We consider a two-period model with missing assets and missing market links, in which money plays a central role and is linked to every instrument in the economy. If there are enough missing market links relative to the ratio of outside to inside money, then monetary equilibrium (ME) exists and money has positive value. The nonexistence of GEI (of the underlying economy) shows up as a liquidity trap in terms of the ME. In sharp contrast to GEI, the ME are generally determinate not only in terms of real, but also financial, variables.
Stock market price/earnings ratios should be influenced by demography. Since demography is predictable, stock returns should be as well. We provide a simple stochastic OLG model with a cyclical structure that generates cyclical P/E ratios. We calibrate the model to roughly fit the cyclical features of historical P/E ratios.
This paper was begun during a visit at the Cowles Foundation in Fall 2000 and revised during a visit in Fall 2002: Michael Magill and Martine Quinzii are grateful for the stimulating environment and the research support provided by the Cowles Foundation. We are also grateful to Bob Shiller for helpful discussions, and to participants at the Cowles Conference on Incomplete Markets at Yale University, the SITE Workshop at Stanford University, the Incomplete Markets Workshop at SUNY Stony Brook during the summer 2001, the Southwest Economic Conference at UCLA, and the Conference for the Advancement of Economic Theory at Rhodes in 2003 for helpful comments. Many thanks to Bill Brainard whose numerous insightful questions and comments greatly improved the final version of the paper. Unfortunately the authors are solely responsible for the remaining weaknesses.
We derive the existence of a Walras equilibrium directly from Nash’s theorem on noncooperative games. No price player is involved, nor are generalized games. Instead we use a variant of the Shapley-Shubik trading-post game.
We build a model of competitive pooling, which incorporates adverse selection and signalling into general equilibrium. Pools are characterized by their quantity limits on contributions. Households signal their reliability by choosing which pool to join. In equilibrium, pools with lower quantity limits sell for a higher price, even though each household’s deliveries are the same at all pools.
The Rothschild-Stiglitz model of insurance is included as a special case. We show that by recasting their hybrid oligopolistic-competitive story into our perfectly competitive framework, their separating equilibrium always exists (even when they say it doesn’t) and is unique.
We build a model of competitive pooling, which incorporates adverse selection and signalling into general equilibrium. Pools are characterized by their quantity limits on contributions. Households signal their reliability by choosing which pool to join. In equilibrium, pools with lower quantity limits sell for a higher price, even though each household’s deliveries are the same at all pools.
The Rothschild-Stiglitz model of insurance is included as a special case. We show that by recasting their hybrid oligopolistic-competitive story into our perfectly competitive framework, their separating equilibrium always exists (even when they say it doesn’t) and is unique.
We build a model of competitive pooling, which incorporates adverse selection and signalling into general equilibrium. Pools are characterized by their quantity limits on contributions. Households signal their reliability by choosing which pool to join. In equilibrium, pools with lower quantity limits sell for a higher price, even though each household’s deliveries are the same at all pools.
The Rothschild-Stiglitz model of insurance is included as a special case. We show that by recasting their hybrid oligopolistic-competitive story in our perfectly competitive framework, their separating equilibrium always exists (even when they say it doesn’t) and is unique.
We construct explicit equilibria for strategic market games used to model an economy with fiat money, one nondurable commodity, countably many time- periods, and a continuum of agents. The total production of the commodity is a random variable that fluctuates from period to period. In each period, the agents receive equal endowments of the commodity, and sell them for cash in a market; their spending determines, endogenously, the price of the commodity. All agents have a common utility function, and seek to maximize their expected total discounted utility from consumption.
Suppose an outside bank sets an interest rate rho for loans and deposits. If 1+rho is the reciprocal of the discount factor, and if agents must bid for consumption in each period before knowing their income, then there is no inflation. However, there is an inflationary trend if agents know their income before bidding.
We also consider a model with an active central bank, which is both accurately informed and flexible in its ability to change interest rates. This, however, may not be sufficient to control inflation.
The possibility of default limits available liquidity. If the potential default draws nearer, a liquidity crisis may ensue, causing a crash in asset prices, even if the probability of default barely changes, and even if no defaults subsequently materialize.
Introducing default and limited collateral into general equilibrium theory (GE) allows for a theory of endogenous contracts, including endogenous margin requirements on loans. This in turn allows GE to explain liquidity and liquidity crises in equilibrium. A formal definition of liquidity is presented.
When new information raises the probability and shortens the horizon over which a fixed income asset may default, its drop in price may be much greater than its objective drop in value for two reasons: the drop in value reduces the relative wealth of its natural buyers and also endogenously raises the margin required for its purchase. The liquidity premium rises, and there may be spillovers in which other assets crash in price even though their probability of default did not change.
Introducing default and limited collateral into general equilibrium theory (GE) allows for a theory of endogenous contracts, including endogenous margin requirements on loans. This in turn allows GE to explain liquidity and liquidity crises in equilibrium. A formal definition of liquidity is presented.
When new information raises the probability a fixed income asset may default, its drop in price may be much greater than its objective drop in value because the drop in value reduces the relative wealth of its natural buyers, who disproportiantely own the asset through leveraged purchases. When the information also shortens the horizon over which the asset might default, its price falls still further because the margin requirement for its purchase endogenously rises. There may be spillovers in which other assets also crash in price even though their probability of default did not change.
We build a model of competitive pooling and show how insurance contracts emerge in equilibrium, designed by the invisible hand of perfect competition. When pools are exclusive, we obtain a unique separating equilibrium. When pools are not exclusive but seniority is recognized, we obtain a different unique equilibrium: the pivotal primary-secondary equilibrium. Here reliable and unreliable households take out a common primary insurance up to its maximum limit, and then unreliable households take out further secondary insurance.