Productive public expenditures, expectation formations and nonlinear dynamics

Hung Ju Chen*, Ming-Chia Li

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

In this paper, we investigate the dynamic properties of an overlapping generations' model with capital accumulation and publicly funded inventions under three different expectations: perfect foresight, myopic expectations and adaptive expectations. We show that considering productive public expenditures in the model will increase the dimension of the dynamical system. To study the dynamic behavior of a high-dimensional dynamical system, we focus on the case when the elasticity of publicly funded invention to output is small and approximate the system by using a one-dimensional dynamical system. This approximation method provides an efficient way to rigorously prove the existence of chaos in high-dimensional dynamical systems. We show that when agents are perfectly foresighted, there exists a unique, nontrivial steady state which is a global attractor. Cycles or even chaos may occur under myopic and adaptive expectations when the inter-temporal elasticity of substitution of consumption is large enough. Furthermore, we find that the impact of fiscal policy is sensible to the expectation formation.

Original languageEnglish
Pages (from-to)109-126
Number of pages18
JournalMathematical social sciences
Volume56
Issue number1
DOIs
StatePublished - 1 Jul 2008

Keywords

  • Chaos
  • Expectation
  • Productive public expenditures

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