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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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RATE-ADAPTIVE BOOTSTRAP FOR POSSIBLY MISSPECIFIED GMM

可能误设的 GMM 模型中的收敛速度自适应 Bootstrap

We consider inference for possibly misspecified GMM models based on possibly nonsmooth moment conditions. While it is well known that misspecified GMM estimators with smooth moments remain $\sqrt {n}$ consistent and asymptotically normal, globally misspecified nonsmooth GMM estimators are $n^{1/3}$ consistent when either the weighting matrix is fixed or when the weighting matrix is estimated at the $n^{1/3}$ rate or faster. Because the estimator’s nonstandard asymptotic…

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Varying-coefficient spatial dynamic panel data models with fixed effects: Theory and application

带固定效应的变系数空间动态面板模型:理论与应用

This paper considers a varying-coefficient spatial dynamic panel data model with fixed effects. We show that a two-point approximation method poses a potential weak identification problem. We propose a robust modified estimator to address this issue. Our two-step estimation procedure incorporates both linear and quadratic moment conditions. We also extend our analysis to a partially linear varying-coefficient model and develop a consistent test for this specification. We…

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Constrained estimation using penalization and MCMC

利用惩罚与 MCMC 的约束估计

We study inference for parameters defined by either classical extremum estimators or Laplace-type estimators subject to general nonlinear constraints on the parameters. We show that running MCMC on the penalized version of the problem offers a computationally attractive alternative to solving the original constrained optimization problem. Bayesian credible intervals are asymptotically valid confidence intervals in a pointwise sense, providing exact asymptotic coverage for…

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BLP estimation using Laplace transformation and overlapping simulation draws

利用拉普拉斯方法与重叠模拟抽样估计 BLP 模型

We derive the asymptotic distribution of the parameters of the Berry et al. (1995) (BLP) model in a many markets setting which takes into account simulation noise under the assumption of overlapping simulation draws. We show that as long as the number of simulation draws R and the number of markets T approach infinity, our estimator is m=min(R,T) consistent and asymptotically normal. We do not impose any relationship between the rates at which R and T go to infinity, thus…

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The numerical bootstrap

This paper proposes a numerical bootstrap method that is consistent in many cases where the standard bootstrap is known to fail and where the $m$-out-of-$n$ bootstrap and subsampling have been the most commonly used inference approaches. We provide asymptotic analysis under both fixed and drifting parameter sequences, and we compare the approximation error of the numerical bootstrap with that of the $m$-out-of-$n$ bootstrap and subsampling. Finally, we discuss applications…

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The numerical delta method

数值 Delta 方法

This paper provides a numerical derivative based Delta method that complements the recent work by Fang and Santos (2014) and also generalizes a previous insight by Song (2014). We show that for an appropriately chosen sequence of step sizes, the numerical derivative based Delta method provides consistent inference for functions of parameters that are only directionally differentiable. Additionally, it provides uniformly valid inference for certain convex and Lipschitz…

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A Bayesian approach to estimation of dynamic models with small and large number of heterogeneous players and latent serially correlated states

含少量或大量异质参与者及潜在序列相关状态的动态模型:贝叶斯估计

We propose a Bayesian approach to estimating dynamic models that can have state variables that are latent, serially correlated, and heterogeneous. Our approach employs sequential importance sampling and is based on deriving an unbiased estimate of the likelihood within a Metropolis chain. Under fairly weak regularity conditions unbiasedness guarantees that the stationary density of the chain is the exact posterior, not an approximation. Results are verified by Monte Carlo…

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Estimating price sensitivity of economic agents using discontinuity in nonlinear contracts

利用非线性合同的不连续性估计经济主体的价格敏感度

This paper proposes a method to estimate price sensitivity of economic agents exploiting discontinuity in nonlinear contracts. As an application, we study contracts between a managed care organization and hospitals for organ transplants. Exploiting donut holes in the reimbursement contracts, we show that the impact of the reimbursement rate on hospitals' provision of health care services varies significantly across patients with different levels of illness severity. Our…

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Estimation of dynamic discrete models from time aggregated data

时间聚合数据下动态离散模型的估计

An important component in dynamic discrete choice models and dynamic discrete games is the transition density of state variables from the current period to the next period. Most empirical dynamic discrete choice models identify the theoretical time interval in the behavioral model with that observed in the data set. However, many empirical data sets are time aggregated. In this paper, we show that when the time interval in the behavioral theory model differs from that in the…

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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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A fast resample method for parametric and semiparametric models

参数与半参数模型的快速重抽样方法

We propose a fast resample method for two step nonlinear parametric and semiparametric models, which does not require recomputation of the second stage estimator during each resample iteration. The fast resample method directly exploits the score function representations computed on each bootstrap sample, thereby reducing computational time considerably. This method is used to approximate the limit distribution of parametric and semiparametric estimators, possibly simulation…

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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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Bayesian averaging, prediction and nonnested model selection

贝叶斯平均、预测与非嵌套模型选择

This paper studies the asymptotic relationship between Bayesian model averaging and post-selection frequentist predictors in both nested and nonnested models. We derive conditions under which their difference is of a smaller order of magnitude than the inverse of the square root of the sample size in large samples. This result depends crucially on the relation between posterior odds and frequentist model selection criteria. Weak conditions are given under which consistent…

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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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Semiparametric efficiency in GMM models with auxiliary data

使用辅助数据的 GMM 模型半参数效率

We study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data. Identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database, when such distribution is common to the two data sets. The auxiliary sample can be independent of the primary sample, or can be…

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Estimation and Confidence Regions for Parameter Sets in Econometric Models

计量经济模型中参数集合的估计与置信区域

This paper develops a framework for performing estimation and inference in econometric models with partial identification, focusing particularly on models characterized by moment inequalities and equalities. Applications of this framework include the analysis of game-theoretic models, revealed preference restrictions, regressions with missing and corrupted data, auction models, structural quantile regressions, and asset pricing models. Copyright The Econometric Society 2007.

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Likelihood Estimation and Inference in a Class of Nonregular Econometric Models

一类非正规计量经济模型中的似然估计与推断

We study inference in structural models with a jump in the conditional density, where location and size of the jump are described by regression curves. Two prominent examples are auction models, where the bid density jumps from zero to a positive value at the lowest cost, and equilibrium job-search models, where the wage density jumps from one positive level to another at the reservation wage. General inference in such models remained a long-standing, unresolved problem,…

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GENERALIZED EMPIRICAL LIKELIHOOD–BASED MODEL SELECTION CRITERIA FOR MOMENT CONDITION MODELS

基于广义经验似然的矩条件模型选择准则

This paper proposes model selection criteria (MSC) for unconditional moment models using generalized empirical likelihood (GEL) statistics. The use of GEL-statistics in lieu of J-statistics (in the spirit of Andrews, 1999, Econometrica 67, 543–564; and Andrews and Lu, 2001, Journal of Econometrics 101, 123–164) leads to an alternative interpretation of the MSCs that emphasizes the common information-theoretic rationale underlying model selection procedures for both…

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