Knowledge that Transforms

The paper studies the implementation problem, first analyzed by Maskin and Moore (1999), in which two agents observe an unverifiable state of nature and may renegotiate inefficient outcomes following play of the mechanism. We develop a first-order approach to characterizing the set of implementable utility mappings in this problem, paralleling Mirrlees's (1971) first-order analysis of standard mechanism design problems. We use this characterization to study optimal contracting in hold-up and risk-sharing models. In particular, we examine when the contracting parties can optimally restrict attention to simple contracts, such as noncontingent contracts and option contracts (where only one agent sends a message).

Strategic behavior in a finite market can cause inefficiency in the allocation, and market mechanisms differ in how successfully they limit this inefficiency. A method for ranking algorithms in computer science is adapted here to rank market mechanisms according to how quickly inefficiency diminishes as the size of the market increases. It is shown that trade at a single market-clearing price in the k-double auction is worst-case asymptotic optimal among all plausible mechanisms: evaluating mechanisms in their least favorable trading environments for each possible size of the market, the k-double auction is shown to force the worst-case inefficiency to zero at the fastest possible rate.

Reinforcement learning and stochastic fictitious play are apparent rivals as models of human learning. They embody quite different assumptions about the processing of information and optimization. This paper compares their properties and finds that they are far more similar than were thought. In particular, the expected motion of stochastic fictitious play and reinforcement learning with experimentation can both be written as a perturbed form of the evolutionary replicator dynamics. Therefore they will in many cases have the same asymptotic behavior. In particular, local stability of mixed equilibria under stochastic fictitious play implies local stability under perturbed reinforcement learning. The main identifiable difference between the two models is speed: stochastic fictitious play gives rise to faster learning.

Rating transition matrices for sovereigns are an important input to risk management of portfolios of emerging market credit exposures. They are widely used both in credit portfolio management and to calculate future loss distributions for pricing purposes. However, few sovereigns and almost no low credit quality sovereigns have ratings histories longer than a decade, so estimating such matrices is difficult. This paper shows how one may combine information from sovereign defaults observed over a longer period and a broader set of countries to derive estimates of sovereign transition matrices.

This paper investigates belief learning. Unlike other investigators who have been forced to use observable proxies to approximate unobserved beliefs, we have, using a belief elicitation procedure (proper scoring rule), elicited subject beliefs directly. As a result we were able to perform a more direct test of the proposition that people behave in a manner consistent with belief learning. What we find is interesting. First to the extent that subjects tend to “belief learn,” the beliefs they use are the stated beliefs we elicit from them and not the “empirical beliefs” posited by fictitious play or Cournot models. Second, we present evidence that the stated beliefs of our subjects differ dramatically, both quantitatively and qualitatively, from the type of empirical or historical beliefs usually used as proxies for them. Third, our belief elicitation procedures allow us to examine how far we can be led astray when we are forced to infer the value of parameters using observable proxies for variables previously thought to be unobservable. By transforming a heretofore unobservable into an observable, we can see directly how parameter estimates change when this new information is introduced. Again, we demonstrate that such differences can be dramatic. Finally, our belief learning model using stated beliefs outperforms both a reinforcement and EWA model when all three models are estimated using our data.

The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative.This paper studies optimization with arbitrary choice sets and shows that the traditional envelope formula holds at any differentiability point of the value function.We also provide conditions for the value function to be, variously, absolutely continuous, left-and right-differentiable, or fully differentiable.These results are applied to mechanism design, convex programming, continuous optimization problems, saddle-point problems, problems with parameterized constraints, and optimal stopping problems.

We develop a √n-consistent and asymptotically normal estimator of the parameters (regression coefficients and threshold points) of a semiparametric ordered response model under the assumption of independence of errors and regressors. The independence assumption implies shift restrictions allowing identification of threshold points up to location and scale. The estimator is useful in various applications, particularly in new product demand forecasting from survey data subject to systematic misreporting. We apply the estimator to assess exaggeration bias in survey data on demand for a new telecommunications service.

Evidence suggests that municipal water utility administrators in the western US price water significantly below its marginal cost and, in so doing, inefficiently exploit aquifer stocks and induce social surplus losses. This paper empirically identifies the objective function of those managers, measures the deadweight losses resulting from their price-discounting decisions, and recovers the efficient water pricing policy function from counterfactual experiments. In doing so, the estimation uses a “continuous-but-constrained- control” version of a nested fixed-point algorithm in order to measure the important intertemporal consequences of groundwater pricing decisions.