We provide a tractable, quantitatively‐oriented theory of innovation and technology diffusion to explore the role of international trade in the process of development. We model innovation and diffusion as a process involving the combination of new ideas with insights from other industries or countries. We provide conditions under which each country's equilibrium frontier of knowledge converges to a Fréchet distribution, and derive a system of differential equations describing the evolution of the scale parameters of these distributions, that is, countries' stocks of knowledge. The model remains tractable with many asymmetric countries and generates a rich set of predictions about how the level and composition of trade affect countries' frontiers of knowledge. We use the framework to quantify the contribution of bilateral trade costs to long‐run changes in TFP and individual post‐war growth miracles. For our preferred calibration, we find that both gains from trade and the fraction of variation of TFP growth accounted for by changes in trade more than double relative to a model without diffusion.

We extend Kreps and Wilson's concept of sequential equilibrium to games with infinite sets of signals and actions. A strategy profile is a conditional ε ‐equilibrium if, for any of a player's positive probability signal events, his conditional expected utility is within ε of the best that he can achieve by deviating. With topologies on action sets, a conditional ε ‐equilibrium is full if strategies give every open set of actions positive probability. Such full conditional ε ‐equilibria need not be subgame perfect, so we consider a non‐topological approach. Perfect conditional ε ‐equilibria are defined by testing conditional ε ‐rationality along nets of small perturbations of the players' strategies and of nature's probability function that, for any action and for almost any state, make this action and state eventually (in the net) always have positive probability. Every perfect conditional ε ‐equilibrium is a subgame perfect ε ‐equilibrium, and, in finite games, limits of perfect conditional ε ‐equilibria as ε → 0 are sequential equilibrium strategy profiles. But limit strategies need not exist in infinite games so we consider instead the limit distributions over outcomes. We call such outcome distributions perfect conditional equilibrium distributions and establish their existence for a large class of regular projective games. Nature's perturbations can produce equilibria that seem unintuitive and so we augment the game with a net of permissible perturbations.

We propose a decomposition of the realized covariance matrix into components based on the signs of the underlying high‐frequency returns, and we derive the asymptotic properties of the resulting realized semicovariance measures as the sampling interval goes to zero. The first‐order asymptotic results highlight how the same‐sign and mixed‐sign components load differently on economic information related to stochastic correlation and jumps. The second‐order asymptotic results reveal the structure underlying the same‐sign semicovariances, as manifested in the form of co‐drifting and dynamic “leverage” effects. In line with this anatomy, we use data on a large cross‐section of individual stocks to empirically document distinct dynamic dependencies in the different realized semicovariance components. We show that the accuracy of portfolio return variance forecasts may be significantly improved by exploiting the information in realized semicovariances.

Theories of bounded rationality often assume a rich dataset of choices from many overlapping menus, limiting their practical applicability. In contrast, we study the problem of identifying the distribution of cognitive characteristics in a population of agents from a minimal dataset that consists of aggregate choice shares from a single menu, and includes no observable covariates of any kind. With homogeneous preferences, we find that “consideration capacity” and “consideration probability” distributions can both be recovered effectively if the menu is sufficiently large. This remains true generically when tastes are heterogeneous with a known distribution. When the taste distribution is unknown, we show that joint choice share data from three “occasions” are generically sufficient for full identification of the cognitive distribution, and also provide substantial information about tastes.