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 World-System. Show all posts
Showing posts with label World-System. Show all posts

Friday, August 28, 2026

World System (1950-2000+): The Economy of Canada


This page is UNDER CONSTRUCTION but you can go ahead an explore the Questions presented below using Wikipedia links and State-Space Models.


Unemployment is an important historical controller in Canada as is the Ecological Footprint. Here is a chatGPT report on the Unemployment effects of a Trump Trade War:



You can run the CA_L20 Model on my Google site using R-code.

Notes


Questions

  1. Do you agree with chatGPT's  analysis of Trump Trade War effects on Unemployment?
  2. What might the effects of a Trump Trade War have on Canada's Ecological Footprint?
  3. What happened between 1978 and 1996 to create feedback cycles with Canada's historical controllers, CA2 and CA3?


CNL20 Model Measurement Matrix



The CAL20 model has three component state variables that explain 98.4% of the variation in the indicator variables (taken from the World Development Indicators), the KOF Index of Globalization, the Human Development Index (HDI) and the Ecological Footprint (EF). CA1 = (Growth), CA2 = (LU-EF) and CA3 = (EF+L-Q-CO2-N).

CNL20 AIC Statistics


The best CN_L20 Attractor Path model takes input from the North America Regional Model (NA_L20).



CNL20 Regional Model




The best CN_L20 Attractor Path model takes input from the North America Regional Model (NA_L20).

NAL20 Model Measurement Matrix









 

Wednesday, May 7, 2025

Historical Feedback Controllers in the World-System: I

 


Taking a systems perspective on societal development involves (1) finding measurable variables of interest for the system and (2) categorizing them using the graphic above. Input variables are external to the system, for example the economic growth of another country or of the World System. Output variables are those under control of the system. The Environment captures the qualitative factors that might influence the performance of the system during a specific historical period. Feedback Control involves (1) the dynamic interactions of the state variables over time and (2) a feedback control loop (for example a PID Controller) imposed on a system to produce desired outputs.

Needless to say, for a macro-economic system, input and output variables could involve an infinite number of measurements. State Variables are the independent set of variables that explain the time path of the system outputs in response to inputs. In Dynamic Component Models, approximate state variables are constructed using Principle Components Analysis. Weightings and signs of indicator variables are used to construct the Measurement Matrix which converts state variables to output variables.



The measurement matrix for the US_M Model (1900-2000) shows a number of controllers. Each row of the matrix is a state variable. The first state variable describes Overall Balanced Growth. The second state variable, US2=(0.663X - 0.555N) describes a Malthusian Export Controller. The third state variable describes a combination of controllers: Malthusian = (0.484 Q - 0.421 N),  Export Prices = (0.33 XREAL - 0.538 X) and Employment = (0.3458 HOURS - 0.268 L). Together, these three state variables explain 0.999% of the variation in the growth indicators.

The time plots for the US1, US2 and US3 state variables are presented above. US1 is the growth component that shows an exponential path across the Long 20th Century. US2 (dashed red line) the Malthusian Export Controller turns negative in the period after 1960. And, US3, the complex Malthusian, Export-Price and Employment controller stays close to the zero point throughout the period.

The three short-cycle minor controllers, US4= (0.650 Q- 0.504 L), (US5=(0.7362 HOURS- 0.490 L)) and (US6=another complex controller), show cyclical paths with decade-long periods.