Inference for the Identified Set in Partially Identified Econometric Models

This paper provides computationally intensive, yet feasible methods for inference in a very general class of partially identified econometric models. Let P denote the distribution of the observed data. The class of models we consider is defined by a population objective function Q(θ, P) for θ∈Θ. The point of departure from the classical extremum estimation framework is that it is not assumed that Q(θ, P) has a unique minimizer in the parameter space Θ. The goal may be either to draw inferences about some unknown point in the set of minimizers of the population objective function or to draw inferences about the set of minimizers itself. In this paper, the object of interest is Θ₀(P)=argmin_θ∈ΘQ(θ, P), and so we seek random sets that contain this set with at least some prespecified probability asymptotically. We also consider situations where the object of interest is the image of Θ₀(P) under a known function. Random sets that satisfy the desired coverage property are constructed under weak assumptions. Conditions are provided under which the confidence regions are asymptotically valid not only pointwise in P, but also uniformly in P. We illustrate the use of our methods with an empirical study of the impact of top‐coding outcomes on inferences about the parameters of a linear regression. Finally, a modest simulation study sheds some light on the finite‐sample behavior of our procedure.     

Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection

The topic of this paper is inference in models in which parameters are defined by moment inequalities and/or equalities. The parameters may or may not be identified. This paper introduces a new class of confidence sets and tests based on generalized moment selection (GMS). GMS procedures are shown to have correct asymptotic size in a uniform sense and are shown not to be asymptotically conservative. The power of GMS tests is compared to that of subsampling, m out of n bootstrap, and “plug‐in asymptotic” (PA) tests. The latter three procedures are the only general procedures in the literature that have been shown to have correct asymptotic size (in a uniform sense) for the moment inequality/equality model. GMS tests are shown to have asymptotic power that dominates that of subsampling, m out of n bootstrap, and PA tests. Subsampling and m out of n bootstrap tests are shown to have asymptotic power that dominates that of PA tests.     

Alternative Models for Moment Inequalities

Behavioral choice models generate inequalities which, when combined with additional assumptions, can be used as a basis for estimation. This paper considers two sets of such assumptions and uses them in two empirical examples. The second example examines the structure of payments resulting from the upstream interactions in a vertical market. I then mimic the empirical setting for this example in a numerical analysis which computes actual equilibria, examines how their characteristics vary with the market setting, and compares them to the empirical results. The final section uses the numerical results in a Monte Carlo analysis of the robustness of the two approaches to estimation to their underlying assumptions.     

On the maximal inequalities for the average of pairwise i.i.d. random variables

We obtain two sided inequalities for the tail of the maximal function of the averages of a multiple sequence of pairwise i.i.d. random variables taking values in a separable Banach space. We then use the results to establish a necessary and sufficient con¬dition, in terms of the common distribution of the norm of the random variables, for the maximal function to be in L , 1< p << &z.rdang;     

Charitable giving and lay morality: understanding sympathy,moral evaluations and social positions

This paper examines how charitable giving offers an example of lay morality, reflecting people's capacity for fellow‐feeling, moral sentiments, personal reflexivity, ethical dispositions, moral norms and moral discourses. Lay morality refers to how people should treat others and be treated by them, matters that are important for their subjective and objective well‐being. It is a first person evaluative relation to the world (about things that matter to people). While the paper is sympathetic to the ‘moral boundaries’ approach, which seeks to address the neglect of moral evaluations in sociology, it reveals this approach to have some shortcomings. The paper argues that although morality is always mediated by cultural discourses and shaped by structural factors, it also has a universalizing character because people have fellow‐feelings, shared human conditions, and have reason to value.     

Moment inequalities for truncated multivariate distributions

In this note some properties of the absolute moments of a doubly truncated arbitrary multivariate distribution are studied and several moment inequalities are derived.     

Nash均衡、变分不等式和广义均衡问题的关系

主要讨论了Nash均衡问题(NE)与变分不等式(VI)和广义均衡问题(GEP)的关系.给出它们之间解的等价关系,以及与之相应的映射之间单调性的关系.研究结果为进一步研究Nash均衡、广义均衡问题理论及其算法提供了理论依据.     

Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities

This paper examines the efficient estimation of partially identified models defined by moment inequalities that are convex in the parameter of interest. In such a setting, the identified set is itself convex and hence fully characterized by its support function. We provide conditions under which, despite being an infinite dimensional parameter, the support function admits √n‐consistent regular estimators. A semiparametric efficiency bound is then derived for its estimation, and it is shown that any regular estimator attaining it must also minimize a wide class of asymptotic loss functions. In addition, we show that the “plug‐in” estimator is efficient, and devise a consistent bootstrap procedure for estimating its limiting distribution. The setting we examine is related to an incomplete linear model studied in Beresteanu and Molinari (2008) and Bontemps, Magnac, and Maurin (2012), which further enables us to establish the semiparametric efficiency of their proposed estimators for that problem.