Controlling Dynamic Components Models

 

For more information on Dynamic Component Models see Pasdirtz, 2007.

Error Correcting Controllers in the World-System

 

Error Correcting Controllers (ECC) are used in Control Theory to generate positive and negative feedback loops to control systems. In economics and sociology, ECCs can be generalized to describe the behavior of macro-economic and macro-social systems starting with Leibenstein's Malthusian Model:

• Malthusian Controller (Q-N) Negative feedback will result when population growth exceeds economic growth.
• Stock Adjustment (Q-K)
• Liberal Market Controller (Q-P) 
• Marxist Controller (Q-L) or (Q-wL) 
• Labor Surplus Controller (Q-LA) 
• Keynesian Controller (Q-G) 
• Environmental Controller (Q-T) 
• Mercantilism Controller (Q-X)
• Modernization Controller (N-V)
• World Price Controller (XR-X)
• Monetarism Controller  (Q-M)
• Fascism Controller (Q-War)
• Globalization Controller (WS-QP)
• Malthusian Trade Controller (N-X)
• Liberal Trade Controller (Q-X)
• Labor Surplus Controller (X-L)
• Class Struggle Controller (L-U)
• Urban Trade Controller (X-U)
• World-System Controller (WS-X)
• Ricardian Trade Controller (X-XWS)

In specific countries during specific historical periods, combinations of controllers are likely to be used. The used of an ECC or multiple ECCs does not imply that the systems is under stable control. For more discussion, see Growth and Control in the World-System. You can run the US_M model code and experiment with the model (here).

Growth and Control in the World-System

 

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.