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     

Inside and outside fiat money, gains to trade, and IS-LM

Summary. 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). At the other extreme, if the government surplus is too large, the economy enters a liquidity trap in which nominal GNP sinks and monetary policy is ineffectual. Received: January 2, 2002; revised version: April 8, 2002 Correspondence to: P. Dubey     

Speculative securities

Summary. A speculative security is an asset whose payoff depends in part on a random shock uncorrelated with economic fundamentals (a sunspot) about which some traders have superior information. In this paper we show that agents may find it desirable to trade such a security in spite of the fact that it is a poorer hedge against their endowment risks at the time of trade, and has an associated adverse selection cost. In the specific institutional setting of innovation of futures contracts, we show that a futures exchange may not have an incentive to introduce a speculative security even when all traders favor it. Received: July 19, 1998; revised version: August 31, 1998     

Devaluation of fixed exchange rates: optimal strategy in the presence of speculation

Summary. This paper analyzes devaluations in a fixed exchange rate system by endogenizing both the speculation and devaluation decisions. It is shown that deterministic devaluation rules are generally sub-optimal for the central bank. In order to deter speculation the central bank introduces uncertainty into the timing of devaluation. The nature this mixed strategy is derived, as is the optimal strategy for speculators. The analysis allows an explanation of successful devaluations that are not precipitated by a speculative attacks, even under perfect capital mobility. Received: May 17, 1999; revised version: June 2, 1999     

Speculative trading with rational beliefs and endogenous uncertainty

Summary. This paper introduces the framework of rational beliefs of Kurz (1994), which makes the assumptions of heterogeneous beliefs of Harrison and Kreps (1978) and Morris (1996) more plausible. Agents hold diverse beliefs that are “rational” in the sense of being compatible with ample observed data. In a non-stationary environment the agents only learn about the stationary measure of observed data, but their beliefs can remain non-stationary and diverse. Speculative trading then stems from disagreements among traders. In a Markovian framework of dividends and beliefs, we obtain analytical results to show how the speculative premium depends on the extent of heterogeneity of beliefs. In addition, we demonstrate that there exists a unique Rational Belief Equilibrium (RBE) generically with endogenous uncertainty (as defined by Kurz and Wu, 1996) and that the RBE price is higher than the rational expectation equilibrium price (REE) under some general conditions Received: March 15, 2001; revised version: April 26, 2002 RID="*" ID="*" We are deeply grateful to Mordecai Kurz for his constant encouragement and inspiring guidance over the years. We wish to express our gratitude to an anonymous referee for the very valuable comments provided. We also thank Kenneth Arrow, Peter Hammond, Roko Aliprantis and Nicholas Yannelis for their helpful suggestions and Academia Sinica and the National Science Council of the R.O.C. for their indispensable support. Correspondence to: H.-M. Wu     

Factors substitutability,heterogeneity and endogenous fluctuations in a finance constrained economy

Summary.   This paper examines the local properties of perfect foresight equilibrium of a finance constrained economy featuring two classes of infinitely-lived agents with heterogeneous general preferences. It is primarily concerned with the conceivability of endogenous fluctuations for large plausible capital-labor elasticities of substitution. It is notably shown that heterogeneity in preferences allows Hopf cycles to be entirely consistent with a wide range of elasticities of substitution including the unitary one (Cobb-Douglas specifications). Received: April 23, 1999; revised version: January 24, 2000     

The analytics of search with posted prices

Summary. This paper investigates the characteristics of the optimal posted price in the standard sequential search paradigm. Much of the intuition gleaned from the extensive sequential search literature in which the seller adopts a reservation price does not carry over to the posted price setting. For example, an increase in buyer valuations can lead to a reduction in the optimal posted price. We do, however, provide sufficient conditions on the hazard rate function h which ensure that an increase in demand induces an increase in the optimal posted price. As exhibited herein, the analysis of the posted price model depends critically upon analytical properties of h. Amongst the issues treated are the elasticity of demand, finite horizon, sale of multiple units, and competitive equilibrium. Received: October 21, 1999; revised version: March 7, 2000     

Equilibrium prices in a random exchange economy with dependent agents

Summary. This paper presents a model of a Walrasian exchange economy in which the preferences and endowments of the agents are random. Stochastic interaction among the agents is formally described in terms of dependency neighborhoods. The main result is a characterization of the distribution of market-clearing prices in a large economy. Received: April 23, 1999; revised version: May 6, 1999     

Agency costs and business cycles

Summary. This paper develops a model with endogenous agency costs that is otherwise quite similar to the canonical real business cycle model. The traditional assumption in the literature is that these agency costs arise in the production of investment goods. In contrast, this paper assumes that these costs are all encompassing in the sense that they arise in the production of aggregate output. The paper explores both the importance of the investment vs. output assumption for business cycle dynamics, and the conditions under which these agency models can deliver amplification and/or persistence. The paper has two principal conclusions. First, in terms of amplification and propagation, the output model performs worse than does the investment model. This arises because a variable distortion in the investment market has more of an impact than a comparable distortion in the output market. Second, in this model with optimal consumption choice by entrepreneurs, there is a clear tension between amplification and persistence. Received: December 30, 1997; revised version: April 1, 1998     

Generic inefficiency of equilibria in the general equilibrium model with incomplete asset markets and infinite time

Summary. We consider a Lucas asset-pricing model with heterogeneous agents, exogenous labor income, and a finite number of exogenous shocks. Although agents are infinitely lived, endowments and dividends are time-invariant functions of the exogenous shock alone and are thus restricted to lie in a finite-dimensional space; genericity analysis can be conducted on sets of zero Lebesgue measure. When financial markets are incomplete, that is, there are fewer financial securities than shocks, we show that generically in individual endowments all competitive equilibria are Pareto inefficient. Received: November 22, 1999; revised version: March 4, 2002 RID="*" ID="*" We are grateful to an anonymous referee for very insightful comments on earlier drafts.     

Human–capital investment and the wage gap

Summary. According to empirical studies, the wage differential by skills evolved non–monotonically in the past decades although the relative supply of skilled labor steadily increased. The present paper provides a theoretical explanation for this finding. In our setting, technological change intertemporally alters the human–capital investment incentives of heterogeneous individuals. As a consequence of changing incentives, the time path of the relative wage is U–shaped while there is a rise in the share of skilled workers. Received: November 28, 2000; revised version: January 30, 2001     

Asymptotic methods for asset market equilibrium analysis

Summary. General equilibrium analysis is difficult when asset markets are incomplete. We make the simplifying assumption that uncertainty is small and use bifurcation methods to compute Taylor series approximations for asset demand and asset market equilibrium. A computer must be used to derive these approximations since they involve large amounts of algebraic manipulation. We use this method to analyze the allocative and welfare effects of introducing a new security. We find that adding any nontrivial derivative security will raise the price of the risky security relative to the bond when risks are small. Received: April 1, 2000; revised version: January 10, 2001     

Effect of credible quality investment with Bertrand and Cournot competition

We show how credible revelation and ability to commit to quality choice effect equilibrium qualities and welfare when product market is either Bertrand or Cournot competition. We show that results depend on the type of competition but not generally on the cost of quality function. We show that with Bertrand competition, the equilibrium qualities are lower with credible commitment. Competition is moderated and producer surplus is higher and consumer surplus lower. With Cournot competition, higher quality will be better but lower quality will be worse with credible commitment. Consumer surplus is always greater with credible commitment and if cost does not increase too quickly with quality, producer surplus will also increase. Thus credible commitment is a collusive device with Bertrand competition but it can improve social welfare with Cournot competition. Received: February 8, 2000; revised version: February 14, 2002 RID="*" ID="*" The idea of this paper originated in the weekly workshops of Mordecai Kurz at Stanford. I am forever in debted to Mordecai and fellow students – Luis Cabral, Peter DeMarzo, John Hillas, Michihiro Kandori, Steve Langois, Patrick McAllister, Steve Sharpe, Peter Streufert, Steve Turnbull and Gyu-Ho Wang – for their criticism and encouragement. I also benefited from comments from Yi-Heng Chen, Jin-Li Hu, Kala Krishna, Jinji Naoto, Thomas J. Prusa, and Shyh-Fang Ueng at various later stages of this work. Last but not least, I am grateful for the detailed comments of the referee.     

Elasticity of substitution and growth: normalized CES in the Diamond model

Summary. It is often asserted that the more substitutable capital and labor are in the aggregate production the more rapidly an economy grows. Recently this has been formally confirmed within the Solow model by Klump and de La Grandville (2000). This paper demonstrates that there exists no such monotonic relationship between factor substitutability and growth in the Diamond overlapping-generations model. In particular, we prove that, if capital and labor are relatively substitutable, a country with a greater elasticity of substitution exhibits lower per capita output growth in transit and in steady state. Received: October 27, 2001; revised version: February 25, 2002     

Real exchange rates,asset prices and terms of trade: A theoretical analysis

This paper develops a continuous-time two-country dynamic equilibrium model, in which the real exchange rates, asset prices, and terms of trade are jointly determined in the presence of nontradable goods. The model determines the relation between the financial markets and real goods markets in the world economy and their responses to various shocks under the home bias assumption. A positive domestic supply shock induces a positive return on the domestic asset markets and a deterioration of terms of trade that improves the foreign output and boosts the foreign asset markets. Demand shocks act in the opposite way. This model also analyses the impact of change in the relative price of nontradable to tradable goods on the terms of trade and asset markets. A higher productivity growth in tradable goods than in nontradable goods leads to a higher relative price of nontradable to tradable goods, which appreciates the real exchange rate, deteriorates the terms of trade, and depresses the domestic and foreign asset markets. A lower relative price of nontradable goods depreciates the real exchange rate, improves the terms of trade, and lifts both the domestic and foreign asset markets.     

Randomization, revelation, and redistribution in a Lerner world

Summary. If total social income is fixed and a social planner is uninformed of the utility representations of different individuals, then Lerner showed that the social optimum is to equally distribute income across individuals. We show that the planner by the use of randomization can in some circumstances induce individuals to reveal information about the curvature of their utility functions and then use the information to move away from equality on average. However, whether this is optimal depends in part on unobservable beliefs of the planner. These may be viewed as an aspect of the planner's ethical judgements or as something entirely arbitrary. Received: January 11, 2000; revised version: June 26, 2001     

The ECFA and its expected effect on cross-strait trade and investment: a Taiwanese perspective

To come to terms with the realization of ASEAN+1, Taiwan had concluded with mainland China a special free trade agreement (FTA), the Economic Cooperation Framework Agreement (ECFA) in June 2010. This framework agreement provides an early harvest agreement of near-term tariff elimination, including detailed product schedules for goods and services from each side, with the final shape of fuller trade liberalization in goods and services taking years to negotiate and realize. The conclusion of the ECFA has been considered as a major breakthrough in cross-strait talks and economic relationships, even though it is by no means free from controversies inside Taiwan. The authors are therefore motivated by hot debates in Taiwan to reflect on the expected trade effect of the ECFA by taking into account the factor of cross-strait global production networks. In particular, we examine with a proposed model and statistical robustness, the trend of Taiwan-based firms' localization in mainland China, driven in part by constant movements in global production networks, which generates complicated and dynamic relationships between Taiwan's investment-induced trade and structural shift in Taiwan's exports to mainland China. Based on our empirical findings, we reflect on the conventional views on the trade effect of the free trade agreement. The results of our analyses tend to support a cautious view about the trade effect of the ECFA. Without denying the significance of the ECFA and deepening cross-strait economic relationships, we argue that the impact of the ECFA should be interpreted in a wider context than just the trade perspective, as the conventional wisdom and the existing evaluations suggested.     

Exact arbitrage and portfolio analysis in large asset markets

Summary. We provide a detailed portfolio analysis for a financial market with an atomless continuum of assets. In the context of an exact arbitrage pricing theory (EAPT), we go beyond the characterization of the existence of important portfolios (normalized riskless, mean, cost, factor and mean-variance efficient portfolios) to furnish exact portfolio compositions in terms of explicit portfolio weights. Such an analysis has not been furnished before in the context of the asymptotic arbitrage pricing theory (APT). We also characterize conditions under which a mean-variance efficient portfolio is a benchmark portfolio used in the EAPT to proxy essential risk. We illustrate our results with several examples of specific financial markets. Received: May 30, 2002; revised version: August 15, 2002 RID="*" ID="*"Some of the results reported here constituted part of Cowles Foundation Discussion Paper– No. 1139 circulated under the title “Hyperfinite Asset Pricing Theory”; additional results were obtained when Sun visited the Department of Economics at Johns Hopkins University during March 2002. This paper was presented at the Conference on Economic Design held at NYU on July 6–9, 2002 Correspondence to: M. A. Khan     

Utility and entropy

Summary. In this paper we study an astonishing similarity between the utility representation problem in economics and the entropy representation problem in thermodynamics. Received: May 17, 1999; revised version: October 16, 2000     

Economic gains from technology-intensive trade: an empirical assessment

National investment in technological activity is commonly justifiedin terms of the positive impacts upon productivity, internationalcompetitiveness and related aspects of national economic performance.This premise has found a supportive theoretical framework inthe new technology and growth models. Based on extended technology-gapmodels, this study examines cross-country empirical evidenceon the relationship between technology-intensive trade performance(as a proxy for technological output) and per capita economicperformance, utilising 1978 to 1992 data for around 45 nations.The results provide some support for a positive relationshipbetween trade performance and economic returns. However, theweak and often inconsistent results suggest that the unconditionalpursuit of technology-intensive trade improvements may not necessarilyhave the expected net benefits.