We study the problem of selling information to a data-buyer who faces a decision problem under uncertainty. We consider the classic Bayesian decision-theoretic model pioneered by Blackwell [Bla51, Bla53]. Initially, the data buyer has only partial information about the payoff-relevant state of the world. A data seller offers additional information about the state of the world. The information is revealed through signaling schemes, also referred to as experiments. In the single-agent setting, any mechanism can be represented as a menu of experiments. A recent paper by Bergemann et al. [BBS18] present a complete characterization of the revenue-optimal mechanism in a binary state and binary action environment. By contrast, no characterization is known for the case with more actions. In this paper, we consider more general environments and study arguably the simplest mechanism, which only sells the fully informative experiment. In the environment with binary state and m ≥ 3 actions, we provide an O(m)-approximation to the optimal revenue by selling only the fully informative experiment and show that the approximation ratio is tight up to an absolute constant factor. An important corollary of our lower bound is that the size of the optimal menu must grow at least linearly in the number of available actions, so no universal upper bound exists for the size of the optimal menu in the general single-dimensional setting. We also provide a sufficient condition under which selling only the fully informative experiment achieves the optimal revenue.
For multi-dimensional environments, we prove that even in arguably the simplest matching utility environment with 3 states and 3 actions, the ratio between the optimal revenue and the revenue by selling only the fully informative experiment can grow immediately to a polynomial of the number of agent types. Nonetheless, if the distribution is uniform, we show that selling only the fully informative experiment is indeed the optimal mechanism.
This study provides new mechanisms for identifying and estimating explosive bubbles in mixed-root panel autoregressions with a latent group structure. A post-clustering approach is employed that combines a recursive k-means clustering algorithm with panel-data test statistics for testing the presence of explosive roots in time series trajectories. Uniform consistency of the k-means clustering algorithm is established, showing that the post-clustering estimate is asymptotically equivalent to the oracle counterpart that uses the true group identities. Based on the estimated group membership, right-tailed self-normalized t-tests and coefficient-based J-tests, each with pivotal limit distributions, are introduced to detect the explosive roots. The usual Information Criterion (IC) for selecting the correct number of groups is found to be inconsistent and a new method that combines IC with a Hausman-type specification test is proposed that consistently estimates the true number of groups. Extensive Monte Carlo simulations provide strong evidence that in finite samples, the recursive k-means clustering algorithm can correctly recover latent group membership in data of this type and the proposed post-clustering panel-data tests lead to substantial power gains compared with the time series approach. The proposed methods are used to identify bubble behavior in US and Chinese housing markets, and the US stock market, leading to new findings concerning speculative behavior in these markets.
This paper studies the social value of closing price differentials in financial markets. We show that arbitrage gaps (price differentials between markets) exactly correspond to the marginal social value of executing an arbitrage trade. We further show that arbitrage gaps and measures of price impact are sufficient to compute the total social value from closing an arbitrage gap. Theoretically, we show that, for a given arbitrage gap, the total social value of arbitrage is higher in more liquid markets. We apply our framework to compute the welfare gains from closing arbitrage gaps in the context of covered interest parity violations and several duallisted companies. The estimates of the value of closing arbitrage gaps vary substantially across applications.
We study rules based on instruments versus targets. Our application is a New Keynesian economy where the central bank has non-contractible information about aggregate demand shocks and cannot commit to policy. Incentives are provided to the central bank via punishment which is socially costly. Instrument-based rules condition incentives on the central bank’s observable choice of policy, whereas target-based rules condition incentives on the outcomes of policy, such as inflation, which depend on both the policy choice and realized shocks. We show that the optimal rule within each class takes a threshold form, imposing the worst punishment upon violation. Target-based rules dominate instrument-based rules if and only if the central bank’s information is sufficiently precise, and they are relatively more attractive the less severe the central bank’s commitment problem. The optimal unconstrained rule relaxes the instrument threshold whenever the target threshold is satisfied.
This paper examines the welfare implications of third-party informational intermediation. A seller sets the price of a product that is sold through an informational intermediary. The intermediary can disclose information about the product to consumers and earns a fixed percentage of sales revenue in each period. The intermediary’s market base grows at a rate that increases with past consumer surplus. We characterize the stationary equilibria and the set of subgame perfect equilibrium payoffs. When market feedback (i.e., the extent to which past consumer surplus affects future market bases) increases, welfare may decrease in the Pareto sense.