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Estimation of a nonlinear panel data model with semiparametric individual effects

带半参数个体效应的非线性面板模型估计

This paper investigates identification and estimation of a class of nonlinear panel data, single-index models. The model allows for unknown time-specific link functions, and semiparametric specification of the individual-specific effects. We develop an estimator for the parameters of interest, and propose a powerful new kernel-based modified backfitting algorithm to compute the estimator. We derive uniform rates of convergence results for the estimators of the link…

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First difference maximum likelihood and dynamic panel estimation

一阶差分极大似然与动态面板估计

First difference maximum likelihood (FDML) seems an attractive estimation methodology in dynamic panel data modeling because differencing eliminates fixed effects and, in the case of a unit root, differencing transforms the data to stationarity, thereby addressing both incidental parameter problems and the possible effects of nonstationarity. This paper draws attention to certain pathologies that arise in the use of FDML that have gone unnoticed in the literature and that…

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The performance of estimators based on the propensity score

基于倾向得分的估计量表现

We investigate the finite sample properties of a large number of estimators for the average treatment effect on the treated that are suitable when adjustment for observed covariates is required, like inverse probability weighting, kernel and other variants of matching, as well as different parametric models. The simulation design used is based on real data usually employed for the evaluation of labour market programmes in Germany. We vary several dimensions of the design…

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Unconditional Quantile Treatment Effects Under Endogeneity

内生性下的无条件分位数处理效应

This article develops estimators for unconditional quantile treatment effects when the treatment selection is endogenous. We use an instrumental variable (IV) to solve for the endogeneity of the binary treatment variable. Identification is based on a monotonicity assumption in the treatment choice equation and is achieved without any functional form restriction. We propose a weighting estimator that is extremely simple to implement. This estimator is root n consistent,…

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Social Networks and the Identification of Peer Effects

社会网络与同伴效应的识别

There is a large and growing literature on peer effects in economics. In the current article, we focus on a Manski-type linear-in-means model that has proved to be popular in empirical work. We critically examine some aspects of the statistical model that may be restrictive in empirical analyses. Specifically, we focus on three aspects. First, we examine the endogeneity of the network or peer groups. Second, we investigate simultaneously alternative definitions of links and…

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Estimation in Partially Linear Single-Index Panel Data Models With Fixed Effects

固定效应部分线性单指标面板数据模型的估计

In this article, we consider semiparametric estimation in a partially linear single-index panel data model with fixed effects. Without taking the difference explicitly, we propose using a semiparametric minimum average variance estimation (SMAVE) based on a dummy variable method to remove the fixed effects and obtain consistent estimators for both the parameters and the unknown link function. As both the cross-section size and the time series length tend to infinity, we not…

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An instrumental variable model of multiple discrete choice

多项离散选择的工具变量模型

This paper studies identification of latent utility functions in multiple discrete choice models in which there may be endogenous explanatory variables, that is explanatory variables that are not restricted to be distributed independently of the unobserved determinants of latent utilities. The model does not employ large support, special regressor or control function restrictions, indeed it is silent about the process delivering values of endogenous explanatory variables and…

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Large sample properties for estimators based on the order statistics approach in auctions

拍卖次序统计量估计方法的大样本性质

For symmetric auctions, there is a close relationship between distributions of order statistics of bidders' valuations and observable bids that is often used to estimate or bound the valuation distribution, optimal reserve price, and other quantities of interest nonparametrically. However, we show that the functional mapping from distributions of order statistics to their parent distribution is, in general, not Lipschitz continuous and, therefore, introduces an irregularity…

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Sensitivity to missing data assumptions: Theory and an evaluation of the U.S. wage structure

对缺失数据假设的敏感性:理论与美国工资结构评估

This paper develops methods for assessing the sensitivity of empirical conclusions regarding conditional distributions to departures from the missing at random (MAR) assumption.We index the degree of nonignorable selection governing the missing data process by the maximal Kolmogorov-Smirnov distance between the distributions of missing and observed outcomes across all values of the covariates.Sharp bounds on minimum mean square approximations to conditional quantiles are…

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A new approach to identifying generalized competing risks models with application to second-price auctions

广义竞争风险模型识别的新方法及其二价拍卖应用

This paper proposes an approach to proving nonparametric identification for distributions of bidders' values in asymmetric second-price auctions. I consider the case when bidders have independent private values and the only available data pertain to the winner's identity and the transaction price. My proof of identification is constructive and is based on establishing the existence and uniqueness of a solution to the system of nonlinear differential equations that describes…

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A central limit theorem in the -model for undirected random graphs with a diverging number of vertices

顶点数增长的无向随机图 β 模型中心极限定理

Chatterjee et al. (2011) established the consistency of the maximum likelihood estimator in the β-model for undirected random graphs when the number of vertices goes to infinity. By approximating the inverse of the Fisher information matrix, we prove asymptotic normality of the maximum likelihood estimator under mild conditions. Simulation studies and a data example illustrate the theoretical results.

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Comparing Distributions by using Dependent Normalized Random-Measure Mixtures

用相依归一化随机测度混合模型比较分布

Summary A methodology for the simultaneous Bayesian non-parametric modelling of several distributions is developed. Our approach uses normalized random measures with independent increments and builds dependence through the superposition of shared processes. The properties of the prior are described and the modelling possibilities of this framework are explored in detail. Efficient slice sampling methods are developed for inference. Various posterior summaries are introduced…

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Quantile and quantile-function estimations under density ratio model

密度比模型下的分位数及分位数函数估计

Population quantiles and their functions are important parameters in many applications. For example, the lower quantiles often serve as crucial quality indices for forestry products. Given several independent samples from populations satisfying the density ratio model, we investigate the properties of empirical likelihood (EL) based inferences. The induced EL quantile estimators are shown to admit a Bahadur representation that leads to asymptotically valid confidence…

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Regressions with Berkson errors in covariates—A nonparametric approach

协变量含 Berkson 型误差的回归:非参数方法

This paper establishes that so-called instrumental variables enable the identification and the estimation of a fully nonparametric regression model with Berkson-type measurement error in the regressors. An estimator is proposed and proven to be consistent. Its practical performance and feasibility are investigated via Monte Carlo simulations as well as through an epidemiological application investigating the effect of particulate air pollution on respiratory health. These…

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Universally consistent vertex classification for latent positions graphs

潜在位置图上的普遍相合顶点分类

In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate feature maps for latent position graphs with positive definite link function $\kappa$, provided that the latent positions are i.i.d. from some distribution $F$. We then consider the exploitation task of vertex classification where the link function $\kappa$ belongs to the class of universal kernels and class labels are observed for a number of vertices tending to…

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Maximum lilkelihood estimation in the $\beta$-model

β 模型中的最大似然估计

We study maximum likelihood estimation for the statistical model for undirected random graphs, known as the $\beta$-model, in which the degree sequences are minimal sufficient statistics. We derive necessary and sufficient conditions, based on the polytope of degree sequences, for the existence of the maximum likelihood estimator (MLE) of the model parameters. We characterize in a combinatorial fashion sample points leading to a nonexistent MLE, and nonestimability of the…

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Identification of first-price auctions with non-separable unobserved heterogeneity

具有不可分未观测异质性的第一价格拍卖识别

We propose a novel methodology for identification of first-price auctions, when bidders’ private valuations are independent conditional on one-dimensional unobserved heterogeneity. We extend the existing literature (Li and Vuong, 1998; Krasnokutskaya, 2011) by allowing the unobserved heterogeneity to be non-separable from bidders’ valuations. Our central identifying assumption is that the distribution of bidder values is increasing in the state. When the state-space is…

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Robust firm pricing with panel data

利用面板数据进行稳健企业定价

Firms often have imperfect information about demand for their products. We develop an integrated econometric and theoretical framework to model firm demand assessment and subsequent pricing decisions with limited information. We introduce a panel data discrete choice model whose realistic assumptions about consumer behavior deliver partially identified preferences and thus generate ambiguity in the firm pricing problem. We use the minimax-regret criterion as a…

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Are there common values in first-price auctions? A tail-index nonparametric test

第一价格拍卖是否存在共同价值?基于尾部指数的非参数检验

We develop a consistent nonparametric test of common values in first-price auctions and apply it to British Columbia Timber Sales data. The test is based on the behavior of the CDF of bids near the reserve price. We show that the curvature of the CDF is drastically different under private values (PV) and common values (CV). We then show that the problem of discriminating between PV and CV is equivalent to estimating the lower tail index of the bid distribution. Our approach…

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Limit theory for panel data models with cross sectional dependence and sequential exogeneity

具有截面依赖与序贯外生性的面板数据模型极限理论

The paper derives a general Central Limit Theorem (CLT) and asymptotic distributions for sample moments related to panel data models with large n. The results allow for the data to be cross sectionally dependent, while at the same time allowing the regressors to be only sequentially rather than strictly exogenous. The setup is sufficiently general to accommodate situations where cross sectional dependence stems from spatial interactions and/or from the presence of common…

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Inference on an extended Roy model, with an application to schooling decisions in France

扩展 Roy 模型的推断及其在法国教育选择中的应用

This paper considers the identification and estimation of an extension of Roy’s model (1951) of sectoral choice, which includes a non-pecuniary component in the selection equation and allows for uncertainty on potential earnings. We focus on the identification of the non-pecuniary component, which is key to disentangling the relative importance of monetary incentives versus preferences in the context of sorting across sectors. By making the most of the structure of the…

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