Knowledge that Transforms

We extend Kyle's (1985) model of insider trading to the case where noise trading volatility follows a general stochastic process. We determine conditions under which, in equilibrium, price impact and price volatility are both stochastic, driven by shocks to uninformed volume even though the fundamental value is constant. The volatility of price volatility appears 'excessive' because insiders choose to trade more aggressively (and thus more information is revealed) when uninformed volume is higher and price impact is lower. This generates a positive relation between price volatility and trading volume, giving rise to an endogenous subordinate stochastic process for prices.

We develop an equilibrium framework that relaxes the standard assumption that people have a correctly-specified view of their environment. Each player is characterized by a (possibly misspecified) subjective model, which describes the set of feasible beliefs over payoff-relevant consequences as a function of actions. We introduce the notion of a Berk-Nash equilibrium: Each player follows a strategy that is optimal given her belief, and her belief is restricted to be the best fit among the set of beliefs she considers possible. The notion of best fit is formalized in terms of minimizing the Kullback-Leibler divergence, which is endogenous and depends on the equilibrium strategy profile. Standard solution concepts such as Nash equilibrium and self-confirming equilibrium constitute special cases where players have correctly-specified models. We provide a learning foundation for Berk-Nash equilibrium by extending and combining results from the statistics literature on misspecified learning and the economics literature on learning in games.

I highlight how reputational concerns provide a natural explanation for “deadline effects, ” the high frequency of deals prior to a deadline in bargaining. Rational agents imitate the demands of obstinate behavioral types and engage in brinkmanship in the face of uncertainty about the deadline's arrival. I also identify how surplus is divided when the prior probability of behavioral types is vanishingly small. If behavioral types are committed to fixed demands, outcomes converge to the Nash bargaining solution regardless of agents' respective impatience. If behavioral types can adopt more complex demand strategies, outcomes converge to the solution of an alternating offers game without behavioral types for the deadline environment.

We study how long it takes for large populations of interacting agents to come close to Nash equilibrium when they adapt their behavior using a stochastic better reply dynamic. Prior work considers this question mainly for 2 × 2 games and potential games; here we characterize convergence times for general weakly acyclic games, including coordination games, dominance solvable games, games with strategic complementarities, potential games, and many others with applications in economics, biology, and distributed control. If players' better replies are governed by idiosyncratic shocks, the convergence time can grow exponentially in the population size; moreover, this is true even in games with very simple payoff structures. However, if their responses are sufficiently correlated due to aggregate shocks, the convergence time is greatly accelerated; in fact, it is bounded for all sufficiently large populations. We provide explicit bounds on the speed of convergence as a function of key structural parameters including the number of strategies, the length of the better reply paths, the extent to which players can influence the payoffs of others, and the desired degree of approximation to Nash equilibrium.

We propose a semiparametric two‐step inference procedure for a finite‐dimensional parameter based on moment conditions constructed from high‐frequency data. The population moment conditions take the form of temporally integrated functionals of state‐variable processes that include the latent stochastic volatility process of an asset. In the first step, we nonparametrically recover the volatility path from high‐frequency asset returns. The nonparametric volatility estimator is then used to form sample moment functions in the second‐step GMM estimation, which requires the correction of a high‐order nonlinearity bias from the first step. We show that the proposed estimator is consistent and asymptotically mixed Gaussian and propose a consistent estimator for the conditional asymptotic variance. We also construct a Bierens‐type consistent specification test. These infill asymptotic results are based on a novel empirical‐process‐type theory for general integrated functionals of noisy semimartingale processes.

The past forty years have seen a rapid rise in top income inequality in the United States. While there is a large number of existing theories of the Pareto tail of the long-run income distributions, almost none of these address the fast rise in top inequality observed in the data. We show that standard theories, which build on a random growth mechanism, generate transition dynamics that are too slow relative to those observed in the data. We then suggest two parsimonious deviations from the canonical model that can explain such changes: “scale dependence” that may arise from changes in skill prices, and “type dependence,” that is, the presence of some “high-growth types.” These deviations are consistent with theories in which the increase in top income inequality is driven by the rise of “superstar” entrepreneurs or managers.

This paper considers equilibrium quit turnover in a frictional labor market with costly hiring by firms, where large firms employ many workers and face both aggregate and firm specific productivity shocks. There is exogenous firm turnover as new (small) startups enter the market over time, while some existing firms fail and exit. Individual firm growth rates are disperse and evolve stochastically. The paper highlights how dynamic monopsony, where firms trade off lower wages against higher (endogenous) employee quit rates, yields excessive job-to-job quits. Such quits directly crowd out the reemployment prospects of the unemployed. With finite firm productivity states, stochastic equilibrium is fully tractable and can be computed using standard numerical techniques.

Call an economic model incomplete if it does not generate a probabilistic prediction even given knowledge of all parameter values. We propose a method of inference about unknown parameters for such models that is robust to heterogeneity and dependence of unknown form. The key is a Central Limit Theorem for belief functions; robust confidence regions are then constructed in a fashion paralleling the classical approach. Monte Carlo simulations support tractability of the method and demonstrate its enhanced robustness relative to existing methods.

Individual heterogeneity is an important source of variation in demand. Allow-ing for general heterogeneity is needed for correct welfare comparisons. We consider general heterogenous demand where preferences and linear budget sets are statis-tically independent. Only the marginal distribution of demand for each price and income is identified from cross-section data where only one price and income is observed for each individual. Thus, objects that depend on varying price and/or income for an indiviual are not generally identified, including average exact con-sumer surplus. We use bounds on income effects to derive relatively simple bounds on the average surplus, including for discrete/continous choice. We also sketch an approach to bounding surplus that does not use income effect bounds. We apply the results to gasoline demand. We find tight bounds for average surplus in this application but wider bounds for average deadweight loss.

We propose a theory of monetary policy and macroprudential interventions in financial markets. We focus on economies with nominal rigidities in goods and labor markets and subject to constraints on monetary policy, such as the zero lower bound or fixed exchange rates. We identify an aggregate demand externality that can be corrected by macroprudential interventions in financial markets. Ex post, the distribution of wealth across agents affects aggregate demand and output. Ex ante, however, these effects are not internalized in private financial decisions. We provide a simple formula for the required financial interventions that depends on a small number of measurable sufficient statistics. We also characterize optimal monetary policy. We extend our framework to incorporate pecuniary externalities, providing a unified approach to both externalities. Finally, we provide a number of applications which illustrate the relevance of our theory.