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Partial identification in asymmetric auctions in the absence of independence

不假定独立性时非对称拍卖的部分识别

This paper examines identification in second‐price and ascending auctions within the private‐values framework. The first part of the paper considers an arbitrary type of dependence of bidders’ values and analyses identification under several observational scenarios, in which the highest bid is never observed. In a basic scenario, only the winner’s identity and the winning price are observed. The most informative is the scenario in which all the identities and all the bids…

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Set inference in latent variables models

潜变量模型中的集合推断

We propose a methodology for constructing valid confidence regions in incomplete models with latent variables satisfying moment equality restrictions. These include moment equality and inequality models with latent variables. The confidence regions are obtained by inverting tests based on the characterization of the identified set derived in Ekeland et al. (2010). A valid bootstrap approximation of the distribution of the test statistic is derived under mild conditions and…

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Intersection Bounds: Estimation and Inference

交集界限:估计与推断

We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or, equivalently, the value of a linear programming problem with a potentially infinite constraint set. We show that many bounds characterizations in econometrics, for instance bounds on parameters under conditional moment inequalities, can be formulated as intersection bounds. Our approach is…

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Average and Quantile Effects in Nonseparable Panel Models

非可分面板模型中的平均效应与分位数效应

Nonseparable panel models are important in a variety of economic settings, including discrete choice. This paper gives identification and estimation results for nonseparable models under time-homogeneity conditions that are like “time is randomly assigned” or “time is an instrument.” Partial-identification results for average and quantile effects are given for discrete regressors, under static or dynamic conditions, in fully nonparametric and in semiparametric models, with…

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Inference Based on Conditional Moment Inequalities

基于条件矩不等式的推断

In this paper, we propose an instrumental variable approach to constructing confidence sets (CS's) for the true parameter in models defined by conditional moment inequalities/equalities. We show that by properly choosing instrument functions, one can transform conditional moment inequalities/equalities into unconditional ones without losing identification power. Based on the unconditional moment inequalities/equalities, we construct CS's by inverting Cramér–von Mises-type or…

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On the uniform asymptotic validity of subsampling and the bootstrap

子抽样与自助法的一致渐近有效性

This paper provides conditions under which subsampling and the bootstrap can be used to construct estimators of the quantiles of the distribution of a root that behave well uniformly over a large class of distributions $\mathbf{P}$. These results are then applied (i) to construct confidence regions that behave well uniformly over $\mathbf{P}$ in the sense that the coverage probability tends to at least the nominal level uniformly over $\mathbf{P}$ and (ii) to construct tests…

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Identifying the Effects of SNAP (Food Stamps) on Child Health Outcomes When Participation Is Endogenous and Misreported

参与内生且存在误报时 SNAP 对儿童健康的效应识别

The literature assessing the efficacy of the Supplemental Nutrition Assistance Program (SNAP), formerly known as the Food Stamp Program, has long puzzled over positive associations between SNAP receipt and various undesirable health outcomes such as food insecurity. Assessing the causal impacts of SNAP, however, is hampered by two key identification problems: endogenous selection into participation and extensive systematic underreporting of participation status. Using data…

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Confidence intervals for the quantile of treatment effects in randomized experiments

随机实验中处理效应分位数的置信区间

In this paper, we explore partial identification and inference for the quantile of treatment effects for randomized experiments. First, we propose nonparametric estimators of sharp bounds on the quantile of treatment effects and establish their asymptotic properties under general conditions. Second, we construct confidence intervals for the bounds and the true quantile by using the approach in Chernozhukov et al. (2009). Third, under additional conditions, we develop a new…

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Testing Predictive Ability and Power Robustification

预测能力检验与功效稳健化

One of the approaches to compare forecasting methods is to test whether the risk from a benchmark prediction is smaller than the others. The test can be embedded into a general problem of testing inequality constraints using a one-sided sup functional. Hansen showed that such tests suffer from asymptotic bias. This article generalizes this observation, and proposes a hybrid method to robustify the power properties by coupling a one-sided sup test with a complementary test.…

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Identification and frequency domain quasi-maximum likelihood estimation of linearized dynamic stochastic general equilibrium models

线性化动态随机一般均衡模型的识别与频域准极大似然估计

This paper considers issues related to identification, inference, and computation in linearized dynamic stochastic general equilibrium (DSGE) models. We first provide a necessary and sufficient condition for the local identification of the structural parameters based on the (first and) second order properties of the process. The condition allows for arbitrary relations between the number of observed endogenous variables and structural shocks, and is simple to verify. The…

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IV models of ordered choice

有序选择的工具变量模型

This paper studies single equation instrumental variable models of ordered choice in which explanatory variables may be endogenous. The models are weakly restrictive, leaving unspecified the mechanism that generates endogenous variables. These incomplete models are set, not point, identifying for parametrically (e.g. ordered probit) or nonparametrically specified structural functions. The paper gives results on the properties of the identified set for the case in which…

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Partial identification using random set theory

利用随机集理论进行部分识别

This paper illustrates how the use of random set theory can benefit partial identification analysis. We revisit the origins of Manski’s work in partial identification (e.g., Manski (1989, 1990)) focusing our discussion on identification of probability distributions and conditional expectations in the presence of selectively observed data, statistical independence and mean independence assumptions, and shape restrictions. We show that the use of the Choquet capacity…

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Set identification via quantile restrictions in short panels

短面板中基于分位数约束的集合识别

This paper studies the identifying power of conditional quantile restrictions in short panels with fixed effects. In contrast to classical fixed effects models with conditional mean restrictions, conditional quantile restrictions are not preserved by taking differences in the regression equation over time. This paper shows however that a conditional quantile restriction, in conjunction with a weak conditional independence restriction, provides bounds on quantiles of…

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Minimax regret treatment choice with covariates or with limited validity of experiments

含协变量或实验有效性受限时的最小最大遗憾处理选择

This paper continues the investigation of minimax regret treatment choice initiated by Manski (2004). Consider a decision maker who must assign treatment to future subjects after observing outcomes experienced in a sample. A certain scoring rule is known to achieve minimax regret in simple versions of this decision problem. I investigate its sensitivity to perturbations of the decision environment in realistic directions. They are as follows. (i) Treatment outcomes may be…

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The impact of the National School Lunch Program on child health: A nonparametric bounds analysis

全国学校午餐计划对儿童健康的影响:非参数界限分析

Children in households reporting the receipt of free or reduced-price school meals through the National School Lunch Program (NSLP) are more likely to have negative health outcomes than observationally similar nonparticipants. Assessing causal effects of the program is made difficult, however, by missing counterfactuals and systematic underreporting of program participation. Combining survey data with auxiliary administrative information on the size of the NSLP caseload, we…

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Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models

利用异方差识别与估计含误测及内生回归变量的模型

This article proposes a new method of obtaining identification in mismeasured regressor models, triangular systems, and simultaneous equation systems. The method may be used in applications where other sources of identification, such as instrumental variables or repeated measurements, are not available. Associated estimators take the form of two-stage least squares or generalized method of moments. Identification comes from a heteroscedastic covariance restriction that is…

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Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure

矩不等式定义参数的推断:一种推荐的矩选择程序

This paper is concerned with tests and confidence intervals for parameters that are not necessarily point identified and are defined by moment inequalities. In the literature, different test statistics, critical-value methods, and implementation methods (i.e., the asymptotic distribution versus the bootstrap) have been proposed. In this paper, we compare these methods. We provide a recommended test statistic, moment selection critical value, and implementation method. We…

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Partial Distributional Policy Effects

部分分布政策效应

In this paper, we propose a method to evaluate the effect of a counterfactual change in the unconditional distribution of a single covariate on the unconditional distribution of an outcome variable of interest. Both fixed and infinitesimal changes are considered. We show that such effects are point identified under general conditions if the covariate affected by the counterfactual change is continuously distributed, but are typically only partially identified if its…

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Set Identified Linear Models

集合识别的线性模型

Before quoting, please ask for the fully revised version We analyze the identification and estimation of parameters β satisfying the incomplete linear moment restrictionsE(z>(xβ−y)) = E(z>u(x))where z is a set of instruments and u(z) an unknown bounded scalar function. We first provide empirically relevant examples of such a set-up. Second, we show that these conditions set identify β where the identified set B is bounded and convex. We provide a sharp characterization of…

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Bayesian and Frequentist Inference in Partially Identified Models

部分识别模型中的贝叶斯与频率学派推断

A large sample approximation of the posterior distribution of partially identified structural parameters is derived for models that can be indexed by a finite-dimensional reduced form parameter vector.It is used to analyze the differences between frequentist confidence sets and Bayesian credible sets in partially identified models.A key difference is that frequentist set estimates extend beyond the boundaries of the identified set (conditional on the estimated reduced form…

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Inference in Nonparametric Instrumental Variables With Partial Identification

部分识别下的非参数工具变量推断

This paper develops methods for hypothesis testing in a nonparametric instrumental variables setting within a partial identification framework. We construct and derive the asymptotic distribution of a test statistic for the hypothesis that at least one element of the identified set satisfies a conjectured restriction. The same test statistic can be employed under identification, in which case the hypothesis is whether the true model satisfies the posited property. An almost…

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Posterior consistency of nonparametric conditional moment restricted models

非参数条件矩限制模型的后验一致性

This paper addresses the estimation of the nonparametric conditional moment restricted model that involves an infinite-dimensional parameter g0. We estimate it in a quasi-Bayesian way, based on the limited information likelihood, and investigate the impact of three types of priors on the posterior consistency: (i) truncated prior (priors supported on a bounded set), (ii) thin-tail prior (a prior that has very thin tail outside a growing bounded set) and (iii) normal prior…

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Set Identification in Models with Multiple Equilibria

We propose a computationally feasible way of deriving the identified features of models with multiple equilibria in pure or mixed strategies. It is shown that in the case of Shapley regular normal form games, the identified set is characterized by the inclusion of the true data distribution within the core of a Choquet capacity, which is interpreted as the generalized likelihood of the model. In turn, this inclusion is characterized by a finite set of inequalities and…

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Non-parametric bounds on quantiles under monotonicity assumptions: with an application to the Italian education returns

单调性假设下分位数的非参数界:意大利教育回报应用

Within the inferential context of predicting a distribution of potential outcomes P[y(t)] under a uniform treatment assignment t ∈ T, this paper deals with partial identification of the α-quantile of the distribution of interest Qα[y(t)] under relatively weak and credible monotonicity-type assumptions on the individual response functions and the population selection process. On the theoretical side, the paper adds to the existing results on non-parametric bounds on quantiles…

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