EQUILIBRIUM INDETERMINACY IN A MODEL OF CONSTRAINED FINANCIAL MARKETS

I present a general equilibrium model with incomplete markets in which assets pay in units of a numéraire good. In this economy, agents are constrained to negotiate the same amount of assets in different states of the world. Different from the standard result of economies with real assets, equilibrium indeterminacy can arise, depending on the structure of the financial markets. Equilibrium fails to be unique when it is not possible to transfer wealth between states in which consumers trade a pair of assets that face the same restriction.     

Money and transaction costs under uncertainty

This paper studies the impact of transaction costs in a fully monetarized exchange economy in which money serves as unit of account, numéraire, medium of exchange, and intertemporal store of value, and proves the existence of a temporary competitive equilibrium when monetary transaction costs are intertemporally uncertain. In addition to the general-equilibrium analysis, the paper also explores individual-agent comparative-statics behavior for the economy under study. The trading behavior of an individual agent is elucidated in detail and conditions are presented under which Slutsky-type properties are obtainable.     

The price normalization problem in imperfect competition and the objective of the firm

Summary. General equilibrium models of oligopolistic competition give rise to relative prices only without determining the price level. It is well known that the choice of a numéraire or, more generally, of a normalization rule converting relative prices into absolute prices entails drastic consequences for the resulting set of Nash equilibria when firms are assumed to maximize profits. This is due to the fact that changing the price normalization amounts to altering the objective functions of the firms. Clearly, the objective of a firm must not be based on price normalization rules void of any economic content. In this paper we propose a definition of the objective of a firm, called maximization of shareholders' real wealth, which takes shareholders' demand explicitly into account. This objective depends on relative prices only. Real wealth maxima are shown to exist under certain conditions. Moreover, we consider an oligopolistic market and prove the existence of a Nash equilibrium in which each firm maximizes the real wealth of its shareholders. Received: July 10, 1997; revised version: July 27, 1998     

Liquidity shocks and equilibrium liquidity premia

We study an equilibrium in which agents face surprise liquidity shocks and invest in liquid and illiquid riskless assets. The random holding horizon from liquidity shocks makes the return of the illiquid security risky. The equilibrium premium for such risk depends on the constraint that agents face when borrowing against future income; it is insignificant without borrowing constraint, but can be very high with borrowing constraint. Illiquidity, therefore, can have large effects on asset returns when agents face liquidity shocks and borrowing constraints. This result can help us understand why some securities have high liquidity premia, despite low turnover frequency.     

Notes on optimal transportation

We study equilibrium in hedonic markets, when consumers and suppliers have reservation utilities, and the utility functions are separable with respect to price. There is one indivisible good, which comes in different qualities; each consumer buys 0 or 1 unit, and each supplier sells 0 or 1 unit. Consumer types, supplier types and qualities can be either discrete of continuous, in which case they are allowed to be multidimensional. Prices play a double role: they keep some agents out of the market, and they match the remaining ones pairwise. We define equilibrium prices and equilibrium distributions, and we prove that equilibria exist, we investigate to what extend equilibrium prices and distributions are unique, and we prove that equilibria are efficient. In the particular case when there is a continuum of types, and a generalized Spence–Mirrlees condition is satisfied, we prove the existence of a pure equilibrium, where demand distributions are in fact demand functions, and we show to what extent it is unique. The proofs rely on convex analysis, and care has been given to illustrate the theory with examples.     

Existence, uniqueness and efficiency of equilibrium in hedonic markets with multidimensional types

We study equilibrium in hedonic markets, when consumers and suppliers have reservation utilities, and the utility functions are separable with respect to price. There is one indivisible good, which comes in different qualities; each consumer buys 0 or 1 unit, and each supplier sells 0 or 1 unit. Consumer types, supplier types and qualities can be either discrete of continuous, in which case they are allowed to be multidimensional. Prices play a double role: they keep some agents out of the market, and they match the remaining ones pairwise. We define equilibrium prices and equilibrium distributions, and we prove that equilibria exist, we investigate to what extend equilibrium prices and distributions are unique, and we prove that equilibria are efficient. In the particular case when there is a continuum of types, and a generalized Spence–Mirrlees condition is satisfied, we prove the existence of a pure equilibrium, where demand distributions are in fact demand functions, and we show to what extent it is unique. The proofs rely on convex analysis, and care has been given to illustrate the theory with examples.     

The Behaviour of Real Exchange Rates: The Case of Japan

This study examines the convergence rate of mean reversion by estimating the half‐lives of sectoral real exchange rates using an extensive product price panel for Japan (with the USA as the numéraire). We find that the half‐lives of sectoral real exchange rates are remarkably distorted when the grouped half‐life is measured inappropriately and the cross‐sectional dependence and potential trend breaks are ignored. After taking account of these problems, the bias‐corrected half‐life for all goods is as low as 3.00 years, close to the bottom of the consensus view of 3 to 5 years. Moreover, the bias‐corrected half‐life of mean reversion is 2.40 years for traded goods, and only approximately half that for non‐traded goods. Finally, our findings also support the view that small‐sample bias correction is critical for half‐life estimations.     

Non-existence of recursive equilibria on compact state spaces when markets are incomplete

This paper analyzes one-good exchange economies with two infinitely lived agents and incomplete markets. It is shown that there are no recursive (Markov) equilibria for which borrowing (debt) constraints never bind if the state space of exogenous and endogenous variables is a compact subset of . Moreover, for large enough (but finite) borrowing limits, no recursive equilibrium with compact state space exists. These non-existence results hold for any economy satisfying the following standard assumptions: preferences are additively separable across time and states; the one-period utility function is time- and state-independent and unbounded from below; endowments are bounded and follow a Markov chain with stationary transition matrix; there is some idiosyncratic risk and no aggregate risk.     

Regularity and Pareto improving on financial equilibria with price-dependent borrowing restrictions

We consider a pure exchange, general equilibrium model, with two periods and a finite number of states, commodities, numeraire assets, and households. Participation in the asset markets is restricted in a household specific manner, imposing upper bounds on the amounts of borrowing which can be obtained using assets. Those bounds are assumed to depend on asset and commodity prices. After establishing existence of equilibria, we show that, generically in the set of the economies, equilibria are finite and regular. Then, we restrict our attention to the significant set of economies in which some associated equilibria exhibit a sufficiently high number of strictly binding participation constraints. We prove that, generically in that set, those equilibria are Pareto improvable through a local change of the participation constraints.     

RECURSIVE EQUILIBRIA IN AN AIYAGARI‐STYLE ECONOMY WITH PERMANENT INCOME SHOCKS

We prove existence of a recursive competitive equilibrium (RCE) for an Aiyagari‐style economy with permanent income shocks and derive important economic implications. We show that there exist equilibria where borrowing constraints are never binding and establish a nontrivial lower bound on the equilibrium interest rate. These results imply distinct consumption dynamics compared to existing studies. We present a new approach to solve the agent's problem that uses lattices of consumption functions to deal with permanent income shocks and an unbounded utility function. The approach provides a theoretical foundation for convergence of the time iteration algorithm widely used in applied work.     

Asset prices in a Huggett economy

This paper explores asset pricing in economies where there is no direct insurance against idiosyncratic risks but other assets can be used for self-insurance, subject to exogenously-imposed borrowing limits. We analyze an endowment economy, based on Huggett (1993) [11], both with and without aggregate risk. Our main innovation is that we obtain full analytical tractability by studying the case with “maximally tight” borrowing constraints. We illustrate by looking at riskless bonds, equity, and the term structure of interest rates, and we show that the model can reproduce many features of observed asset prices when idiosyncratic risks are quantitatively reasonable.     

Adaptive behavior,demand and preferences

This paper extends the work on endogenous change of tastes of Von Weizsäcker to the n-commodity framework and for a general adaptive behavior process. The paper examines the relation between the effect of taste changes to income and price changes. It provides sufficient conditions for stability of the underlying dynamic process, establishes uniqueness of the equilibrium demand vector and some useful relations between the long-run demand functions and the equilibrium short-run demand functions. It is also shown that the long-run demand functions can be rationalized by a utility function if and only if the short-run utility function is such that any good that experiences learning or taste change is separable from all other goods.     

ON THE SUSTAINABILITY OF GOVERNMENT BORROWING IN A DYNAMIC GENERAL EQUILIBRIUM

Abstract.  This paper constructs a dynamic general equilibrium model with money in consumers' utility functions and investigates the equilibrium dynamics of government's debt. The limitation level of the government borrowing for which a dynamic equilibrium and the no Ponzi Game condition are compatible with each other is explicitly derived. The critical level depends on the long-run interest rate, primary balance, money supply etc.     

Borrowing constraints and the trade balance–output comovement

The countercyclical trade balance ratio is among the key stylized facts about open economies. The magnitude of the correlation between the trade balance and output, however, differs from country to country. In particular, the trade balance ratio is more negatively correlated with output in emerging economies than in developed economies, suggesting that the trade balance is more sensitive to output changes in the former than in the latter. This paper explores whether this difference is caused by international borrowing constraints imposed on emerging economies.By modeling borrowing constraints as conditional on macroeconomic performance, this paper shows that when there is a positive shock takes place in an emerging economy, GDP increases and the borrowing constraint becomes less binding, resulting in a decreased incentive to accumulate foreign assets. When there is a negative shock, by contrast, GDP falls, and the representative household must increase the trade balance to avoid possible binding borrowing constraints.     

Adaptive behavior and the existence of Weizsäcker's long-run indifference curves

Suppose that past consumptions of the first r commodities (r < n) influence present consumption. Then, the long-run demand function to which demand converges maximizes the equilibrium short-run utility function only under very restrictive conditions. The long-run demand functions can be rationalized by a utility function, different from the equilibrium short-run utility function, if and only if the short-run utility function is such that past consumptions of any good that experience, learning, or taste changes is separable from all other goods. The class of such utility functions has been found.     

Self-insurance in a life-cycle model of labour supply and savings

This paper analyses the incentives to work and to save over the life cycle in the presence of incomplete markets. In a calibrated, partial equilibrium model, flexibility in hours worked changes asset age-profiles: borrowing when young is greater and saving when middle-aged is greater than when labour supply is fixed. Uncertainty causes individuals to work longer hours and to consume less when young. With flexibility over hours, accumulating precautionary assets incurs less of a utility cost and so the level of saving is greater. Further, allowing for flexibility and uncertainty means simulated hours of work and consumption more closely match the age profiles in the data.     

COLLATERAL REQUIREMENTS AND ASSET PRICES

Many assets derive their value not only from future cash flows but also from their ability to serve as collateral. In this article, we investigate this collateral premium and its impact on asset returns in an infinite‐horizon general equilibrium model with heterogeneous agents. We document that borrowing against collateral substantially increases the return volatility of long‐lived assets. Moreover, otherwise identical assets with different degrees of collateralizability exhibit substantially different return dynamics because their prices contain a sizable collateral premium that varies over time. This premium can be positive even for assets that never pay dividends.     

Determinacy of Equilibrium in an Overlapping Generations Model with Heterogeneous Agents

We study the determinacy of perfect foresight equilibrium near a steady state in an overlapping generations model with production and both altruistic and non-altruistic agents having distinct utility functions. The proportion of each type of consumer is exogenously given. Our main results show that when there are positive stationary bequests, some standard assumptions on preferences and technology rule out local indeterminacy for any positive value of the proportions. In the particular case of a separable utility function for altruistic agents, we prove that the determinacy property does not depend on the size of the “infinite lived” altruistic dynasties. Journal of Economic Literature Classification Numbers: C62, D91, O21, O41.     

How Borrowing Constraints Hinder Migration: Theoretical Insights from a Random Utility Maximization Model*

We provide a theoretical framework to analyze how financial constraints hinder migration. Introducing wealth heterogeneity and borrowing constraints into a random utility maximization model of migration, we find evidence of multilateral resistance to migration stemming from borrowing constraints. We calibrate the model on 22 European countries, and we show that omitting the constraints biases upward the estimation of bilateral migration rates. We then simulate an increase in the bilateral cost of migration to the United Kingdom. We find that omitting the constraints biases downward the change entailed by the cost increase in the bilateral rates of migration to all destinations.     

Education and growth with endogenous debt constraints

When future human capital cannot be alienated, households are allowed to borrow up to the point where it is in their own interest not to default. In such a framework, endogenous borrowing limits arise as the outcome of individual rationality constraint. In a model where education is the engine of growth, we show that endogenous borrowing constraints imply global indeterminacy. Comparing outcomes across the various equilibria we show that the relation between growth and yields is hump-shaped. Maximum growth can arise in an equilibrium with binding borrowing constraints, specially if the elasticity of human capital to education spending is large. Deepening financial markets promotes long-run growth in the case of a poverty trap, but not necessarily otherwise. On the methodological side, our approach stresses the importance of studying borrowing limits in general equilibrium, not only in small open economies. Philippe Michel passed away on July 22, 2004. His death is a great loss for his friends and for the overlapping generations and optimal control community.