Macroeconomic variables exhibit inertia. On the face of it, such inertia sits uncomfortably with the behavior of rational, forward-looking agents who form expectations on the basis of the best information available at the time. Christopher Sims (2003, sect. 8) offers a three-fold taxonomy of attempts to rationalize inertia. The first is the idea of Robert Lucas (1973) and Edmund Phelps (1970) that agents face a signal extraction problem, so that their actions react only partially to shifts in fundamentals due to the residual uncertainty. The second is the sticky expectations approach of N. Gregory Mankiw and Ricardo Reis (2002), where otherwise rational and forward-looking agents receive information with some delay. The third is the rational inattention approach favored by Sims himself, where agents with informationprocessing constraints choose the optimal coarsening of their information (Sims, 2003). Our approach is a variation on the signalextraction theme but has implications for the sticky-expectations and rational-inattention approaches. As explained recently by Michael Woodford (2003), the original contribution of Lucas (1973) had limited success in explaining the persistence of macroeconomic aggregates due to the feature that the underlying fundamentals are fully revealed after a delay of one period. Without this simplifying feature, however, the complexity of the problem increases rapidly as expectations of others’ expectations become relevant in one’s calculations (Robert Townsend, 1983; Phelps, 1983). Tractability aside, the approach holds much promise. When agents are differentially informed, events in the distant past are “more common knowledge” than events in the recent past. Not only has enough time elapsed for the agents to ascertain the facts in the distant past, but more importantly, enough time has elapsed for each agent to be more confident that other agents have ascertained the facts. When common knowledge is important (as in coordination problems, for example) events in the distant past take on significance. Paradoxically, the farther the agents peer into the future, the farther they must look into the past to establish the informational platform for their actions. To an outside observer, the aggregate action betrays all the outward signs of adaptive expectations. In order to demonstrate this principle in a transparent way, we employ other drastic simplifications but do not assume that realizations are revealed after a delay of one period. We thereby preserve the nontrivial nature of dynamic, higher-order beliefs and show how persistence arises as a natural consequence of the original Lucas and Phelps insight.

What are the welfare effects of enhanced dissemination of public information through the media and disclosures by market participants with high public visibility? We examine the impact of public information in a setting where agents take actions appropriate to the underlying fundamentals, but they also have a coordination motive arising from a strategic complementarity in their actions. When the agents have no socially valuable private information, greater provision of public information always increases welfare. However, when agents also have access to independent sources of information, the welfare effect of increased public disclosures is ambiguous.

We describe a methodology for making counterfactual predictions in settings where the information held by strategic agents and the distribution of payoff-relevant states of the world are unknown. The analyst observes behavior assumed to be rationalized by a Bayesian model, in which agents maximize expected utility, given partial and differential information about the state. A counterfactual prediction is desired about behavior in another strategic setting, under the hypothesis that the distribution of the state and agents’ information about the state are held fixed. When the data and the desired counterfactual prediction pertain to environments with finitely many states, players, and actions, the counterfactual prediction is described by finitely many linear inequalities, even though the latent parameter, the information structure, is infinite dimensional.

We revisit the revenue comparison of standard auction formats, including first-price, second-price, and English auctions. We rank auctions according to their revenue guarantees, i.e., the greatest lower bound of revenue across all informational environments, where we hold fixed the distribution of bidders’ values. We conclude that if we restrict attention to the symmetric affiliated models of Milgrom and Weber (1982) and monotonic pure-strategy equilibria, first-price, second-price, and English auctions are revenue guarantee equivalent: they have the same revenue guarantee, which is equal to that of the first-price auction as characterized by Bergemann, Brooks, and Morris (2017). If we consider all equilibria or if we allow more general models of information, then first-price auctions have a greater revenue guarantee than all other auctions considered.

In a financial market where traders are risk averse and short lived and prices are noisy, asset prices today depend on the average expectation today of tomorrow’s price. Thus (iterating this relationship) the date 1 price equals the date 1 average expectation of the date 2 average expectation of the date 3 price. This will not, in general, equal the date 1 average expectation of the date 3 price. We show how this failure of the law of iterated expectations for average belief can help understand the role of higher-order beliefs in a fully rational asset pricing model.

We explore the impact of private information in sealed-bid first-price auctions. For a given symmetric and arbitrarily correlated prior distribution over values, we characterize the lowest winning-bid distribution that can arise across all information structures and equilibria. The information and equilibrium attaining this minimum leave bidders indifferent between their equilibrium bids and all higher bids. Our results provide lower bounds for bids and revenue with asymmetric distributions over values. We also report further characterizations of revenue and bidder surplus including upper bounds on revenue. Our work has implications for the identification of value distributions from data on winning bids and for the informationally robust comparison of alternative auction mechanisms.

Do large investors increase the vulnerability of a country to speculative attacks in the foreign exchange markets? To address this issue, we build a model of currency crises where a single large investor and a continuum of small investors independently decide whether to attack a currency based on their private information about fundamentals. Even abstracting from signalling, the presence of the large investor does make all other traders more aggressive in their selling. Relative to the case in which there is no large investor, small investors attack the currency when fundamentals are stronger. Yet, the difference can be small, or non-existent, depending on the relative precision of private information of the small and large investors. Adding signalling makes the influence of the large trader on small traders' behaviour much stronger.

We analyze the welfare consequences of a monopolist having additional information about consumers' tastes, beyond the prior distribution; the additional information can be used to charge different prices to different segments of the market, i.e., carry out “third degree price discrimination.” We show that the segmentation and pricing induced by the additional information can achieve every combination of consumer and producer surplus such that: (i) consumer sur plus is nonnegative, (ii) producer surplus is at least as high as profits under the uniform monopoly price, and (iii) total surplus does not exceed the surplus generated by efficient trade.

We consider the efficient allocation of a single good with interdependent values in a quasilinear environment. We present an approach to modeling interdependent preferences distinguishing between “payoff types” and “belief types” and report a characterization of when the efficient allocation can be partially Bayesian implemented on a finite type space. The characterization can be used to unify a number of sufficient conditions for efficient partial implementation in this classical auction setting. We report how a canonical language for discussing interdependent types - developed in a more general setting by Bergemann, Morris and Takahashi (2011) - applies in this setting and note by example that this canonical language will not allow us to distinguish some types in the payoff type - belief type language.

We analyze a nonlinear pricing model where the seller controls both product pricing (screening) and buyer information about their own values (persuasion). We prove that the optimal mechanism always consists of finitely many signals and items, even with a continuum of buyer values. The seller optimally pools buyer values and reduces product variety to minimize informational rents. We show that value pooling is optimal even for finite value distributions if their entropy exceeds a critical threshold. We also provide sufficient conditions under which the optimal menu restricts offering to a single item.