This paper introduces a novel bootstrap procedure to perform inference in a wide class of partially identified econometric models. We consider econometric models defined by finitely many weak moment inequalities,2 which encompass many applications of economic interest. The objective of our inferential procedure is to cover the identified set with a prespecified probability.3 We compare our bootstrap procedure, a competing asymptotic approximation, and subsampling procedures in terms of the rate at which they achieve the desired coverage level, also known as the error in the coverage probability. Under certain conditions, we show that our bootstrap procedure and the asymptotic approximation have the same order of error in the coverage probability, which is smaller than that obtained by using subsampling. This implies that inference based on our bootstrap and asymptotic approximation should eventually be more precise than inference based on subsampling. A Monte Carlo study confirms this finding in a small sample simulation.

A unifying framework to test for causal effects in nonlinear models is proposed. We consider a generalized linear-index regression model with endogenous regressors and no parametric assumptions on the error disturbances. To test the significance of the effect of an endogenous regressor, we propose a statistic that is a kernel-weighted version of the rank correlation statistic (tau) of Kendall (1938). The semiparametric model encompasses previous cases considered in the literature (continuous endogenous regressors (Blundell and Powell (2003)) and a single binary endogenous regressor (Vytlacil and Yildiz (2007))), but the testing approach is the first to allow for (i) multiple discrete endogenous regressors, (ii) endogenous regressors that are neither discrete nor continuous (e.g., a censored variable), and (iii) an arbitrary “mix” of endogenous regressors (e.g., one binary regressor and one continuous regressor).

We study optimal taxation when consumers have temptation and self-control problems. Embedding the class of preferences developed by Gul and Pesendorfer into a standard macroeconomic setting, we first prove, in a two-period model, that the optimal policy is to subsidize savings when consumers are tempted by “excessive” impatience. The savings subsidy improves welfare because it makes succumbing to temptation less attractive. We then study an economy with a long but finite horizon which nests, as a special case, the Phelps–Pollak–Laibson multiple-selves model (thereby providing guidance on how to evaluate welfare in this model). We prove that when period utility is logarithmic, the optimal savings subsidies increase over time for any finite horizon. Moreover, as the horizon grows large, the optimal policy prescribes a constant subsidy, in contrast to the well known Chamley–Judd result.

The minimax argument represents game theory in its most elegant form: simple but with stark predictions. Although some of these predictions have been met with reasonable success in the field, experimental data have generally not provided results close to the theoretical predictions. In a striking study, Palacios-Huerta and Volij ( 2008) presented evidence that potentially resolves this puzzle: both amateur and professional soccer players play nearly exact minimax strategies in laboratory experiments. In this paper, we establish important bounds on these results by examining the behavior of four distinct subject pools: college students, bridge professionals, world-class poker players, who have vast experience with high-stakes randomization in card games, and American professional soccer players. In contrast to Palacios-Huerta and Volij's results, we find little evidence that real-world experience transfers to the lab in these games-indeed, similar to previous experimental results, all four subject pools provide choices that are generally not close to minimax predictions. We use two additional pieces of evidence to explore why professionals do not perform well in the lab: (i) complementary experimental treatments that pit professionals against preprogrammed computers and (ii) post-experiment questionnaires. The most likely explanation is that these professionals are unable to transfer their skills at randomization from the familiar context of the field to the unfamiliar context of the lab. Copyright 2010 The Econometric Society.