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Generalized Method of Moments and Empirical Likelihood

广义矩估计与经验似然

Generalized method of moments (GMM) estimation has become an important unifying framework for inference in econometrics in the last 20 years. It can be thought of as encompassing almost all of the common estimation methods, such as maximum likelihood, ordinary least squares, instrumental variables, and two-stage least squares, and nowadays is an important part of all advanced econometrics textbooks. The GMM approach links nicely to economic theory where orthogonality…

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RANK ESTIMATORS FOR A TRANSFORMATION MODEL

变换模型的秩估计量

We establish [square root] n -consistency and asymptotic normality of Han's (1987a, Journal of Econometrics 35, 191–209) estimator of the parameters characterizing the transformation function in a semiparametric transformation model. We verify a Vapnik–Cervonenkis (VC) condition for the parameterizations of Box and Cox (1964, Journal of the Royal Statistical Society, Series B 34, 187–200) and Bickel and Doksum (1981, Journal of the American Statistical Association 76,…

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Invariance, Identifiability, and Morphometrics

不变性、可识别性与形态测量

The form of an object is that characteristic that remains invariant under a group of transformations comprising translation, rotation, and possibly reflection. Group invariance thus naturally plays an important role in the statistical analysis of forms. We examine the existing methods for the statistical analysis of form from the invariance perspective. We begin with a review of the important basic ideas behind invariance and derive a maximal invariant under the group of…

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Identification of Shared Components in Large Ensembles of Time Series Using Dimension Reduction

利用降维识别大规模时间序列集合中的共享成分

In this article we present a framework for parsimonious modeling of large ensembles of time series. The idea is to identify a small number of stochastic time series components such that each series in the ensemble is a weighted sum of series-specific realizations of the components. We present an estimation procedure that is computationally tractable for large datasets. Through simulations, we argue that the estimators perform well. We illustrate the method using two…

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Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression

We propose a novel statistic for conducting joint tests on all the structural parameters in instrumental variables regression. The statistic is straightforward to compute and equals a quadratic form of the score of the concentrated log–likelihood. It therefore attains its minimal value equal to zero at the maximum likelihood estimator. The statistic has a χ2 limiting distribution with a degrees of freedom parameter equal to the number of structural parameters. The limiting…

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Youth Labor Markets in the United States: Shopping Around vs. Staying Put

美国青年劳动力市场:频繁换工作还是保持稳定

The need for school-to-work programs or other means of increasing early job market stability is predicated on the view that the "chaotic" nature of youth labor markets in the United States is costly because workers drift from one job to another without developing skills, behavior, or other characteristics that in turn lead to higher adult earnings. However, there is also ample evidence that workers receive positive returns to job shopping. This paper asks whether youths in…

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Alcohol abuse and employment: a second look

酒精滥用与就业:重新考察

Abstract Based on data from the 1988 Alcohol Supplement of the National Health Interview Survey, Mullahy and Sindelar ( 1996 ) (M&S) find, for both men and women, that alcohol abuse results in reduced employment and increased unemployment. The estimates from which they drew these inferences were obtained via the instrumental variables (IV) method, which was implemented in order to account for the potential endogeneity of problem drinking. Though these IV estimates…

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The sampling properties of conditional independence graphs for structural vector autoregressions

结构向量自回归条件独立图的抽样性质

Structural vector autoregressions allow contemporaneous series dependence and assume errors with no contemporaneous correlation. Models of this form, that also have a recursive structure, can be described by a directed acyclic graph. An important tool for identification of these models is the conditional independence graph constructed from the contemporaneous and lagged values of the process. We determine the large‐sample properties of statistics used to test for the…

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Estimating a Changepoint, Boundary, or Frontier in the Presence of Observation Error

观测误差下的变点、边界与前沿估计

A range of problems in economics and statistics involve calculation of the boundary, or frontier, of the support of a distribution. Several practical and attractive solutions exist if the sampled distribution has a sharp discontinuity at the frontier, but accuracy can be greatly diminished if the data are observed with error. Indeed, if the error is additive and has variance σ2 then inaccuracies are usually of order σ, for small σ. In this article we suggest an elementary…

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Hierarchical Bayesian Nonresponse Models for Binary Data From Small Areas With Uncertainty About Ignorability

可忽略性不确定下的小区域二元数据分层贝叶斯无响应模型

In the National Crime Survey (NCS), data on victimization can be poststratified into domains determined by urbanization, type of place, and poverty level. There is much difficulty in the analysis of binary data with substantial nonresponse. We consider three Bayesian hierarchical models for binary nonresponse data, like those from the NCS, which are clustered within a number of domains or areas. As in small area estimation, one key feature is that each model “borrows…

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STRUCTURAL CHANGES AND SEEMINGLY UNIDENTIFIED STRUCTURAL EQUATIONS

结构变化与表面未识别的结构方程

This paper introduces structural equations that do not satisfy the rank and/or order condition(s) for identification but still are identifiable. These equations are called seemingly unidentified structural equations. The key to the identifiability of these equations is that the right-hand-side endogenous variables undergo structural changes with respect to the exogenous and/or predetermined variables. To estimate the seemingly unidentified structural equations, this paper…

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INSTRUMENTAL VARIABLE INTERPRETATION OF COINTEGRATION WITH INFERENCE RESULTS FOR FRACTIONAL COINTEGRATION

协整的工具变量解释与分数协整推断

In this paper we propose an alternative characterization of the central notion of cointegration, exploiting the relationship between the autocovariance and the cross-covariance functions of the series. This characterization leads us to propose a new estimator of the cointegrating parameter based on the instrumental variables (IV) methodology. The instrument is a delayed regressor obtained from the conditional bivariate system of nonstationary fractionally integrated…

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EFFICIENT IV ESTIMATION FOR AUTOREGRESSIVE MODELS WITH CONDITIONAL HETEROSKEDASTICITY

条件异方差自回归模型的有效工具变量估计

This paper analyzes autoregressive time series models where the errors are assumed to be martingale difference sequences that satisfy an additional symmetry condition on their fourth-order moments. Under these conditions quasi maximum likelihood estimators of the autoregressive parameters are no longer efficient in the generalized method of moments (GMM) sense. The main result of the paper is the construction of efficient semiparametric instrumental variables estimators for…

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Spatial Price Competition: A Semiparametric Approach

We investigate the nature of price competition among firms that produce differentiated products and compete in markets that are limited in extent. We propose an instrumental variables series estimator for the matrix of cross price response coefficients, demonstrate that our estimator is consistent, and derive its asymptotic distribution. Our semiparametric approach allows us to discriminate among models of global competition, in which all products compete with all others,…

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CONSISTENCY AND EFFICIENCY OF LEAST SQUARES ESTIMATION FOR MIXED REGRESSIVE, SPATIAL AUTOREGRESSIVE MODELS

混合回归与空间自回归模型中最小二乘的一致性和效率

Least squares estimation has casually been dismissed as an inconsistent estimation method for mixed regressive, spatial autoregressive models with or without spatial correlated disturbances. Although this statement is correct for a wide class of models, we show that, in economic spatial environments where each unit can be influenced aggregately by a significant portion of units in the population, least squares estimators can be consistent. Indeed, they can even be…

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Bootstrap Tests for Distributional Treatment Effects in Instrumental Variable Models

工具变量模型中分布处理效应的自助法检验

This article considers the problem of assessing the distributional consequences of a treatment on some outcome variable of interest when treatment intake is (possibly) nonrandomized, but there is a binaryinstrument available for the researcher. Such a scenario is common in observational studies and in randomized experiments with imperfect compliance. One possible approach to this problem is to compare the counterfactual cumulative distribution functions of the outcome with…

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Clustering of Translocation Breakpoints

染色体易位断点的聚集分析

Translocation, a physical movement of genetic material from one chromosome to another, can result in the aberrant linkage of two cellular genes. This type of fusion may disrupt cellular function by producing novel, biologically active fused genes, or by triggering the activation of normally quiescent growth-associated genes. Either of these mechanisms provides a putative oncogenic stimulus, and indeed, several gene fusions from translocations have been identified in…

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Shift Restrictions and Semiparametric Estimation in Ordered Response Models

有序响应模型中的平移限制与半参数估计

We develop a √n-consistent and asymptotically normal estimator of the parameters (regression coefficients and threshold points) of a semiparametric ordered response model under the assumption of independence of errors and regressors. The independence assumption implies shift restrictions allowing identification of threshold points up to location and scale. The estimator is useful in various applications, particularly in new product demand forecasting from survey data subject…

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Inference on Regressions with Interval Data on a Regressor or Outcome

解释变量或结果具有区间数据时的回归推断

This paper examines inference on regressions when interval data are available on one variable, the other variables being measured precisely. Let a population be characterized by a distribution P(y, x, v, v0, v1), where y∈R1, x∈Rk, and the real variables (v, v0, v1) satisfy v0≤v≤v1. Let a random sample be drawn from P and the realizations of (y, x, v0, v1) be observed, but not those of v. The problem of interest may be to infer E(y|x, v) or E(v|x). This analysis maintains…

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Edgeworth approximations for semiparametric instrumental variable estimators and test statistics

半参数工具变量估计量与检验统计量的 Edgeworth 近似

We establish the validity of higher order asymptotic expansions to the distribution of a version of the nonlinear semiparametric instrumental variable considered in Newey (1990) as well as to the distribution of a Wald statistic derived from it. We employ local polynomial smoothing with variable bandwidth, which includes local linear, kernel, and [a version of] nearest neighbour estimates as special cases. Our expansions are valid to order n^(-2ϵ) for some 0 < ϵ < ½, where ϵ…

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ON INTERCEPT ESTIMATION IN THE SAMPLE SELECTION MODEL

样本选择模型中的截距估计

We provide a proof of the consistency and asymptotic normality of the estimator suggested by Heckman (1990, American Economic Review 80, 313–318) for the intercept of a semiparametrically estimated sample selection model. The estimator is based on “identification at infinity,” which leads to nonstandard convergence rate.

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OPTIMAL INFERENCE WITH MANY INSTRUMENTS

多工具变量情形下的最优推断

In this paper, I derive the efficiency bound of the structural parameter in a linear simultaneous equations model with many instruments. The bound is derived by applying a convolution theorem to Bekker's (1994, Econometrica 62, 657–681) asymptotic approximation, where the number of instruments grows to infinity at the same rate as the sample size. Usual instrumental variables estimators with a small number of instruments are heuristically argued to be efficient estimators in…

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