An endogenous social effect exists if the propensity of an individual to behave in some way varies with the prevalence of that behavior in some reference group containing the individual. This paper investigates aspects of the problem of identifying endogenous effects from data on actual behavior. Empirical researchers have long been sensitive to the problem of distinguishing social effects from reference-group fixed effects. The present analysis reveals that the identification of endogenous effects is tenuous even in the absence of reference-group fixed effects. There are two main findings. First, a researcher who does not a priori know how individuals form their reference groups cannot infer this from data on actual behavior and cannot determine whether social effects really are present. Second, suppose that individual behavior is known to be affected directly by specified variables z •and that an individual's reference group is known to be the sub-population having specified attributes x. Then the effect of reference-group behavior on individual behavior is not identified if x and z are either functionally dependent or statistically independent.

To predict choice behavior, the standard practice of economists has been to infer decision processes from data on observed choices. When decision makers act with partial information, economists typically assume that persons form probabilistic expectations for unknown quantities and maximize expected utility. Observed choices may be consistent with many alternative specifications of preferences and expectations, so researchers commonly assume particular sorts of expectations. It would be better to measure expectations in the form called for by modern economic theory; that is, subjective probabilities. Data on expectations can be used to relax or validate assumptions about expectations. Since the early 1990's, economists have increasingly undertaken to elicit from survey respondents probabilistic expectations of significant personal events. This article discusses the history underlying the new literature, describes some of what has been learned thus far, and looks ahead towards making further progress. Copyright The Econometric Society 2004.

Economists have long been ambivalent about whether the discipline should focus on the analysis of markets or should be concerned with social interactions more generally. Recently the discipline has sought to broaden its scope while maintaining the rigor of modern economic analysis.Major theoretical developments in game theory, the economics of the family, and endogenous growth theory have taken place. Economists have also performed new empirical research on social interactions, but the empirical literature does not show progress comparable to that achieved in economic theory. This paper examines why and discusses how economists might make sustained contributions to the empirical analysis of social interactions.

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We propose a bootstrap-based calibrated projection procedure to build confidence intervals for single components and for smooth functions of a partially identified parameter vector in moment (in)equality models. The method controls asymptotic coverage uniformly over a large class of data generating processes. The extreme points of the calibrated projection confidence interval are obtained by extremizing the value of the component (or function) of interest subject to a proper relaxation of studentized sample analogs of the moment (in)equality conditions. The degree of relaxation, or critical level, is calibrated so that the component (or function) of θ, not θ itself, is uniformly asymptotically covered with prespecified probability. This calibration is based on repeatedly checking feasibility of linear programming problems, rendering it computationally attractive. Nonetheless, the program defining an extreme point of the confidence interval is generally nonlinear and potentially intricate. We provide an algorithm, based on the response surface method for global optimization, that approximates the solution rapidly and accurately. The algorithm is of independent interest for inference on optimal values of stochastic nonlinear programs. We establish its convergence under conditions satisfied by canonical examples in the moment (in)equalities literature. Our assumptions and those used in the leading alternative approach (a profiling based method) are not nested. An extensive Monte Carlo analysis confirms the accuracy of the solution algorithm and the good statistical as well as computational performance of calibrated projection, including in comparison to other methods. Keywords: Partial identification; Inference on projections; Moment inequalities; Uniform inference. * We are grateful to Elie Tamer and three anonymous reviewers for very useful suggestions that substantially improved the paper. We thank for their comments Ivan Canay and seminar and conference participants at Bonn, BC/BU joint workshop, Brown,

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