Information structures with unawareness

I construct a state space model with unawareness following [R.J. Aumann, Agreeing to disagree, Ann. Stat. 76 (1976) 1236-1239]. Dekel et al. [E. Dekel, B.L. Lipman, A. Rustichini, Standard state-space models preclude unawareness, Econometrica 66 (1998) 159-173] show that standard state space models are incapable of representing unawareness. The model circumvents the impossibility result by endowing the agent with a subjective state space that differs from the full state space when he has the unawareness problem. Information is modeled as a pair, consisting of both factual information and awareness information. The model preserves the central properties of the standard information partition model.     

Trust in triads: effects of exit, control, and learning

This paper provides theoretical background for some effects of social networks on trust. We study the implications of a model with rational actors in two settings with three actors. In the first setting, there are two trustees who are involved in transactions with one truster implying that the truster has an exit option. In the second setting, two trusters play with one trustee, which gives the trusters options for voice, i.e., complaining and informing each other about the trustee's behavior. We compare these models with a baseline model in which there is only one truster and one trustee. It turns out that the opportunities for placing and honoring trust do not change for the exit model compared to the baseline model. The opportunities for trust in the voice model differ from the baseline model only if both trusters inform each other at a rate that is high enough. Only if the possibilities for receiving information and transmitting information are large enough for both trusters, trust will increase due to the information exchange possibilities in the voice model.     

Steady state properties of multi‐state economic models

A simple method to derive optimal steady states of multi‐state dynamic economic systems with minimal assumptions on the underlying processes is developed. This is accomplished by an n‐dimensional function defined over the n‐dimensional state space in terms of the model's primitives. The location and stability properties of optimal steady state candidates are characterized by the roots and derivatives of this function. A resource management example illustrates the simplicity and applicability of the method.     

Informal work networks

Abstract We present a model of time allocation between formal and informal labour supply, where workers learn of informal job opportunities from their peers. In addition to formal income taxation and enforcement, individuals’ labour supply decisions depend on the number of their peers with informal jobs and the strength of social ties. Workers allocate more time to informal activities when tax enforcement is lax and job information transmission is good. More connected social networks (e.g., wheel, complete) feature lower average income but higher average utility than poorly connected social networks (e.g., star, empty). Average income may be non‐monotonic in tax enforcement.     

The Zero-root Property: Permanent vs Temporary Terms-of-trade Shocks

In this contribution, we show that the persistence and the time of occurrence of a terms‐of‐trade shock matter in determining steady‐state changes: (i) a strong persistent (temporary) terms‐of‐trade worsening induces a long‐run decline in the real expenditure greater than after a permanent disturbance; (ii) an adverse permanent shift in the terms of trade raises the real expenditure in the long run if the shock is expected to occur in the distant future. Finally, according to whether a temporary terms‐of‐trade worsening is anticipated or not, the current account displays a monotonic or a nonmonotonic adjustment.     

Predators in the market: implications of market interaction on optimal resource management

A two-species bioeconomic model is analyzed, but in contrast to most similar models, there is no biological interaction between the species, only economic. The interaction takes place in the market where the quantity of either species may affect the price of the other. The effects of cross-price elasticities on the optimal steady state and on the optimal paths in the sole-owner case are investigated both analytically (steady states) and numerically (optimal paths). First, it is shown that if the harvest of one species has impact on the price of another species, then this has a positive effect on its steady-state stock. The effect increases with the stock-elasticity in the cost function. Further, in the case of linear demand functions, the steady state outcome depends solely on the sum of the cross-price parameters and not their individual values. Secondly, in the investigation of optimal paths, it is shown that if the harvest of one species has impact on the price of the other, optimal trajectories reach steady state faster for itself and slower for the other species. Further, when cross-price elasticities are sufficiently high, the paths go from being monotonic to feature over- or undershooting.     

How common are common priors?

To answer the question in the title we vary agents? beliefs against the background of a fixed knowledge space, that is, a state space with a partition for each agent. Beliefs are the posterior probabilities of agents, which we call type profiles. We then ask what is the topological size of the set of consistent type profiles, those that are derived from a common prior (or a common improper prior in the case of an infinite state space). The answer depends on what we term the tightness of the partition profile. A partition profile is tight if in some state it is common knowledge that any increase of any single agent?s knowledge results in an increase in common knowledge. We show that for partition profiles that are tight the set of consistent type profiles is topologically large, while for partition profiles that are not tight this set is topologically small.     

Aggregate fluctuations, financial constraints and risk sharing

Summary. Private information and costly state verification often result in credit rationing in models with smooth investment, affecting both loan size and total investment. The optimal contract is derived in a dynamic stochastic growth model with capital for two types of models: one with symmetric information and the other with asymmetric information and costly state verification. When all information is observed costlessly, the equilibrium optimal contract provides complete insurance to risk-averse savers against aggregate fluctuations. When information is asymmetric and there is costly state verification, the equilibrium optimal contract provides only partial insurance against aggregate shocks. The extent of insurance is measured by the marginal rate of transformation of consumption between borrowers and lenders which is closely linked to the user cost of capital. The deadweight monitoring costs create a wedge between a borrower's cost of capital and a lender's stochastic discount factor, with two results: (i) fluctuations in the user cost of capital provides a mechanism by which aggregate shocks can be␣propagated; (ii) the distribution of capital's share of output among borrowers, lenders, and monitoring costs varies even if capital's share is constant. Capital market frictions not only amplify aggregate fluctuations but also generate cross-sectional fluctuations that may not be observable in aggregate data. Received: November 17, 1997; revised version: April 20, 1998     

On the Dynamics of Basic Growth Models: Ratio Stability vs. Convergence and Divergence in State Space

Abstract. We show for a class of basic growth models that convergence in ratios does not imply the pathwise convergence to the corresponding balanced growth path in the state space. We derive conditions on parameters and on the elasticity of the savings function for convergence or divergence and apply our results to the Solow model, an augmented Solow model as well as to an optimal growth model. An implication for the convergence debate is that two economies that differ only in the initial capital stock and converge in per capita terms might diverge to infinity in absolute terms.     

Risk sharing and retrading in incomplete markets

At a competitive equilibrium of an incomplete-markets economy agents’ marginal valuations for the tradable assets are equalized ex-ante. We characterize the finest partition of the state space conditional on which this equality holds for any economy. This leads naturally to a necessary and sufficient condition on information that would induce agents to retrade, if such information was to become publicly available after the initial round of trade.     

Pricing, learning, and strategic behavior in a single-sale model

Summary. We analyze an infinite horizon model where a seller who owns an indivisible unit of a good for sale has incomplete information about the state of the world that determines not only the demand she faces but also her own valuation for the good. Over time, she randomly meets potential buyers who may have incentives to manipulate her learning process strategically. We show that i) the seller's incentives to post a high price and to experiment are not necessarily monotonic in the information conveyed by a buyer's rejection; and ii) as the discount factors tend to one, there are equilibria where the seller always ends up selling the good at an ex-post individually rational price. Received: January 6, 1999; revised version: July 15, 2000     

Opting out and topping up reconsidered: Informal care under uncertain altruism

We study the design of public long‐term care (LTC) insurance when the altruism of informal caregivers is uncertain. We consider non‐linear policies where the LTC transfer depends on the level of informal care, which is assumed to be observable, while children's altruism is not. Our policy encompasses two policies traditionally considered in the literature: topping up policies consisting of a transfer independent of informal care, and opting out policies entailing a positive transfer only if children fail to provide care. We show that both total and informal care should increase with the children's level of altruism. This is obtained under full and asymmetric information. Public LTC transfers, on the other hand, may be non‐monotonic. Under asymmetric information, public LTC transfers are lower than their full information level for the parents whose children are the least altruistic, while it is distorted upward for the highest level of altruism. This is explained by the need to provide incentives to highly altruistic children. In contrast to both topping up and opting out policies, the implementing contract is always such that social care increases with informal care.     

Keynes‐Marx and Keynes‐Wicksell Models of Monetary Growth: A framework for future analysis

This paper reconsiders and generalizes a dichotomizing two-sector real growth model of Marglin which claims that the steady state of capitalist economies is plagued by secular inflation. We show that this implication need not be true from the perspective of a more general steady state analysis and that the Marglin model can be embedded into a general Keynes‐Marx‐Friedman or Keynes‐Wicksell framework where money is superneutral, where therefore inflation is due solely to excessive monetary growth, where the private sector is basically asymptotically stable and where there is a steady state rate of employment that differs from the 'natural' rate of employment of monetarist models of inflation. We consider this model a benchmark model that requires equally general alternatives if the above implications are to be rejected.     

Status-Seeking, Catching-Up, and Comparative Statics in a Dynamic Heckscher–Ohlin Model

This paper examines a two‐country dynamic general equilibrium model with status‐seeking agents. We show that the introduction of status‐seeking behavior brings about new properties in equilibrium dynamics. While there exists a continuum of steady states in the standard dynamic models, the present framework demonstrates that, under some conditions, there uniquely exists an incompletely specialized steady state, which is locally saddle‐point stable. Therefore, catching‐up and overtaking phenomena seen in economic development can be explained, and comparative statics analysis also is made possible. Our comparative statics analysis illustrates, for example, that trade pattern is determined in the Heckscher–Ohlin manner; the patient country acts just like a capital abundant one to export the capital‐intensive good. Furthermore, as distinct from the existing literature, the present study shows that the existence of an incompletely specialized steady state can be ensured even if the two countries conduct different policies.     

Competitive prices for a stochastic input–output model with infinite time horizon

Consider a one-sector stochastic input–output model with infinite time horizon. The technology in each time period exhibits constant returns to scale on positive linear combinations of a finite number of basic input–output pairs. Furthermore, perfect information is available as a filtration generated by finite partitions of the state space. By definition, competitive prices require expected profit maximization in every time period. The Riesz representation of a sequence of competitive price functionals yields a state-price deflator with a supermartingale property. We show that there exists a competitive price system for some feasible program if and only if there is No Free Production (NFP). Furthermore, there exists a competitive price system for a particular program if and only if if NFP holds and the program is short-run efficient. This model includes a securities market model with or without convex cone trading constraints as a special case. Under these circumstances, NFP reduces to No Arbitrage and we recover a version of the fundamental theorem of asset pricing. The author expresses gratitude for the advice of two anonymous referees, one who pointed out the simple way to prove the key lemma and the other who helped integrate the conclusions into the existent literature.     

OPTIMAL PRICE SETTING IN FIXED‐ODDS BETTING MARKETS UNDER INFORMATION UNCERTAINTY

This paper develops a model of optimal pricing under information uncertainty for fixed‐odds betting markets. The model suggests that bookmakers require a premium for quoting the odds several days before an event. This premium reflects the uncertainty of public information that can be exploited by expert bettors. The model predicts that when bookmakers set optimal prices, expected returns to bettors increase as a monotonic function of winning probabilities. In this manner, an information‐based explanation is given for the celebrated favourite‐longshot bias in fixed‐odds. Using an extensive data‐set of football odds from two major European bookmakers, we estimate the probability of informed betting.     

Price Convergence and Information Efficiency in German Natural Gas Markets

In 2007, Germany changed network access regulation in the natural gas sector and introduced a so‐called entry–exit system. The spot market effects of the reregulation remain to be examined. We use cointegration analysis and a state space model with time‐varying coefficients to study the development of natural gas spot prices in the two major trading hubs in Germany and the interlinked spot market in the Netherlands. To analyse information efficiency in more detail, the state space model is extended to an error correction model. Overall, our results suggest a reasonable degree of price convergence between the corresponding hubs. Market efficiency in terms of information processing has increased considerably among Germany and the Netherlands.     

PARTY CUES,POLITICAL TRENDS,AND FISCAL INTERACTIONS IN THE UNITED STATES

Recent theoretical and empirical research has suggested that similarities in party affiliations across space will alter voters' comparisons, thus influencing fiscal policy mimicking. We employ a two‐regime spatial panel data model applied to U.S. state governors from 1970 to 2012, and find rather weak empirical evidence of influence of political party affiliations in fiscal yardstick competition. Our observed cross‐state interdependence in fiscal policies suggests voters may not weigh party affiliation heavily in their measure of comparative quality, treating each incumbent individually and independently. Incumbents strategically choose policy accordingly. This provides indirect support for the median voter theorem, in which incumbents' objective function is to maximize votes, independent of political affiliation. (JEL D72, H2, H7)     

Linear exchange economies with a continuum of agents

The purpose of this paper is to study how the equilibrium prices vary with respect to the initial endowments in a linear exchange economy with a continuum of agents. We first state the model and give conditions of an increasing strength for existence, uniqueness and continuity of equilibrium prices. Then, if we restrict ourselves to economies with essentially bounded initial endowments and if we assume that there is, from the point of view of preferences, only a finite number of types of agents, we show that, on an open dense subset of the space of initial endowments, the equilibrium price vector is an infinitely differentiable function of the initial endowments. The proof of this claim is based on a formula allowing to compute the equilibrium price vector around a so-called “regular” endowment where it is known.     

A simple proof of the monotonicity of the state trajectories in autonomous control problems

This paper deals with the question whether in optimal control problems with one state variable cyclical solutions and other nonmonotonicities can be optimal. It is shown that this can only occur if exogeneous shocks are brought into the model while for autonomous problems the state trajectory must always be monotonic. The proof also applies for nondifferentiable control problems as it does not use any regularity assumptions for the model functions.