Time-inconsistent preferences in a general equilibrium model

This paper introduces time-inconsistent preferences in a multicommodity general equilibrium framework with incomplete markets. The standard concept of competitive equilibrium is extended in order to allow for changes in intertemporal preferences. Depending on whether or not agents recognize that their intertemporal preferences change, agents are called sophisticated or naïve. This paper presents competitive equilibrium notions for economies with naïve agents and economies with sophisticated agents and provides assumptions under which both types of equilibria exist. Surprisingly, the set of naïve equilibria in societies populated by time-consistent households is not allocationally equivalent to the set of competitive equilibria. For sophisticated equilibria, the equivalence holds. Time-inconsistency also raises conceptual issues about the appropriate concept of efficiency. Choices have to be made concerning the incorporation of future preferences and the appropriate instruments to create Pareto improvements. For both naïve and sophisticated societies, we present four possible efficiency concepts. Suitable conditions are specified for which both naïve and sophisticated equilibria satisfy appropriate efficiency concepts.     

Public Goods,Social Norms,and Naïve Beliefs

An individual's contribution to a public good may be seen by others as a signal of attributes such as generosity or wealth. An individual may, therefore, choose their contribution so as to send an appropriate signal to others. In this paper, we question how the inferences made by others will influence the amount contributed to the public good. Evidence suggests that individuals are naïve and biased toward taking things at “face value.” We contrast, therefore, contributions made to a public good if others are expected to make rational inferences versus contributions if others are expected to make naïve inferences.     

Linear economies are “gross substitute” systems

The uniqueness of the equilibrium price in linear exchange economies is proved by exploiting their “gross substitute” properties. A necessary and sufficient condition for the uniqueness is that no equilibrium price decomposes the economy. By a familiar mathematical tool — restriction and projection, the demand correspondence becomes a smooth function. We can then apply properties of the Jacobian matrix, which always has a dominant or quasi-dominant diagonal. The combination of convex and differential analysis can be used in piecewise linear economies. The uniqueness of the equilibrium price is a special case of the equilibrium index formula for regular piecewise linear economies.     

What to stabilize in the open economy*

We consider the question how “best” to maintain price‐level stability in an open economy, and evaluate three possible policy choices: (a) a constant money growth rate rule; (b) a fixed exchange rate; and (c) a policy of explicit commitment to a price‐level target. In each case we assume that policy is conducted by injecting reserves into or withdrawing reserves from the “banking system.” In evaluating the three regimes, we adopt the criterion that the “best” policy should leave the least scope for indeterminacy and “excessive” economic volatility. In a steady‐state equilibrium, the choice of regime is largely irrelevant; any steady‐state equilibrium under one regime can be duplicated by an appropriate choice of the “control” variable under any other regime. However, we show that the sets of equilibria under the three regimes are dramatically different. When all countries follow the policy of fixing a constant rate of money growth, there are no equilibria displaying endogenously arising volatility and there is no indeterminacy of equilibrium. Under a regime of fixed exchange rates, indeterminacies and endogenously arising fluctuations are impossible if and only if the country with the low “reserve‐to‐deposit” ratio is charged with maintaining the fixed rate. Finally, when one country targets the time path of its price level, under very weak conditions, there will be indeterminacy of equilibrium and endogenously arising volatility driven by expectations.     

Multiple equilibria, coordination, and transitional growth

We study a small open economy with two sectors and two factors of production. In one of the sectors, external economies of scale are generated through the industry-level capital input. This leads to a divergence between private and social production possibility frontiers as well as to multiple equilibria. The equilibrium selection problem that arises is solved by agents who follow a simple trial-and-error learning rule. The growth path of the economy as agents learn lies below the production possibility frontier and may display cyclical transitional dynamics. We also show that coordination problems which may prevent the economy from attaining the “good” equilibrium may be alleviated by the temporary use of policy instruments that shape the allocation of resources.     

Inefficient lobbying,populism and oligarchy

This paper analyzes the efficiency consequences of lobbying in a production economy with imperfect commitment. We first show that the Pareto efficiency result found for truthful equilibria of common agency games in static exchange economies no longer holds under these more general conditions. We construct a model of pressure groups where the set of efficient truthful common agency equilibria has measure zero. Second, we show that, under fairly general assumptions, the equilibrium will be biased against the group with the highest productivity of private capital, reflecting the fact that, on the margin, less productive groups find lobbying relatively more rewarding. Finally, as an application, if lobbies representing the “poor” and the “rich” have identical organizational capacities, we show that the equilibrium is biased towards the poor, who have a comparative advantage in politics, rather than in production. If the pressure groups differ in their organizational capacity, both pro-rich (oligarchic) and pro-poor (populist) equilibria may arise, all of which are inefficient with respect to the constrained optimum.     

On the completeness of complete markets

We reconsider the allocational invariance of equilibria to different formulations of market completeness. We identify the so-far neglected assumption of sophisticated behavior as being crucial. First, the Arrow–Debreu setting is considered, where markets do not reopen in the future. Second, sequentially complete markets are analyzed, where goods on the spot markets and all contingent one-period ahead commodities can be traded in every state. Finally, complete markets are analyzed, where all possible contingent commodities can be traded at every state. Preferences may be time-consistent or time-inconsistent. A distinction is made between naïve and sophisticated behavior.     

Distance measures between free trade and autarky for the world economy

We develop a methodology to determine numerically how globalized the world economy is. We present a global general equilibrium model capturing major OECD economies and a residual rest of world for which alternative metrics of distance between observed, free trade and autarky equilibria can be developed. We use data for 2000 and report a number of distance measures between the 2000 observed trade restricted equilibrium and both free trade and autarky equilibria noting the absence of prior literature on metrics of distance between equilibria. The measures are used to determine the degree to which the world economy is globalized.     

SIZE,OPENNESS, AND MACROECONOMIC INTERDEPENDENCE

One common, simplifying assumption in open economy macroliterature is that the rest of the world can be thought of as a representative economy. This article formally investigates conditions under which this assumption can be justified using a multicountry general equilibrium model as a laboratory. We derive the conditions that ensure the existence of the equilibrium and study the properties of the equilibrium using large N asymptotics. Thereby, we show that the two‐country framework is a valid approximation only for economies that have diversified trade linkages and only when there is no globally dominant economy among the foreign economies.     

Enforcement of Property Rights and Underdevelopment

The authors formalize the role of legal infrastructure in economic development in a general‐equilibrium model with endogenously determined property rights enforcement. The mutual importance of property rights protection and market production is illustrated by the model's multiplicity of equilibria. In one equilibrium, property rights are enforced, and market activity unhampered. In the other, property rights are not enforced, discouraging economic activity, which leaves the economy without the resources and the incentives to enforce property rights. Even identically endowed economies may therefore find themselves in very different equilibria.     

The existence of fully rational expectations approximate equilibria with noisy price observations

Nonrevealing fully rational expectations approximate equilibria exist in microeconomic pure exchange economies in which uninformed agents have suitably dispersed noisy price observations. Such traders maximize a state-dependent expected utility conditional on the price vector they observe, the distributions of noisy price observations, and the correct equilibrium relationship between states of the world and prices. In equilibrium, aggregate excess demand is small with high probability in every state of the world (and its expectation is also small); this magnitude diminishes as the noisy price observations become more accurate. Equilibria are obtained by applying a fixed point argument to state-dependent excess demand functions which are smooth because of the noisy price observations.     

On persistent disequilibrium

Consider a standard model of a Walrasian economy where the time derivative of price change is a sign preserving function of excess demand. The only steady states of such a system are the Walrasian equilibria. For if the system is not at a Walrasian equilibrium then there must be excess demands or supplies in some market and thus those prices must be changing. Walras' law implies that all prices cannot change in the same direction, and thus relative prices must change.However, it seems that in real world economies there have been states of persistent disequilibrium. How can this be? How can there be stationary states of an economy that are not Walrasian equilibria?The answer presented in this paper goes something like this: the demands actually presented to the market, i.e., the demands that affect price movements, are not the Walrasian demands. Rather, these demands, the effective demands, are a function of both price and quantity signals. There is no reason why there cannot be equilibria of the effective demand system that are not equilibria of the Walrasian demand system.In this paper, I present a simple abstract model of effective demand systems and given a condition for this system to have non-Walrasian equilibria. I also present a simple example of this phenomena. Finally I discuss the real world implications of this model. Related concepts of effective demand are discussed in [A1H], [2], [3], [L5], and [L6].     

Existence of equilibrium in the Helpman–Krugman model of international trade with imperfect competition

Helpman and Krugman (Market structure and foreign trade. Increasing returns, imperfect competition, and the international economy. MIT Press, Cambridge, 1985) provide a synthesis of the traditional factor proportions theory of international trade and the theory of international trade due to the exploitation of scale economies in imperfectly competitive markets. They derive illuminating results about trade patterns and gains from trade, among other things, leaving unanswered the question of existence of equilibrium, however. The central significance of their characterization of properties of free trade equilibria with inter-industry and intra-industry trade calls for an analysis of existence of equilibrium. This is the object of the present paper. We prove the existence of equilibrium for the integrated multi-sector multi-factor Helpman–Krugman economy without national borders. Well-known conditions ensure that the world economy under free trade reproduces this equilibrium and thus establishes existence of a free trade equilibrium. Since an equilibrium of the integrated economy is not necessarily unique, the same holds true for a free trade equilibrium.     

Continuous time limits of repeated games with imperfect public monitoring

In a repeated game with imperfect public information, the set of equilibria depends on the way that the distribution of public signals varies with the players' actions. Recent research has focused on the case of “frequent monitoring,” where the time interval between periods becomes small. Here we study a simple example of a commitment game with a long-run and short-run player in order to examine different specifications of how the signal distribution depends upon period length. We give a simple criterion for the existence of efficient equilibrium, and show that the efficiency of the equilibria that can be supported depends in an important way on the effect of the player's actions on the variance of the signals, and whether extreme values of the signals are “bad news” of “cheating” behavior, or “good news” of “cooperative” behavior.     

Approximate equilibria in microeconomic rational expectations models

For general equilibrium models in which prices transmit information among asymmetrically informed traders, strict rational expectations approximate equilibria are defined. A state-dependent price function is an ε-equilibrium if, when agents use their own information and that conveyed by prices, aggregate excess demand (in each state of the world) does not exceed ε. For any positive ε, existence requires only very mild assumptions—continuity and compact support. Moreover, there are revealing ε-equilibria for all smooth economies satisfying a dimensionality condition. In an open neighborhood of this case, existence of maximally revealing ε-equilibria holds.     

Information,trade and common knowledge

In any voluntary trading process, if agents have rational expectations, then it is common knowledge among them that the equilibrium trade is feasible and individually rational. This condition is used to show that when risk-averse traders begin at a Pareto optimal allocation (relative to their prior beliefs) and then receive private information (which disturbs the marginal conditions), they can still never agree to any non-null trade. On markets, information is revealed by price changes. An equilibrium with fully revealing price changes always exists, and even at other equilibria the information revealed by price changes “swamps” each trader's private information.     

Competitive signalling

With imperfect information about product quality there are incentives for buyers to make use of proxy variables as “signals”, and hence for sellers to invest in the activity of signalling. Received theory suggests that there are plausible circumstances under which there exist a whole family of potential “signalling equilibria” each of which successfully distinguish quality differences.In this paper it is shown that from the family of “equilibria” only one, the Pareto-dominant member, survives plausible experimentation by buyers. With moderately more sophisticated experimentation it is further shown that there is no competitive equilibrium.     

Walrasian equilibria as limits of noncooperative equilibria. Part II: Pure strategies

We examine the connection between Walrasian equilibria of a limit economy (with infinitesimal firms) and noncooperative (Cournot) equilibria of approximating finite economies (with significant firms). Nonconvex production sets, decreasing returns in the aggregate, and endogenous determination of the number of active firms are allowed. A Walrasian equilibrium is a limit of pure strategy noncooperative equilibria only if a condition (loosely analogous to downward sloping demand in the partial equilibrium constant returns to scale case) holds. The condition is also sufficient to guarantee the existence of a robust sequence of pure strategy noncooperative equilibria which converges to the Walrasian equilibrium.     

More on economies with a finite set of Walrasian equilibria

Proposition. The graph of the Walrasian equilibrium correspondence is a piecewise continuously differentiable manifold. Furthermore, there exists an open dense set of economies, Ω, such that for all w in Ω (a) the number of equilibria of the economy w is finite; and (b) there exists a neighborhood V(w) on which the set of equilibria is represented by a finite family of piecewise continously differentiable functions.     

Hyperbolic Discounting,Borrowing Aversion and Debt Holding

Analysis of an original Internet‐based survey reveals that debt holding is related to time discounting through: (i) present bias, measured by the degree of declining impatience in the generalized hyperbolic discount function; (ii) borrowing aversion, captured by a sign effect in that future losses are discounted at lower rates than future gains; and (iii) impatience, measured by the overall discount rate. Hyperbolic respondents are classified naïve if their answers reveal them to be time‐inconsistent procrastinators, and otherwise sophisticated. Naïve respondents with more steeply declining impatience are more likely to be debtors. The sign effect relates negatively to borrowing. Survey responses indicative of high or declining impatience are associated with credit card borrowing and other overborrowing indicators.