Knowledge that Transforms

Ž. THE REGRESSION DISCONTINUITY RD data design is a quasi-experimental design with the defining characteristic that the probability of receiving treatment changes discontinuously as a function of one or more underlying variables. This data design arises frequently in economic and other applications but is only infrequently exploited as a source of identifying information in evaluating effects of a treatment. In the first application and discussion of the RD method, Thistlethwaite and Campbell Ž. 1960 study the effect of student scholarships on career aspirations, using the fact that awards are only made if a test score exceeds a threshold. More recently, Van der Klaauw Ž. 1997 estimates the effect of financial aid offers on students’ decisions to attend a particular college, taking into account administrative rules that set the aid amount partly on the basis of a discontinuous function of the students’ grade point average and SAT Ž. score. Angrist and Lavy 1999 estimate the effect of class size on student test scores, taking advantage of a rule stipulating that another classroom be added when the average Ž. class size exceeds a threshold level. Finally, Black 1999 uses an RD approach to estimate parents’ willingness to pay for higher quality schools by comparing housing prices near geographic school attendance boundaries. Regression discontinuity methods have potentially broad applicability in economic research, because geographic boundaries or rules governing programs often create discontinuities in the treatment assignment mechanism that can be exploited under the method. Although there have been several discussions and applications of RD methods in the literature, important questions still remain concerning sources of identification and ways of estimating treatment effects under minimal parametric restrictions. Here, we show that identifying conditions invoked in previous applications of RD methods are often overly strong and that treatment effects can be nonparametrically identified under an RD design by a weak functional form restriction. The restriction is unusual in that it requires imposing continuity assumptions in order to take advantage of the known discontinuity in the treatment assignment mechanism. We also propose a way of nonparametrically estimating treatment effects and offer an interpretation of the Wald estimator as an RD estimator.

The paper first develops an economic analysis of the concept of shareholder value, describes its approach and discusses some open questions. It emphasizes the relationship between pledgeable income, monitoring and control rights using a unifying and simple framework. The paper then provides a first and preliminary analysis of the concept of the stakeholder society. It investigates whether the managerial incentives and the control structure described in the first part can be modified so as to promote the stakeholder society. It is shown that the implementation of the stakeholder society strikes three rocks: dearth of pledgeable income, deadlocks in decision-making, and lack of clear mission for management. While it fares better on those three grounds, shareholder value generates biased decision-making; the paper analyzes the costs and benefits of various methods of protecting noncontrolling stakeholders: covenants, exit options, flat claims, enlarged fiduciary duty.

We study efficient, Bayes-Nash incentive compatible mechanisms in a social choice setting that allows for informational and allocative externalities. We show that such mechanisms exist only if a congruence condition relating private and social rates of information substitution is satisfied. If signals are multi-dimensional, the congruence condition is determined by an integrability constraint, and it can hold only in nongeneric cases where values are private or a certain symmetry assumption holds. If signals are one-dimensional, the congruence condition reduces to a monotonicity constraint and it can be generically satisfied. We apply the results to the study of multi-object auctions, and we discuss why such auctions cannot be reduced to one-dimensional models without loss of generality.

This paper evaluates the effectiveness of four econometric approaches intended to identify the learning rules being used by subjects in experiments with normal form games. This is done by simulating experimental data and then estimating the econometric models on the simulated data to determine if they can correctly identify the rule that was used to generate the data. The results show that all of the models examined possess difficulties in accurately distinguishing between the data generating processes.

We study the incentives of candidates to strategically affect the outcome of a voting procedure. We show that the outcomes of every nondictatorial voting procedure that satisfies unanimity will be affected by the incentives of noncontending candidates (i.e., who cannot win the election) to influence the outcome by entering or exiting the election.

This paper reports an experiment comparing three stag hunt games that have the same best-response correspondence and the same expected payoff from the mixed equilibrium, but differ in the incentive to play a best response rather than an inferior response.In each game, risk dominance conflicts with payoff dominance and selects an inefficient pure strategy equilibrium.We find statistically and economically significant evidence that the differences in the incentive to optimize help explain observed behavior.

This paper derives sufficient conditions for a class of games of incomplete information, such as first price auctions, to have pure strategy Nash equilibria (PSNE).The paper treats games between two or more heterogeneous agents, each with private information about his own type (for example, a bidder's value for an object or a firm's marginal cost of production), and the types are drawn from an atomless joint probability distribution which potentially allows for correlation between types.Agents' utility may depend directly on the realizations of other agents' types, as in MUgrom and Weber's (1982) formulation of the "mineral rights" auction.The restriction we consider is that each player's expected payoffs satisfy the following single crossing condition: whenever each opponent uses a nondecreasing strategy (that is, an opponent who has a higher type chooses a higher action), then a player's best response strategy is also nondecreasing in her type.The paper has two main results.The first result shows that, when players are restricted to choose among a finite set of actions (for example, bidding or pricing where the smallest unit is a penny), games where players' objective functions satisfy this single crossing condition wUl have PSNE.The second result demonstrates that when players' utility functions are continuous, as well as in mineral rights auction games and other games where "winning" creates a discontinuity in payoffs, the existence result can be extended to the case where players choose from a continuum of actions.The paper then applies the theory to several classes of games, providing conditions on utility ftanctions and joint distributions over types under which each class of games satisfies the single crossing condition.In particular, the single crossing condition is shown to hold in all first-price, private value auctions with potentially heterogeneous, risk-averse bidders, with either independent or affiliated values, and with reserve prices which may differ across bidders; mineral rights auctions with two heterogeneous bidders and affiliated values; a class of pricing games with incomplete information about costs; a class of all-pay auction games; and a class of noisy signaling games.Finally, the formulation of the problem introduced in this paper suggests a straightforward algorithm for numerically computing equilibrium bidding stiategies in games such as first price auctions, and we present numerical analyses of several auctions under alternative assumptions about the joint distribution of types.

We develop a new test of a parametric model of a conditional mean function against a nonparametric alternative. The test adapts to the unknown smoothness of the alternative model and is uniformly consistent against alternatives whose distance from the parametric model converges to zero at the fastest possible rate. This rate is slower than n[superscript -1/2]. Some existing tests have nontrivial power against restricted classes of alternatives whose distance from the parametric model decreases at the rate n[superscript -1/2]. There are, however, sequences of alternatives against which these tests are inconsistent and ours is consistent. As a consequence, there are alternative models for which the finite-sample power of our test greatly exceeds that of existing tests. This conclusion is illustrated by the results of some Monte Carlo experiments.