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.

Wednesday, October 29, 2025

World-System (0-2000) What Caused the Industrial Revolution?

                 

The graphic above is a time plot of World Aggregate Production (W_Q) taken from Maddison (see the Boiler Pate).  The growth of Capitalism is typically data from 1500-Present with a clear visible take-off starting in the 19th Century. The burning question is "Why"!


ChatGPT (an AI Systems) produces the graphic above as an answer to the question "What Caused the Industrial Revolution".*** One can quibble with some of the links in the graph ("Why aren't Profits plowed back into the production process?", "What about Environmental Impacts?", etc.), but the graph is a good place to start.


The Kaya Identity is another good place to start (notice the Kaya Identity does not have feedback loops).

The causes of the Industrial Revolution are not possible to consider in one post, but I think there is a causal explanation that has been missed and I will investigate it in future posts.


Notes


*** Actually, my question was about feedback loops in the Industrial Revolution but you can asked the "What Caused" question yourself here. Google AI provides the following answer:

AI Overview
The main causes of the Industrial Revolution include 
  • combination of the Agricultural Revolutionwhich freed up labor and increased foodproduction;
  • technological innovations like the steam engine and new machinery that mechanized production;
  • access to natural resources such as coal and iron;
  • economic and political factors like capitalismavailable capitaland supportive government policies;
  • and an increase in population growth and made, which created both work force and demand for goods.

Agricultural advancements

The enclosure movement:Landowners consolidated smaller plots of land, making farming more efficient and forcing many rural laborers to seek work in cities.
New farming techniques:Innovations like Jethro Tull's seed drill increased crop yields, supporting a larger population.

Technological innovation

New inventions:

Key inventions like the spinning jenny, water frame, and steam engine revolutionized production in the textile and other industries.

Mechanization:
Machines could produce goods faster and more cheaply than by hand, leading to the development of the factory system.
Economic and political factors
Capitalism:
An economic system with private property and free enterprise encouraged investment and risk-taking.
Available capital:
A large amount of money was available for investment in new businesses and technologies.
Supportive government:
Policies, such as those protecting property rights and patents, encouraged innovation and industrial growth.
Abundant natural resources:
Britain, the birthplace of the revolution, had large deposits of coal for power and iron for machinery, often located near waterways for transport.
Growing population:
Population growth provided both a large workforce for factories and a bigger market for consumer goods.
Improved transportation:
Systems like canals and later railroads made it cheaper and faster to transport raw materials and finished products.

References















Thursday, October 16, 2025

World-System (1960-2150) La French TECH Cycles



In a prior post (here) and in prior posts on the French Economy (here), I have found that the French Economy (or at least my model of it) is approaching a Steady State. My hypothesis is that the approaching steady state might (in addition to a lot of other forces) be creating Political Instability. However, no one knows the Future and we have to entertain other hypotheses.

The current 2025 Noble Prize in Economics offers another hypothesis. History teaches us that new technologies and Creative Destruction will eventually break steady states and send Economic Systems on to new Attractor Paths. The hypothesis is the essential argument of Kondratiev Wave Theory (here) and is embraced by World-Systems Theory. An alternative forecast for France is that the Steady State will not happen due to La French TECH.

The graphic above plots two historical forms of French Technology: Productivity (TECHP) and Efficiency (TECHE) (see the Notes below). Notice that they are both cyclical (echoes of Schumpeter's Creative Destruction model which is also cyclical but unstable). Notice also that TECHP (productivity) peaks before TECHE (efficiency): once a productivity peak is reached, focus turns toward efficiency until all gains are exhausted.

Unfortunately for France, both of these technological peaks (at least in my model which is estimated from World Development Data) are going to be reached in the near future: (1) reinforcing the steady state or (2) creating more instability and a search for new technologies to put the economy on another growth path. Since we do not know the Future, nothing is guaranteed.

For more on Stable French Technology Cycles see the post hereSchumpeter's Creative Destruction model predicts unstable Creative Destruction cycles and the French Technology Cycles are stable.
 

Notes

FR TECH Measurement Models


The two types of Technological Change  (TECHP and TECHE) are explained in a post on Technology in the United Kingdom which also is a good comparison to the French Model. Essentially, TECHP is productivity (output per capita)  and TECHE is efficiency (for example, CO2 emissions relative to energy consumption).

Friday, October 10, 2025

Friday, September 26, 2025

World-System (1960-2500) Unstable System Cycles in Latin America

 


In an earlier post (here and here), I found that the best forecasting model for Argentina was the LA20 Model (Latin America Regional Economy). Out until 2100 (the furthest out the IPCC is willing to go on Global Emission Scenarios), it looks as if Latin American Integration would provide a desirable future, at least for Argentina (here). This post explores what happens after 2100, out to 2500. Of course, no one knows the future (especially out to 2500), but the LA20 Model is a computer program that can be run out to any date. Sometimes it is insightful just to see what happens!


The LA20 Model is unstable and cyclical (the eigenvalues and AIC statistics are presented in the graphic above for the Business as Usual BAU model).  In the Phase Plot, above, time moves from left to right and cycles increase in magnitude and severity.** Although the short-term future might look endurable, the long-term future is not. Luckily, a lot (maybe everything) can change after 2100, especially in the face of Environmental Crisis.

Another reason to look at long-run cycles in Latin America is that cycles (particularly Kondratiev Waves or K-Waves) are discussed extensively and qualitatively in World-Systems Theory. It is refreshingly concrete to see actual historical cycles tested with a statistically estimated model. However, a future of unstable cycles is probably one reason why Latin American Integration has been so problematic.


Notes

** And will require that bailouts increase in magnitude and severity.


LA20 BAU Measurement Matrix:

The State Space of the LA20 model has three components that explain 99% of the variation in the indicators: LA1=(Overall Growth), LA2=(LU-Q-EG) an Unemployment Controller and LA3=(N+L-CO2-Q) a Population Controller. LA1 reinforces the conclusions of Balanced Growth Theory (all major parts of the Economy have to grow together). LA2 balances Unemployment (LU) against overall production (Q) and Energy Use (EG)--reducing LU requires increasing energy-intensive production. LA3 is a Malthusian-Environmental component balancing Population (N) and Labor Force (L) Growth against Emission (CO2) intensive production (Q).

The unstable LA20 BAU model has cyclical periods under a decade but no effective damping time (table above). 
The stable LA20 BAU model also has cyclical periods under a decade but damping times of about 150 years.

NOTE: Periods in both models are longer than those assumed by Kondratiev Waves or K-Wave models (45-60 years). LA2 could be expanded to a Marxian Economic component with (0.901 L - 0.272 Q - 0.239 EG - 0.144 L) where the standard Marxian Economic component is (Q - wL) assuming fixed Ricardian wages. Most of these ideas (MalthusianMarxian EconomicBalanced Growth Theory and Kondratiev Waves or K-Wave) can be combined in Systems Theory models. However, the result for LA does not mean that the ideas can be generalized to all regions, countries and time periods (see Unified Growth Theory).

You can experiment with the LA20 BAU model hereSuggestions are given in the code for how to stabilize the model.

Ex. 1.0 Can you find a way to eliminate cycles once the model has been stabilized? 

The solution to this Exercise can be found in the LA_TECHP model which I will describe in a future post. 

Descriptions of the how the Dynamic Component State Space models are constructed are given in the Boiler Plate.




Sunday, September 7, 2025

World-System (1950-2100) The New "Axis of Evil" BAU Scenario

 

In a prior post (here) I found that most scenarios for the "New Axis of Evil" (Russia, China and India) led to collapse of the system, except for one: the BAU (Business as Usual) Scenario. In one interpretation of the BAU scenario, the AXIS is allowed to dominate the World System and the US without interference from other countries. Although the scenario seems unlikely and might well lead to World War III, in this post I will take it seriously and see what happen between the present and the year 2100.

In another interpretation of the BAU Scenario, the AXIS is necessary to drive exponential growth of the World-System and of the Hegemonic leader (the US). I like the Functionalist explanation. Functionalism suggests we focus on the World-System, which I think is the right focus. In this post, I will present a model that demonstrates the Functionalist explanation for the New Axis of Evil.

The Functionalist explanation hypothesizes that the Axis-of-Evil is necessary to stimulate military spending and growth of all participants.

Politicians, on the other hand, seem to have no concept of a World-System which leads to a Contradiction: are there systemic considerations that affect the AXIS? The graphic above shows the non-system view: exponential growth forever, the US1 and the World System (W1) driven independently by the Axis.


The graphic above shows the US1 growth system forecast when driven by the AXIS model. The function of the AXIS is to stabilize the system, at least in terms of US growth.



The same is not true for World System growth (W1) in the graphic above. In other words, US growth, given AXIS input, is at the expense of the World System.


You can run the AXIS_of_Evil models here.




Tuesday, August 26, 2025

What is Historical Dialectic Materialism?

 



I was first introduced to the terms Dialectic Materialism and Historical Materialism in an advanced sociology course on Marxism at the University of Wisconsin, Madison. At the time, I didn't understand how important the concepts were to understanding Quantitative History. Hopefully, I can communiate my understanding in this post.




Notes

The drawing at the beginning of this post pictures Marx and the British museum in the process of researching. When I visited the British Museum, I asked where Marx sat when he was writing and they didn't know but it was probably somewhere in the Socials Science section (reasonably). So, I sat in a chair there and contemplated!

World-System (1950-2100) How to Balance the World System


In an earlier post (here), I found that the US-MX-CA World Trading System could reach a Steady State in a number of ways.

Creating a Steady State in the World System, keeping Industrialization and Environmental Degradation in balance, involves mitigating the cascading effects of Collapsing Oil Markets and collapsing Agricultural markets.

This fictional future is controversial: (1) As long as population growth and technological change continue to increase, the Neoclassical Economic Growth model will never reach equilibrium (unlimited growth forever), (2) In World-Systems Theory, although we live in a World of interacting economic systems, because there is no World Government to legislate a Steady State, there is no governed World System** and (3) the IPCC Emission Scenarios (see the Boiler Plate and the BAU Scenario) envision a scenario where the World-System is eventually in a Steady StateContinued uncontrolled industrialization seems inevitable and, at the same time, inconsistent with environmental balance.

And, worse yet, the best scenario for the US-MX-CA Trading System (using the AIC to evaluate models) is growth-and-collapse (SSP2.0-6.0 in the IPCC Scenarios) when driven by the World System (here). In this post I will explore ways to create a Steady State in the World System because (1) the WL203 Model  is often, in my experience, a good input for country-level World-System models, (2) the IPCC Emission Scenarios are all conducted in terms of the World System, (3) Limits-to-Growth policy recommendations are directed at the World System and (4) I want to address the issue of how environmental balance is supposed to happen without World government.
 



The graphic above presents a number of experiments with the WL203 Model (you can run the experiments yourself here). These futures look a lot like the IPCC Emission Scenarios because growth of the entire World System produces emissions. 

There are three growth-and-collapse scenarios: WL20, F[1,2] = 0 and F[2,3]=0. The magnitude of collapse is increased by reducing the effects of feedback loops from Food Production (F[1,2]=0) and decreased by reductions in the feedback effects of Oil Production (F[2,3]=0). Reducing both feedback effects to zero produces a high-level steady state (F[1,2] = 0 and F[2,3]=0). Setting growth in the World System to a Random Walk produces an immediate steady state (F[1,1]=0). 

The counterfactual experiments are discussed more fully in the Notes below. But, what do the model results mean in a practical sense for policy action:
  • Oil and food production (through the oil-driven Green Revolution) are essential for Industrial society. We typically don't think of oil markets and agricultural markets as historical feedback controllers, but they will become controllers when Peak Oil is reached (oil is a non-renewable resources). Electric vehicles, wind and solar energy serve to reduce feedback effects from Oil Markets.
  • Current uses of oil (burning in combustion engines, making plastic bottles, medical devices, industrial fertilizers, etc.) will be restricted after Peak Oil. It would be prudent to reduce industrial growth rates and conserve existing supplies of all scare, non-renewable resources.
All of these policy measures are being attempted to some extent (but reducing growth rates seems to be the most difficult). My assumption is that the only way to motivate global action is from entering growth-and-collapse mode and then focussing political action, if it is not too late (result from the WL203 Model here suggest that there will be a rebound (see the Recovery Forecast below in the Notes) after 2115 and the World System could recover). Environmental Mitigation will most likely not be undertaken voluntarily.

Notes

** In World-Systems Theory, the hyphen between "World" and "System" indicates a world of systems. The term "World System" indicates a one-world system. The World System is typically used by the IPCC in Integrated Assessment Models (IAMS). The Contradiction here is that there is no World Government to manage environmental degradation.


The time plot above shows the dominant component from the WL203 Model. From 1950 to 2008, the blue line tracks the actual data. From 2008 to 2108, the different time paths are created by setting various elements in the WL203 Model System Matrix (F) to zero or one. Let me first describe how the state space is constructed and then describe the System Matrix (F) (more information about the models is available in the Boiler Plate).

The approximate state space is constructed using Principal Components Analysis (PCA). The PCA measurement matrix is presented above. The first component (W1) is the dominant component and explains 87.4% of the variation in the underlying indicators. The other two components (W2 and W3) are historical feedback controllers. 

The first component, W1=(Growth-LP), is overall growth compared to the Living Planet Index (LP)an indicator of the state of global biological diversity. Over time the LP Index peaks after 1975 and declines after that (see the graphic above). In the future, the (Growth-LP) historical controller might become more important but right now, the decline in global biological diversity will just continue.


The second component, W2=(LP+P.Wheat.-GWP-TEMP), is an historical feedback controller that links the LP index and the Agricultural market (P.Wheat.) to Gross World Product and Global Surface Temperature. For the period from 1970-2000, W2 was in positive territory. From 2000 to the present, W2 has become negative meaning that GWP and Global Temperature are not in balance with Biodiversity and Agricultural production.

The third component, W3=(P.Oil.-OIL-EF), is also an historical feedback controller for Oil Markets and the Ecological Footprint. From the graphic above, the Oil-Market-Footprint controller seems to be reaching a steady state (Peak Oil) but this can mean that  (1) Oil Prices will keep climbing as supplies dwindle or (2) Prices will decline as demand declines.


The System Matrix, F (above), shows the interaction between the three state variables (column [,4] is the constant term in the statistical model). The system is stable (ignoring the constant) and cyclical (periods and damping time over hundreds of years). 



Results of manipulating the System Matrix:
  • WL20 In the graphic above, the dark black line is the basic model forecast: slowing growth in the present and collapse shortly after that.
  • F[1,2] = 0 The coefficient -0.02519461 is the negative feedback effect of food production, W2. Without this feedback effect, collapse happens more rapidly.
  • F[2,3] = 0 The coefficient -0.05250691 is the negative effect of the Oil-Market-Footprint W3, on food production, W2. Eliminating this feedback effect reduces the amount of collapse after 2050.
  • F[2,3] = F[3,2] = 0 Eliminating the interaction between W2 and W3, leads to gradual growth and then a steady state after 2100.
  • F[1,1] = 1 Finally, setting growth to a Random Walk, results in an immediate steady state.

What do these results mean in terms of balancing and controlling the World System? 

First, the World system has it's own feedback mechanisms that will limit growth. It should be no surprise that Peak Oil and damage to Agricultural production systems will put the World System in a growth and collapse mode. The two systems (Oil Production and the Green Revolution) are intimately linked and can fail together to provide energy and food for the Industrial Revolution

Second, a World Government would be helpful in minimizing the effects of collapse but I can't see nations agreeing to be governed before 2100 (current effects by the United Nations have been unsuccessful). 

Third, our current Integrate Assessment Models (for example, the DICE model) seem to have none of these feedback effects. 

Fourth, my results seem to align with the IPCC Emission Scenarios which makes sense because system growth, energy emissions and global temperature are intimately liked (I will do a more detailed comparison on a future post).

No one knows the future; all we have are projections from models. Politicians who claim that all the model projections are a hoax simply rely on their gut instincts to say that everything will be fine--a massive act of ignorance, denial and hubris before the fall.

Recovery Forecast

Since the WL203 model (here) is cyclical and stable, the prediction for the far-distant future (after 2130) is for recovery. But notice that the system does not reach the same level it had reached in 2000; Entropy takes it's toll.