| Three essays explore issues pertinent to developing a theory of speculative bubbles as dynamic instabilities rather than as discrepancies from "fundamental values." The focus is on the ultimate construction of a dynamic model of trading under asymmetric information and institutional constraints. The five primary contributions are: (1) A notion of dynamic instability, which I call 'exaggeration,' that is better suited to economic processes than the well-worn Lyapunov-style concepts. The new concept spotlights 'episodes of positive feedback' that are indiscriminately designated as stable by the traditional concepts. It does not presume a dynamical systems format nor the associated continuity properties. (2) A review and critique of the existing definitions of deterministic and stochastic stability and instability. I demonstrate that in a model of growing bubbles the fundamental solution is stochastically stable with respect to bubble perturbations. Another example shows how an "endogenous" process can exhibit episodes of positive feedback, according to the realization of a stochastic "exogenous" process, and yet be stochastically stable. (3) The definition of a latent demand function. The concept is developed within a static equilibrium model of trading under asymmetric information and order-form constraints. The Nash equilibrium is not a Green-Lucas rational expectations equilibrium, although the equilibrium price is fully revealing. The latent demands are "backward bending," reflecting the discrepancy between the price and the information revealed. (4) The application of the generalized Slutsky equation to trading under asymmetric information. Other financial economists have observed that asymmetric information can cause the demand for a noninferior good to have a positive own-price derivative, but they have not formally applied the generalized Slutsky decomposition to this observation. An information effect complements the familiar substitution and income effects and spoils the symmetry and negative semidefiniteness of the Slutsky observables matrix. I also provide counterexamples to assumptions employed by other authors. (5) Two propositions on generalized integrability that strengthen previous results. Going beyond the fact that the Slutsky observables matrix need not be symmetric and negative semidefinite, they show that virtually any demand function can be rationalized by a price-dependent utility function. |
