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.
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 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.
Keywords: Inflation, strategic market games, control, interest rate, central bank, equilibrium
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.
This paper explores the general equilibrium impact of social security portfolio diversification into private securities, either through the trust fund or private accounts. The analysis depends critically on heterogeneities in saving, production, assets, and taxes. Limited diversification weakly increases interest rates, reduces the expected return on short-term investment (and the equity premium), decreases safe investment, increases risky investment and increases a suitably weighted social welfare function. However, the effects on aggregate investment, long-term capital values, and the utility of young savers hinges on assumptions about technology. Aggregate investment and long-term asset values can move in opposite directions.
Keywords: Social security, privatization, diversification
This paper explores the general equilibrium impact of social security portfolio diversification into private securities, either through the trust fund or private accounts. The analysis depends critically on heterogeneities in saving, production, assets, and taxes. Limited diversification weakly increases interest rates, reduces the expected return on short-term investment (and the equity premium), decreases safe investment, increases risky investment and increases a suitably weighted social welfare function. However, the effects on aggregate investment, long-term capital values, and the utility of young savers hinges on assumptions about technology. Aggregate investment and long-term asset values can move in opposite directions.
Keywords: Social security, privatization, diversification
In our previous paper we built a general equilibrium model of default and punishment in which equilibrium always exists and endogenously determines asset promises, penalties, and sales constraints. In this paper we interpret the endogenous sales constraints as equilibrium signals. By specializing the default penalties and imposing an exclusivity constraint on asset sales, we obtain a perfectly competitive version of the Rothschild-Stiglitz model of insurance. In our model their separating equilibrium always exists even when they say it doesn’t.
We extend the standard model of general equilibrium with incomplete markets to allow for default and punishment. The equilibrating variables include expected delivery rates, along with the usual prices of assets and commodities. By reinterpreting the variables, our model encompasses a broad range of moral hazard, adverse selection, and signalling phenomena (including the Akerlof lemons model and Rothschild-Stiglitz insurance model) in a general equilibrium framework.
We impose a condition on the expected delivery rates for untraded assets that is similar to the trembling hand refinements used in game theory. Despite earlier claims about the nonexistence of equilibrium with adverse selection, we show that equilibrium always exists, even with exclusivity constraints on asset sales, and transactions-liquidity costs or information-evaluation costs for asset trade.
We show that more lenient punishment which encourages default may be Pareto improving because it allows for better risk spreading.
We also show that default opens the door to a theory of endogenous assets.
This paper explores the general equilibrium impact of social security portfolio diversification into private securities, either through the trust fund or via private accounts. The analysis depends critically on heterogeneity in saving, in production, in assets, and in taxes. Under fairly general assumptions we show that limited diversification increases a neutral social welfare function, increases interest rates, reduces the expected return on short-term equity (and thus the equity premium), decreases safe investment and increases risky investment. However, the effect on aggregate investment, long-term capital values, and the utility of young savers hinges on delicate assumptions about technology. Aggregate investment and long-term asset values often move in the opposite direction. Thus social security diversification might reduce long-term equity value while it increases aggregate investment.
We build a one-period general equilibrium model with money. Equilibrium exists, and fiat money has positive value, as long as the ratio of outside money to inside money is less than the gains to trade available at autarky. We show that the nominal effects of government fiscal and monetary policy can be completely described by a diagram identical in form to the IS-LM curves introduced by Hicks to describe Keynes’ general theory. IS-LM analysis is thus not incompatible with full market clearing, multiple commodities, and heterogeneous households. We show that as the government deficit approaches a finite threshold, hyperinflation sets in (prices converge to infinity and real trade collapses). If the government surplus is too large, the economy enters a liquidity trap in which nominal GNP sinks and monetary policy is ineffectual.
Keywords: Bank, gains to trade, inside money, IS-LM, outside money
We extend the standard model of general equilibrium with incomplete markets (GEI) to allow for default. The equilibrating variables include aggregate default levels, as well as prices of assets and commodities. Default can be either strategic, or due to ill-fortune. It can be caused by events directly affecting the borrower, or indirectly as part of a chain reaction in which a borrower cannot repay because he himself has not been repaid.
Each asset is defined by its promises A, the penalties lambda for default, and the limitations Q on its sale. The model is thus named GE(A,λ,Q). Each asset is regarded as a pool of promises. Different sellers will often exercise their default options differently, while each buyer of an asset receives the same pro rata share of all deliveries. This model of assets represents for example the securitized mortgage market and the securitized credit card market.
Given any collection of assets, we prove that equilibrium exists under conditions similar to those necessary to guarantee the existence of GEI equilibrium. We argue that default is thus reasonably modeled as an equilibrium phenomenon. Moreover, we show that more lenient lambda which encourage default may be Pareto improving because they allow for better risk spreading.
Our definition of equilibrium includes a condition on expected deliveries for untraded assets that is similar to the trembling hand refinements used in game theory. Using this condition, we argue that the possibility of default is an important factor in explaining which assets are traded in equilibrium. Asset promises, default penalties, and quantity constraints can all be thought of as determined endogenously by the forces of supply and demand.
Our model encompasses a broad range of moral hazard, adverse selection, and signalling phenomena (including the Akerlof lemons model and Rothschild-Stiglitz insurance model) in a general equilibrium framework. Many authors (including Akerlof , Rothschild and Stiglitz) have suggested that equilibrium may not exist in the presence of adverse selection. But our existence theorem shows that it must. The problem is the inefficiency of the resulting equilibrium, not its nonexistence. The power of perfect competition simplifies many of the complications attending the finite player, game theoretic analyses of the same topics.
The Modigliani-Miller theorem typically fails to hold when there is the possibility that the firm or one of its investors might default.
One approach to representing knowledge or belief of agents, used by economists and computer scientists, involves an infinite hierarchy of beliefs. Such a hierarchy consists of an agent’s beliefs about the state of the world, his beliefs about other agents’ beliefs about the world, his beliefs about other agents’ beliefs about other agents’ beliefs about the world, and so on. (Economists have typically modeled belief in terms of a probability distribution on the uncertainty space. In contrast, computer scientists have modeled belief in terms of a set of worlds, intuitively, the ones the agent considers possible.) We consider the question of when a countably infinite hierarchy completely describes the uncertainty of the agents. We provide various necessary and sufficient conditions for this property. It turns out that the probability-based approach can be viewed as satisfying one of these conditions, which explains why a countable hierarchy suffices in this case. These conditions also show that whether a countable hierarchy suffices may depend on the “richness” of the states in the underlying state space. We also consider the question of whether a countable hierarchy suffices for “interesting” sets of events, and show that the answer depends on the definition of “interesting.”
We enlarge the standard model of general equilibrium with incomplete market (GEI), to incorporate liquidity constraints as well as the possibility of bankruptcy and default. A new equilibrium results, which we abbreviate GELBI (general equilibrium with liquidity, bankruptcy and incomplete markets). When the supply of bank money and bankruptcy/default penalties are taken sufficiently high (the high regime), GEI occur as GELBI. But outside the high regime many new phenomena appear: money is (almost) never neutral, it has positive value and its optimum quantity is often finite; bankruptcy and default not only occur in equilibrium but can have welfare improving consequences for everyone; there is no real indeterminacy even with financial assets.
JEL Classification: 021, 022
Keywords: Incomplete markets, general equilibrium, bankruptcy, liquidity constraints