Forward and Backward Feedback in Growth Models
|Author:||Ing. Jan Plešingr, PhD.|
|Year:||2001 - winter|
|Leaders:|| prof. Ing. Miloslav Vošvrda CSc.
|Work type:|| Dissertations
|Awards and prizes:|
|Abstract:||The traditional approach of the optimal representative household behavior in the Ramsey-Cass-Koopmans (RCK) model is reconsidered under the assumption of a time shift in the optimal feedback. A situation when the representative households apply a consumption level that would be optimal in the future is modelled by a positive time shift (a negative delay) and is called forward feedback. Analogically, the situation when the applied consumption level has been optimal in pastness is modelled by a negative time shift (a positive delay) and is called backward feedback. The main conclusion presented in this work is that the forward feedback slows down the convergence to a steady state, and the backward feedback speeds it up. If the time shift of the forward feedback is too large, the system can become unstable and start to diverge with right consumption and declining capital.
The concept of forward and backward feedback is applied to endogenous growth models, too. This category of models is characterized by an asymptotically positive growth rate of the per capita consumption and capital and therefore also by an absence of a steady state in the sense of the RCK model. As a result, contrary to the RCK model, any nonzero time shift in the feedback causes divergence. Endogenous growth models are thus very sensitive to the feedback delay and unstable if the delay is nonzero.
The work is accompanied by a Matlab toolbox that provides a computational framework for various numerical and graphical analyses within the RCK model with forward or backward feedback. Most of the 53 figures and 3 animations have been prepared using this toolbox.