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.

Thursday, June 18, 2026

Unstable Feedback Loops

 


Everyone has probably heard intended or unintended audio feedback effects at a Rock Concert or a public event with a PA System.  What is probably not well understood is that unstable feedback loops can be found in any system (see examples below) under certain conditions. 

Ii have been studying social systems and feedback loops since the 1980's. Some AI summaries, first from ChatGPT and then from Google AI are presented below.

Contrary to the AI conclusions, for example that the Great Depression was a result of unstable feedback loops, the US_E20 Model does not have unstable secondary feedback loops, neither does the DEL19D Model for 19th Century Germany, contrary to my initial hypotheses.

Notes

Pasdirtz, G.W. Instability and Late Nineteenth Century German Development. The DEL19D Model does not have unstable feedback loops but does have an unstable growth component and is an example of the Moving Equilibrium model.


ChatGPT

What are the effects if unstable feedback loops in systems?

Unstable feedback loops occur when a system's responses amplify disturbances rather than dampening them. Instead of returning to equilibrium after a shock, the system moves farther away from it.

General Effects of Unstable Feedback Loops

  1. Exponential Growth or Decline
    • Small changes become large changes.
    • The system may experience runaway growth or collapse.
    • Example: A bank run, where withdrawals trigger more withdrawals.
  2. Increased Volatility
    • Fluctuations become larger over time.
    • The system becomes difficult to predict or control.
    • Example: Financial bubbles and crashes.
  3. Loss of Equilibrium
    • Stable operating points disappear.
    • The system may shift to a completely different state.
    • Example: An ecosystem losing a key species and reorganizing into a new ecological regime.
  4. Overshoot and Collapse
    • Growth exceeds sustainable limits, followed by rapid decline.
    • Example: Population growth that exhausts resources.
  5. Tipping Points
    • A critical threshold is crossed, after which change becomes self-reinforcing.
    • Returning to the previous state may become difficult or impossible.
    • Example: Climate systems reaching irreversible ice-sheet loss.
  6. System Failure
    • Components become overloaded and break down.
    • Example: Electrical grids experiencing cascading blackouts.

Examples Across Different Systems

SystemUnstable Feedback LoopPossible Outcome
EconomyRising asset prices attract more buyersBubble and crash
ClimateWarming melts ice, reducing reflectivityAccelerated warming
PoliticsPolarization creates more polarizationInstitutional breakdown
EcologySpecies loss reduces ecosystem resilienceEcosystem collapse
TechnologySocial media engagement rewards outrageInformation instability
MilitaryArms race encourages further armamentEscalating conflict

Why Some Systems Survive

Many real-world systems contain negative feedback loops that counteract instability:

  • Central banks raising interest rates during inflation.
  • Predator populations limiting prey populations.
  • Thermostats regulating temperature.
  • Democratic institutions constraining political power.

When these stabilizing mechanisms are weaker than the reinforcing feedbacks, instability grows.

A Systems Theory Perspective

From the perspective of the academic field of Systems Theory, the most dangerous systems are not those with feedback loops alone—every system has feedback loops—but those where:

  1. Positive feedback dominates negative feedback.
  2. Delays prevent corrective action.
  3. Actors do not perceive the consequences until thresholds are crossed.

Many major historical crises—from the Great Depression to financial crashes and ecological collapses—can be understood as situations where self-reinforcing feedbacks overwhelmed stabilizing forces.

A useful rule is:

Stable systems absorb shocks; unstable systems amplify them.


Google AI




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