with the LA20 BAU model here. Instructions for modifying the model to produce stable and/or cyclical patterns are given in the code. I believe that the BAU model describes how policy makers think about their own economy, regardless of what Systems Theory right tell them about "Best or Worst Models" (an important Contradiction).


Notes

LA_SYS Model Summary:






Friday, September 19, 2025

World-System (1980-2100) Six Forecasts for the United Kingdom

 


The US and the United Kingdom (UK) recently signed Technological Prosperity Deal (I posted about the Deal here). After Brexit (the withdrawal of the UK from the European Union, EU), it seems that the purpose of the deal is obvious: the UK needs friends and Geopolitical Alliances after having essentially snubbed the EU. The US is the obvious next choice. But, the question remains: what would be the best Geopolitical Alliance for the UK? This post explores that question using the UKL20 Model (for more information about how the model was created, see the Boiler Plate).

The best Geopolitical Alliance for the UK is none, that is, to remain independent in the World-System and conduct Business as Usual (BAU) muddling through as necessary (RW).

In the graphic above are six growth forecasts for the UK1 state space component. From the Political Perspective, the UK-BAU Business As Usual models are the best, better than staying linked to the EU (a rationale for Brexit). The BAU models are unstable (largest eigenvalue greater than 1.0). The weaker models (EU, US, and W) are all stable and lead eventually to a Steady State Economy (a better result for reducing Environmental Degradation). The best short-term, year-to-year model is the Random Walk (RW), just muddling through.

You can experiment with the UKL20 Model and investigate the Technology models (TECHE and TECHP) here.


Notes



The  UKL20 Model Measurement Matrix is presented above. The state space components are UK1=(Growth-CO2-LU),   UK2=(CO2+E-Q),     UK2=(L+N+LU+EF-HDI). Note that all the components are historical feedback controllers, particularly Growth (UK1) is controlled by CO2 Emissions and Unemployment (LU).

The models (AIC = Akaike Information Criterion, smaller is better):
  • RW Random Walk [11.69 < AIC = 20.71 < 30.63]
  • BAU Business As Usual [81.86 <  AIC = 87.22 < 91.8 ]
  • W World WL20 Input [34.58 < AIC = 60.83 < 82.67]
  • US USL20 Input [29 < AIC =  63.25 < 90.17] 
  • UK UK2_UK3 BAU Input [83.88 < AIC = 89.88 < 94.15]
  • EU European Union [60.47 < AIC = 79.99 < 97.75]
  • TECHP Technical Productivity [27.43 < AIC = 48.29 < 66.77]
  • TECHE Technical Efficiency [61.16  < AIC = 73.08 < 82.33 ]

Thursday, September 18, 2025

World-System (1960-2100) Technological Change in the United Kingdom


On September 18, 2025 Donald Trump and Keir Starmer signed a Technological Prosperity Deal between the US and the UK covering joint technological advancement. Aside from giving the US President a chance to ride in the Golden State Carriage with King Charles, what was the motivation for the visit and the Technological Prosperity Deal?

The Economy of the UK is driven by Technological Productivity (TECHP) change;  without accelerated Technological Productivity growth, the UK is facing a Steady State Economy or even Limits to Growth

In this post, I present results from the UKL20_TECHP model to explain the forecast. The TECHP Indicators and index construction are explained in the Notes.


The forecast for a steady state TECHP, with 98% bootstrap confidence intervals, is presented above. There have been spurts of growth in TECHP, one when the UK joined the EC (European Community, precursor to the EU, in1973) and one after Brexit. The first TECHP component, 

TECHP1=(-0.511 co2 + 0.182 e + 0.616 q - 0.571 l)

explains 60% of the variance in the productivity indicators. TECHP1 is an historical feedback controller balancing CO2 emissions per capita (quality of capital, co2and Employment per capita (l) with Output per capita (q) and Energy per capita (e). In other words, higher quality capital stock (lower CO2 emissions and energy use) is associated with greater productivity and lower employment (capital-labor substitution). The UKL20_TECHP model predicts that this process is reaching a steady state.

The Technological Prosperity Deal is an attempt to put off the steady state and approach the 98% upper confidence interval where TECHP reaches a much higher level, but still a steady  state.

You can experiment with the full TECHP model here.

Notes

The Measurement Matrix for the TECHP state space:


The indicators are co2 (Carbon Dioxide Productivity), e (Energy Productivity), (Output Productivity) and l (Labor Productivity). TECHP1 explains 60% of the variation in the indicators.

The System matrix for the full UKL20_TECHP model:

The  UKL20 Model Measurement Matrix is presented below (TECHP is one of the better drivers for the UKL20 Model--see the Akaike Information Criterion statistics below)



The state space components are UK1=(Growth-CO2-LU),   UK2=(CO2+E-Q),     UK2=(L+N+LU+EF-HDI). Note that all the components are historical feedback controllers, particularly Growth (UK1) is controlled by CO2 Emissions and Unemployment (LU).

The models (AIC = Akaike Information Criterion, smaller is better):
  • RW Random Walk [11.69 < AIC = 20.71 < 30.63]
  • BAU Business As Usual [81.86 <  AIC = 87.22 < 91.8 ]
  • W World WL20 Input [34.58 < AIC = 60.83 < 82.67]
  • US USL20 Input [29 < AIC =  63.25 < 90.17] 
  • UK UK2_UK3 BAU Input [83.88 < AIC = 89.88 < 94.15]
  • EU European Union [60.47 < AIC = 79.99 < 97.75]
  • TECHP Technical Productivity [27.43 < AIC = 48.29 < 66.77]
  • TECHE Technical Efficiency [61.16  < AIC = 73.08 < 82.33 ]