Fluctuations and Limitations of a Multi-Sector Economic Model with Delays

in The proceedings of the 2010 American Control Conference (ACC) (2010)

A general multi-sector model of the economy is investigated. A sector's input to production, labor, evolves according to a jump Markov process. Labor jumps between sectors to balance supply and demand ... [more ▼]

A general multi-sector model of the economy is investigated. A sector's input to production, labor, evolves according to a jump Markov process. Labor jumps between sectors to balance supply and demand, where each sector differs by its productivity. The jump model captures the intrinsic noise of the micro agents on the macro level, which is represented by the random timing of labor jumps. Quantifying this noise is a central theme of this paper. An operator theoretic approach is utilized to capture the fluctuations of a linearized jump system exactly. As an illustrative example two sector and three sector economies are studied. In each case the optimal aggressiveness, gain, of a sector is determined for minimal variance. Delays are then introduced into the model. It is shown that the presence of a delay creates a limit on the minimum variance achievable and that high gain is destabilizing. For both the two and three sector models the nonlinear jump systems are simulated. It is shown that the operator theoretic approach is an appropriate method for quantifying the second moments. [less ▲]

Heterogeneous agent models in economics: a study of heterogeneous productivity of sectors

in Proceedings of the 2008 American Control Conference (2008)

Macroeconomic modeling is undergoing a change from the ground up. Previously models based on fully rational representative agents were constructed to give macroeconomics soli microeconomic foundations ... [more ▼]

Macroeconomic modeling is undergoing a change from the ground up. Previously models based on fully rational representative agents were constructed to give macroeconomics soli microeconomic foundations. However the representative agent models have been shown to be inconsistent with empirical evidence and a new method of approach has emerged, one based on heterogeneity of agents. Recently heterogenous models have been used to simulate expected outcomes but due to their complexity little analytic work has been done. In this paper a basic model of the macro economy, with heterogeneous sectors differentiated by productivity, and driven by a jump Markov process, is investigated and steady state solutions for a sector’s output variance are discovered. We adjust the model to include a gain term, to represent a sector’s reaction to its error signal, excess demand, and then linearize the transition rates and apply the fluctuation dissipation theorem to solve the model. [less ▲]