Payment uncertainty, the division of labor, and productivity declines in great depressions

This paper proposes a simple model that formalizes a variant of Ohanian's conjecture explaining the productivity declines observed in the Great Depression [Ohanian, L.E., 2001. Why did productivity fall so much during the Great Depression? American Economic Review 91 (2), 34–38]. If a large payment shock like an asset-price collapse renders many firms insolvent, other economic agents become exposed to a higher risk of not being paid (payment uncertainty). The payment uncertainty causes endogenous disruptions of the division of labor among firms, thereby lowering macroeconomic productivity.The prediction of the model is that productivity correlates negatively with bankruptcies and positively with the cost share of intermediate inputs, which is consistent with the data from depression episodes. The model implies that the so-called failure of macroeconomic policy in the United States during the early 1930s, when a rash of bankruptcies occurred, could actually have been welfare enhancing, since the quick exit of insolvent agents can resolve payment uncertainty quickly.     

Some extensions of a claim of Aumann in an axiomatic model of knowledge

The paper begins by presenting an axiomatic model of simple and iterated knowledge. A formal definition of the intuitive notion of common knowledge is given and shown equivalent to previous characterizations. It is shown that agents have information partitions. The second part generalizes Aumann's (Ann. Statist.4 (1976), 1236–1239) well-known propositions about common knowledge between two rational agents of each other's probability assignments. It is shown that: common knowledge of decisions—if these are rational—implies a common decision for like-minded agents; and that a “dialogue” in decisions leads to a common decision. A “no-trade” theorem is given which includes trade under complete uncertainty.     

Preference for Flexibility and Dynamic Consistency

Dekel, Lipman, and Rustichini [3] characterize preferences over menus of lotteries that can be represented by the use of a unique subjective state space and a prior. We investigate what would be the appropriate version of Dynamic Consistency in such a setup. The condition we find, which we call Flexibility Consistency, is linked to a comparative theory of preference for flexibility. When the subjective state space is finite, we show that Flexibility Consistency is equivalent to a subjective version of Dynamic Consistency and that it implies that the decision maker is a subjective state space Bayesian updater. Later we characterize when a collection of signals can be interpreted as a partition of the subjective state space of the decision maker.     

Intertemporal equilibria with Knightian uncertainty

We study a dynamic and infinite-dimensional model with incomplete multiple prior preferences. In interior efficient allocations, agents share a common risk-adjusted prior and subjective interest rate. Interior efficient allocations and equilibria coincide with those of economies with subjective expected utility and priors from the agents? multiple prior sets. A specific model with neither risk nor uncertainty at the aggregate level is considered. Risk is always fully insured. For small levels of ambiguity, there exists an equilibrium with inertia where agents also insure fully against Knightian uncertainty. When the level of ambiguity exceeds a critical threshold, full insurance no longer prevails and there exist equilibria with inertia where agents do not insure against uncertainty at all. We also show that equilibria with inertia are indeterminate.     

Completing the State Space with Subjective States

We define an opportunity act as a mapping from an exogenously given objective state space to a set of lotteries over prizes, and consider preferences over opportunity acts. We allow the preferences to be possibly uncertainty averse. Our main theorem provides an axiomatization of the maxmin expected utility model. In the theorem we construct subjective states to complete the objective state space. As in E. Dekel et al. (Econometrica, in press), we obtain a unique subjective state space. We also allow for preference for flexibility in some of the subjective states and commitment in others. Journal of Economic Literature Classification Number: D81.     

On the Economic Meaning of Machina's Fréchet Differentiability Assumption

This note shows that M. J. Machina's (1982, Econometrica50, 277-323) assumption that preferences over lotteries are smooth has some economic implications. We show that Fréchet differentiability implies that preferences represent second order risk aversion (as well as conditional second order risk aversion). This implies, among other things, that decision makers buy full insurance only at the absence of marginal loading. We also show that with constant absolute and relative risk aversion, expected value maximization, second order risk aversion, and Fréchet differentiability are equivalent. Journal of Economic Literature Classification Number: D81.     

Technology adoption in markets with network effects: Theory and experimental evidence

We examine a technology-adoption game with network effects in which coordination on either technology A or technology B constitutes a Nash equilibrium. Coordination on technology B is assumed to be payoff dominant. We define a technology’s critical mass as the minimal share of users, which is necessary to make the choice of this technology the best response for any remaining user. We show that the technology with the lower critical mass implies risk dominance and selection by the maximin criterion. We present experimental evidence that both payoff dominance and risk dominance explain participants’ choices in the technology-adoption game. The relative riskiness of a technology can be proxied using either technologies’ critical masses or stand-alone values absent any network effects.     

Recursive preferences and balanced growth

We study a class of utility functions that are defined recursively by an aggregator W(x,y) where u_t=W(c_t,u_t+1). In single-agent economies it is known that a sufficient condition for the existence of a balanced growth path is that utility should be homogenous of degree γ. In the context of a multi-agent economy we show that this restriction implies that either a balanced growth equilibrium fails to exist or all agents have the same constant discount factor. We suggest a generalization of recursive preferences wherein the intertemporal utility function is time dependent. Within this class we establish that there may exist a balanced growth equilibrium even if agents are different.     

Choice under uncertainty with the best and worst in mind: Neo-additive capacities

We develop the simplest generalization of subjective expected utility that can accommodate both optimistic and pessimistic attitudes towards uncertainty—Choquet expected utility with non-extreme-outcome-additive (neo-additive) capacities. A neo-additive capacity can be expressed as the convex combination of a probability and a special capacity, we refer to as a Hurwicz capacity, that only distinguishes between whether an event is impossible, possible or certain. We show that neo-additive capacities can be readily applied in economic problems, and we provide an axiomatization in a framework of purely subjective uncertainty.     

Should a team be homogeneous?

Should an organization hire people with similar backgrounds or with different backgrounds? We formulate this question within the framework of team theory. The team is formed by n agents. The type of each agent is endogenous and determines his information structure and his cost for the team. We show that the sign of complementarity between jobs determines workforce homogeneity. With positive complementarities, the team should be composed of agents of the same type, while, with negative complementarities, workforce heterogeneity is optimal. These results do not rely on the restrictions on the way uncertainty is modeled or on the feasible set of agent types: they can be explained in terms of correlation between errors committed by different agents.     

Subjective random discounting and intertemporal choice

This paper provides an axiomatic foundation for a particular type of preference shock model called the random discounting representation where a decision maker believes that her discount factors change randomly over time. For this purpose, we formulate an infinite horizon extension of [E. Dekel, B. Lipman, A. Rustichini, Representing preferences with a unique subjective state space, Econometrica 69 (2001) 891-934], and identify the behavior that reduces all subjective uncertainties to those about future discount factors. We also show uniqueness of subjective belief about discount factors. Moreover, a behavioral comparison about preference for flexibility characterizes the condition that one's subjective belief second-order stochastically dominates the other. Finally, the resulting model is applied to a consumption-savings problem.     

Individual option prices for climate change mitigation

Willingness-to-pay for climate change mitigation depends on people's perceptions about just how bad things will get if nothing is done. Individual subjective distributions for future climate conditions are combined with stated choices over alternative climate policies to estimate individual option prices (the appropriate ex ante welfare measure in the face of uncertainty) for climate change mitigation. We find statistically significant sensitivity of estimated option prices to both expected future conditions and uncertainty about future conditions.     

Optimal consumption and the timing of the resolution of uncertainty

As is well-known, consumers want to accumulate precautionary savings in the face of income risks when their marginal utility is convex (prudence). In this paper, we explore the effect of the timing of the resolution of income uncertainty on savings. An agent faces uncertainty about his income at date t+2. What is the effect of being informed that the uncertainty will be resolved at date t+1 on the consumption at date t? We show that the effect is positive, if and only if, marginal utility is convex (prudence), when either the risk free rate is equal to the rate of pure preference for the present, or when the utility function is HARA. The intuition is that an early resolution of uncertainty allows for time-diversifying the risk. It therefore plays a role similar to a reduction of the income risk, whose effect on savings is negative under prudence.     

Performance incentives and planning under uncertainty

The paper discusses the use of the performance-incentive function (PIF) by planning organizations when there is subjective or objective uncertainty. It is proved that a PIF can be constructed that achieves both allocational and distributional optimality, when there is subjective uncertainty about the conditions of production and both the center and the producer are risk-averse. When there is objective uncertainty, however, it is shown that it is not, in general, possible for the center to achieve these two objectives simultaneously. J. Comp. Econ., Sept. 1979, 3(3), pp. 217–232. United States Air Force Academy, Colorado 80840; and University of California, Berkeley, California 94720.     

Anticipated regret as an explanation of uncertainty aversion

The paper provides a psychological explanation of uncertainty aversion based on the fear of regret. We capture an agent’s regret using a reference-dependent utility function in which the agent’s utility depends on the performance of his chosen option relative to the performance of the option that would have been best ex post. An uncertain option is represented as a compound lottery. The basic idea is that selecting a compound lottery reveals information, which alters the ex post assessment of what the best choice would have been, inducing regret. We provide sufficient conditions under which regret implies uncertainty aversion in the sense of quasi-concave preferences over compound lotteries.     

Precautionary saving in the presence of labor income and interest rate risks

This paper deals with the classic issue of precautionary saving in a standard two-period setting. The literature has identified conditions on the individual??s utility function under which either labor income uncertainty or interest-rate uncertainty can lead to positive precautionary saving. We allow for both sources of uncertainty simultaneously. We extend the Jensen inequality from one risk to two positively quadrant dependent risks. The main result of the paper is that ??positive quadrant dependent?? uncertainty raises saving if and only if ??partial relative prudence?? is larger than 2. We characterize the condition that ??partial relative prudence?? exceeds 2 via preferences over simple binary lotteries, in the style of Eeckhoudt and Schlesinger (Am Econ Rev 96:280?C289, 2006).     

Risk sharing and industrial specialization in China

We investigate how risk sharing shapes industrial specialization across prefecture-level cities in China. By unbundling the mechanisms of risk sharing, we find that ex ante risk sharing generates a first-order stimulant effect on the geographical concentration of manufacturing industries, particularly for non-state-owned enterprises and cyclical industries. Ex post risk sharing matters only for state-owned enterprises. This result remains robust to instrument variable estimation and controlling for other determinants of industrial specialization. Finally, we show that interregional labor migration (special fiscal transfers) plays an important role in promoting interregional ex ante (ex post) risk sharing. The study implies that much more risk sharing and efficiency gains from industrial specialization would be achieved if capital markets and credit markets are better developed.     

The impossibility of compromise: some uniqueness properties of expected utility preferences

Summary. We focus on the following uniqueness property of expected utility preferences: Agreement of two preferences on one interior indifference class implies their equality. We show that, besides expected utility preferences under (objective) risk, this uniqueness property holds for subjective expected utility preferences in Anscombe-Aumann's (partially subjective) and Savage's (fully subjective) settings, while it does not hold for subjective expected utility preferences in settings without rich state spaces. Indeed, when it holds the uniqueness property is even stronger than described above, as it needs only agreement on binary acts. The extension of the uniqueness property to the subjective case is possible because beliefs in the mentioned settings are shown to satisfy an analogous property: If two decision makers agree on a likelihood indifference class, they must have identical beliefs. Received: November 15, 1999; revised version: December 29, 1999     

Communication, consensus and order. Who wants to speak first?

Parikh and Krasucki [R. Parikh, P. Krasucki, Communication, consensus and knowledge, J. Econ. Theory 52 (1990) 178-189] show that, in a group of rational agents, communication of the value of a function f leads to a consensus on the value of f, provided some conditions on the communication protocol and the function f hold. In this article, we address the issue of the influence of the protocol on the outcome of the communication process, when agents value information positively. We show that, if it is common knowledge in a group of agents that some of them disagree on two protocols, then the consensus value of f must be the same for both protocols.     

The economic impacts of river rehabilitation: A regional Input-Output analysis

We developed a model to predict the impacts of river rehabilitation activities on the local economy. The model is based on the Input-Output analysis technique and was applied to the planned rehabilitation project for the River Thur in northern Switzerland, along the 4 km stretch between the communities of Bürglen and Weinfelden. We estimated changes in local employment and local economic output resulting from government spending on rehabilitation, associated changes in adjacent land use, and increased recreational activity. Accounting for land use changes required a modification of the conventional Input-Output analysis technique which should be of general interest. We accounted for uncertainty in the data and in some of the model assumptions by using a probabilistic formulation and propagating uncertainty through the model equations. As time-consuming local surveys were beyond the scope of this study, we used the Location Quotient non-survey technique to construct the local technical coefficients from national data and local employment data. This implies that the model can be applied quite easily to a different study area in Switzerland as long as local employment data are available. For each CHF 1 million expenditure per year on rehabilitation activities in our study region, we estimate an extra 8 fulltime employment equivalents (standard deviation, σ = 0.4 fte) and an increased output of CHF 1.4 million (σ = CHF 0.05 million). The low uncertainty of these estimates can be partly attributed to the structure of Input-Output analysis and partly to the fact that we estimated changes in the economic output, rather than output itself. In addition to the above impacts, we estimate that increased recreational use of the area will increase output by as much as CHF 0.17 million (σ = CHF 0.12 million) and employment by as much as 1.7 fulltime employment equivalents (σ = 1.3 fte), depending on the specific rehabilitation option selected.