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Endogenous demand composition across sectors due to income elasticity differences, or Engel's Law for brevity, affects (i) sectoral compositions in employment and in value-added, (ii) variations in innovation rates and in productivity change across sectors, (iii) intersectoral patterns of trade across countries, and (iv) product cycles from rich to poor countries. Using a two-country model of directed technical change with a continuum of sectors under nonhomothetic preferences, which is rich enough to capture all these effects as well as their interactions, this paper offers a unifying perspective on how economic growth and globalization affect the patterns of structural change, innovation, and trade across countries and across sectors in the presence of Engel's Law. Among the main messages is that globalization amplifies, instead of reducing, the power of endogenous domestic demand composition differences as a driver of structural change.

We propose a novel model of stochastic choice: the single-crossing random utility model (SCRUM). This is a random utility model in which the collection of preferences satisfies the single-crossing property. We offer a characterization of SCRUMs based on two easy-to-check properties: the classic Monotonicity property and a novel condition, Centrality. The identified collection of preferences and associated probabilities is unique. We show that SCRUMs nest both single-peaked and single-dipped random utility models and establish a stochastic monotone comparative result for the case of SCRUMs.

A key feature of communication with evidence is skepticism: a receiver will attribute any incomplete disclosure to the sender concealing unfavorable evidence. I study when a change in the receiver\"s prior belief about the sender's evidence induces more skepticism, i.e., induces the receiver, regardless of his preferences, to take an equilibrium action that is less favorable for the sender following every message. I provide a definition of when one receiver's prior belief expects more evidence than another and show that this characterizes more skepticism. As an input, I fully characterize receiver optimal equilibrium outcomes in general verifiable disclosure games.

We introduce a notion of substitutability for correspondences and establish a monotone comparative static result. More precisely, we introduce the notions of unified gross substitutes and nonreversingness and show that if Q:P⇉Q is a supply correspondence defined on a set of prices P, which is a sublattice of RN, and Q satisfies these two properties, then the set of equilibrium prices Q−1(q) associated with a vector of quantities q ∈ Q is a sublattice of P and is increasing (in the strong set order) in q. We establish connections between our notion of substitutes and existing notions, and examine applications such as the structure of inverse demand, profit maximization, the structure of competitive equilibria, matching games, hedonic pricing, and routing problems.

The single crossing property plays a crucial role in economic theory, yet there are important instances where the property cannot be directly assumed or easily derived. Difficulties often arise because the property cannot be aggregated: the sum or convex combination of two functions with the single crossing property need not have that property. We introduce a new condition characterizing when the single crossing property is stable under aggregation, and also identify sufficient conditions for the preservation of the single crossing property under multidimensional aggregation. We use our results to establish properties of objective functions (convexity, logsupermodularity), the monotonicity of optimal decisions under uncertainty, and the existence of monotone equilibria in Bayesian games.

In many theories and applications with uncertainty, using intervals to characterize uncertainty is simple and operable. It is crucial to choose a proper order for an interval method. In general, a total order is superior to a partial order for those applications in which we have to make a final decision. Motivated by this idea, we generalized interval-valued monotone comparative statics (MCS) with a partial order to interval-valued MCS with a total order, to be more precise, with an admissible order. The generalization was not trival. We obtained a necessary and sufficient condition for MCS by a series of new concepts such as an interval-valued quasi-super-modular function and an interval-valued single crossing property with an admissible order. The same condition was only sufficient in the existing literature. Furthermore, we illustrated the efficiency of the interval-valued MCS with the lexicographical orders and XY-order, which are well-known admissible orders. Finally, we applied our results in interval games with strategic complements to get the monotonity of the best response correspondence for player i.

We develop a nonparametric and ordinal approach for testing pure strategy Nash equilibrium play in games with monotone best responses, such as those with strategic complements/substitutes. The approach makes minimal assumptions on unobserved heterogeneity, requires no parametric assumptions on payoff functions, and no restriction on equilibrium selection from multiple equilibria. The approach can also be extended in order to make inferences and predictions. Both model-testing and inference can be implemented by a tractable computation procedure based on column generation. To illustrate how our approach works, we include an application to an IO entry game.

We explore costly deliberation by two differentially informed and possibly biased jurors: A hawk Lones and a dove Moritz alternately insist on a verdict until one concedes. Debate assumes one of two genres, depending on bias: A juror, say Lones, is intransigent if he wishes to prevail and reach a conviction for any type of Moritz next to concede. In contrast, Lones is ambivalent if he wants the strongest conceding types of Moritz to push for acquittal. Both jurors are ambivalent with small bias or high delay costs. As Lones grows more hawkish, he argues more forcefully for convictions, mitigating wrongful acquittals. If dovish Moritz is intransigent, then he softens (strategic substitutes), leading to more wrongful convictions. Ambivalent debate is new, and yields a novel dynamic benefit of increased polarization. For if Moritz is ambivalent, then he toughens (strategic complements), and so, surprisingly, a more hawkish Lones leads to fewer wrongful acquittals and convictions. So more polarized but balanced debate can improve communication, unlike in static cheap talk. We also show that patient and not too biased jurors vote against their posteriors near the end of the debate, optimally playing devil’s advocate. We shed light on the adversarial legal system, peremptory challenges, and cloture rules.

Many questions of interest in economics can be stated in terms of monotone comparative statics: If a parameter of a constrained optimization problem increases, when does its solution increase as well. We characterize monotone comparative statics in different directions in finite-dimensional Euclidean space by extending the monotonicity theorem of Milgrom and Shannon (Econometrica 62(1): 157–180, 1994) to constraint sets ordered in Quah (Econometrica 75(2):401–431, 2007)'s set order. Our characterizations are ordinal and retain the same flavor as their counterparts in the standard theory, showing new connections to the standard theory and presenting new results. The results are highlighted with several applications (in consumer theory, producer theory, and game theory) which were previously outside the scope of the standard theory of monotone comparative statics.

International trade has experienced a Ricardian revival. In this article, we offer a user guide to assignment models, which we refer to as Ricardo-Roy (R-R) models, that have contributed to this revival.