Knowledge that Transforms

This paper studies the nonparametric identification of the first-price auction model with risk averse bidders within the private value paradigm. First, we show that the benchmark model is nonindentified from observed bids. We also derive the restrictions imposed by the model on observables and show that these restrictions are weak. Second, we establish the nonparametric identification of the bidders' utility function under exclusion restrictions. Our primary exclusion restriction takes the form of an exogenous bidders' participation, leading to a latent distribution of private values that is independent of the number of bidders. The key idea is to exploit the property that the bid distribution varies with the number of bidders while the private value distribution does not. We then extend these results to endogenous bidders' participation when the exclusion restriction takes the form of instruments that do not affect the bidders' private value distribution. Though derived for a benchmark model, our results extend to more general cases such as a binding reserve price, affiliated private values, and asymmetric bidders. Last, possible estimation methods are proposed.

A player's pure strategy is called relevant for an outcome of a game in extensive form with perfect recall if there exists a weakly sequential equilibrium with that outcome for which the strategy is an optimal reply at every information set it does not exclude. The outcome satisfies forward induction if it results from a weakly sequential equilibrium in which players' beliefs assign positive probability only to relevant strategies at each information set reached by a profile of relevant strategies. We prove that if there are two players and payoffs are generic, then an outcome satisfies forward induction if every game with the same reduced normal form after eliminating redundant pure strategies has a sequential equilibrium with an equivalent outcome. Thus in this case forward induction is implied by decision-theoretic criteria. Copyright 2009 The Econometric Society.

We propose a new regression method to evaluate the impact of changes in the distribution of the explanatory variables on quantiles of the unconditional (marginal) distribution of an outcome variable. The proposed method consists of running a regression of the (recentered) influence function (RIF) of the unconditional quantile on the explanatory variables. The influence function, a widely used tool in robust estimation, is easily computed for quantiles, as well as for other distributional statistics. Our approach, thus, can be readily generalized to other distributional statistics.

Can incentives be effective in encouraging the development of good habits? We investigate the post-intervention effects of paying people to attend a gym a number of times during one month. In two studies we find marked attendance increases after the intervention relative to attendance changes for the respective control groups. This is entirely driven by people who did not previously attend the gym on a regular basis. In our second study, we find improvements on health indicators such as weight, waist size, and pulse rate, suggesting the intervention led to a net increase in total physical activity rather than to a substitution away from nonincentivized ones. We argue that there is scope for financial intervention in habit formation, particularly in the area of health.

We define belief-free equilibria in two-player games with incomplete information as sequential equilibria for which players' continuation strategies are best replies after every history, independently of their beliefs about the state of nature. We characterize a set of payoffs that includes all belief-free equilibrium payoffs. Conversely, any payoff in the interior of this set is a belief-free equilibrium payoff. The characterization is applied to the analysis of reputations. Copyright 2009 The Econometric Society.

This paper applies some general concepts in decision theory to a linear panel data model. A simple version of the model is an autoregression with a separate intercept for each unit in the cross section, with errors that are independent and identically distributed with a normal distribution. There is a parameter of interest Gamma and a nuisance parameter τ, a N×K matrix, where N is the cross-section sample size. The focus is on dealing with the incidental parameters problem created by a potentially high-dimension nuisance parameter. We adopt a "fixed-effects" approach that seeks to protect against any sequence of incidental parameters. We transform tau to (delta, rho, omega), where delta is a J x K matrix of coefficients from the least-squares projection of tau on a N x J matrix x of strictly exogenous variables, rho is a K x K symmetric, positive semidefinite matrix obtained from the residual sums of squares and cross-products in the projection of tau on x, and omega is a (N - J) x K matrix whose columns are orthogonal and have unit length. The model is invariant under the actions of a group on the sample space and the parameter space, and we find a maximal invariant statistic. The distribution of the maximal invariant statistic does not depend upon omega. There is a unique invariant distribution for omega. We use this invariant distribution as a prior distribution to obtain an integrated likelihood function. It depends upon the observation only through the maximal invariant statistic. We use the maximal invariant statistic to construct a marginal likelihood function, so we can eliminate omega by integration with respect to the invariant prior distribution or by working with the marginal likelihood function. The two approaches coincide. Copyright 2009 The Econometric Society.

The property of an allocation rule to be implementable in dominant strategies by a unique payment scheme is called revenue equivalence. We give a characterization of revenue equivalence based on a graph theoretic interpretation of the incentive compatibility constraints. The characterization holds for any (possibly infinite) outcome space and many of the known results are immediate consequences. Moreover, revenue equivalence can be identified in cases where existing theorems are silent.

We reappraise the significance and robustness of indeterminacy in overlapping-generations models. In any of Gale's example economies with an equilibrium that is not locally unique, for instance, perturbing the economy by judiciously splitting each of Gale's goods into two close substitutes restricts that indeterminacy to each period's allocation of consumption between those substitutes. In particular, prices, interest rates, the commodity value of nominal savings (including money), and utility levels become determinate. Any indeterminacy of equilibrium consumption in the perturbed economy is thus insignificant to consumers, and some forecasting and comparative-statics policy exercises become possible.

A norm of 50–50 division appears to have considerable force in a wide range of economic environments, both in the real world and in the laboratory. Even in settings where one party unilaterally determines the allocation of a prize (the dictator game), many subjects voluntarily cede exactly half to another individual. The hypothesis that people care about fairness does not by itself account for key experimental patterns. We consider an alternative explanation, which adds the hypothesis that people like to be perceived as fair. The properties of equilibria for the resulting signaling game correspond closely to laboratory observations. The theory has additional testable implications, the validity of which we confirm through new experiments.

Consider a weather forecaster predicting a probability of rain for the next day. We consider tests that, given a finite sequence of forecast predictions and outcomes, will either pass or fail the forecaster. Sandroni showed that any test which passes a forecaster who knows the distribution of nature can also be probabilistically passed by a forecaster with no knowledge of future events. We look at the computational complexity of such forecasters and exhibit a linear-time test and distribution of nature such that any forecaster without knowledge of the future who can fool the test must be able to solve computationally difficult problems. Thus, unlike Sandroni's work, a computationally efficient forecaster cannot always fool this test independently of nature.