This paper provides an analysis of aggregate behavioral outcomes when individual utility exhibits social interaction effects. We study generalized logistic models of individual choice which incorporate terms reflecting the desire of individuals to conform to the behavior of others in an environment of noncooperative decisionmaking. Laws of large numbers are generated in such environments. Multiplicity of

CAPRi Working Papers contain preliminary material and research results, and are circulated prior to a full peer review in order to stimulate discussion and critical comment. It is expected that most Working Papers will eventually be published in some other form, and that their content may also be revised. CAPRi WORKING PAPER NO. 17

JEL No. C10 The major contributions of twentieth century econometrics to knowledge were the definition of causal parameters when agents are constrained by resources and markets and causes are interrelated, the analysis of what is required to recover causal parameters from data (the identification problem), and clarification of the role of causal parameters in policy evaluation and in forecasting the effects of policies never previously experienced. This paper summarizes the development of those ideas by the Cowles Commission, the response to their work by structural econometricians and VAR econometricians, and the response to structural and VAR econometrics by calibrators, advocates of natural and social experiments, and by nonparametric econometricians and statisticians.

For nearly a century, investigators in the social sciences have used regression models to deduce cause-and-effect relationships from patterns of association. Path models and automated search procedures are more recent developments. In my view, this enterprise has not been successful. The models tend to neglect the difficulties in establishing causal relations, and the mathematical complexities tend to obscure rather than clarify the assumptions on which the analysis is based. Formal statistical inference is, by its nature, conditional. If maintained hypotheses A, B, C,... hold, then H can be tested against the data. However, if A, B, C,... remain in doubt, so must inferences about H. Careful scrutiny of maintained hypotheses should therefore be a critical part of empirical work-- a principle honored more often in the breach than the observance.

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CentER and CentERdata is gratefully acknowledged. We thank Hanneke Dam, Marcel Das and Corrie Vis of

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We present the application of a recently introduced nonparametric predictive inferential method to compare two groups of data, consisting of observed event times and right-censoring times. Comparison is based on imprecise probabilities concerning one future observation per group.

The importance of social programs to a diverse population creates a legitimate concern that the findings of evaluations be widely credible. The weaker are the assumptions imposed, the more widely credible are the findings. The classical argument for random assignment of treatments is viewed by many as enabling evaluation under weak assumptions, and has generated much interest in the conduct of experiments. But the classical argument does impose assumptions, and there often is good reason to doubt their realism. Some researchers, finding the classical assumptions implausible, impose other assumptions strong enough to identify treatment effects of interest. In contrast, the recent literature examined in this article explores the inferences that may be drawn from experimental data under assumptions weak enough to yield widely credible findings. This literature has two branches. One seeks out notions of treatment effect that are identified when the experimental data are combined with weak assumptions. The canonical finding is that the average treatment effect within some context-specific subpopulation is identified. The other branch specifies a population of a priori interest and seeks to learn about treatment effects in this population. Here the canonical finding is a bound on average treatment effects. The various approaches to the analysis of experiments are complementary from a mathematical perspective, but in tension as guides to evaluation practice. The reader of an evaluation reporting that some social program "works" or has "positive impact" should be careful to ascertain what treatment effect has been estimated and under what assumptions.

Bidders’ values in discriminatory and uniform-price auctions are not point-identified under the assumptions of equilibrium bidding and independent private values, but meaningful policy analysis can proceed from bounds on bidder values. This paper provides upper and lower bounds on values, under the additional (and standard) assumption of non-increasing marginal values. Novel testable implications of the best response hypothesis are also provided, again under the assumption of non-increasing marginal values.