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.
Showing posts with label US. Show all posts
Showing posts with label US. Show all posts

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.
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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











Thursday, July 31, 2025

World-System (2015-2100) US Attempts to Dominate India

 


Reuters is reporting (here) that the Trump II Administration is planning to impose 25% Tariffs on India and, not surprisingly, creating Political Chaos in India. My first question is "What is really going on here?" Trump's Trade War makes little economic sense and is opposed to conventional Republican Right-Wing Free-Market Ideology.

If Trump's Trade War isn't about Economics, what is it about? My best guess (and there might not be a rational explanation) is that the Trade War is about Political Power. Trump is intent on the Economic Domination of every country in the World-System and has decided that a Trade War is the way to do it. And, right now, he seems to be winning--most countries appear anxious to capitulate. How the Trade War helps Trump personally or the US Economy, if at all, remains to be seen.


Another (and maybe more important questions) is what kind of Geopolitical Alignment is best for India (or any other country, for that matter)? In terms of the models I have estimate, the World-System Linkage model (W)** is the best for India [-99.33, AIC=-60.09, -28.39]*** while in terms of predicted performance, the BAU model [-9.571, AIC=26.53, 57.61] is best (graphic above). In the long-run, US domination will lead to collapse of the Indian Economy (I would assume that the Trump II Administration isn't thinking this far ahead).

Russian domination (RU) is another interesting case. Russia is itself a cyclical economy (think of the Collapse of the Soviet Union) and that cyclicality would be transmitted Geopolitically to India. There would be periods of success and periods of failure.

In the end, my guess is that Indian (and any other country, really) would prefer the BAU model, that is, to be left alone to find their own attractor path

You can experiment yourself with the IN_LM_BAU model here. You can learn more about how the models were constructed in the Boiler Plate. For more discussion of the Indian Economy, see India as a Small Regional Economy.


Notes

** Other types of Geopolitical Alignments estimated in my models are discussed in the Boiler Plate.

***Akaike Information Criterion (AIC) Smaller is better.

The BRICS (of which India is a member) are actually an intergovernmental organization of ten countries but the name comes from just five: Brazil, Russia, India, China, South Africa. You can experiment with the BRICS BAU state space models on the following sites:
  • Brazil (BR_20 Model) An unstable model that leads to collapse (stabilizing the model also leads to collapse). There are strong historical unemployment and environmental Controllers. See if you can find a steady state for this economy!
  • Russia (RU_LM Model) An unstable model with strong Export-Employment historical controllers. Becomes cyclical when stabilized.
  • India (IN_LM Model) A Malthusian Economy currently in collapse mode. Stabilizing the economy is beneficial.
  • China (CN_LM Model) An unstable economy with strong historical Export-Employment controllers. Stabilizing the economy produces a steady state after 2100.
  • South Africa (ZA_20 Model) An unstable economy with strong Globalization-Environmental historical controllers. Stabilizing the economy would lead to a steady state in the distant future (well after 2100).

The BRICS are not a uniform set of Semi-Peripheral countries. They have different dynamics and different historical patterns of development. Neoclassical Economics makes a mistake when applying the same Exogenous Growth Model to these countries.

Trump doesn't think much of either the Indian or the Russian economies (here) and calls them "dead economies". Obviously, the Trade War is not meant to help other countries in the World-System but rather to dominate them (read more about Trump's Trade War here from a World-System Perspective).

Wednesday, February 5, 2025

World-System (2015-2030) US Egg-Price Controversey

 


To be honest, I never thought I would be blogging about Egg Prices, but evidently the price of eggs and other grocery items may have helped Trump win a second term. Had Biden imposed price controls during his administration, there would have been a terrible outcry among pundits and economists. There appears to be no consensus about price controls and Neoliberalism insists on leaving the markets alone to set prices.

What interests me about the Egg-Price Controversy is that Americans do not seem to understand how markets work. For those that have gone to college, they must have been asleep in ECON 101 or have not connected Supply and Demand Curves to the US Capitalist System. Shocks such as COVD-19 or the Bird Flu (H5N1) Pandemic affect the supply of chickens (eggs) as herds are culled and, according to ECON 101, if supply decreases then prices increase. I guess Americans think prices will always be constant and if they aren't then it is the fault of the unlucky Presidential Administration in charge during the shock. 

Part of the problem here is the ECON 101 understanding of how markets work. Adjustment to Supply shocks is supposed to be instantaneous. But, time to adjustment is most likely a function of the size of the shock.

The graphic above shows shocks to Egg Prices from 1980 to the present. The shocks during COVID and the Bird Flu were very large by historical standards. There is not a lot of historical experience to predict how the market will respond, but it won't be instantaneous.


The graphic above shows the response of egg prices to systemic shocks.  The strongest forces (statistically) driving egg prices come from the World-System (something likely not discussed in ECON 101). The first graph above shows the Price of Eggs in January as a function of growth shocks to the World System. As the World System grows in response to shocks, egg prices increase. The assertion by Techno-Optimists that markets always reduce prices has to be tested in each market; it fails in the Market for Eggs.

The second graph shows shocks to the World-Market compared to Global Temperature. Regardless of what markets do, shocks to Global Temperature reduce egg prices (chickens must like a warmer climate, to a point). Finally, the third graph shows World-Market conditions compared to the Ecological Footprint. World-Market shocks increase egg prices. It takes almost ten years (at least in the model)  to work the shocks out of the system. Since, during the decade, there are likely to be more shocks, establishing dynamic causality is always difficult and contentious.

What is the Working Class in a Capitalist System to do? You are supposed to play by the rules and reduce your demand for eggs. Instead, you ask for the Socialist solution of Price Controls or elect a Far Right Wing Presidential Candidate to solve the problem who thinks that eggs come from a machine in the back room at McDonalds. Wouldn't it be easier and make more sense to switch to a vegan breakfast without eggs until everything blows over? Let the Price Gougers pound sand. Capitalism is certainly full of Contradictions that can make life miserable for consumers.

If you notice from the forecast at the beginning of this post, things are only going to get worse for Egg Prices! Shocks seem to be getting bigger as do the model's prediction intervals.  Keep in mind that no one knows the future and a model is not reality. The important issue is to understand how to protect yourself in a Capitalist System, a system that will not change soon and, when it does change, will produce massive shock waves that might make COVID and the Bird Flu look mild.

NOTES


Here is a more detailed look at the Error-Correcting Controllers (ECCs, a concept from Systems Theory not Economics) The second ECC shows how environmental conditions control egg prices (0.775 LP + 0.411 P.Wheat. + 0.241 P.Oil. - 0.235 TEMP) where LP is the Living Planet Index, P.Wheat. is the price of Wheat, P.Oil. is the price of Oil and TEMP is global temperature (see the Measurement Matrix above). In other words, favorable environmental conditions in the World System reduce the price of eggs. Finally, the third ECC shows another environmental World-Market controller  (0.712 P.Oil. + 0.461 P.Wheat - 0.241 Oil, - 0.293 EF) where Oil is World Oil production and EF is the Ecological Footprint. World Markets, when compared to Environmental conditions. Against a background of Egg Producer Price Gouging, World Markets and Environmental conditions are also taking their toll.

Another aspect of the Egg-Price controversy is the role of Technology. The Techno-Optimist Manifesto and  Neoliberalism both claim that Technology will drive prices down in a free market. I don't see that happening in the Egg Market. Technology (in the form of Vaccines) could reduce the impact of Bird Flu  but there is a problem: it is expensive to inoculate an entire herd of chickens, especially those that are going quickly to the slaughter house. There is some discussion of inoculating laying hens, but inoculation will only add to egg prices. Because there is a World market for chickens, culling the herd is (surprisingly) more cost effective since many countries will not accept chickens from infected herds. So, the effect of Technology (productivity increase) is not very clear in this market.

You can experiment  with the effect of Technology on Egg Prices here. You can see that the effect, at least in the short run, is not to lower prices as claimed by The Techno-Optimist Manifesto and  NeoliberalismSweeping claims about markets and technology always have to be tested.





Saturday, January 18, 2025

World-System (1950-2080) US Capitalist Accumulation Crises

 



Reading between the lines in the Classical Capitalist Model (see Higgins, 1985, Chapter 4) and the Neoliberal Model, Capitalism and Inequality go together.  Higher concentration of wealth ensures that funds are available for investment in the unceasing drive to accumulate capital. Too high concentrations of capital result in the Crisis of Capitalism. Too low concentrations require Neoliberal Renewal of Unfettered Capitalism.


I can develop these insights by starting with Higgins Classical Model and adding a GINI Coefficient (0 = perfect equality, 1= perfect inequality) as an output of the Classical System State in the causal diagram above, O=(L,Q,T). By applying the ideas of Systems Theory, the Capitalist Error Correcting Controller (ECC) is now the major output. What this means is that the relationship between Inequality (GINI) and Capital Accumulation (K) has to be monitored in a Capitalist System. From the perspective of Systems Theory, this ECC is one way to possibly maintain Capitalist growth, by continuing to keep (GINI > K).

When I apply the Marxist and Neoliberal insights to the US (see the Measurement Matrix in the Notes below), we get three components: Classic1 is the overall growth in Capital, Investment and Inequality explaining about 96% of the variation. Classic2 is the important controller here, ECC2=( 0.80 GINI - 0.778 K) that explains only about 3% of the variation. Classic3 is another controller for Investment, ECC3 = (0.548 GINI - 0.795 I) and explains another 0.08% of the variation. What the small explained variance for the ECCs means is that, in the Post WWII period, it has not been necessary to exert much control over capital accumulation in the US. 

When we put Classic2 in a state space model (here), and construct an attractor path for the US, the result is presented in the time series plot at the beginning of this post. Numbers above zero (dark black line) indicate increasing Inequality available for capital accumulation. The attractor path (dashed red line) indicates that Inequality has been well below expected levels and has plenty of room to increase under the Trump II administration. But somehow, since the 1980s, the US has stayed fairly close to (GINI - K) = 0.



What is notable is that there was a Neoliberal accumulation crisis during the Reagan years (the start of Neoliberalism in the US) and an impending Marxist Overaccumulation Crisis starting after 2000. But still, the US is below the World System attractor path. 

The attractor path at the beginning of this post is driven by the World System, overall growth of the system, environmental effects on agriculture and world markets. The graphic above takes the World System out of the model and allows ECC2 to work as expected. 

European Neoliberalism after WWII was meant to reintegrated the World System after the shock of Fascism. The Trump II administration is signaling that Neoliberalism is at an end in the US and that some type of Right-Wing Authoritarianism is being planned along with Isolationism.

The World System attractor path reaches a steady state after 2060 which may signal an impending Crisis of Capitalism in the US or simply that there would now be enough inequality to ensure continued accumulation for ever. Although the current Trump II Administration is committed to increasing inequality to really high levels, it is also committed to detaching from the World System--contradictory policies that may cancel each other out. 

You can run the USL20_Capitalism model here. Other futures for the USL20 model are available here.


Notes


The Measurement Matrix above was constructed using Principal Components Analysis with standardized data from the World Development Indicators. The USL20 Capitalism model with input from the World System is stable and cyclical (Eigenvalues = (0.8023969+0.119491i 0.8023969-0.119491i) and it is the best model out of the ones tested [-285.6 > AIC = -254.2 > -231.5]). For the BAU model [-260.2 > AIC = -242.3 > -220.5].

The confidence intervals for AICs of the W-input and BAU model overlap and are not statistically different even though the W-input AIC is better. What this means is that, even though the outputs of the two models are very different, political forces within the US could easily switch back and forth between either model--another reason why the future is unknowable. In a future post, I will discuss the importance of the World System for Neoliberalism.

 The full USL20 Capitalism model is available here (both W-input and BAU).

Terms

   US = United States, K = Capital Stock, Q = Production, I = Investment, 
    GINI = Gini Coefficient [0,1], L = Labor,T = Technology, N = Population, 
    O = Output, ECC = Error Correcting Controller
    Neoliberal Accumulation Crisis = (GINI < K),   
    Marxist Accumulation Crisis = (GINI > K)

References



Saturday, December 21, 2024

World-System (1970-2060) US Debt Crisis

The US just had another debt crisis to join France (here), Germany (here) and Canada (here). Debt Crises have been quite the political spectacle, almost closing down the government in the US and toppling governments in European countries. Hitting the Debt Ceiling and Government shutdowns are nothing new for the US (here). Deficit Hawks have used the repeated crisis to impose Austerity on the US Government, threatening to dismantle Social Security, Health Care and Welfare programs while giving tax cuts to the wealthy. 

What is somewhat confusing about all this is that there is a branch of Economics called Modern Monetary Theory (MMT) that suggests that there can be no debt crises when governments control their own currency, as do the governments in the US, France, Germany and Canada. Populist  Deficit Hawks argue that everyone understands that we can accumulate too much debt and wind up in bankruptcy. MMT counters that if individuals go into too much debt they cannot simply print money to get out of debt as modern governments can. As long as there are slack resources in the US Economy, government deficit spending will not create inflation. If you are not familiar with the theoretical arguments, the controversies make interesting reading (here and here).

From the perspective of Systems Theory, Debt Crises reveal yet another Error Correcting Controller (ECC) that is being used to control outputs of the Political System. Regardless of theoretical and rational considerations, the DEBT ECC triggers an important feedback loop we need to understand. If governments have to go into debt to address the Climate Crisis or any other of the many Overlapping Crises, ideas about DEBT will assert themselves as a constraint on spending.

In the graphic above, I have displayed a history of US Debt from 1970 to the present and a forecast for the future out to 2060 by political administration. Debt has been fairly close to the (increasing) attractor path except during the Clinton Administration when it went down, during the Obama Administration when it went up and during the Trump I Administration when it went way up (above the 98% prediction interval) as a result of the COVID-19 Pandemic. The USL20 model's forecast for the future is that US Debt will be declining but with rather wide prediction intervals. Given the historical data, almost anything can happen.

Notes

Data are 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. The Akaike Information Criterion (AIC) is used for model selection.

You can run the WL20W US BAU Model here. From my perspective, the future of US Debt depends on the future of the US economy, which is unknowable but about which I have a forecast (here).
 

Thursday, November 21, 2024

US Inequality

ChatGPT a generative artificial intelligence model lists eight causes of increasing income inequality in the US (Wikipedia list twelve--see below). A GINI coefficient measures the level of income inequality as a percentage with 0=(complete equality) and 1=(complete inequality, one person owns all the wealth). Above 50% is considered high and the US (above 40% right before COVID-19) is considered a country in the middle range.

The history of income inequality after 1970 (in the graphic above) shows major deviations from the bootstrap 98% prediction intervals: (1) during the Ford and Carter administrations (low), (2) during the Bush I, Clinton and Bush II administrations (high) and (3) during the Trump I administration, low as a result of COVID-19


One commonly mentioned cause (regressive taxation) that I can test easily is displayed above. Effective taxation, over the period 1980-2024, is mostly steady with shocks during the Bush I, Trump (result of COVID-19) and Biden administrations.



What will happen in the future under the Trump II administration is speculative. Results from my four models (see below) are displayed above: (1) The RW and BAU models predict continuing high inequality and (2) the US and World System models show peaking and declining inequality, the greatest decline being as a result of World System forces. Clearly, the RW and BAU models would be favored by Trump and any future Republican administrations. As a practical matter, World System linkage would be similar to policies favored by the Obama Administration even though the effects were cyclical.

My tentative conclusion is that Income Inequality would stay high until the end of the Trump II administration and certainly not go down. After that, we would need policies driven by something other than Neoliberalism.

Causes of Income Inequality

Typical causes include: (1) Globalization, (2) Technological Change, (3) Decline in Unions, (4) Stagnant Wages, (5) Executive Compensation, (6) Education, (7) Skills mismatch, (8) Regressive Tax Policy, (9) Erosion of Social Safety Nets, (10) Inheritance, (11) Real Estate and Investment gains, (12) Racial and Gender Inequality, (13) The history of Segregation, (14) Rising Healthcare Costs, (15) Affordable Housing Shortage, (16) Lobbying by the wealthy and powerful, (17) Campaign Finance, and (18) Neoliberalism.

I have tested four models using the AIC: (1) A Random Walk (RW) Model, (2) A Business As Usual Model (BAU), (3) a US Economy Model and (4) a World System model. In the short run (year to year), the RW model is best. As an attractor path, the BAU model (no input variables) is best. From the discussion above, my conclusion is that, in addition to historical determinants, generating inequality is simply an output of the US Capitalist System.