Conclusion

In this chapter, we have investigated bubbles in linear dynamic models and nonlinear models characterized by indeterminacy and sunspot equilibria. These are models in which expectational factors determine the dynamic path of the economy, and in which expectations turn out to be self-fulfilling.

We have discussed the conditions under which unstable bubbles can be ruled out in both partial and general equilibrium models, and investigated how sunspot equilibria and endogenous cycles can arise in nonlinear models, such as the Samuelson OLG model.

The examples discussed go beyond the property of uniqueness characterizing the steady state solutions of most of the models used in the rest of this text. Although the approach taken in this chapter does not necessarily invalidate the analytical strategy adopted in the rest of this book, models of bubbles and sunspots can potentially explain why economies sometimes enter unsustainable paths, display endogenous business cycles, or shift from one equilibrium to another.

1. Examples of exceptions include the Samuelson and Diamond overlapping generations models and the Calvo public debt model.

2. See Blanchard and Watson [1982] for an early analysis of bubbles versus fundamentals under rational expectations. A more recent and comprehensive survey can be found in Brunnermeier [2008].

3. For a comprehensive survey of this literature, see Benhabib and Farmer [1999].

4. This section follows Blanchard and Watson [1982].

5. See Farmer [1999] for an extensive discussion of models with self-fulfilling prophecies. Farmer considers inherently stable models to be the “regular case” and inherently unstable models to be the “irregular case.”

6. See Abreu and Brunnermeier [2003] for a model in which a bubble can be sustained because of unsychronized trading in the presence of informational asymmetries.

7. See Kindleberger and Aliber [2005] for a history of what have been termed financial market bubbles.

8. See Brunnermeier [2008] for a survey of the empirical evidence.

9. This model is a version of an example first used by Azariadis [1981].

10. In this definition, Cass and Shell [1983] differ from Jevons [1884], who developed a sunspot theory of agricultural cycles, based on the idea that sunspot activity affected agricultural output, through its impact on the weather. The Jevons theory is based on fundamentals and intrinsic uncertainty and not extrinsic uncertainty as in the case of Cass and Shell [1983] sunspot equilibria.

11. Note that this is a more general version of the Samuelson model than the one presented in chapter 12, which relied on logarithmic preferences. The elasticity of intertemporal substitution in the model of this section is allowed to differ from unity.

12. The offer curve approach to the analysis of the Samuelson OLG model with money was introduced by Cass et al. [1979].

13. Note that in the case of logarithmic preferences (i.e., θ = 1), this money demand function reduces to the one analyzed in chapter 12, namely, equation (12.15).

14. Comprehensive treatments of the macroeconomics of self-fulfilling prophecies and sunspots can be found in Azariadis [1993] and Farmer [1999].