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Expectation formation in an overlapping generation model with production.

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This study examines economic dynamics in an overlapping generations model, comparing perfect, myopic, and adaptive expectations. Adaptive expectations can lead to complex dynamics and multistability, unlike myopic expectations.

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Area of Science:

  • Economics
  • Mathematical Economics

Background:

  • Overlapping generations models are crucial for understanding macroeconomic dynamics.
  • Expectations formation significantly impacts economic stability and outcomes.

Purpose of the Study:

  • To analyze the dynamic properties of an overlapping generations model with capital accumulation.
  • To compare the effects of perfect foresight, myopic foresight, and adaptive expectations on model dynamics.
  • To investigate the conditions leading to complex dynamics and multistability under adaptive expectations.

Main Methods:

  • Analytical investigation of model stability under different expectation mechanisms.
  • Detailed analysis of adaptive expectations, including local and global stability.
  • Numerical simulations to explore complex dynamics and multistability.

Main Results:

  • The steady state is invariant across all expectation mechanisms.
  • Global stability is proven for perfect foresight.
  • Adaptive and myopic expectations can generate periodic and chaotic dynamics when agents allocate significant time to labor in their second period.
  • Multistability, characterized by the coexistence of a stable steady state and chaotic attractors, emerges under adaptive expectations, but not under myopic expectations.

Conclusions:

  • Reduced rationality, particularly adaptive expectations, can introduce significant complexity and multistability into economic models.
  • The findings highlight the importance of considering sophisticated expectation formation for understanding economic fluctuations.
  • Agents may benefit from learning by observing forecasting errors to improve their predictions.