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, 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 ]


Wednesday, September 10, 2025

World-System (1975-2150) Breaking Cycles of Austerity in France

 



The background graphic above was from a protest in Aug 2012 (you can see the small peak in AUST1--see the Operational Definitions in the Notes below--in the overlay time series plot). Emmanuel Macron took office in 2017, right after AUST1 hit bottom. His government has been riding the AUST1 Recovery wave since then. From my Business-As-Usual (BAU) model of French Austerity (here), AUST1 can be expected to peak in the next few years and decline after that. However, the decreasing Cycles of AUST1 will continue well past 2150. 



The BAU model, however, is not the best model for French Austerity. In the long-run, AUST is better seen as being driven by the EUL20 model (which is also steady state). In future posts, I will look at Austerity in the European Union (EU). In the short run, the best model is a Random Walk (RW)--validated by the Macron Administration's inability to form a government and retain a Prime Minister. The attractor path for the RW model is presented above (dashed red line). The RW attractor path suggests that AUST1 should be kept at a low level aside from random movements.

Austerity is a difficult component of Neoliberal Theory (see below). Especially, the dominant controller, AUST1, depends on external forces such as US Military support and the Russian-Ukrainian War which is forcing military expenditure up and creating the budgetary crisis with Health, Education and Welfare.

For an understanding of why Austerity has become such an issue in France, keep in mind that the Economy of France is becoming a Steady State Economy (see the FRL20 Model). One interesting hypothesis is that cyclical processes such as Austerity become more important as the system reaches a steady state and the dream of unending exponential growth (Techno-Optimism) is over. Promises can no longer be made that growth will solve Social Inequality problems. The New Axis of Evil can be used to motivate increased military expenditure but, to avoid reducing Social Expenditure, Debt will have to be used to drive the economy, creating another focus for Protest and wide-spread civil unrest.

You can experiment with the FR_AUST model here. For more information about how the models are constructed see the Boiler Plate.

Notes

More reading:



Austerity, as a theoretical concept, is part of Neoliberalism (see the graphic above and Shefner, 2015 here and here). I will explore the other aspects of French Neoliberalism in future posts.





The data for the AUST index is taken from the World Development Indicators (WDI). The indicators and definitions are listed in the table above. NOTE: AUST is entirely measured by budgetary categories as percentages; the cyclical nature of the index is a result of percentages hitting up against limits [0%,100%].




The AUST index contains three components that explain 94% of the variation in the indicators. 

AUST1 = (0.433 GED + 0.4571 MIL - 0.4477 G - 0.393 GE - 0.4701 GH)  
AUST2 = (0.822 GHE - 0.357 GED - 0.377 GE) 
AUST3 = (Overall Growth) 

AUST1 and AUST2 are historical feedback controllers for the budgetary categories defining Austerity. AUST1 focuses on controlling Education, Military expenditure, Overall Government Expenditure and Health Expenditure. AUST2 focuses on controlling Health and Education Expenditure.




In the Economy of France, Austerity, Debt and Globalization (KOF) are closely related. The relationship can be seen from the Measurement Matrix above when DEBT and WorldGlobal (KOF) are added to the model. In future posts, I will investigate all the indicators of Neoliberalism in France.



The state space of the French Economy is dominated by three components explaining 98% of the variation in the underlying indicators: 

FR1=(Overall Growth)
FR2= (CO2+EF-KOF)
FR3=(LU-L-N

FR2 and FR3 are Historical Feedback Controllers regulating Environmental Impacts of Globalization and Unemployment, respectively. EF is the Ecological Footprint and KOF is the Index of Globalization.

You can run the FRL20 Model with code available in Google Sites.




Friday, September 5, 2025

World-System (1960-2100) A New "Axis of Evil"?

 


On September 1, 2025, in the Chinese port city of Tianjin, Chinese President Xi Jinping held a summit in response to the Trump II Administration tariff policies that included leaders of Russia and India and other representatives from the Global South (here). Xi declared that "Global governance has reached a new crossroads," in the fight against US Hegemonic Power. Did Xi just announce the birth of the New Axis of Evil? And, what might this mean for the future?

The conclusion from my World-System models is that the future forecasts for the New Axis of Evil all lead to collapse of the system (except for one worrisome scenario).

In prior posts (see the Notes below), I have looked at the issue of US Hegemonic Dominance and the economic performance of Russia, India and China. In this post, I will look specifically at how the three countries (RU, IN and CN) could interact with the current World-System.

The Measurement Matrix (see the Boiler Plate for more information about Dynamic Component Models) is presented in the Notes below. In terms of overall growth, the first growth components for each country are relatively equally weighted (AXIS1). The historical feedback controller (AXIS2) is dominated by Russia. From the graphic above, Russia's dominance peaked before 1990 and then decline after the Fall of the Soviet Union.
--


For the late Twentieth Century, the system was dominated by the US. If that domination were to continue until 2100, the AXIS System would collapse--pretty strong motivation for eliminating US influence.


If the AXIS System were to align itself with the World-System (graphic above), the forecast for the future is also collapse.


If the AXIS System were to go it alone (as a BAU System), the countries could grow exponentially but it would involve the decline of the Russian historical feedback controller (AXIS2) -- a loss that would probably not be tolerated by Russia.


Unstable exponential growth will not minimize Environmental Damage from growth, so another option for an AXIS system not dominated by Russia is to stabilize growth (graphic above). Stability leads to a steady state after 2100 but would also probably not be tolerated by the AXIS participants.

In summary, none of the Geopolitical Alignments for the AXIS System look very promising. Either the system will eventually collapse or it's reason for existence (unending exponential growth) will not be consistent with World System Balance.

However, pursuing World System Balance does not seem to be a priority of any potential Hegemonic or Multipolar Leaders in the World-System.  In the Functionalist explanation, the AXIS System is necessary for the military-fueled expansion of all the participants .I will investigate the AXIS BAU scenario in a future post (here).

You can run the WL20_AXIS model here, the WL20_RU model here, the WL20_CN model here and the WL20_IN model here

You can run the AXIS_of_Evil models here.

Notes

Other relevant postings:



Thursday, August 21, 2025

World-System (1960-2100) Geopolitical Linkages: Canada, Mexico and the US

 



A recent article in the New York Times (here) suggests that Trump II Administration bullying (Trade Threats to both Canada and Mexico) might bring the two countries (CA and MX) closer together. It's hard to imagine Geopolitical Linkages between Canada and Mexico without the US. Mexico has strong cultural and economic relations with the Southwestern US and Canada has solid culture and economic relationships with the entire Northern US. There are strong inertial forces that will keep the Free Trade Agreements between the three countries moving forward well beyond the limited and inconsistent influence of the Trump II Administration.

The results presented below also suggest (not unexpectedly) that President Trump is tinkering with a system that he does not understand.

In this post, I will put the Growth Components (CA1, MX1, and US1, presented in the Notes below) of the three countries (CA, MX, US) together in a systems model and see what shape the future dynamics might take.** The first question would be which model would be best (from an AIC perspective), the two country model (CA1, MX1) or the three country model (CA1, MX1, US1)? The AICs  for the models are presented in the Notes below. From the AIC perspective, the three-country World-System linkage model is best.

But, let me clarify these results. I assume that politicians follow a BAU strategy: "our country is able to make it's own decisions without regard for other countries or the World System". The reality is, however, that each country is part of the World-System, whether they like it or not and whether they do or do not take into account World-System forces. The BAU results in the Notes suggest that CA and MX might reasonably consider going it alone together. The history of US, Canada and Mexico Free Trade Agreements also suggests that the countries understand the importance of the US as Hegemonic Leader of the World-System. Strong inertial forces will keep the three countries trading with each other long past the Trump II Administration. Inertia does not mean that there are not tensions and contradictions in the system!

The problem with forecasts from the WS-linkage model (above) is that each country will face a possible growth-and-collapse, Limits-to-Growth future. The US will peak a little later (2050) than CA or MX (2025). So, right out of the gate, World System linkage will seem like a bad idea to growth-obsessed politicians. From the standpoint of Environmental Damage from growth, Degrowth would be a positive outcome. So my assumption is that growth-obsessed politicians will turn away from a Limits-to-Growth future and focus on a BAU strategy such as NAFTA or the USMCA (the Trump I version of  NAFTA).

If each country (MX, CA, US) focuses on business-as-usual and their existing linkages (which  is very likely after the Trump II Administration), each country could experience unlimited exponential growth well after 2150 driven by the US, which is the unstable part of the system (you can experiment with the MX_CA_US model using the code provided here). At least unstable, unlimited growth was the vision prior to the Trump II Administration



I have suggested here that the Trump II Administration  is essentially taking the US on a Random Walk. If Trump is successful, the result (graphic above) could be a steady state (well after 2150) for all three countries if the US Random Walk persists (you can experiment with setting the US to an RW here; try to determine when the steady state will occur--it's way off in the future)




In the short-run (year-to-year), the Mexican Economy is also a Random Walk (here). Additionally, setting the Mexican Economy to a Random Walk (graphic above) destabilizes the system and pushes the US into collapse mode. President Trump has to be careful with his RW-policy-approach because it can also destabilize the system.


All of the above is a round-about but necessary way of getting to the question of what effect will Trump Shocks have on the USMCA system? The graphic above shows how a negative shock to the US will affect each country, to include the US. Both MX and CA will be affected negatively to about the same extent and take over twenty years to reach equilibrium again. The US will respond positively in the first years (a prediction of the Shock Doctrine) but will eventually have to deal with the negative consequences for about the same twenty years. In other words, 

the Trade War works in the short run but in the long run helps none of the parties.

You can experiment with the MX_CA_US Model here and the MX_CA_US_W Input Model here. You can experiment with the MXL20 model here, the USL20 model here, the CA_LM model here and the WL20 model here.

In a future post, I will explore finding a steady state for the World System and what it's effect on the MX_CA_US_W Model could be.




 Notes

** More information about how the dynamic component state space models can be found in the Boiler Plate.

AICs

The AICs are: (CA1MX1 = [104 > AIC=121.6, 137.5]) and (CA1MX1US1 [112.5 > AIC=138.5 > 163]) for the Business-as-Usual Models (BAU) and (CA1MX1 = [58.03  > AIC=101.6 > 134.2]) and (CA1MX1US1 = [ 51.14 < AIC=94.59 < 132.4]) for the World System (WS) input model (smaller is better for the AIC).

MX Components


CA Components


US Components


World Components