Testing theories with learnable and predictive representations

We study the problem of testing an expert whose theory has a learnable and predictive parametric representation, as do standard processes used in statistics. We design a test in which the expert is required to submit a date T by which he will have learned enough to deliver a sharp, testable prediction about future frequencies. We show that this test passes an expert who knows the data-generating process and cannot be manipulated by a uninformed one. Such a test is not possible if the theory is unrestricted.     

Search theory,competitive equilibrium,and the Nash bargaining solution

We investigate a canonical search-theoretic model without entry. Two agents are randomly matched with a long side being rationed. The matched agents face a pair of randomly drawn non-transferable payoffs, and then choose whether or not to form a partnership subject to a small probability of exogenous break down. As this probability and friction vanish, the Nash bargaining solution emerges as the unique undominated strategy equilibrium outcome if the mass of each party is the same. If the size of one party is larger than the other, the short side extracts the entire surplus, a sharp contrast to Rubinstein and Wolinsky (1985) [16].     

Robust estimation and control under commitment

In a Markov decision problem with hidden state variables, a decision maker expresses fear that his model is misspecified by surrounding it with a set of alternatives that are nearby as measured by their expected log likelihood ratios (entropies). Sets of martingales represent alternative models. Within a two-player zero-sum game under commitment, a minimizing player chooses a martingale at time 0. Probability distributions that solve distorted filtering problems serve as state variables, much like the posterior in problems without concerns about misspecification. We state conditions under which an equilibrium of the zero-sum game with commitment has a recursive representation that can be cast in terms of two risk-sensitivity operators. We apply our results to a linear quadratic example that makes contact with findings of T. Ba?ar and P. Bernhard [H^∞-Optimal Control and Related Minimax Design Problems, second ed., Birkhauser, Basel, 1995] and P. Whittle [Risk-sensitive Optimal Control, Wiley, New York, 1990].     

Recursive robust estimation and control without commitment

In a Markov decision problem with hidden state variables, a posterior distribution serves as a state variable and Bayes’ law under an approximating model gives its law of motion. A decision maker expresses fear that his model is misspecified by surrounding it with a set of alternatives that are nearby when measured by their expected log likelihood ratios (entropies). Martingales represent alternative models. A decision maker constructs a sequence of robust decision rules by pretending that a sequence of minimizing players choose increments to martingales and distortions to the prior over the hidden state. A risk sensitivity operator induces robustness to perturbations of the approximating model conditioned on the hidden state. Another risk sensitivity operator induces robustness to the prior distribution over the hidden state. We use these operators to extend the approach of Hansen and Sargent [Discounted linear exponential quadratic Gaussian control, IEEE Trans. Automat. Control 40(5) (1995) 968-971] to problems that contain hidden states.     

Inverse demand systems and choice of functional form

Barten (Empirical Economics 18 (1993) 129) recently advocated estimation of a synthetic demand system that mechanically nests four other popular differential demand models. This paper follows a similar strategy, but in the context of four inverse share-equation demand systems: The Inverse Translog Demand System (ITLDS); the Inverse Almost Ideal Demand System (IAIDS); the Inverse Lewbel Demand System (ILDS); and the Inverse Non-Separable Linear Expenditure System (INLES). Each of these specifications is artificially nested in a Hybrid Inverse Demand System (HIDS). An empirical application to three categories of quarterly U.S. meat demand data over the period 1961-1996 indicates the HIDS is a preferred specification.     

The strategy of manipulating joint decision-making

We study a model of strategic persuasion based on the theory of cheap talk, in which a better-informed agent manipulates two decision-makers’ joint decision on alternative proposals. With the heterogeneity of two decision-makers’ value of the outside option, only the decision-maker with the better outside option is critical in determining whether communication is truthful, overselling, or ineffective.     

Mechanism design with side payments: Individual rationality and iterative dominance

We investigate the collective decision with incomplete information and side payments. We show that a direct mechanism associated with the social choice function that satisfies budget balancing, incentive compatibility, and interim individual rationality exists for generic prior distributions. We consider the possibility that a risk-averse principal extracts full surplus in agency problems with adverse selection. With regard to generic prior distributions, we show that there exists a modified direct mechanism associated with the virtual social choice function, which satisfies budget balancing and interim individual rationality, such that truth telling is the unique three times iteratively undominated message rule profile.     

Financial constraints and occupational choice in Thai villages

Financial constraints and entrepreneurship are key factors affecting economic performance in developing countries. I formulate and solve a model of occupational choice with moral hazard under three alternative financial market environments: savings only, borrowing and lending with default and moral hazard constrained insurance. I use computationally efficient techniques based on mechanism design, genetic algorithms and maximum likelihood to estimate and statistically test these models of financial constraints. Using occupational choice data from Thai villages I find evidence that the saving only regime is rejected in favor of regimes allowing for borrowing and/or insurance, especially in higher-wealth data stratifications. A direct test between the borrowing and insurance regimes reveals that neither can be rejected in favor of the other. Allowing ex-ante lotteries over wealth improves the explanatory power of the model. I also find evidence for differences in the best fitting regimes by region, wealth, and access to formal credit.     

The micro economics of group behavior: General characterization

We study the demand function of a group of S members facing a global budget constraint. Any vector belonging to the budget set can be consumed within the group, with no restriction on the form of individual preferences, the nature of individual consumptions or the form of the decision process beyond efficiency. Moreover, only the group aggregate behavior, summarized by its demand function, is observable. We provide necessary and (locally) sufficient restrictions that fully characterize the group's demand function, with and without distribution factors. We show that the private or public nature of consumption within the group is not testable from aggregate data on group behavior.     

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.     

Why do people place lower weight on advice far from their own initial opinion?

Experimental studies find that the weight put on advice is negatively related to the distance between the advice and the decision-maker’s initial opinion. We show that this can be rational if the decision-maker has imperfect knowledge about the advisor’s competence.     

Introduction to Incompleteness and Uncertainty in Economics

This introduces the symposium on incompleteness and uncertainty in economics.     

The choice of a foreign price measure in a Bayesian estimated new-Keynesian model for Israel

We estimate a small DSGE model by full information Bayesian techniques on the basis of Israeli data from 1995 to 2006. The model was first developed and estimated by means of classical GMM in Argov and Elkayam (2010), and since then it has been used at the Bank of Israel for monetary policy analysis. It is widely believed that in 2007 (out of sample year) as elsewhere worldwide, inflation rose in Israel due to high commodity prices in global markets. However, our baseline model attributes most of the high inflation in 2007 to supply shocks. One conjecture is that this model's result derives from the inappropriate original use of the unit value of imported consumer goods (which do not include unprocessed food and energy) as the main foreign price measure. We test this conjecture by re-estimating the model with various other foreign price measures that typically do reflect the global rise in commodity prices and compare the log-marginal likelihoods. We find that no other price measure outperforms the original choice in the sample period. Only the foreign trade-weighted CPI equals the performance of the original choice while improving the 2007 interpretation of inflation, and should therefore be considered the main foreign price measure. The proposed methodology for comparing the suitability of alternative measures for observable variables can be applied to any model with exogenous variables that are characterized by univariate equations.     

Internal rationality, imperfect market knowledge and asset prices

We present a decision theoretic framework in which agents are learning about market behavior and that provides microfoundations for models of adaptive learning. Agents are ‘internally rational’, i.e., maximize discounted expected utility under uncertainty given dynamically consistent subjective beliefs about the future, but agents may not be ‘externally rational’, i.e., may not know the true stochastic process for payoff relevant variables beyond their control. This includes future market outcomes and fundamentals. We apply this approach to a simple asset pricing model and show that the equilibrium stock price is then determined by investors? expectations of the price and dividend in the next period, rather than by expectations of the discounted sum of dividends. As a result, learning about price behavior affects market outcomes, while learning about the discounted sum of dividends is irrelevant for equilibrium prices. Stock prices equal the discounted sum of dividends only after making very strong assumptions about agents? market knowledge.     

The communication requirements of social choice rules and supporting budget sets

The paper examines the communication requirements of social choice rules when the (sincere) agents privately know their preferences. It shows that for a large class of choice rules, any minimally informative way to verify that a given alternative is in the choice rule is by verifying a “budget equilibrium”, i.e., that the alternative is optimal to each agent within a “budget set” given to him. Therefore, any communication mechanism realizing the choice rule must find a supporting budget equilibrium. We characterize the class of choice rules that have this property. Furthermore, for any rule from the class, we characterize the minimally informative messages (budget equilibria) verifying it. This characterization is used to identify the amount of communication needed to realize a choice rule, measured with the number of transmitted bits or real variables. Applications include efficiency in convex economies, exact or approximate surplus maximization in combinatorial auctions, the core in indivisible-good economies, and stable many-to-one matchings.     

Justifiable group choice

We study the judgment aggregation problem from the perspective of justifying a particular collective decision by a corresponding aggregation on the criteria. In particular, we characterize the logical relations between the decision and the criteria that enable justification of a majority decision through a proposition-wise aggregation rule with no veto power on the criteria. While the well-studied “doctrinal paradox” provides a negative example in which no such justification exists, we show that genuine possibility results emerge if there is a gap between the necessary and the sufficient conditions for the decision. This happens, for instance, if there is only a partial consensus about the appropriate criteria for the decision, if only a subset of these criteria can be elicited, or if the judgment on criteria is based on probabilistic acceptance thresholds.     

Match choice and Ghettoization in evolutionary games

I study how having a choice about who to play affects the conventions that arise in a population playing a 2×2 common interest game. Match choice allows agents playing “fragile but efficient” strategies to isolate themselves, raising their returns but making it harder for outsiders to duplicate their success. When agents are myopic, the second effect dominates: long run play can shift toward either the risk-dominant equilibrium (with common interests in matching) or toward the inefficient equilibrium (with opposing interests in matching). In contrast, when agents are patient, supra-Nash payoffs can be sustained.     

Commitment and choice of partner in a negotiation with a deadline

This paper analyses the effects of partially revocable endogenous commitments of a seller in a negotiation with a deadline. In particular, we examine when commitment is a source of strength, a source of inefficiency and when it does not affect the bargaining outcome at all. We show that when commitment possesses a minimum amount of irrevocability this crucially determines the bargaining outcome. In the bilateral bargaining case, commitment becomes a source of inefficiency since it causes a deadline effect. In the choice of partner framework, however, the deadline effect disappears and there is an immediate agreement and, moreover, commitment becomes a source of strength since it increases the seller's equilibrium payoff by triggering off competition between the buyers.     

A note on undominated Bertrand equilibria

This note shows that the conventional outcome associated with Bertrand competition with homogenous products and different marginal costs is obtained in every Nash equilibrium in which firms use undominated strategies. This strengthens an existence result due to Blume (2003).     

Private versus verifiable interim performance evaluations under uncertainty

I study the trade-off between private and verifiable interim performance evaluations under uncertainty. More uncertainty leads to higher agency costs if the interim evaluation is public and verifiable but lower agency costs if the interim evaluation is private and unverifiable.