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An IV Model of Quantile Treatment Effects

分位数处理效应的工具变量模型

The ability of quantile regression models to characterize the heterogeneous impact of variables on different points of an outcome distribution makes them appealing in many economic applications. However, in observational studies, the variables of interest (e.g., education, prices) are often endogenous, making conventional quantile regression inconsistent and hence inappropriate for recovering the causal effects of these variables on the quantiles of economic outcomes. In…

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Efficient Semiparametric Estimation via Moment Restrictions

基于矩限制的有效半参数估计

Conditional moment restrictions can be combined through GMM estimation to construct more efficient semiparametric estimators. This paper is about attainable efficiency for such estimators. We define and use a moment tangent set, the directions of departure from the truth allowed by the moments, to characterize when the semiparametric efficiency bound can be attained. The efficiency condition is that the moment tangent set equals the model tangent set. We apply these results…

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Panel Binary Variables and Sufficiency: Generalizing Conditional Logit

面板二元变量与充分性:推广条件 Logit

This paper extends the conditional logit approach (Rasch, Andersen, Chamberlain) used in panel data models of binary variables with correlated fixed effects and strictly exogenous regressors. In a two-period two-state model, necessary and sufficient conditions on the joint distribution function of the individual-and-period specific shocks are given such that the sum of individual binary variables across time is a sufficient statistic for the individual effect. By extending a…

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Consistent Testing of Cointegrating Relationships

协整关系的一致检验

In this paper we investigate methods for testing the existence of a cointegration relationship among the components of a nonstationary fractionally integrated (NFI) vector time series. Our framework generalizes previous studies restricted to unit root integrated processes and permits simultaneous analysis of spurious and cointegrated NFI vectors. We propose a modified F-statistic, based on a particular studentization, which converges weakly under both hypotheses, despite the…

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Estimation of Continuous-Time Markov Processes Sampled at Random Time Intervals

随机时间间隔采样下连续时间马尔可夫过程的估计

We introduce a family of generalized-method-of-moments estimators of the parameters of a continuous-time Markov process observed at random time intervals. The results include strong consistency, asymptotic normality, and a characterization of standard errors. Sampling is at an arrival intensity that is allowed to depend on the underlying Markov process and on the parameter vector to be estimated. We focus on financial applications, including tick-based sampling, allowing for…

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Empirical Likelihood-Based Inference in Conditional Moment Restriction Models

条件矩限制模型中的经验似然推断

This paper proposes an asymptotically efficient method for estimating models with conditional moment restrictions. Our estimator generalizes the maximum empirical likelihood estimator (MELE) of Qin and Lawless (1994). Using a kernel smoothing method, we efficiently incorporate the information implied by the conditional moment restrictions into our empirical likelihood-based procedure. This yields a one-step estimator which avoids estimating optimal instruments. Our…

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Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models

空间自回归模型准最大似然估计量的渐近分布

This paper investigates asymptotic properties of the maximum likelihood estimator and the quasi-maximum likelihood estimator for the spatial autoregressive model. The rates of convergence of those estimators may depend on some general features of the spatial weights matrix of the model. It is important to make the distinction with different spatial scenarios. Under the scenario that each unit will be influenced by only a few neighboring units, the estimators may have -rate…

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Confidence Intervals for Partially Identified Parameters

部分识别参数的置信区间

In the last decade a growing body of research has studied inference on partially identified parameters (e.g., Manski, 1990, 2003). In many cases where the parameter of interest is realvalued, the identification region is an interval whose lower and upper bounds may be estimated from sample data. Confidence intervals may be constructed to take account of the sampling variation in estimates of these bounds. Horowitz and Manski (1998, 2000) proposed and applied interval…

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Polarization: Concepts, Measurement, Estimation

极化:概念、测量与估计

We develop the measurement theory of polarization for the case in which income distributions can be described using density functions. The main theorem uniquely characterizes a class of polarization measures that fits into what we call the “identity-alienation” framework, and simultanously satisfies a set of axioms. Second, we provide sample estimators of population polarization indices that can be used to compare polarization across time or entities. Distribution-free…

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Wavelet-Based Testing for Serial Correlation of Unknown Form in Panel Models

面板模型中未知形式序列相关的小波检验

Wavelet analysis is a new mathematical method developed as a unified field of science over the last decade or so. As a spatially adaptive analytic tool, wavelets are useful for capturing serial correlation where the spectrum has peaks or kinks, as can arise from persistent dependence, seasonality, and other kinds of periodicity. This paper proposes a new class of generally applicable wavelet-based tests for serial correlation of unknown form in the estimated residuals of a…

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Likelihood-Based Estimation of Latent Generalized ARCH Structures

潜在广义 ARCH 结构的似然估计

GARCH models are commonly used as latent processes in econometrics, financial economics, and macroeconomics. Yet no exact likelihood analysis of these models has been provided so far. In this paper we outline the issues and suggest a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a Bayesian solution in O(T) computational operations, where T denotes the sample size. We assess the performance of our…

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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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Consistent Estimation of Models Defined by Conditional Moment Restrictions

In econometrics, models stated as conditional moment restrictions are typically estimated by means of the generalized method of moments (GMM). The GMM estimation procedure can render inconsistent estimates since the number of arbitrarily chosen instruments is finite. In fact, consistency of the GMM estimators relies on additional assumptions that imply unclear restrictions on the data generating process. This article introduces a new, simple and consistent estimation…

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Jackknife and Analytical Bias Reduction for Nonlinear Panel Models

Fixed effects estimators of panel models can be severely biased because of the well-known incidental parameters problem. We show that this bias can be reduced by using a panel jackknife or an analytical bias correction motivated by large T. We give bias corrections for averages over the fixed effects, as well as model parameters. We find large bias reductions from using these approaches in examples. We consider asymptotics where T grows with n, as an approximation to the…

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Efficient Semiparametric Estimation of Censored and Truncated Regressions via a Smoothed Self-Consistency Equation

An asymptotically efficient likelihood-based semiparametric estimator is derived for the censored regression (tobit) model, based on a new approach for estimating the density function of the residuals in a partially observed regression. Smoothing the self-consistency equation for the nonparametric maximum likelihood estimator of the distribution of the residuals yields an integral equation, which in some cases can be solved explicitly. The resulting estimated density is…

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Statistical Treatment Rules for Heterogeneous Populations

An important objective of empirical research on treatment response is to provide decision makers with information useful in choosing treatments. Manski (2000, 2002, 2003) showed how identification problems generate ambiguity about the identity of optimal treatment choices. This paper studies treatment choice using sample data. I consider a planner who must choose among alternative statistical treatment rules, these being functions that map observed covariates of population…

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A PANIC Attack on Unit Roots and Cointegration

This paper develops a new methodology that makes use of the factor structure of large dimensional panels to understand the nature of nonstationarity in the data. We refer to it as PANIC-Panel Analysis of Nonstationarity in Idiosyncratic and Common components. PANIC can detect whether the nonstationarity in a series is pervasive, or variable-specific, or both. It can determine the number of independent stochastic trends driving the common factors. PANIC also permits valid…

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Twicing Kernels and a Small Bias Property of Semiparametric Estimators

The purpose of this note is to show how semiparametric estimators with a small bias property can be constructed. The small bias property (SBP) of a semiparametric estimator is that its bias converges to zero faster than the pointwise and integrated bias of the nonparametric estimator on which it is based. We show that semiparametric estimators based on twicing kernels have the SBP. We also show that semiparametric estimators where nonparametric kernel estimation does not…

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The Error in Rejection Probability of Simple Autocorrelation Robust Tests

A new class of autocorrelation robust test statistics is introduced. The class of tests generalizes the Kiefer, Vogelsang, and Bunzel (2000) test in a manner analogous to Anderson and Darling's (1952) generalization of the Cramér–von Mises goodness of fit test. In a Gaussian location model, the error in rejection probability of the new tests is found to be O(T-1logT), where T denotes the sample size.

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Simple Finite Horizon Bubbles Robust to Higher Order Knowledge

An asymmetric information model of a finite horizon “nth order” rational asset price bubble is presented, where (all agents know that)n the asset is worthless. Also, the model has only two agents, so the first order version of the bubble is simpler than other first order bubbles in the literature.

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Behavior in a Dynamic Decision Problem: An Analysis of Experimental Evidence Using a Bayesian Type Classification Algorithm

Different people may use different strategies, or decision rules, when solving complex decision problems. We provide a new Bayesian procedure for drawing inferences about the nature and number of decision rules present in a population, and use it to analyze the behaviors of laboratory subjects confronted with a difficult dynamic stochastic decision problem. Subjects practiced before playing for money. Based on money round decisions, our procedure classifies subjects into…

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the Block-Block Bootstrap: Improved Asymptotic Refinements

The asymptotic refinements attributable to the block bootstrap for time series are not as large as those of the nonparametric iid bootstrap or the parametric bootstrap. One reason is that the independence between the blocks in the block bootstrap sample does not mimic the dependence structure of the original sample. This is the join-point problem. In this paper, we propose a method of solving this problem. The idea is not to alter the block bootstrap. Instead, we alter the…

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Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics

This paper analyses multivariate high frequency financial data using realized covariation. We provide a new asymptotic distribution theory for standard methods such as regression, correlation analysis, and covariance. It will be based on a fixed interval of time (e.g., a day or week), allowing the number of high frequency returns during this period to go to infinity. Our analysis allows us to study how high frequency correlations, regressions, and covariances change through…

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