Discrepancies between ex ante and ex post efficiency under identical subjective probabilities

Summary. Starr (1973) showed that, if people have different subjective probabilities, ex ante and ex post efficiency conflict. Conversely, under the simple preferences that he considered, the discrepancy between ex ante and ex post efficiency disappears when subjective probabilities are identical. Here I consider identical subjective probabilities, but more general preferences. First, risk attraction is admitted. Second, I dispense with the double requirement (dubbed IZU) of additive separability and state-independence of the utility of zero-date consumption, an unrealistic requirement when modeling the investment in durable goods. I find that, under IZU, and as long as ex post preferences satisfy the natural assumption of quasiconcavity (and satisfy some technical qualifications), an ex ante efficient allocation is indeed ex post efficient, but the converse is not necessarily true under risk attraction. If, on the other hand, IZU is violated, then one can have ex ante efficient allocations that are not ex post efficient, and vice-versa, even under risk aversion. Received: June 25, 1999; revised version: March 2001     

Equilibrium selection in common-value second-price auctions

This note considers equilibrium selection in common-value second-price auctions with two bidders. We show that for each ex post equilibrium in continuous and undominated strategies, a sequence of “almost common-value” auctions can be constructed such that each of them possesses a unique undominated and continuous equilibrium and the corresponding sequence of equilibria converges to that ex post equilibrium. As an implication, no equilibrium selection of this model based on perturbations seems to be more convincing than others.     

Does High‐skilled Migration Affect Publicly Financed Investments?

This paper analyzes the interaction between migration of high‐skilled labor and publicly financed investment. We develop a theoretical model with multiple, ex ante identical jurisdictions where individuals decide on education and subsequent emigration. Migration decisions are based on differences in net income across jurisdictions which may occur endogenously. The interaction between income differences and migration flows gives rise to the potential of multiple equilibria: a symmetric equilibrium without migration and an asymmetric equilibrium in which net income levels differ among jurisdictions and trigger migration flows. In the former equilibrium, all jurisdictions have the same public investment level. In the latter one, public investment is high in host economies of skilled expatriates and low in source economies. We empirically test the hypothesis that emigration rates are negatively associated with publicly financed investment levels for OECD countries.     

Indeterminacy of equilibrium in stochastic OLG models

Summary. This paper studies the equilibria of a stochastic OLG exchange economies consisting of identical agents living for two periods, and having the opportunity to trade a single infinitely-lived asset in constant supply. The agents have uncertain endowments and the stochastic process determining the endowments is Markovian. For such economies, the literature has focused on studying strongly stationary equilibria in which quantities and prices are functions of the exogenous states of nature which describe the uncertainty: such equilibria are generalizations of deterministic steady states, and this paper investigates if they have the same special status as asymptotic limits of other equilibrium paths. The difficulty in extending the analysis of equilibria beyond the class of strongly stationary equilibria comes from the presence of indeterminacy: we propose a procedure for overcoming this difficulty which can be decomposed into two steps. First backward induction arguments are used to restrict the domain of possible prices; then if some indeterminacy is left, expectation functions are introduced to make the forward equilibrium equations determinate. The properties of the resulting trajectories, in particular their asymptotic properties, can then be studied. For the class of models that we study this procedure provides a justification for focusing on strongly stationary equilibria. For the model with positive dividends (equity or land) the justification is complete, since we show that the strongly stationary equilibrium is the unique equilibrium. For the model with zero dividends (money) there is a continuum of self-fulfilling expectation functions resulting in a continuum of equilibrium paths starting from any admissible initial condition: under conditions given in the paper, these equilibrium paths converge almost surely to one of the strongly stationary equilibria-either autarchy or the stochastic analogue of the Golden Rule. Received: November 19, 2001; revised version: March 22, 2002 RID="*" ID="*" We are grateful for the stimulating environment and research support provided by the Cowles Foundation at Yale University during the Fall 2000 when this paper was first conceived. We are also grateful to the participants of the SITE Workshop at Stanford University and the Incomplete Markets Workshop at SUNY Stony Brook during the summer 2001 for helpful discussions. Correspondence to: M. Magill     

Comparing Environmental Policy Instruments Within an Incomplete Contract Framework

This paper compares three different legal means—no environmental policy (the pollutee pays), full liability (the polluter pays), and pollution standards—to reduce and regulate neighborhood externalities within an incomplete contract framework. It turns out that the relative efficiency of these instruments depends, in general, on details. However, moderate standards are preferable to no environmental policy and tight (but not too tight) standards dominate liability. This provides under the given assumptions (neighborhood externalities, incomplete contracts) a justification for “sensible” standards for three reasons. First, unilateral allocations of property rights are biased that distort allocations even if ex post bargaining takes place. Second, a standard is superior in the following sense: if it is set equal to the outcome under any allocation of rights, it will be improved in the process of ex post bargaining. Third, unilateral property rights encourage strategic ex ante investments up to the point that committing to no bargaining would be beneficial (if possible).     

Reclaim-proof allocation of indivisible objects

We study desirability axioms imposed on allocations in indivisible object allocation problems. The existing axioms in the literature are various conditions of robustness to blocking coalitions with respect to agentsʼ ex ante (individual rationality and group rationality) and ex post (Pareto efficiency) endowments. We introduce a stringent axiom that encompasses and strengthens the existing ones. An allocation is reclaim-proof if it is robust to blocking coalitions with respect to any conceivable interim endowments of agents. This is an appealing property in dynamic settings, where the assignments prescribed by an allocation to be implemented need to be made in multiple rounds rather than all in one shot. We show that an allocation is reclaim-proof if and only if it is induced by a YRMH–IGYT mechanism (introduced by Abdulkadiroğlu and Sönmez, 1999) and if and only if it is a competitive allocation.     

An empirical investigation into the impact of US federal government budget deficits on the real interest rate yield on intermediate-term treasury issues, 1972–2012

This study provides new empirical evidence on the impact of the federal budget deficit on the real interest rate yields on intermediate-term debt issues of the US Treasury, represented herein by the ex post real interest rate yields on 3-year Treasury notes and 7-year Treasury notes, two interest rate measures that have received essentially no attention in the economics and finance literature in recent years. This study is couched within a loanable funds model that includes two ex post real interest rate yields, the monetary base as a per cent of GDP, the change in per capita real GDP, net financial capital inflows as a per cent of GDP and the budget deficit as a per cent of GDP. This study uses annual data for the study period 1972 to 2012, a time period that includes ‘quantitative easing’ monetary policies by the Federal Reserve. Two-stage least squares estimations reveal that the federal budget deficit, expressed as a per cent of GDP, exercised a positive and statistically significant impact on the ex post real interest rate yields on both 3-year and 7-year Treasury notes, even after allowing for quantitative easing and other factors. The study also considers the time period 1980 to 2012 and offers simple robustness testing.     

Nonlinear Modelling Using the Generalized Exponential Family of Distributions

This paper introduces an approach to nonlinear modelling which is based on the use of the generalized exponential family of distributions. The flexibility of the approach is illustrated using hypothetical data based on an economic model which exhibits multiple equilibria for certain periods of time and a unique equilibrium for other periods. The distributional analogue of multiple equilibria is multimodality. An advantage of this framework is that discrete jumps can be modelled without the need for identifying the timing of jumps ex post. The framework also has the advantage of explaining how smooth changes in market fundamentals can give rise to large and sudden changes in prices. The introduction of economic assumptions into nonlinear models is explained, and it is shown how an explicit form for the distribution of the dependent variable can be derived. It is suggested that the approach has considerable potential in a wide variety of economic contexts.     

Private investment with social benefits under uncertainty: The dark side of public financing

We develop a game‐theoretic model of private–public contribution to a long‐term project with sequential actions and moral hazard. A private agent is one who is in charge of both the financial contribution and the management effort, these two actions entailing private costs and uncertain ex‐post private and social benefits. A public agent is one who decides the amount of public funding to this quasi‐public good, knowing that the size and the probability of attaining a surplus ex post depend on the private agent's effort. We consider four public‐funding scenarios: benefit‐sharing versus cost‐sharing crossed with ex‐ante versus ex‐interim government intervention. We test our theoretical predictions by means of an experiment that confirms the main result of the model: Cost‐sharing public intervention is more effective than benefit‐sharing in boosting private financial contribution to the project. Furthermore, when public intervention comes after private contribution ( ex‐interim government intervention), both public‐funding scenarios have a negative impact on the private management effort. In our model, the latter result is explained by the private agent's high degree of risk aversion. These results have policy implications for strategic investments with long‐term social consequences. In deciding the optimal timing and method of the contribution, governments should also consider the indirect effects on agents’ long‐term management efforts.     

Collusion and Renegotiation in a Principal–Supervisor–Agent Relationship

We describe a principal–supervisor–agent relationship in which agent and supervisor may collude. To prevent collusion, the principal may contract on a noisy signal which is correlated with the occurrence of collusion. When the signal is informative enough, the principal uses it and no collusion occurs in equilibrium. These contracts, however, are ex post inefficient and are only optimal if the principal can commit not to renegotiate. With renegotiation it is never optimal for the principal to prevent collusion and, at the same time, condition contracts on the signal. In fact, when the signal is informative enough collusion occurs in equilibrium.     

Optimal Universal and Categorical Benefit Provision with Classification Errors and Imperfect Enforcement

We determine the optimal combination of a universal benefit and categorical benefit when individuals differ in their ability to work and, if able to work, their productivity. The categorical benefit is conditioned ex ante on applicants being unable to work and ex post on recipients not working. The awards test makes Type I/II errors. If the ex post condition is (i) not enforced, the optimal categorical benefit is positive only if the awards test has discriminatory power, while maximum welfare falls with both error propensities; but if (ii) fully enforced, the optimal categorical benefit is positive always and maximum welfare can increase with the Type II error propensity.     

Optimal algorithms and lower partial moment: ex post results

Portofolio management in the finance literature has typically used optimization algorithms to determine security allocations within a portfolio in order to obtain the best trade-off between risk and return. These algorithms, despite some improvements, are restrictive in terms of an investor's risk aversion (utility function). Since individual investors have different levels of risk aversion, this paper proposes two portfolio-optimization algorithms that can be tailored to the specific level of risk aversion of the individual investor and performs ex postevaluation tests of the algorithm performance.     

Speculative Attacks with Multiple Sources of Public Information*

We propose a speculative attack model in which agents receive multiple public signals. Diverse pieces of public information can be taken into account differently by different players and are likely to lead to different appreciations ex post. This process defines players' expected private values of a successful attack. The main result shows that equilibrium uniqueness depends on two conditions: (i) signals are sufficiently dispersed and (ii) private beliefs about signals' relative precision differ sufficiently. We derive some implications for information dissemination policy. Transparency in this context is multidimensional: it concerns the publicity of announcements, the number of signals disclosed and their precision.     

An Evolutionary Interpretation of Mixed-Strategy Equilibria

A convincing interpretation of mixed-strategy equilibria describes them as steady states in a large population in which players use pure strategies but the population as a whole mimics a mixed strategy. I study the conditions under which an evolutionary, stochastic learning process converges to the appropriate distribution over pure strategies in the population. I find that not all mixed equilibria can be justified as the result of an evolutionary process even if the equilibrium is unique. For symmetric 2 × 2 and 3 × 3 games I give necessary and sufficient conditions for convergence, which are related to the concept of an ESS, and forn × ngames I give a sufficient condition.Journal of Economic LiteratureClassification Numbers: C73, D83.     

累积创新中的内生许可证

This paper analyzes the endogeneity of licensing arrangements in cost-reducing cumulative innovation. There exists the following results. First, for the first-generation patentee, ex post licensing matters for rent extraction while ex ante licensing matters for efficiency. Second, if the second-generation innovator does not exit, then the firms’ profits as well as social welfare are all irrelevant to whether ex ante licensing is allowed. Third, costly litigation can occur on the equilibrium path and its occurrence is also irrelevant to ex ante licensing. Interestingly, the conditional probability of the first-generation patentee winning litigation first decreases and then increases in patent breadth. Fourth, optimal patent breadth depends on the tradeoff between litigation costs and antitrust effect. Translated from Shijie Jingji Wenhui 世界经济文汇 (World Economic Papers), 2006, (6): 1–29     

Note on the non-existence of sunspot equilibrium

In this note, we emphasize the role of consumers’ risk aversion in the non-existence of sunspot equilibria in incomplete market economies. We prove that there are no sunspot equilibria if the fundamentals of the underlying economy admit a unique equilibrium for any distribution of endowments. This substantiates Mas-Colell’s (Economic analysis of markets and games: essays in honor of Frank Hahn. MIT, Cambridge, 1992) conjecture. We also prove that, in a two-consumer economy, no sunspot equilibrium exists under the more relaxed condition that the underlying economy admits a unique equilibrium for the initial endowment. This is a generalization of Corollaries 1 and 2 of Hens and Pilgrim (Econ Theory 24:583–602, 2004).      

Bayesian Equilibrium in a Public Good Economy

This paper studies the provision of a public good via voluntary contributions in an economy with uncertainty and differential information. Consumers differ in their private information regarding their future endowment as well as in their preferences. Each consumer selects her consumption ex ante, i.e., before knowing the state of nature. Contributions to the provision of the public good are determined ex post, i.e., when the state of nature is realized. Assuming that some normality conditions hold, a Bayesian equilibrium exists. Further, equilibrium is unique, regardless of the number of consumers, when either (1) the information partitions of consumers can be ranked from the finest to the coarsest, or (2) there are only two types of consumers.     

Information, Informal Finance, and SME Financing

Informal finance exists extensively and has been playing an important role in small- and medium-sized enterprise (SME) financing in developing economies. This paper tries to rationalize the extensiveness of informal finance. SME financing suffers more serious information asymmetry to the extent that most SMEs are more opaque and can only provide less collateral. Informal lenders have an advantage over formal financial institutions in collecting “soft information” about SME borrowers. This paper establishes a model including formal and informal lenders and high- and low-risk borrowers with or without sufficient collateral and shows that the credit market in which informal finance is eliminated will allocate funds in some inefficient way, and the efficiency of allocating credit funds can be improved once informal finance is allowed to coexist with formal finance. Translated from Economic Research Journal, 2005, 7 (in Chinese)     

Optimal Liquidity Provision Through a Demand Deposit Scheme: The Jacklin Critique Revisited

We derive conditions such that optimal liquidity provisions through a demand deposit scheme can be sustainably implemented in a subgame perfect Nash equilibrium under the assumption that renegade investors have free access to ex post asset markets. As our qualitative main finding we demonstrate that such sustainability is more likely for ‘poor’ than for ‘rich’ scheme participants in terms of future income. By establishing sustainability for low future income populations, our formal analysis therefore offers an important qualification of Jacklin's (1987) influential claim that an optimal demand deposit scheme is not sustainable whenever there exists the possibility of an ex post asset market.     

Growth with many agents and wages paid ex ante

In this paper, we consider a one-sector model of economic growth with several infinitely-lived heterogeneous agents, who are endowed with diverse discount factors as well as preferences over consumption. In line with the classical Ramsey model, agents are not allowed to borrow against future income. Unlike the traditional assumption of ex post wage payment, wages are paid ex ante in our model. We first explain the difference between the assumptions of wages being paid ex ante and wages being paid ex post in the framework of a simple illustrative two-class model. Our main result shows that in contrast to the many-agent Ramsey model with ex post wage payment, the capital stock sequence converges to the steady state stock irrespective of production technology employed by the firms. Further, all impatient agents own zero capital stock, whereas the most patient agent owns the entire capital stock from some time onward. Thus, we have shown that a slight modification in the timing of wage payment in growth models can lead to significant changes in the stability properties of equilibrium dynamics.