Pareto improving financial innovation in incomplete markets

Summary. In this paper we develop a differential technique for investigating the welfare effects of financial innovation in incomplete markets. Utilizing this technique, and after parametrizing the standard competitive, pure-exchange economy by both endowments and utility functions, we establish the following (weakly) generic property: Let S be the number of states, I be the number of assets and H be the number of households, and consider a particular financial equilibrium. Then, provided that the degree of market incompleteness is sufficiently larger than the extent of household heterogeneity, S−I≥2H−1 [resp. S−I≥H+1], there is an open set of single assets [resp. pairs of assets] whose introduction can make every household better off (and, symmetrically, an open set of single assets [resp. pairs of assets] whose introduction can make them all worse off ). We also devise a very simple nonparametric procedure for reducing extensive household heterogeneity to manageable size, a procedure which not only makes our restrictions on market incompleteness more palatable, but could also prove to be quite useful in other applications involving smooth analysis. Received: August 14, 1995; revised version: April 14, 1997     

Support restrictions and sequential equilibria

We consider equilibrium concepts which require that the support of beliefs at an information set be contained in the supports of beliefs at preceding information sets. We analyze by means of an example why such equilibria often fail to exist in extensive form games. We find that support restrictions may exclude very salient equilibria.     

Stochastic equilibria with incomplete financial markets

We demonstrate the existence of equilibria with incomplete financial markets for stochastic economies whose information structure is given by an event tree, restricting attention to purely financial securities, those paying in units of account (e.g., “dollars”). Financial markets may be incomplete: some consumption streams may be impossible to obtain by any trading strategy. Securities may be individually precluded from trade at arbitrary states and dates. Sufficient conditions for the existence of stochastic equilibria are: continuous, convex, strictly monotonic preferences and strictly positive aggregate endowments. These conditions are weakened. A corollary states that any regime of security prices precluding arbitrage can be embedded in an equilibrium.     

Observable restrictions of general equilibrium models with financial markets

This paper examines whether general equilibrium models of exchange economies with incomplete financial markets impose restrictions on prices of commodities and assets given the stochastic processes of dividends and aggregate endowments. We show that the assumption of time-separable expected utility implies restriction on the cross-section of asset prices as well as on spot commodity prices. However, a relaxation of the assumption of time separability will generally destroy these restriction.     

Pareto optima and equilibria when preferences are incompletely known

An exchange economy in which agents have convex incomplete preferences defined by families of concave utility functions is considered. Sufficient conditions for the set of efficient allocations and equilibria to coincide with the set of efficient allocations and equilibria that result when each agent has a utility in her family are provided. Welfare theorems in an incomplete preferences framework therefore hold under these conditions and efficient allocations and equilibria are characterized by first order conditions.     

Existence of financial market equilibria with transaction costs

The purpose of this paper is to give an existence proof of equilibria in a two-period exchange economy with incomplete markets and transaction costs. When tradings on financial markets incur real transaction costs —interpreted as costs of enforcement of financial contracts or real taxation of financial revenues —the set of individual portfolios is bounded by the limited resources of the economy. Existence of equilibria then follows from Kakutani 's fixed point theorem.     

Government financing in an endogenous growth model with financial market restrictions

Summary. In this paper, we develop an endogenous growth model with market regulations on explicitly modeled financial intermediaries to examine the effects of alternative government financing schemes on growth, inflation, and welfare. In the presence of binding regulation, there is always a unique equilibrium. We perform four alternative policy experiments; a change in the seigniorage tax rate, a change in the seigniorage tax base, a change in the income tax and a change in the fiscal-monetary policy mix. We find that in the presence of binding legal reserve requirements, a marginal increase in government spending need not result in a reduction in the rate of economic growth if it is financed with an increase in the seigniorage tax rate. Raising the seigniorage tax base by means of an increase in the reserve requirement retards growth and it has an ambiguous effect on inflation. An increase in income tax financed government spending also suppresses growth and raises inflation although not to the extent that the required seigniorage tax rate alternative would. Switching from seigniorage to income taxation as a source of government finance is growth reducing but deflationary. From a welfare perspective, the least distortionary way of financing an increase in the government spending requirements is by means of a marginal increase in the seigniorage tax rate. Under the specification of logarithmic preferences, the optimal tax structure is indeterminate. Received: March 20, 2000; revised version: June 26, 2001     

Misallocation and financial market frictions: Some direct evidence from the dispersion in borrowing costs

Financial frictions distort the allocation of resources among productive units—all else equal, firms whose financing choices are affected by such frictions face higher borrowing costs than firms with ready access to capital markets. As a result, input choices may differ systematically across firms in ways that are unrelated to their productive efficiency. We propose an accounting framework that allows us to assess empirically the magnitude of the loss in aggregate resources due to such misallocation. To a second-order approximation, the framework requires only information on the dispersion in borrowing costs across firms, which we measure—for a subset of U.S. manufacturing firms—directly from the interest rate spreads on their outstanding publicly-traded debt. Given the observed dispersion in borrowing costs, our approximation method implies a relatively modest loss in efficiency due to resource misallocation—on the order of 1 to 2 percent of measured total factor productivity (TFP). In our framework, the correlation between firm size and borrowing costs has no bearing on TFP losses under the assumption that financial distortions and firm-level efficiency are jointly log-normally distributed. To take into account the effect of covariation between firm size and borrowing costs, we consider a more general framework, which dispenses with the assumption of log-normality and which implies somewhat higher estimates of the resource losses—about 3.5 percent of measured TFP. Counterfactual experiments indicate that dispersion in borrowing costs must be an order of magnitude higher than that observed in the U.S. financial data, in order for misallocation—arising from financial distortions—to account for a significant fraction of measured TFP differentials across countries.     

The structure of the set of sunspot equilibria in economies with incomplete financial markets

Summary This paper considers the set of equilibria of two-period, sunspot economies withS purely extrinsic states of nature in the second period andI assets with linearly independent nominal payoffs. The span of the payoff matrix contains the vector [1, ... , 1] (i.e., inside money). The set of economies is described in terms of (sunspot-invariant) utility functions. IfS>I> 0, there is an open, dense set of economies such that, given a vector of no arbitrage asset prices, the set of equilibrium allocations contains a smooth manifold of dimensionS—I. Such a manifold contains at least one nonsunspot equilibrium (and at most a finite number of such equilibria).The paper was written while I was a visitor at C.O.R.E., Universitè Catholique de Louvain, with the financial support of a S.P.E.S. fellowship. I would like to thank D. Cass, H. Polemarchakis and P. Siconolfi for their helpful comments.     

Monetary policy with heterogeneous agents and borrowing constraints

We show that the long-run neutrality of inflation on capital accumulation obtained in complete market models no longer holds when households face binding credit constraints. Borrowing-constrained households are not able to rebalance their financial portfolio when inflation varies, and thus adjust their money holdings differently compared to unconstrained households. This heterogeneity leads to a new precautionary savings motive, which implies that inflation increases capital accumulation. We quantify the importance of this new channel in an incomplete market model where the traditional redistributive effects of inflation are also introduced. We show that this model provides a quantitative rationale for the observed hump-shaped relationship between inflation and capital accumulation.     

The set of sunspot equilibria in economies with incomplete financial markets: variable asset prices

Summary. I consider the set of equilibria of two-period economies with S extrinsic states of nature in the second period and I assets with linearly independent nominal payoffs. Asset prices are variable. If the number of agents is greater than (S-I), the payoff matrix is in general position and S 2I, the set of equilibrium allocations generically (in utility function space) contains a smooth manifold of dimension (S-1). Moreover, the map from states o f nature to equilibrium allocations (restricted to this manifold) is one-to-one at each equilibrium. Received: February 23, 1998; revised version: June 1, 2000     

A note on Eaton and Gersovitz's model of borrowing

Eaton and Gersovitz's model of borrowing with default risk was re-estimated using data from 1977 and 1981. The results of the re-estimation indicated that the developing countries were less credit constrained in the late seventies/early eighties than in the early dseventies. However, the model did not describe the later sample period as well as the earlier sample period. One reason for the reduced explanatory power of their model is that the model does not incorporate many of the changes that occured in the world economy after 1974 and does not reflect the current structure of indebtedness of the developing countries.     

On the first-order approach in principal-agent models with hidden borrowing and lending

We provide sufficient conditions for the validity of the first-order approach for two-period dynamic moral hazard problems where the agent can save and borrow secretly. The first-order approach is valid if the following conditions hold: (i) the agent has non-increasing absolute risk aversion utility (NIARA), (ii) the output technology has monotone likelihood ratios (MLR), and (iii) the distribution function of output is log-convex in effort (LCDF). Moreover, under these three conditions, the optimal contract is monotone in output. We also investigate a few possibilities of relaxing these requirements.     

Equilibria and Pareto optima of markets with adverse selection

Summary This paper examines the efficiency properties of competitive equilibrium in an economy with adverse selection. The agents (firms and households) in this economy exchange contracts, which specify all the relevant aspects of their interaction. Markets are assumed to be complete, in the sense that all possible contracts can, in principle, be traded. Since prices are specified as part of the contract, they cannot be used as free parameters to equate supply and demand in the market for the contract. Instead, equilibrium is achieved by adjusting the probability of trade. If the contract space is sufficiently rich, it can be shown that rationing will not be observed in equilibrium. A further refinement of equilibrium is proposed, restricting agents' beliefs about contracts that are not traded in equilibrium. Incentive-efficient and constrained incentive-efficient allocations are defined to be solutions to appropriately specified mechanism design problems. Constrained incentive efficiency is an artificial construction, obtained by adding the constraint that all contracts yield the same rate of return to firms. Using this notion, analogues of the fundamental theorems of welfare economics can be proved: all refined equilibria are constrained incentive-efficient and all constrained incentive-efficient allocations satisfying some additional conditions can be decentralized as refined equilibria. A constrained incentive-efficient equilibrium is typically not incentive-efficient, however. The source of the inefficiency is the equilibrium condition that forces all firms to earn the same rate of return on each contract.Notation ={ ₁,..., _k } set of outcomes - : ₊ generic contract or lottery - A = () ; - A_o A{, where denotes the null contract or no trade - S={1,...,¦S¦} set of seller types - L(s) number of type-s sellers - M number of buyers - u: × S seller's utility function, which can be extended toA× S by puttingu(, s) ; - v. × S buyer's utility function, which can be extended toA × S by puttingv(, s) ; - f:A ₀ ×S ₊ allocation of sellers - g:A ₀ ×S ₊ allocation of buyers - A ₊ sellers' trading function - :A ×S ₊ buyers' trading function This paper has had a long gestation period, during which I have been influenced by helpful conversations with many persons, by their work, or both. Among those who deserve special mention are Martin Hellwig, Roger Myerson, Edward Prescott, Robert Townsend and Yves Younés. Earlier versions were presented to the NBER/CEME Conference on Decentralization at the University of Toronto and the NBER Conference on General Equilibrium at Brown University. I would like to thank John Geanakoplos, Walter Heller, Andreu Mas Colell, Michael Peters, Michel Poitevin, Lloyd Shapley, John Wooders, Nicholas Yannelis and an anonymous referee for their helpful comments and especially Robert Rosenthal for his careful reading of two drafts. The financial support of the National Science Foundation under Grant No. 912202 is gratefully acknowledged.     

An empirical re-examination of extreme tail behavior: testing the assumptions of the power laws and the generalized Pareto distribution on the financial series

This study investigates whether the power laws and the associated generalized Pareto distribution (GPD) exist in the extreme tail behavior of financial return series. We include 10 series of five major financial categories over the period 1971–2018 for empirical analysis. For the former assumption, we test three representative power-law distributions. For the latter, we employ an innovative bootstrap goodness-of-fit test of GPD modeling. We also discuss the relationship between both assumptions. The empirical outcomes indicate that both assumptions do not necessarily hold for all tail series due to the outlying observations. The rejection of the power laws assumption leads to the rejection of the GPD assumption. This rejection does not promise the non-rejection of power laws either. However, the non-rejection of either assumption does not imply non-rejection of the other assumption. Power-law distribution and exponential distribution outperform log-normal distribution in tail fitting. GPD fits better at the 1% quantile level than at the 5% level. Overall, we need to acknowledge the considerable gap between the goodness-of-fit testing outcomes of both the power laws and GPD assumptions.