Knowledge that Transforms

This paper develops methods for hypothesis testing in a nonparametric instrumental variables setting within a partial identification framework. We construct and derive the asymptotic distribution of a test statistic for the hypothesis that at least one element of the identified set satisfies a conjectured restriction. The same test statistic can be employed under identification, in which case the hypothesis is whether the true model satisfies the posited property. An almost sure consistent bootstrap procedure is provided for obtaining critical values. Possible applications include testing for semiparametric specifications as well as building confidence regions for certain functionals on the identified set. As an illustration we obtain confidence intervals for the level and slope of Brazilian fuel Engel curves. A Monte Carlo study examines finite sample performance.

This paper considers the estimation problem of structural models for which empirical restrictions are characterized by a fixed point constraint, such as structural dynamic discrete choice models or models of dynamic games. We analyze a local condition under which the nested pseudo likelihood (NPL) algorithm converges to a consistent estimator, and derive its convergence rate. We find that the NPL algorithm may not necessarily converge to a consistent estimator when the fixed point mapping does not have a local contraction property. To address the issue of divergence, we propose alternative sequential estimation procedures that can converge to a consistent estimator even when the NPL algorithm does not.

The standard dual-self model of self-control, with a shorter-run self who cares only about the current period, is excessively sensitive to the timing of decisions and to the interpolation of additional "no-action" time periods in between the dates when decisions are made.We show that when the shorter-run self is not completely myopic, this excess sensitivity goes away.To accommodate the combination of short time periods and convex costs of self-control, we introduce a cognitive resource variable that tracks how the control cost depends on the self-control that has been used in the recent past.We consider models with both linear and convex control costs, illustrating the theory through a series of examples.We examine when opportunities to consume will be avoided or delayed, and we consider the way in which the marginal interest declines with delay.

We introduce and derive the asymptotic behavior of a new measure constructed from high-frequency data which we call the realized Laplace transform of volatility. The statistic provides a nonparametric estimate for the empirical Laplace transform function of the latent stochastic volatility process over a given interval of time and is robust to the presence of jumps in the price process. With a long span of data, that is, under joint long-span and infill asymptotics, the statistic can be used to construct a nonparametric estimate of the volatility Laplace transform as well as of the integrated joint Laplace transform of volatility over different points of time. We derive feasible functional limit theorems for our statistic both under fixed-span and infill asymptotics as well as under joint long-span and infill asymptotics which allow us to quantify the precision in estimation under both sampling schemes.

We report an experiment on effects of varying institutional format and dynamic structure of centipede games and Dutch auctions. Centipede games with a clock format unravel, as predicted by theory but not reported in previous literature on two-player tree-format centipede games. Dutch auctions with a tree format produce bids close to risk neutral Nash equilibrium bids, unlike previous literature on clock-format Dutch auctions. Our data provide a new, expanded set of stylized facts which may provide a foundation for unified modeling of play in a class of games that includes centipede games and Dutch auctions.

For a finite game with perfect recall, a refinement of its set of Nash equilibria selects closed connected subsets, called solutions. Assume that each solution's equilibria use undominated strategies and some of its equilibria are quasi-perfect, and that all solutions are immune to presentation effects; namely, if the game is embedded in a larger game with more pure strategies and more players such that the original players' feasible mixed strategies and expected payoffs are preserved regardless of what other players do, then the larger game's solutions project to the original game's solutions. Then, for a game with two players and generic payoffs, each solution is an essential component of the set of equilibria that use undominated strategies, and thus a stable set of equilibria as defined by Mertens (1989).

For such a model, we show that consistency of the quasi-maximum likelihood estimator for the population parameter values, on which consistency of the test is based, does not hold. We describe a condition that ensures consistency of the estimator and discuss the consistency of the test in the absence of consistency of the estimator. In Cho and White (2007), Testing for Regime Switching, the authors stud ied the asymptotic behavior of a statistic that tests the null hypothesis of one regime against the alternative of Markov switching between two regimes. A key insight is that a consistent test can be based on a quasi-likelihood that ignores the Markov structure of regime switching and treats the state variables that indicate regimes as a sequence of independent and identically distributed ran dom variables. Consistency of the test follows from consistency of the quasi maximum likelihood estimator (QMLE) under the alternative, which appears as Theorem 1(b) in Cho and White. Consistency of the QMLE requires that the expected quasi-log-likelihood attain a global maximum at the population parameter values. We show that this requirement does not hold for the au toregressive process analyzed in Cho and White. Thus, for models of regime switching in which the conditional mean contains autoregressive components, consistency of the test proposed by Cho and White has not been established. For the observable random variables {X, e Md}=1, d e N, the Markov regime-switching autoregressive process analyzed by Cho and White (Sec tion 3, p. 1697) is

We examine challenges to estimation and inference when the objects of interest are nondifferentiable functionals of the underlying data distribution. This situation arises in a number of applications of bounds analysis and moment inequality models, and in recent work on estimating optimal dynamic treatment regimes. Drawing on earlier work relating differentiability to the existence of unbiased and regular estimators, we show that if the target object is not differentiable in the parameters of the data distribution, there exist no estimator sequences that are locally asymptotically unbiased or α-quantile unbiased. This places strong limits on estimators, bias correction methods, and inference procedures, and provides motivation for considering other criteria for evaluating estimators and inference procedures, such as local asymptotic minimaxity and one-sided quantile unbiasedness.

How can price elasticities be identified when agents face optimization frictions such as adjustment costs or inattention? I derive bounds on structural price elasticities that are a function of the observed effect of a price change on demand, the size of the price change, and the degree of frictions. The degree of frictions is measured by the utility losses agents tolerate to deviate from the frictionless optimum. The bounds imply that frictions affect intensive margin elasticities much more than extensive margin elasticities. I apply these bounds to the literature on labor supply. The utility costs of ignoring the tax changes used to identify intensive margin labor supply elasticities are typically less than 1% of earnings. As a result, small frictions can explain the differences between micro and macro elasticities, extensive and intensive margin elasticities, and other disparate findings. Pooling estimates from existing studies, I estimate a Hicksian labor supply elasticity of 0.33 on the intensive margin and 0.25 on the extensive margin after accounting for frictions.

In this paper, we introduce a notion of continuous implementation and characterize when a social choice function is continuously implementable. More specifically, we say that a social choice function is continuously (partially) implementable if it is (partially) implementable for types in the model under study and it continues to be (partially) implementable for types "close" to this initial model. Our results show that this notion is tightly connected to full implementation in rationalizable strategies.