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Statistical inference of optimal allocations I: Regularities and their implications

最优分配的统计推断之一:正则性及其含义

In this paper, we develop a functional differentiability approach for solving statistical optimal allocation problems. We derive Hadamard differentiability of the value functions through analyzing the properties of the sorting operator using tools from geometric measure theory. Building on our Hadamard differentiability results, we apply the functional delta method to obtain the asymptotic properties of the value function process for the binary constrained optimal allocation…

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On uniform inference in nonlinear models with endogeneity

内生性非线性模型中的一致推断

This paper explores the uniformity of inference for parameters of interest in nonlinear econometric models with endogeneity. Here the notion of uniformity arises because the behavior of estimators of parameters of interest is shown to vary with where either they or nuisance parameters lie in the parameter space. As a result, inference becomes nonstandard in a fashion that is loosely analogous to inference complications found in the unit root and weak instruments literature,…

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Regularised orthogonal machine learning for nonlinear semiparametric models

非线性半参数模型的正则化正交机器学习

Summary This paper proposes a Lasso-type estimator for a high-dimensional sparse parameter identified by a single index conditional moment restriction (CMR). In addition to this parameter, the moment function can also depend on a nuisance function, such as the propensity score or the conditional choice probability, which we estimate by modern machine learning tools. We first adjust the moment function so that the gradient of the future loss function is insensitive (formally,…

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Identification, data combination, and the risk of disclosure

识别、数据合并与信息披露风险

It is commonplace that the data needed for econometric inference are not contained in a single source. In this paper we analyze the problem of parametric inference from combined individual‐level data when data combination is based on personal and demographic identifiers such as name, age, or address. Our main question is the identification of the econometric model based on the combined data when the data do not contain exact individual identifiers and no parametric…

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Information structure and statistical information in discrete response models

离散响应模型中的信息结构与统计信息

Strategic interaction parameters characterize the impact of actions of one economic agent on the payoff of another economic agent, and are of great interest in both theoretical and empirical work. In this paper, by considering econometric models involving simultaneous discrete systems of equations, we study how the information available to economic agents regarding other economic agents can influence whether or not these strategic information parameters can be inferred from…

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Extremum estimation and numerical derivatives

极值估计与数值导数

Finite-difference approximations are widely used in empirical work to evaluate derivatives of estimated functions. For instance, many standard optimization routines rely on finite-difference formulas for gradient calculations and estimating standard errors. However, the effect of such approximations on the statistical properties of the resulting estimators has only been studied in a few special cases. This paper investigates the impact of commonly used finite-difference…

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Efficient local IV estimation of an empirical auction model

经验拍卖模型的有效局部工具变量估计

In this paper we examine semiparametric efficiency bounds and efficient estimators for the case of a linear local instrument variable (LIV) model under the assumptions studied in Abadie et al. (2002). We apply the semiparametrically efficient estimation method to analyze the relation between bid dispersion and early bidding in an online auction dataset, which is collected from a natural experiment conducted in Nekipelov (2007). The results confirm the theoretical findings…

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Semiparametric efficiency in nonlinear LATE models

非线性 LATE 模型中的半参数效率

In this paper we study semiparametric efficiency for the estimation of a finite-dimensional parameter defined by generalized moment conditions under the local instrumental variable assumptions. These parameters identify treatment effects on the set of compliers under the monotonicity assumption. The distributions of covariates, the treatment dummy, and the binary instrument are not specified in a parametric form, making the model semiparametric. We derive the semiparametric…

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Estimating Static Models of Strategic Interactions

策略互动静态模型的估计

We study the estimation of static games of incomplete information with multiple equilibria. A static game is a generalization of a discrete choice model, such as a multinomial logit or probit, which allows the actions of a group of agents to be interdependent. While the estimator we study is quite flexible, in most cases it can be easily implemented using standard statistical packages such as STATA. We also propose an algorithm for simulating the model which finds all…

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