Does uncertainty justify intensity emission caps?

Environmental policies often set “relative” or “intensity” emission caps, i.e. emission limits proportional to the polluting firm's output. One of the arguments put forth in favour of relative caps is based on the uncertainty on business-as-usual output: if the firm's production level is higher than expected, so will be business-as-usual emissions, hence reaching a given level of emissions will be more costly than expected. As a consequence, it is argued, a higher emission level should be allowed if the production level is more important than expected. We assess this argument with a stochastic analytical model featuring two random variables: the business-as-usual emission level, proportional to output, and the slope of the marginal abatement cost curve. We compare the relative cap to an absolute cap and to a price instrument, in terms of welfare impact. It turns out that in most plausible cases, either a price instrument or an absolute cap yields a higher expected welfare than a relative cap. Quantitatively, the difference in expected welfare is typically very small between the absolute and the relative cap but may be significant between the relative cap and the price instrument.     

Choquet Rationality

Consider a decision problem under uncertainty for a decision maker with known (utility) payoffs over prizes. We say that an act is Choquet (Shafer, Bernoulli) rational if for some capacity (belief function, probability) over the set of states, it maximizes her “expected” utility. We show that an act may be Choquet rational without being Bernoulli rational, but it is Choquet rational if and only if it is Shafer rational. Journal of Economic Literature Classification Numbers: C72, D81.     

Influence and inefficiency in the internal capital market

I model inefficient resource allocations in M-form organizations due to influence activities by division managers that skew capital budgets in their favor. Corporate headquarters receives two types of signals about investment opportunities: private signals that can be distorted by managers, and public signals that are undistorted but noisy. Headquarters faces a tradeoff between the cost of attaining an accurate private signal and the value of the information the signal provides. In contrast to existing models of “socialism” in internal capital markets, I show that investment sensitivity to Tobin's Q is higher than first-best in firms where division managers hold equity (a result consistent with evidence presented in Scharfstein, 1998). When managers face high private costs from distorting information (equity holdings), headquarters may commit to investment contracts that place “too little” weight on private signals and “too much” weight on public signals (i.e. Q). This result has implications for managers in the design of capital budgeting processes and incentive compensation systems.     

A Bayesian Model of Voting in Juries

We model voting in juries as a game of incomplete information, allowing jurors to receive a continuum of signals. We characterize the unique symmetric equilibrium of the game, and give a condition under which no asymmetric equilibria exist under unanimity rule. We offer a condition under which unanimity rule exhibits a bias toward convicting the innocent, regardless of the size of the jury, and give an example showing that this bias can be reversed. We prove a “jury theorem” for our general model: As the size of the jury increases, the probability of a mistaken judgment goes to zero for every voting rule except unanimity rule. For unanimity rule, the probability of making a mistake is bounded strictly above zero if and only if there do not exist arbitrarily strong signals of innocence. Our results explain the asymptotic inefficiency of unanimity rule in finite models and establishes the possibility of asymptotic efficiency, a property that could emerge only in a continuous model. Journal of Economic Literature Classification Numbers: C72, D72.     

Conditional Universal Consistency

Players choose an action before learning an outcome chosen according to an unknown and history-dependent stochastic rule. Procedures that categorize outcomes, and use a randomized variation on fictitious play within each category are studied. These procedures are “conditionally consistent:” they yield almost as high a time-average payoff as if the player knew the conditional distributions of actions given categories. Moreover, given any alternative procedure, there is a conditionally consistent procedure whose performance is no more than epsilon worse regardless of the discount factor. We also discuss cycles, and argue that the time-average of play should resemble a correlated equilibrium. Journal of Economic Literature Classification Numbers: C72, C73, C63, D83.     

Non-Additive Beliefs and Strategic Equilibria

This paper studies n-player games where players' beliefs about their opponents' behaviour are modelled as non-additive probabilities. The concept of an “equilibrium under uncertainty” which is introduced in this paper extends the equilibrium notion of Dow and Werlang (1994, J. Econom. Theory64, 305–324) to n-player games in strategic form. Existence of such an equilibrium is demonstrated under usual conditions. For low degrees of ambiguity, equilibria under uncertainty approximate Nash equilibria. At the other extreme, with a low degree of confidence, maximin equilibria appear. Finally, robustness against a lack of confidence may be viewed as a refinement for Nash equilibria. Journal of Economic Literature Classification Numbers: C72, D81.     

The inflationary bias of real uncertainty and the harmonic Fisher equation

Summary. We argue that real uncertainty itself causes long-run nominal inflation. Consider an infinite horizon cash-in-advance economy with a representative agent and real uncertainty, modeled by independent, identically distributed endowments. Suppose the central bank fixes the nominal rate of interest. We show that the equilibrium long-run rate of inflation is strictly higher, on almost every path of endowment realizations, than it would be if the endowments were constant.Indeed, we present an explicit formula for the long-run rate of inflation, based on the famous Fisher equation. The Fisher equation says the short-run rate of inflation should equal the nominal rate of interest less the real rate of interest. The long-run Fisher equation for our stochastic economy is similar, but with the rate of inflation replaced by the harmonic mean of the growth rate of money.Received: 25 February 2005, Revised: 26 May 2005, JEL Classification Numbers: C7, C73, D81, E41, E58.An earlier version of this paper “Inflationary Bias in a Simple Stochastic Economy,” as a 2001 Cowles Foundation Discussion Paper No. 1333.     

Benefit and Distance Functions

We explore the relationship between R. W. Shephard's input distance function (“Cost and Production Functions,” Princeton Univ. Press, Princeton, 1953) and D. G. Luenberger's benefit function (J. Math. Econ.21(1992a), 461–481). We point out that the latter can be recognized in a production context as a directional input distance function which can exhaustively characterize technologies in both price and input space. D. McFadden's (Cost, revenue, and profit functions,in“Production Economics: A Dual Approach to Theory and Applications, “North-Holland/Elsevier, New York, 1978) composition rules for input sets and input distance functions are then extended to the directional input distance function.Journal of Economic LiteratureClassification Numbers : D21, D24, D29.     

Contracts and externalities: How things fall apart

A single principal interacts with several agents, offering them contracts. The crucial assumption of this paper is that the outside-option payoffs of the agents depend positively on how many uncontracted or “free” agents there are. We study how such a principal, unwelcome though he may be, approaches the problem of contract provision to agents when coordination failure among the latter group is explicitly ruled out. Two variants are considered. When the principal cannot re-approach agents, there is a unique equilibrium, in which contract provision is split up into two phases. In phase 1, simultaneous offers at good (though varying) terms are made to a number of agents. In phase 2, offers must be made sequentially, and their values are “discontinuously” lower: they are close to the very lowest of all the outside options. When the principal can repeatedly approach the same agent, there is a multiplicity of equilibria. In some of these, the agents have the power to force delay. They can hold off the principal's overtures temporarily, but they must succumb in finite time. In both models, despite being able to coordinate their actions, agents cannot resist an “invasion” by the principal and hold to their best payoff. It is in this sense that “things [eventually] fall apart”.     

Optimizing the shares of native tree species in forest plantations with biased financial parameters

Addressing uncertainty is a key requirement to follow the principle of precaution in sustainable ecosystem management. The maximization of worst-case outcomes according to the “maximin” decision rule, based on the two parameters mean and variance of a financial indicator, is a prominent approach to integrate uncertainty in decision-making. In forestry, the problem of selecting the optimum tree species combination for a forest plantation investment can be seen as a problem of optimal portfolio selection, to be solved according to the “maximin” decision rule. Yet, it is well known that portfolios computed from expected means and variances are highly sensitive to changes in the estimated parameters. The financial results may be poor if we rely too much on the historical data. This paper tests an extended worst-case model that considers a lower bound for the expected mean net present value (NPV) of a tree species portfolio and an upper bound for its variance. Biased expected mean NPVs, variances and correlations for the tree species Picea abies [L.] Karst. (Spruce) and Fagus sylvatica L. (Beech) were used to test the variability of the resulting tree species portfolios (27 scenarios). A comprehensive simulated data set, which was adopted from an existing study and defined as the independent reference, served to evaluate the financial performance of the tree species portfolios obtained from optimization with the biased data. Compared with the results of classical worst-case optimization instances, it was feasible to reduce the variability of tree species shares effectively when the optimization was carried out with the extended worst-case approach. Furthermore, the financial performance of this approach was better when tested with the independent data. The worst-case forest NPVs achieved with the extended approach were on average 10% (statistical confidence 0.95) or 147% (statistical confidence 0.99) greater in comparison to the results of the classical approach. The influence of the uncertainty parameter selection was tested and the results were discussed against the controversial viewpoints on the usefulness of the “information-gap decision theory”. Finally, the significance of our results for sustainable ecosystem management is pointed out.     

Welfare costs of monetary policy uncertainty in the economy with shifting trend inflation

We study welfare costs of the uncertainty about monetary policy in the economy featuring shifting trend inflation. We follow Ruge-Murcia (J Econ Dyn Control 36: 914–-938, 2012) to employ the SMM approach to fit the model to the US data (1979Q1-2015Q1). We find that the monetary policy uncertainty affects economic welfare through different dimensions. On the one hand, the policy uncertainty itself distorts the economic welfare negligibly, not only by increasing volatilities of consumption and leisure, but also by decreasing their average levels. A higher level of trend inflation then signifies these changes to produce greater welfare costs. Furthermore, the adverse impacts of policy uncertainty on the economy, documented by the impulse response functions of macroeconomic variables to policy uncertainty shock, become larger when central banks raise their inflation targets. On the other hand, the costs of exogenous variations in trend inflation are larger if there is policy uncertainty.     

On the Existence of Stable Roommate Matchings

This paper identifies a condition called “no odd rings” that is sufficient for the existence of stable roommate matchings in the weak preferences case. It shows that the process of allowing randomly chosen blocking pairs to match converges to a stable roommate matching with probability one as long as there are no odd rings. This random-paths-to-stability result generalizes that of Roth and Vande Vate (1990, Econometrica58, 1475–1480) and may not hold if there are odd rings. The “no odd rings” condition can also be used to prove a number of other sufficient conditions that are more economically interpretable. Journal of Economic Literature Classification Numbers: C78, D71.     

Direct Foreign Investment and Welfare in the Transforming Economies: The Case of Central Asia

This paper studies the welfare effects of foreign investment into an economy with a trade regime of export taxes and/or import subsidies. This regime is characteristic of the Central Asian economies but has received no consideration in previous literature. We show that in many circumstances, foreign investment into an economy with a Central-Asian-type trade regime reduces welfare. In particular, we find that foreign investment is most likely to immiserize when it is directed toward nondistorted traded sectors or free trade zones.J. Comp. Econom.,June 1997,24(3), pp. 297–312. University of Miami, P.O. Box 248126, Coral Gables, Florida 33124.     

Selective Acceptance and Inefficiency in a Two-Issue Complete Information Bargaining Game

This paper explores the effects of a “selective acceptance” rule on the outcome of two-issue negotiations. The alternating-offer game introduced here allows for the possibility that settlement may be reached on one issue while negotiation continues about the other. This model captures features of laws that are generally believed to increase efficiency. The analysis shows that if one issue is indivisible, there are inefficient subgame perfect equilibria with no Pareto-improving alternative equilibria. With opposing valuations, rapid communication guarantees inefficiency. These are unique examples of this strong form of inefficiency in an alternating-offer bargaining game with complete (and perfect) information. Journal of Economic Literature Classification Numbers: C72, J30.     

Undominated Nash Implementation with Collusion and Renegotiation

This article looks at implementation in economic environments when agents have perfect information about the state of the world, but cannot commit not to renegotiate bad outcomes or to collude against each other. If renegotiation satisfies a weak condition of disagreement point monotonicity, then any Pareto-efficient social choice function can be implemented if there are at least three agents who play undominated Nash equilibria. The mechanism does not use modulo or integer games, has no bad mixed strategy equilibria, and is “bounded.”Journal of Economic LiteratureClassification Number: D71.     

INCOME UNCERTAINTY,CONSUMER DURABLES INVESTMENTS,AND HOME PRODUCTION: EVIDENCE FROM CHINA

We investigate the effect of uncertainty on home durable purchase decisions, and empirically evaluate the efficacy of consumer durable policies under uncertainty. A model of lumpy home capital adjustment shows that elevated uncertainty leads households to adopt a cautionary perspective and postpone their capital adjustment. We test this prediction using microevidence from China where both uncertainty and home production are substantial. We exploit a wide‐scale rebate program funded by the Chinese government as a natural experiment, and examine the impact on household investment. We find strong, significant, and robust evidence that greater income uncertainty inhibits durable adjustment. Our findings highlight the impediment that income uncertainty poses to investment in home durables, which are often considered as “engines of liberation” in emerging economies. (JEL E21, E64, J22, O16, O23, D91)     

The equivalence of the Dekel–Fudenberg iterative procedure and weakly perfect rationalizability

Summary. Two approaches have been proposed in the literature to refine the rationalizability solution concept: either assuming that a player believes that with small probability her opponents choose strategies that are irrational, or assuming that their is a small amount of payoff uncertainty. We show that both approaches lead to the same refinement if strategy perturbations are made according to the concept of weakly perfect rationalizability, and if there is payoff uncertainty as in Dekel and Fudenberg [J. of Econ. Theory 52 (1990), 243–267]. For both cases, the strategies that survive are obtained by starting with one round of elimination of weakly dominated strategies followed by many rounds of elimination of strictly dominated strategies. Received: 10 December 1998; revised version: 26 April 1999     

Eliciting Preferences to Assign Positions and Compensation

We describe strategy-proof rules for economies where an agent is assigned a position (e.g., a job) plus some of a divisible good. For the 2-agent–2-position case we derive a robust characterization. For the multi-agent–position case, many “arbitrary” such rules exist, so we consider additional requirements. By also requiring coalitional strategy-proofness or nonbossiness, the range of a solution is restricted to the point that such rules are not more complex than those for the Shapley–Scarf housing model (no divisible good). Third, we show that essentially only constant solutions are immune to manipulations involving “bribes.” Finally, we demonstrate a conflict between efficiency and strategy-proofness. The results extend to models (without externalities) in which agents share positions. Journal of Economic Literature Classification Numbers: C72, D70.     

When is reputation bad?

In traditional reputation models, the ability to build a reputation is good for the long-run player. In [Ely, J., Valimaki, J., 2003. Bad reputation. NAJ Econ. 4, 2; http://www.najecon.org/v4.htm. Quart. J. Econ. 118 (2003) 785–814], Ely and Valimaki give an example in which reputation is unambiguously bad. This paper characterizes a class of games in which that insight holds. The key to bad reputation is that participation is optional for the short-run players, and that every action of the long-run player that makes the short-run players want to participate has a chance of being interpreted as a signal that the long-run player is “bad.” We allow a broad set of commitment types, allowing many types, including the “Stackelberg type” used to prove positive results on reputation. Although reputation need not be bad if the probability of the Stackelberg type is too high, the relative probability of the Stackelberg type can be high when all commitment types are unlikely.     

Dynamic stability and reform of political institutions

This paper examines endogenous institutional change in a class of dynamic political games. The political aggregation rules used at date t+1 are instrumental choices under rules at date t. Effectively, rules are “players” who can strategically delegate future policy-making authority to different rules. A political rule is stable if it selects itself. A reform occurs when an alternative rule is selected. The stability of a political rule is shown to depend on whether its choices are dynamically consistent. For instance, simple majority rules can be shown to be dynamically consistent in many common environments where wealth-weighted voting rules are not. The result extends to political rules that incorporate private activities such as extra-legal protests, threats, or private investment. The approach is one way of understanding various explanations of institutional change proposed in the literature. A parametric model of public goods provision gives an illustration.