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Nonparametric Estimation with Nonlinear Budget Sets

非线性预算集下的非参数估计

Choice models with nonlinear budget sets are important in econometrics.In this paper we propose a nonparametric approach to estimation of choice models with nonlinear budget sets.The basic idea is to think of the choice, in our case hours of labor supply, as being a function of the entire budget set.Then we can ac- count nonparametrically for a nonlinear budget set by estimating a nonparametric regression where the variable in the regression is the budget set.We reduce the…

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Identification of Standard Auction Models

标准拍卖模型的识别

We present new identification resiilts for models of first-price, second-price, ascending (English), and descending (Dutch) auctions.We analyze a general specification of bidders' preferences and the underlying information structure, nesting as special cases the pure private values and pure common values models, and allowing both ex ante symmetric and asymmetric bidders.We address identification of a series of such models and propose strategies for discriminating between…

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Mobility and the Return to Education: Testing a Roy Model with Multiple Markets

迁移与教育回报:多市场 Roy 模型的检验

Self-selected migration presents one potential explanation for why observed returns to a college education in local labor markets vary widely even though U.S. workers are highly mobile.To assess the impact of self-selection on estimated returns, this paper first develops a Roy model of mobility and earnings where workers choose in which of the 50 states (plus the District of Columbia) to live and work.Available estimation methods are either infeasible for a selection model…

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Equilibrium Wage Dispersion with Worker and Employer Heterogeneity

劳动者与雇主异质性下的均衡工资离散

We construct and estimate an equilibrium search model with on–the–job–search. Firms make take–it–or–leave–it wage offers to workers conditional on their characteristics and they can respond to the outside job offers received by their employees. Unobserved worker productive heterogeneity is introduced in the form of cross–worker differences in a “competence” parameter. On the other side of the market, firms also are heterogeneous with respect to their marginal productivity of…

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Mobility and the Return to Education: Testing a Roy Model with Multiple Markets

Self–selected migration presents one potential explanation for why observed returns to a college education in local labor markets vary widely even though U.S. workers are highly mobile. To assess the impact of self–selection on estimated returns, this paper first develops a Roy model of mobility and earnings where workers choose in which of the 50 states (plus the District of Columbia) to live and work. Available estimation methods are either infeasible for a selection model…

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Equilibrium Wage Dispersion with Worker and Employer Heterogeneity

劳动者与雇主异质性下的均衡工资离散

We construct and estimate an equilibrium search model with on-the-job-search. Firms make take-it-or-leave-it wage offers to workers conditional on their characteristics and they can respond to the outside job offers received by their employees. Unobserved worker productive heterogeneity is introduced in the form of cross-worker differences in a "competence" parameter. On the other side of the market, firms also are heterogeneous with respect to their marginal productivity of…

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Discrete-Time Approximations of the Holmstrom-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision

This paper studies the relation between discrete–time and continuous–time principal–agent models. We derive the continuous–time model as a limit of discrete–time models with ever shorter periods and show that optimal incentive schemes in the discrete–time models approximate the optimal incentive scheme in the continuous model, which is linear in accounts. Under the additional assumption that the principal observes only cumulative total profits at the end and the agent can…

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Identification of Standard Auction Models

This paper presents new identification results for models of first–price, second–price, ascending (English), and descending (Dutch) auctions. We consider a general specification of the latent demand and information structure, nesting both private values and common values models, and allowing correlated types as well as ex ante asymmetry. We address identification of a series of nested models and derive testable restrictions enabling discrimination between models on the basis…

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Nonparametric Estimation with Nonlinear Budget Sets

Choice models with nonlinear budget sets provide a precise way of accounting for the nonlinear tax structures present in many applications. In this paper we propose a nonparametric approach to estimation of these models. The basic idea is to think of the choice, in our case hours of labor supply, as being a function of the entire budget set. Then we can do nonparametric regression where the variable in the regression is the budget set. We reduce the dimensionality of this…

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Particle Filtering for Partially Observed Gaussian State Space Models

部分观测高斯状态空间模型的粒子滤波

Summary Solving Bayesian estimation problems where the posterior distribution evolves over time through the accumulation of data has many applications for dynamic models. A large number of algorithms based on particle filtering methods, also known as sequential Monte Carlo algorithms, have recently been proposed to solve these problems. We propose a special particle filtering method which uses random mixtures of normal distributions to represent the posterior distributions…

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Generalized Method of Moments Estimation When a Parameter Is on a Boundary

参数位于边界时的广义矩估计

This article establishes the asymptotic distributions of generalized method of moments (GMM) estimators when the true parameter lies on the boundary of the parameter space. The conditions allow the estimator objective function to be nonsmooth and to depend on preliminary estimators. The boundary of the parameter space may be curved and/or kinked. The article discusses three examples: (1) instrumental variables (IV) estimation of a regression model with nonlinear equality…

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An Adaptive, Rate-Optimal Test of Linearity for Median Regression Models

中位数回归模型线性性的自适应速率最优检验

This article is concerned with testing the hypothesis that a conditional median function is linear against a nonparametric alternative with unknown smoothness. We develop a test that is uniformly consistent against alternatives whose distance from the linear model converges to zero at the fastest possible rate. The test does not require knowledge of the distribution of the model's random noise component, and it permits conditional heteroscedasticity of unknown form. The…

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A Unified Approach to Conjoint Analysis Models

联合分析模型的统一方法

We present a unified approach to conjoint analysis models using a Bayesian framework. One data source is used to form a prior distribution for the partworths, whereas full-profile evaluations under a rating scale, ranking, discrete choice, or constant-sum scale constitute the likelihood data (“one model fits all”). Standard existing models for conjoint analysis, considered in the literature, become particular cases of the proposed specification, and explicit formulas for the…

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Accounting for the Black–White Wealth Gap

解释黑人与白人的财富差距

Many applications involve a decomposition of the mean intergroup difference in a given variable into the portion attributable to differences in the distribution of one or more explanatory variables and that due to differences in the conditional expectation function. This article notes two interrelated reasons why the Blinder–Oaxaca (B–O) method—the approach most commonly used in the literature—may yield misleading results. We suggest a natural solution that both provides a…

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Three-Step Censored Quantile Regression and Extramarital Affairs

三步删失分位数回归与婚外情应用

This article suggests very simple three-step estimators for censored quantile regression models with a separation restriction on the censoring probability. The estimators are theoretically attractive (i.e., asymptotically as efficient as the celebrated Powell's censored least absolute deviation estimator). At the same time, they are conceptually simple and have trivial computational expenses. They are especially useful in samples of small size or models with many regressors,…

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The Optimality of a Simple Market Mechanism

Strategic behavior in a finite market can cause inefficiency in the allocation, and market mechanisms differ in how successfully they limit this inefficiency. A method for ranking algorithms in computer science is adapted here to rank market mechanisms according to how quickly inefficiency diminishes as the size of the market increases. It is shown that trade at a single market-clearing price in the "k"-double auction is "worst-case asymptotic optimal" among all plausible…

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Estimation in a semiparametric model for longitudinal data with unspecified dependence structure

依赖结构未指定的纵向数据半参数模型估计

This paper considers an extension of M‐estimators in semiparametric models for independent observations to the case of longitudinal data. We approximate the nonparametric function by a regression spline, and any M‐estimation algorithm for the usual linear models can then be used to obtain consistent estimators of the model and valid large‐sample inferences about the regression parameters without any specification of the error distribution and the covariance structure.…

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Analysis of clustered data: A combined estimating equations approach

聚类数据分析:组合估计方程方法

Examples of clustered data include data from longitudinal studies and data sampled within groups. This paper proposes a regression analysis method for clustered data that optimally weights and combines contrasts of the data through a combination of estimating equations. Examples of combining between‐cluster, within‐cluster and longitudinal data contrasts are presented. The method results in increased estimation efficiency relative to generalised estimating equations with…

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Bayesian analysis of covariance matrices and dynamic models for longitudinal data

纵向数据协方差矩阵与动态模型的贝叶斯分析

Parsimonious modelling of the within‐subject covariance structure while heeding its positive‐definiteness is of great importance in the analysis of longitudinal data. Using the Cholesky decomposition and the ensuing unconstrained and statistically meaningful reparameterisation, we provide a convenient and intuitive framework for developing conditionally conjugate prior distributions for covariance matrices and show their connections with generalised inverse Wishart priors.…

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Testing model adequacy for dynamic panel data with intercorrelation

具有相互相关性的动态面板模型适合性检验

We give several definitions of residual autocorrelations and derive their joint asymptotic distribution for the panel time series model of Hjellvik & Tjøstheim (1999a). A portmanteau goodness‐of‐fit test arises naturally from the asymptotic distribution. Simulation results show that the asymptotic standard errors compared satisfactorily with the empirical standard errors, that the goodness‐of‐fit test has reasonable empirical size, and that it is powerful enough to be useful…

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Chain Graph Models and their Causal Interpretations

链图模型及其因果解释

Summary Chain graphs are a natural generalization of directed acyclic graphs and undirected graphs. However, the apparent simplicity of chain graphs belies the subtlety of the conditional independence hypotheses that they represent. There are many simple and apparently plausible, but ultimately fallacious, interpretations of chain graphs that are often invoked, implicitly or explicitly. These interpretations also lead to flawed methods for applying background knowledge to…

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