Knowledge that Transforms

We assess the empirical content of equilibrium models of labor market sorting based on unobserved (to economists) characteristics. In particular, we show theoretically that all parameters of the classic model of sorting based on absolute advantage in Becker, 1973 with search frictions can be nonparametrically identified using only matched employer?employee data on wages and labor market transitions. In particular, these data are sufficient to nonparametrically estimate the output of any individual worker with any given firm. Our identification proof is constructive and we provide computational algorithms that implement our identification strategy given the limitations of the available data sets. Finally, we add on-the-job search to the model, extend the identification strategy, and apply it to a large German matched employer?employee data set to describe detailed patterns of sorting and properties of the production function.

This paper develops characterizations of identified sets of structures and structural features for complete and incomplete models involving continuous or discrete variables.Multiple values of unobserved variables can be associated with particular combinations of observed variables.This can arise when there are multiple sources of heterogeneity, censored or discrete endogenous variables, or inequality restrictions on functions of observed and unobserved variables.The models generalize the class of incomplete instrumental variable (IV) models in which unobserved variables are singlevalued functions of observed variables.Thus the models are referred to as generalized IV (GIV) models, but there are important cases in which instrumental variable restrictions play no significant role.Building on a definition of observational equivalence for incomplete models the development uses results from random set theory that guarantee that the characterizations deliver sharp bounds, thereby dispensing with the need for case-by-case proofs of sharpness.The use of random sets defined on the space of unobserved variables allows identification analysis under mean and quantile independence restrictions on the distributions of unobserved variables conditional on exogenous variables as well as under a full independence restriction.The results are used to develop sharp bounds on the distribution of valuations in an incomplete model of English auctions, improving on the pointwise bounds available until now.Application of many of the results of the paper requires no familiarity with random set theory.

We provide general conditions under which principal-agent problems admit mechanisms that are optimal for the principal. Our result covers as special cases those in which the agent has no private information – i.e., pure moral hazard – as well as those in which the agent’s only action is a participation decision – i.e., pure adverse selection. We allow multi-dimensional actions and signals, as well as both …nancial and non-financial rewards. Beyond measurability, we require no a priori restrictions on the space of mechanisms. Consequently, our optimal mechanisms are optimal among all measurable mechanisms. A key to obtaining our result is to permit randomized mechanisms. We also provide conditions under which randomization is unnecessary.

A growing number of school districts use centralized assignment mechanisms to allocate school seats in a manner that reflects student preferences and school priorities. Many of these assignment schemes use lotteries to ration seats when schools are oversubscribed. The resulting random assignment opens the door to credible quasi-experimental research designs for the evaluation of school effectiveness. Yet the question of how best to separate the lottery-generated randomization integral to such designs from non-random preferences and priorities remains open. This paper develops easily-implemented empirical strategies that fully exploit the random assignment embedded in a wide class of mechanisms, while also revealing why seats are randomized at one school but not another. We use these methods to evaluate charter schools in Denver, one of a growing number of districts that combine charter and traditional public schools in a unified assignment system. The resulting estimates show large achievement gains from charter school attendance. Our approach generates efficiency gains over ad hoc methods, such as those that focus on schools ranked first, while also identifying a more representative average causal effect. We also show how to use centralized assignment mechanisms to identify causal effects in models with multiple school sectors.

We characterize optimal mechanisms for the multiple-good monopoly problem and provide a framework to find them.We show that a mechanism is optimal if and only if a measure µ derived from the buyer's type distribution satisfies certain stochastic dominance conditions.This measure expresses the marginal change in the seller's revenue under marginal changes in the rent paid to subsets of buyer types.As a corollary, we characterize the optimality of grand-bundling mechanisms, strengthening several results in the literature, where only sufficient optimality conditions have been derived.As an application, we show that the optimal mechanism for n independent uniform items each supported on [c, c + 1] is a grand-bundling mechanism, as long as c is sufficiently large, extending Pavlov's result for 2 items [Pav11].At the same time, our characterization also implies that, for all c and for all sufficiently large n, the optimal mechanism for n independent uniform items supported on [c, c + 1] is not a grand bundling mechanism.

We present a flexible and scalable method for computing global solutions of highdimensional stochastic dynamic models.Within a time iteration or value function iteration setup, we interpolate functions using an adaptive sparse grid algorithm.With increasing dimensions, sparse grids grow much more slowly than standard tensor product grids.Moreover, adaptivity adds a second layer of sparsity, as grid points are added only where they are most needed, for instance, in regions with steep gradients or at nondifferentiabilities.To further speed up the solution process, our implementation is fully hybrid parallel, combining distributed and shared memory parallelization paradigms, and thus permits an efficient use of high-performance computing architectures.To demonstrate the broad applicability of our method, we solve two very different types of dynamic models: first, high-dimensional international real business cycle models with capital adjustment costs and irreversible investment; second, multiproduct menu-cost models with temporary sales and economies of scope in price setting.

We solve a general class of dynamic rational-inattention problems in which an agent repeatedly acquires costly information about an evolving state and selects actions. The solution resembles the choice rule in a dynamic logit model, but it is biased towards an optimal default rule that does not depend on the realized state. We apply the general solution to the study of (i) the sunk-cost fallacy; (ii) inertia in actions leading to lagged adjustments to shocks; and (iii) the tradeoff between accuracy and delay in decision-making.

In this paper we prove the existence of recursive equilibria in stochastic production economies with infinitely lived agents and incomplete financial markets. We consider a general dynamic model with several commodities, which encompasses heterogeneous agent versions of both the Lucas asset pricing model and the stochastic neo-classical growth model as special cases. Our main assumption is that there are atomless shocks to fundamentals that have a purely transitory component and a component that does not depend on last period's shocks directly.

We study a dynamic principal–agent relationship with adverse selection and limited commitment. We show that when the relationship is subject to productivity shocks, the principal may be able to improve her value over time by progressively learning the agent's private information. She may even achieve her first‐best payoff in the long run. The relationship may also exhibit path dependence, with early shocks determining the principal's long‐run value. These findings contrast sharply with the results of the ratchet effect literature, in which the principal persistently obtains low payoffs, giving up substantial informational rents to the agent.

We develop econometric tools for studying jump dependence of two processes from high-frequency observations on a fixed time interval. In this context, only segments of data around a few outlying observations are informative for the inference. We derive an asymptotically valid test for stability of a linear jump relation over regions of the jump size domain. The test has power against general forms of nonlinearity in the jump dependence as well as temporal instabilities. We further propose an efficient estimator for the linear jump regression model that is formed by optimally weighting the detected jumps with weights based on the diffusive volatility around the jump times. We derive the asymptotic limit of the estimator, a semiparametric lower efficiency bound for the linear jump regression, and show that our estimator attains the latter. The analysis covers both deterministic and random jump arrivals. In an empirical application, we use the developed inference techniques to test the temporal stability of market jump betas.