Stability, instability and complex behavior in macrodynamic models with policy lag. (English) Zbl 0980.34070

Asada, Toichiro; Yoshida, Hiroyuki

Discrete Dyn. Nat. Soc. 5, No. 4, 281-295 (2001).

The authors consider simple macrodynamic models with policy lag by means of mixed difference and differential equations, and study how lags in policy response affect the macrodynamic (in)stability. Local dynamics of the prototype model are studied analytically, and the global dynamics of the prototype and the extended models are studied by means of numerical simulations. They show that the government can stabilize the intrinsically unstable economy if the policy lag is sufficiently short, but the system becomes locally unstable when the policy lag is too long. They also show the existence of cycles and complex behavior in some range of the policy lag.

Reviewer: Marcos Lizana (Merida)

MSC:

34K20	Stability theory of functional-differential equations
34K18	Bifurcation theory of functional-differential equations
91B64	Macroeconomic theory (monetary models, models of taxation)
37N40	Dynamical systems in optimization and economics
37G15	Bifurcations of limit cycles and periodic orbits in dynamical systems
34K35	Control problems for functional-differential equations
34H05	Control problems involving ordinary differential equations

Keywords:

policy lag; mixed difference and differential equations; dynamic stability; Hopf bifurcation; complex behavior; macrodynamic models