Multi-asset Accumulation

Multi-asset Accumulation

The pricing of assets — and hence the allocation of investment — is central to macroeconomics. My paper with Joe Stiglitz in the QJE (1967) and with Chris Caton in the RES (1971) show how the apparent plethora of perfect-foresight equilibria is substantially reduced by boundary conditions arising from the non-negativity of prices.

My paper in the RES (1969) with Sidrauski and Stiglitz shows how different “money models” can be from “real models.” Boundary conditions do rule out hyper-deflation, but they do not rule out hyperinflation. For this reason, multiplicity of equilibrium trajectories is more likely in monetary economies. The phase-diagram analysis in Shell-Sidrauski-Stiglitz (1969) is the same as in the later bubble analysis of Tirole (1985). Conraria and Shell (2005, 2006) have extended the analysis of Shell-Stiglitz to OG economies with a focus on bursting bubbles.

Perfect-foresight economies generate perturbed Hamiltonian dynamical systems. My work with Dave Cass on Hamiltonian dynamics is in part an outgrowth of his work with Stiglitz and Sidrauski. Cass and Shell (1976) showed how the geometry of the Hamiltonian function generating the perturbed Hamiltonian dynamical system determines the long-run development of the economy.

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