Knowledge that Transforms

This paper presents new identification results for models of first–price, second–price, ascending (English), and descending (Dutch) auctions. We consider a general specification of the latent demand and information structure, nesting both private values and common values models, and allowing correlated types as well as ex ante asymmetry. We address identification of a series of nested models and derive testable restrictions enabling discrimination between models on the basis of observed data. The simplest model—symmetric independent private values—is nonparametrically identified even if only the transaction price from each auction is observed. For richer models, identification and testable restrictions may be obtained when additional information of one or more of the following types is available: (i) the identity of the winning bidder or other bidders; (ii) one or more bids in addition to the transaction price; (iii) exogenous variation in the number of bidders; (iv) bidder–specific covariates. While many private values (PV) models are nonparametrically identified and testable with commonly available data, identification of common values (CV) models requires stringent assumptions. Nonetheless, the PV model can be tested against the CV alternative, even when neither model is identified.

We construct and estimate an equilibrium search model with on?the?job?search. Firms make take?it?or?leave?it wage offers to workers conditional on their characteristics and they can respond to the outside job offers received by their employees. Unobserved worker productive heterogeneity is introduced in the form of cross?worker differences in a ?competence? parameter. On the other side of the market, firms also are heterogeneous with respect to their marginal productivity of labor. The model delivers a theory of steady?state wage dispersion driven by heterogenous worker abilities and firm productivities, as well as by matching frictions. The structural model is estimated using matched employer and employee French panel data. The exogenous distributions of worker and firm heterogeneity components are nonparametrically estimated. We use this structural estimation to provide a decomposition of cross?employee wage variance. We find that the share of the cross?sectional wage variance that is explained by person effects varies across skill groups. Specifically, this share lies close to 40% for high?skilled white collars, and quickly decreases to 0% as the observed skill level decreases. The contribution of market imperfections to wage dispersion is typically around 50%.

This paper examines inference on regressions when interval data are available on one variable, the other variables being measured precisely. Let a population be characterized by a distribution P(y, x, v, v0, v1), where y∈R1, x∈Rk, and the real variables (v, v0, v1) satisfy v0≤v≤v1. Let a random sample be drawn from P and the realizations of (y, x, v0, v1) be observed, but not those of v. The problem of interest may be to infer E(y|x, v) or E(v|x). This analysis maintains Interval (I), Monotonicity (M), and Mean Independence (MI) assumptions: (I) P(v0≤v≤v1)=1; (M) E(y|x, v) is monotone in v; (MI) E(y|x, v, v0, v1)=E(y|x, v). No restrictions are imposed on the distribution of the unobserved values of v within the observed intervals [v0, v1]. It is found that the IMMI Assumptions alone imply simple nonparametric bounds on E(y|x, v) and E(v|x). These assumptions invoked when y is binary and combined with a semiparametric binary regression model yield an identification region for the parameters that may be estimated consistently by a modified maximum score (MMS) method. The IMMI assumptions combined with a parametric model for E(y|x, v) or E(v|x) yield an identification region that may be estimated consistently by a modified minimum-distance (MMD) method. Monte Carlo methods are used to characterize the finite-sample performance of these estimators. Empirical case studies are performed using interval wealth data in the Health and Retirement Study and interval income data in the Current Population Survey.

A principal and an agent enter into a sequence of agreements. The principal faces an interim participation constraint at each date, but can commit to the current agreement; in contrast, the agent has the opportunity to renege on the current agreement. We study the time structure of agreement sequences that satisfy participation and no-deviation constraints and are (constrained) efficient. We show that every such sequence must, after a finite number of dates, exhibit a continuation that maximizes the agent's payoff over all such efficient, self-enforcing sequences. Additional results are provided for situations with transferable payoffs.

When a continuous-time diffusion is observed only at discrete dates, in most cases the transition distribution and hence the likelihood function of the observations is not explicitly computable. Using Hermite polynomials, I construct an explicit sequence of closed-form functions and show that it converges to the true (but unknown) likelihood function. I document that the approximation is very accurate and prove that maximizing the sequence results in an estimator that converges to the true maximum likelihood estimator and shares its asymptotic properties. Monte Carlo evidence reveals that this method outperforms other approximation schemes in situations relevant for financial models.

In the context of common agency adverse-selection games we illustrate that the revelation principle cannot be applied to study equilibria of the multi-principal games. We then demonstrate that an extension of the taxation principle - what we term the delegation principle - can be used to characterize the set of all common agency equilibria.