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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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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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Regressions, Short and Long

短回归与长回归

We study the problem of identi cation of the long regression E(y j x � z) when the short conditional distributions P (y j x) and P (z j x) are known but the long conditional distribution P (y j x � z) is not known. This problem often arises when a researcher utilizes data from two separate data sets. (A leading example is the ecological inference problem of political science, where voting behavior across electoral districts is observed from administrative records, the…

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Monotone Instrumental Variables: With an Application to the Returns to Schooling

单调工具变量:教育回报的应用

Econometric analyses of treatment response commonly use instrumental variable (IV) assumptions to identify treatment effects.Yet the credibility of IV assumptions is often a matter of considerable disagreement.There is therefore good reason to consider weaker but more credible assumptions.To this end, we introduce monotone instrumental variable (MIV) assumptions and the important special case of monotone treatment selection (MTS).We study the identifying power of MIV…

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Nonparametric Analysis of Randomized Experiments with Missing Covariate and Outcome Data

协变量和结局缺失的随机实验非参数分析

Analysis of randomized experiments with missing covariate and outcome data is problematic, because the population parameters of interest are not identified unless one makes untestable assumptions about the distribution of the missing data. This article shows how population parameters can be bounded without making untestable distributional assumptions. Bounds are also derived under the assumption that covariate data are missing completely at random. In each case the bounds…

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Monotone Treatment Response

单调处理响应

This paper investigates what may be learned about treatment response when it is assumed that response functions are monotone, semimonotone, or concave-monotone. Nothing is assumed about the process of treatment selection and cross-individual restrictions on response are not imposed. The idea is to determine, for every member of the population, the response functions that pass through the realized (treatment, outcome) pair and that are consistent with the assumption imposed.…

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Identification and Robustness with Contaminated and Corrupted Data

数据污染与损坏下的识别及稳健性

Robust estimation aims at developing point estimators that are not highly sensitive to errors in data. However, the population parameters of interest are not identified under the assumptions of robust estimation, so the rationale for point estimation is not apparent. This paper shows that, under error models used in robust estimation, unidentified population parameters can often be bounded. The bounds provide information that is not available in robust estimation. For…

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Alternative Estimates of the Effect of Family Structure during Adolescence on High School Graduation

青少年时期家庭结构对高中毕业影响的不同估计

Many studies have reported significant empirical associations between family structure during childhood and children's outcomes later in life. It may be that living in a nonintact family has adverse consequences for children. On the other hand, it may be that some unobserved process jointly determines family structure and children's outcomes. How then should one interpret the empirical evidence on the relationship between family structure and children's outcomes? The answer…

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Identification of Binary Response Models

二元反应模型的识别

This article studies identification of the threshold-crossing model of binary response. Most research on binary response has considered specific estimators and tests. The study of identification exposes the foundations of binary response analysis by making explicit the assumptions needed to justify different methods. It also clarifies the connections between reduced-form and structural analyses of binary response data. Assume that the binary outcome z is determined by an…

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Estimation by the Analogy Principle

基于类比原则的估计

The analogy principle proposes that population parameters be estimated by sample statistics which make known properties of the population hold as closely as possible in the sample. Applications of the analogy principle are ubiquitous. Nevertheless, estimation theory has not been studied from a consistent analog perspective. This paper makes a start.

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Monte Carlo Evidence on Adaptive Maximum Likelihood Estimation of a Regression

回归自适应最大似然估计的 Monte Carlo 证据

This paper reports Monte Carlo evidence on the fixed sample size properties of adaptive maximum likelihood estimates of a linear regression. The focus is on the problem of selecting the smoothing and trimming parameters used in estimating the score function. We examine the performance of adaptive maximum likelihood estimators when these parameters are preselected or, alternatively, are determined by a data-based bootstrap method.

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Semiparametric Analysis of Random Effects Linear Models from Binary Panel Data

基于二元面板数据的随机效应线性模型半参数分析

Andersen_(1970) considered the problem of inference on random effects linear models from binary response panel data, and showed that inference is possible if the disturbances for each panel member are known to be white noise with the logistic distribution. The present paper shows that inference remains possible if the disturbances are known only to be time-stationary. A conditional version of the maximum score estimator consistently estimates the parameters up to scale.…

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Estimation of Response Probabilities from Augmented Retrospective Observations

利用增补辅助信息的回溯观测估计响应概率

When augmented by suitable auxiliary information, retrospective data can identify response probabilities. The auxiliary information may take the form of data on marginal distributions or appropriate structural assumptions. When a combination of retrospective observation and auxiliary information suffices in principle to identify response probabilities, practical use of this fact requires that statistically sound and computationally tractable estimation methods be available.…

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The Estimation of Choice Probabilities from Choice Based Samples

基于选择结果抽样的选择概率估计

Ti-H CONCERN of this paper is the estimation of the parameters of a probabilistic choice model when choices rather than decision makers are sampled. Existing estimation methods presuppose an exogeneous sampling process, that is one in which a sequence of decision makers are drawn and their choice behaviors observed. In contrast, in choice based sampling processes, a sequence of chosen alternatives are drawn and the characteristics of the decision makers selecting those…

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