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, April 17, 2025

World-System (1450-1640): The German Economy

 



The expansion of the German Economy after 1450 (a discussion of the period before 1450 can be found here)  was brought to an end by the Urbanization Controller (Q-U) which peaked about 1550 which was also associated with a mild Malthusian crisis (Q-N). Eventually, growth reached a plateau after 1600.

During the early part of the Long Sixteenth Century (1450-1650), the Great Bullion Famine also limited economic growth. Precious metals were necessary to conduct overland and maritime commerce and the European mines were being played out. The voyages of Columbus were motivated by the search for gold necessary to mint coin.


Notes


The measurement matrix for the DEL16 state space model is presented above showing the weightings for the Urbanization (0.634 Q - 0.768 U) and the Malthusian (0.524 Q - 0.7821 N) Error Correcting Controllers (ECCs).



The system matrix for the DEL16 state space model is presented above. The model is unstable (dominant eigenvalue greater than 1.0). The model can be stabilized by reducing the coefficient for the Urbanization ECC (F[2,2] = 1.017812347) or you can turn the Urbanization and the Malthusian ECCs into random walks by setting (F[2,2] = F[3,3] = 1.0).



The result of setting the ECCs to random walks is to create a cyclical system (see the forecast above). What is interesting is that this cyclical system, without German Unification in 1871, enters the Twentieth Century, right before WWI, on a downward cycle. Germany would have been unable to wage war without Unification (see Pasdirtz, 1981).

State Space models for the period (1450-1640) can be found here.




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