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, February 25, 2025

World-System (1960-2100) Six Futures for the World System


In January of 2025, the IMF released an update to the World Economic Outlook (WEO) which addressed growth, inflation and other economic indicators for the World-System. The general conclusion was that global growth is "divergent and uncertain". The WEO does not provide forecasts or scenarios (see the IPCC Emission Scenarios) for the World-System and only looks back over a handful of years when analyzing economic trends. In this post, I will take a Systems Perspective and look at the World System growth component (W1, see below in the Notes) from 1960 to 2100.

In their analysis, the IMF was primarily focused on the rate of change in GDP. From Systems Perspective, we can look at the rate of change in overall system growth from (1960-2010, above). The average rate of change was -11.52884%  but the mean is heavily weighted by the period around the 1980's when the World System was in crisis (the early 1980's recession). Although growth rates are decreasing in the World System, it is difficult from the graph above to decide whether or not the system is stagnating or reaching a steady state. For that answer we need to estimate system models.

I've estimate six systems models. The difference between the models involves only the input variables which are chosen based on different Geopolitical Alignments for the World System (see below in the Notes).




The first group of models (graphed above) compares the US and the World model (WL20) to a Random Walk (RW) and to the Business As Usual (BAU) model. These models provide a range of growth from stable linear growth (BAU) to growth-and-collapse models (WL20 and US). The Random Walk (RW) provides the baseline.



The next set of models (graphed above) compares stable exponential growth (the RULM model, late Modern) to a stable decline model (WL20W). Again, the RW model provides a baseline. 
In the final set of models (graphed above), I compare the China Model (CH, stable growth) to the Russian Late 20th Century model (RUL20, unstable cyclical growth). Geopolitical Alignments with Russia and China, in these models, would end up in the same place in 2100, but the RUL20 model would be a rougher ride.


The six models above offer a range of reasonable futures for the World System but there are some surprises.  The RULM model (stable exponential growth), the Growth and Collapse models (US and WL20) and the collapse model (CH) would probably not have been predicted in advance from arm-chair speculations. But, no one knows the future. The models themselves are speculative (but at least estimated from historical data) and meant for discussion and analysis. However, the alternative models, I would argue, are better than presenting one simple BAU model (for example, the DICE model) and assuming that growth will continue linearly for the foreseeable future.

The results of the forecasts above are a direct result of the behavior of the country model assumed to be the hegemonic leader dominating the World System. Using the AIC (see below), the best model is the WL20 model (AIC=-3.91), a BAU model that assumes no hegemonic leader.

Notes

The World System growth component is the  first principal component state variable for the WL20 model.


The Measurement Matrix for the WL20 model is presented above. The W1 Component (state variable) is an approximately equal and positive weighting of all the indicators except for the Living Planet Index (the planet is becoming less livable) and measures overall growth in the World System (rather than just GDP).

The six models estimated for the World System WL20 model are based on six different Geopolitical Alignments:
  • BAU The Business As Usual (BAU) model assumes no input variables and thus no preferred hegemonic geopolitical alignment for the World System
  • RW The Random Walk (RW) model assumes that the World System responds randomly to shocks from the member states. Today is like tomorrow except for random shocks (just one damned thing after another).
  • W The World System model (W) assumes that the W1 state variable is driven entirely by other state variables in the system, W2 and W3 respectively (in some analyses, more state variables could be added).
  • US The United States (US) model assumes that the US is the hegemonic leader of the world system.
  • RU The Russia (RU) model assumes that Russia is the hegemonic leader of the World System.
  • CH The China (CH) model assumes that China is the hegemonic leader of the World System.
Of the geopolitical linkage models, the US model (AIC=109.57), the WL20 model (AIC=-3.91), the RU model (AIC=117.95) and the CH model (AIC=136.50) were the best using the Akaike Information Criterion (AIC). Of these models, the WL20, the US, the CH and the RU models were stable (dominant eigenvalue < 1.0).

In general, the 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 models used for input variables can be viewed and run here.



 

Monday, February 24, 2025

World-System (1960-2100) Six Futures for Germany

 



In a prior post (here) I presented results from the DEL20 Model that suggested the German Economy may have reached a steady state sometime after the year 2000. I have also argued (here) that the Steady State Economy, although it will solve some environmental problems by stabilizing CO2 emissions, might create other Geopolitical problems by becoming the target of predatory economies focused on World domination (e.g., Germany in the Nineteenth Century) The question for this post is whether some (new?) Geopolitical Alignment might protect Germany from the (possible) fate of stagnant steady-state economics. The answer isn't encouraging.

From the graphic above, you can see that alignment with the European Union (EU) or Business as Usual (BAU, NS, RW) don't shock the German Economy out of the steady state. Alignments with the World System (W) or the United States (US) are even worse. Here are the specific results:
  • Random Walk (RW)
  • Nation State (NS)
  • European Union (EU)
  • Business as Usual (BAU)
  • World System (W)
  • United States (US)
  • Russia (RU)


NOTES

Thursday, February 6, 2025

World-System (1980-2100) Eight Futures for Canada


The Trump II administration has threatened a Trade War with Canada and the imposition of tariffs has been delayed while negotiations proceed (here). Canada, Mexico, China and the EU are the US's largest trading partners. I have presented the MXL20 (Mexico Late 20th Century) model here with eight future growth forecasts. In this post, I will do the same for Canada.

The Canadian forecasts are a little different in that they group clearly into two classes: Growth and Steady State (presented above) or Collapse (presented below) when compared against a the Random Walk (RW)--I give more detail about the classes of models with the MXL20 model here--the best two forecasts are the TECHE (Technical Efficiency) forecast and the Business as Usual (BAU) forecast. The forecasts do not predict growth forever (the Techno-Optimist forecast) but rather a steady-state after 2100 (the type of forecast one would get with a Classical Economic model).

The forecast for Geopolitical Alignment with the United States is very interesting and, I would argue, speaks directly to the threatened Trade War. The forecast with the USL20 model driving inputs to the CAL20 model suggests a Growth-and-Collapse scenario with a peak around 2025 at the start of the Trump II administration. In other words, the benefits of Canada's alignment with US have reached their peak and are not forecast to continue into the future--and my forecasts start in 2010!

Both the IMF (here) and the OECD (here) argue (as of 2024) that Canada needs to focus on internal structural issues and Technology, the BAU and the TECHE (Technical Efficiency) forecasts above. Reorienting the Canadian Economy will be difficult during a Trade War with the US, to say the least.


It would be reasonable to argue that some other Geopolitical Alignment might serve Canada better than alignment with the US, which appears to be ending.  I have estimated three other alignment models: World System (W), North America (NA) and China (CN). All of these models (presented above) predict collapse, some collapses being severe (NA and CN, respectively). Even focusing on Technical Productivity (TECHP) is worse than a Random Walk (RW, tomorrow being like today except for random shocks).

In summary, the CAL20 model suggests that Canada should concentrate on getting it's structural house in order and implementing efficiency-producing technologies, two steps that the IMF and the OCED have been emphasizing for the last twenty years. Let the Trade War with the US play it's way out. Geopolitical Alignment with the US has run it's course.

The IMF (here) and the OECD (here) economic reports about Canada bring up many other macro-economic issues. I'll look at those issues in the future. Setting the big picture for the Canadian Economy will help put detailed policy issues in a better perspective. I want to emphasize again that the future is unknowable. All I am doing is creating scenarios based on state space models. We will have to wait for the future to understand how useful such models might be.

NOTES

The Measurement Matrix for the CAL20 model is:


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 second two components: CA2=(0.721 LU - 0.675 EF) and CA3 = (0.586 LU + 0.680 EF - 0.249 CO2 - 0.263 Q - 0.2076 N) describe Environmental and Unemployment Error Correction Controllers (ECCs). I will present the behavior of the Canadian ECCs in a future post.

You can run the CAL20 model here. The Bootstrap confidence intervals for the coefficients are:


You can convert the model into a Techno-Optimist model by setting F[1,1] = 1.0 in the System Matrix, but that would be an improbable value although it is close to the Upper Confidence Interval (UCI) of 0.990595.


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.





Monday, February 3, 2025

World-System (1970-2100) Eight Futures for Mexico

 



The Trump II administration has threatened a Trade War with Mexico and the imposition of tariffs has been delayed while negotiations proceed (here). Canada, Mexico, China and the EU are the US's largest trading partners. Trump has threatened tariffs on all four if his demands on immigration and drug trafficking are not met. The common assumption is that the US "Gorilla" will impose it's will on other nations in the world and will get what it wants. But a World Economic Order where the US imposes it's hegemony on the rest of the World-System is not the only option and it may not be the best for any particular country.

In this post, I will create future paths for the development of Mexico based on different assumptions about possible Geopolitical Alignments. First, there is some history here between Mexico and the two Trump Administrations. In 1994, the US signed the North American Free Trade Agreement (NAFTA), but the impetus for free trade started in the Reagan Administration and is a central assumption of Neoliberalism. In 2017, with the start of the Trump I Administration, NAFTA was renegotiated into the United States-Mexico-Canada Agreement (Trump thought NAFTA was a "bad deal"). Now, in the Trump II Administration, the United States-Mexico-Canada Agreement (that Trump negotiated in 2017) is itself a "bad deal" and Trump thinks that the US is being treated very "unfairly". In the future, trading partners might no longer want to deal with the US and a US Republican party that can't decide whether Neoliberal free trade is a good or bad thing.

Currently, Mexico has an important role to play in the Globalization of its trading partners (CN, CA and US) but does not exert much control over the system (here). Future Geopolitical alignments, to include giving up on the World-System, might be one of the the following (presented visually in the time plot at the beginning of this post):  

  • BAU [119.6 < AIC124 < 128] The Business as Usual (BAU) model is not a bad option (you can experiment with it here--see the bootstrap confidences intervals for coefficients below). It would essentially involve Isolationism and would insulate Mexico from US bullying tactics.

  • LAC [73.36 < AIC = 131.5 < 170.1] The Latin American Regional (LAC) Alignment would direct Mexico to trade with it's Latin American Neighbors. It would not mean isolation from the World-System but rather Latin American Integration or a confederation of Latin American countries that would interface with the World-System (an unrealized idea that goes back to the 19th Century). In the MXL20 model, it would result in a steady-state after 2040.

  • RW [38.14 < AIC = 48.06 < 57.18] The Random Walk (RW) model would open Mexico up to all types of shocks from the World-System, with Mexico becoming a Small Country, possibly dominated by some other World hegemonic leader. In the short-run (year-to-year) it is not a bad description of 20th Century Mexican history as one damned thing after another.

  • W [69.96 < AIC = 91.55 < 104.3] Hierarchy Theory would argue that linking Mexico to the World System would be the best way to control growth, environmental problems and unemployment (see the Measurement Matrix below for the MX1, MX2 and MX3 state variable components). For Mexico, such a linkage would mean Degrowth after 2040.

  • US [104.7 < AIC = 112.8 < 119.5] Hegemony Theory would suggest that linking to the Hegemonic World Leader (the US, in this case) would be the best strategy for a Semi-peripheral country such as Mexico. The US and Mexico have been strengthening ties (off and on) over the last three decades, but the Trump Administrations seem intent on severing the relationship. For Mexico, Hegemonic linkage would also mean Degrowth after 2040.

  • CN [103.2 AIC = 116.5 < 129.1] Mexico has also had a history of strengthening relations with China. If the US cuts Mexico free, China may well move into the Geopolitical vacuum. Of the choices uncovered by the MXL20 model, linking with China would be the worst and would lead to almost immediate collapse. The reason is the predicted collapse of the CN21 Model (to be covered in a future post).

  • TECH1 Productivity [63.11 < AIC = 102.8 < 135.3] Mexico could also choose to improve the technological advancement of their economy. One aspect of Technological change is productivity (output per worker, output per energy input, etc.). Although an attractive alternative suggested by Economic Growth Theory, it would be equivalent to a steady-state in Mexico (see LAC above). 

  • TECH2 Efficiency [81.42 < AIC = 130.8 < 160.6] Another aspect of Technological change is efficiency, for example, decreasing energy use per unit of GDP. In Mexico, increases in Economic Efficiency would not be much better than a Random Walk (RW).

As with the IPCC Emission Scenarios the Geopolitical options for Mexico are not forecasts. The future is unknowable. Using different inputs to the MXL20 model, alternate futures can be extrapolated. We will have to wait to see what direction Mexico actually choses, but shocks from the Trump II administration may push the country into making choices.

Notes

MX1 is the dominant state variable of the MXL20 system with data taken from the World Development Indicators (WDI). The methodology used to create forecasts is similar to the one used by the Atlanta Federal Reserves GDPNow app but produces growth scenarios similar to the IPCC Emission Scenarios. Prediction intervals are generated using a Bootstrap algorithm in the R programming language. The AIC can be used to evaluate the quality of models but does not determine which model provides the best forecast. An explanation of Dynamic Component Models (DCMs) can be found here.

The MX1 state variable was created from the following weighted indicators (the first row of the Measurement Matrix) and explain 98% of the variation. 


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 second two components: MX2=(0.892 EF- 0.34 LU - 0.22 HDI) and MX3 = (0.847 LU - 0.305 GDP) describe Environmental and Unemployment Error Correction Controllers (ECCs).

You can run the MXL20-BAU model here. The bootstrap confidence intervals for coefficients are:


You can change parameters in the System Matrix (F) in the MXL20 BAU model to any number you want, but the ranges presented above would not be too extreme and would have reasonable probability values.

IPCC Emission Scenarios


Most of the IPCC Scenarios seem to produce a steady state around 2100 (after controlled growth or Degrowth) but there are some outlier scenarios that seem to grow forever. Te MXL20 BAU model is stable and would eventually also reach a steady state (well after 2100).

Saturday, February 1, 2025

World-System (1990-2060) Globalization and Trump II Tariffs

 

The Trump II Administration announced today (here) that it is imposing stiff tariffs on goods from Mexico, Canada and China because "...they haven't treated us fairly on trade...". The Wall Street Journal (here) is calling the move "...the dumbest trade war in history...". Other than the Trump II administration breaking decisively with Neoliberalism (free trade and Globalization were key elements of Neoliberal orthodoxy), what is going on here?

Let's first look at the state of Globalization among the trading partners (US, CN, CA, and MX) using the KOF Index of Globalization. The dominant state variable attractor path for the trading system is displayed above as being driven by the USL20 model. From 1990 to 2000, the system had its ups and downs but did stay pretty much within the 98% prediction intervals for the attractor path. In 2010, the system was right on the attractor path. After that, the US-dominated system is predicted to peak somewhere around 2040. Trump is throwing a tariff-wrench in the system and, as with prior swings in Globalization, the policy may have little impact and we can expect a return to the attractor path after Trump II is gone.

But, does Trump understand that the Globalization system is reaching a peak and might well collapse in the future? Is Trump attempting to pull globalized US industries back on-shore before system collapse? Trump claims to act intuitively and his ample gut might tell him that the global World-System is collapsing. At this point, my goal is to get a stake in the ground to understand what has happened after the Trump II Administration is over.


Notes


The Measurement Matrix for this KOF Index of Globalization system is presented above. KOF1=overall growth, KOF2 is dominated by the US and KOF3 is dominated by Canada. All look at KOF2 and KOF3 in future posts.