Some Issue on Modelling Unobservable Variables

基于本质上不可观察的变量的模型经常出现在经济学、心理学和其他社会科学中。它们可能是由于被分析数据中的错误，或者是因为代理人的行为反应部分是由无法观察或测量的特征决定的。要从不可观测变量发挥作用的模型中获得有意义的见解，要么需要用更精确的测量来扩展数据集，要么需要开发一个分析框架，从现有数据中提取有关不可观测变量的相关信息。前者往往成本过高，甚至不可能实现，尤其是在研究大型联邦统计数据集的时候。该项目考察了在使用联邦数据的计量经济学研究中广泛使用的两种分析模型，即变量误差模型和享乐模型。从误差结构的各种假设、模型识别和统计推断的角度研究了变量误差模型。利用享乐模型，本项目建立了潜在特征和观察变量之间的对应关系。它还推导了有关系数的识别、估计和解释的条件。基于本质上不可观察的变量的模型经常出现在经济学、心理学和其他社会科学中。它们可能是由于被分析数据中的错误，或者是因为代理人的行为反应部分是由无法观察或测量的特征决定的。大型联邦数据集，例如由人口普查局或劳工统计局收集的数据，通常包含分组数据。出于保密或便于收集的原因，可能会要求一个家庭列出其收入范围，例如在1.5万美元至2.5万美元之间，而不是其确切收入。如果计量经济学分析使用这些数据，假设它们是精确的测量，结果可能会误导或错误。要从不可观测变量发挥作用的模型中获得有意义的见解，要么需要用更精确的测量来扩展数据集，要么需要开发一个分析框架，从现有数据中提取有关不可观测变量的相关信息。前一种方法更可取，但往往过于昂贵，特别是当研究人员使用大型联邦统计数据集时。本项目侧重于后一种更具分析性的策略。它开发了一个计量经济学框架，以提高基于联邦数据的研究的可靠性和有用性，其中潜在变量模型是合适的。

Models based on variables which are inherently unobservable are found very often in economics, psychology, and other social sciences. They might arise from errors in the data being analyzed, or because the behavioral responses of agents are in part determined by characteristics which cannot be observed or measured. Obtaining meaningful insight from models in which unobservable variables play a role requires either expanding the data set with more precise measurement or developing an analytical framework to extract the relevant information on the unobserved variables from the existing data. The former is often too costly or even impossible, particularly when large Federal statistical data sets are being studied. The project examines two analytical models widely used in econometric studies using Federal data, namely the errors-in-variables model and the hedonic model. The errors-in-variables model is studied from the standpoint of various assumptions regarding the structure of the errors, and model identification, and statistical inference. Using the hedonic model this project establishes correspondences between the underlying characteristics and the observed variables. It also derives conditions regarding identification, estimation, and interpretation of the coefficients. %%% Models based on variables which are inherently unobservable are found very often in economics, psychology, and other social sciences. They might arise from errors in the data being analyzed, or because the behavioral responses of agents are in part determined by characteristics which cannot be observed or measured. Large Federal data sets, such as those collected by the Bureau of the Census or the Bureau of Labor Statistics, often contain grouped data. For reasons of confidentiality or ease of collection, a household might be asked to list its income range, for instance between $15,000 and $25,000, rather than its exact income. If an econometric analysis uses these data on the assumption that they are precise measurements, the results can be misleading or erroneous. Obtaining meaningful insight from models in which unobservable variables play a role requires either expanding the data set with more precise measurement or developing an analytical framework to extract the relevant information on the unobserved variables from the existing data. The former approach is more desirable, but often too costly, particularly when a researcher is using large Federal statistical data sets. This project focuses on the latter, more analytical strategy. It develops an econometric framework to enhance the reliablity and usefulness of research based on Federal data where latent variable models are appropriate.