The virtues and vices of equilibrium and the future of financial economics

The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then we present a critique and describe why this approach is inherently limited, and why economics needs to move in new directions if it is to continue to make progress. We stress that this shouldn't be a question of dogma, but should be resolved empirically. There are situations where equilibrium models provide useful predictions and there are situations where they can never provide useful predictions. There are also many situations where the jury is still out, i.e., where so far they fail to provide a good description of the world, but where proper extensions might change this. Our goal is to convince the skeptics that equilibrium models can be useful, but also to make traditional economists more aware of the limitations of equilibrium models. We sketch some alternative approaches and discuss why they should play an important role in future research in economics.Comment: 68 pages, one figur

Leverage Causes Fat Tails and Clustered Volatility

We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called "value investing", i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are normally distributed and uncorrelated across time. All this changes when the funds are allowed to leverage, i.e. borrow from a bank, to purchase more assets than their wealth would otherwise permit. During good times competition drives investors to funds that use more leverage, because they have higher profits. As leverage increases price fluctuations become heavy tailed and display clustered volatility, similar to what is observed in real markets. Previous explanations of fat tails and clustered volatility depended on "irrational behavior", such as trend following. Here instead this comes from the fact that leverage limits cause funds to sell into a falling market: A prudent bank makes itself locally safer by putting a limit to leverage, so when a fund exceeds its leverage limit, it must partially repay its loan by selling the asset. Unfortunately this sometimes happens to all the funds simultaneously when the price is already falling. The resulting nonlinear feedback amplifies large downward price movements. At the extreme this causes crashes, but the effect is seen at every time scale, producing a power law of price disturbances. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility gets high, making these extreme fluctuations even worse.Comment: 19 pages, 8 figure

Inside and Outside Money, Gains to Trade, and IS-LM

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.

Insurance Contracts Designed by Competitive Pooling

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.

Hyperbolic Discounting Is Rational: Valuing the Far Future with Uncertain Discount Rates

Conventional economics supposes that agents value the present vs. the future using an exponential discounting function. In contrast, experiments with animals and humans suggest that agents are better described as hyperbolic discounters, whose discount function decays much more slowly at large times, as a power law. This is generally regarded as being time inconsistent or irrational. We show that when agents cannot be sure of their own future one-period discount rates, then hyperbolic discounting can become rational and exponential discounting irrational. This has important implications for environmental economics, as it implies a much larger weight for the far future.Hyperbolic discounting, Environment, Time consistent, Exponential discounting, Geometric random walk, Term structure of interest rates

The Virtues and Vices of Equilibrium and the Future of Financial Economics

The use of equilibrium models in economics springs from the desire for parsimonious models of economic phenomena that take human reasoning into account. This approach has been the cornerstone of modern economic theory. We explain why this is so, extolling the virtues of equilibrium theory; then we present a critique and describe why this approach is inherently limited, and why economics needs to move in new directions if it is to continue to make progress. We stress that this shouldn’t be a question of dogma, but should be resolved empirically. There are situations where equilibrium models provide useful predictions and there are situations where they can never provide useful predictions. There are also many situations where the jury is still out, i.e., where so far they fail to provide a good description of the world, but where proper extensions might change this. Our goal is to convince the skeptics that equilibrium models can be useful, but also to make traditional economists more aware of the limitations of equilibrium models. We sketch some alternative approaches and discuss why they should play an important role in future research in economics.Equilibrium, Rational expectations, Efficiency, Arbitrage, Bounded rationality, Power laws, Disequilibrium, Zero intelligence, Market ecology, Agent based modeling

Default and Punishment in General Equilibrium

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.

Leverage Causes Fat Tails and Clustered Volatility

We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called "value investing," i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are normally distributed and uncorrelated across time. All this changes when the funds are allowed to leverage, i.e. borrow from a bank, to purchase more assets than their wealth would otherwise permit. During good times competition drives investors to funds that use more leverage, because they have higher profits. As leverage increases price fluctuations become heavy tailed and display clustered volatility, similar to what is observed in real markets. Previous explanations of fat tails and clustered volatility depended on "irrational behavior," such as trend fol­lowing. Here instead this comes from the fact that leverage limits cause funds to sell into a falling market: A prudent bank makes itself locally safer by putting a limit to leverage, so when a fund exceeds its leverage limit, it must partially repay its loan by selling the asset. Unfortunately this sometimes happens to all the funds simultaneously when the price is already falling. The resulting nonlinear feedback amplifies large downward price movements. At the extreme this causes crashes, but the effect is seen at every time scale, producing a power law of price disturbances. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility gets high, making these extreme fluctuations even worse.Systemic risk, Clustered volatility, Fat tails, Crash, Margin calls, Leverage