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The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models
About: This article is published in Annals of Economic and Social Measurement.The article was published on 1976-10-01 and is currently open access. It has received 5063 citations till now. The article focuses on the topics: Truncation (statistics) & Errors-in-variables models.
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01 Jan 2001
TL;DR: This is the essential companion to Jeffrey Wooldridge's widely-used graduate text Econometric Analysis of Cross Section and Panel Data (MIT Press, 2001).
Abstract: The second edition of this acclaimed graduate text provides a unified treatment of two methods used in contemporary econometric research, cross section and data panel methods. By focusing on assumptions that can be given behavioral content, the book maintains an appropriate level of rigor while emphasizing intuitive thinking. The analysis covers both linear and nonlinear models, including models with dynamics and/or individual heterogeneity. In addition to general estimation frameworks (particular methods of moments and maximum likelihood), specific linear and nonlinear methods are covered in detail, including probit and logit models and their multivariate, Tobit models, models for count data, censored and missing data schemes, causal (or treatment) effects, and duration analysis. Econometric Analysis of Cross Section and Panel Data was the first graduate econometrics text to focus on microeconomic data structures, allowing assumptions to be separated into population and sampling assumptions. This second edition has been substantially updated and revised. Improvements include a broader class of models for missing data problems; more detailed treatment of cluster problems, an important topic for empirical researchers; expanded discussion of "generalized instrumental variables" (GIV) estimation; new coverage (based on the author's own recent research) of inverse probability weighting; a more complete framework for estimating treatment effects with panel data, and a firmly established link between econometric approaches to nonlinear panel data and the "generalized estimating equation" literature popular in statistics and other fields. New attention is given to explaining when particular econometric methods can be applied; the goal is not only to tell readers what does work, but why certain "obvious" procedures do not. The numerous included exercises, both theoretical and computer-based, allow the reader to extend methods covered in the text and discover new insights.
28,298 citations
TL;DR: In this article, the bias that results from using non-randomly selected samples to estimate behavioral relationships as an ordinary specification error or "omitted variables" bias is discussed, and the asymptotic distribution of the estimator is derived.
Abstract: Sample selection bias as a specification error This paper discusses the bias that results from using non-randomly selected samples to estimate behavioral relationships as an ordinary specification error or «omitted variables» bias. A simple consistent two stage estimator is considered that enables analysts to utilize simple regression methods to estimate behavioral functions by least squares methods. The asymptotic distribution of the estimator is derived.
23,995 citations
TL;DR: 2 general approaches that come highly recommended: maximum likelihood (ML) and Bayesian multiple imputation (MI) are presented and may eventually extend the ML and MI methods that currently represent the state of the art.
Abstract: Statistical procedures for missing data have vastly improved, yet misconception and unsound practice still abound. The authors frame the missing-data problem, review methods, offer advice, and raise issues that remain unresolved. They clear up common misunderstandings regarding the missing at random (MAR) concept. They summarize the evidence against older procedures and, with few exceptions, discourage their use. They present, in both technical and practical language, 2 general approaches that come highly recommended: maximum likelihood (ML) and Bayesian multiple imputation (MI). Newer developments are discussed, including some for dealing with missing data that are not MAR. Although not yet in the mainstream, these procedures may eventually extend the ML and MI methods that currently represent the state of the art.
10,568 citations
TL;DR: In this article, the authors proposed a global test statistic for multivariate data with missing values, that is, whether the missing data are missing completely at random (MCAR), that is whether missingness depends on the variables in the data set.
Abstract: A common concern when faced with multivariate data with missing values is whether the missing data are missing completely at random (MCAR); that is, whether missingness depends on the variables in the data set. One way of assessing this is to compare the means of recorded values of each variable between groups defined by whether other variables in the data set are missing or not. Although informative, this procedure yields potentially many correlated statistics for testing MCAR, resulting in multiple-comparison problems. This article proposes a single global test statistic for MCAR that uses all of the available data. The asymptotic null distribution is given, and the small-sample null distribution is derived for multivariate normal data with a monotone pattern of missing data. The test reduces to a standard t test when the data are bivariate with missing data confined to a single variable. A limited simulation study of empirical sizes for the test applied to normal and nonnormal data suggests th...
6,045 citations
TL;DR: In this paper, conditions for obtaining cosistency and asymptotic normality of a very general class of estimators (extremum estimators) are given to enable approximation of the SDF.
Abstract: Asymptotic distribution theory is the primary method used to examine the properties of econometric estimators and tests We present conditions for obtaining cosistency and asymptotic normality of a very general class of estimators (extremum estimators) Consistent asymptotic variance estimators are given to enable approximation of the asymptotic distribution Asymptotic efficiency is another desirable property then considered Throughout the chapter, the general results are also specialized to common econometric estimators (eg MLE and GMM), and in specific examples we work through the conditions for the various results in detail The results are also extended to two-step estimators (with finite-dimensional parameter estimation in the first step), estimators derived from nonsmooth objective functions, and semiparametric two-step estimators (with nonparametric estimation of an infinite-dimensional parameter in the first step) Finally, the trinity of test statistics is considered within the quite general setting of GMM estimation, and numerous examples are given
2,954 citations
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6,456 citations
1,907 citations
TL;DR: A good bit of attention has been paid to the effect of the price the woman assigns to her time as discussed by the authors, and it is argued that these time inputs constitute a predominant part of the costs of production of "child services", in particular while the child is young.
Abstract: Much recent economic literature on the socioeconomic factors affecting fertility has focused on the "price" of children. A good bit of attention has been paid to the effect of the price the woman assigns to her time. It is argued that these time inputs constitute a predominant part of the costs of production of "child services," in particular while the child is young.' The price of time has figured as a main determinant of almost every dimension of fertility: the amount of child services produced, the trade off between the quality of children and the number of children, the timing of the first child, and the spacing of the various children. The first endeavors were to associate the woman's price of time with the wage rate of working women who have the same market characteristics. An objection to this procedure is that the wage rate of working women is net of her general on-the-job training costs and that a true measure of the price women have to pay for having children should include the costs of depreciation of their market skills as well as the value of appreciation of their nonmarket skills (Michael and Lazear 1971). Furthermore, over three-fifths of all American married women as yet abstain from entering into the labor force in any given week, implying in their behavior that they reject the wage offered to them by the market as an adequate compensation for the loss of nonmarket productivity (Willis 1969 [rev. 1971]; Gronau
277 citations
TL;DR: Gronau as mentioned in this paper considered a group of persons who differ in their home price of time, but who are alike in having the same discount rate r, search cost C, and distribution (W) of market wage offers W.
Abstract: These comments on selectivity biases in wage comparisons stem from Gronau's paper on the subject in this issue of the Journal and assume that the reader is familiar with his paper. Consider a group of persons who differ in their home price of time W0, but who are alike in having the same discount rate r, search cost C, and distribution (W) of market wage offers W. I shall call such a group a "homogeneous" group. Let E be the mean market wage of persons in the group who, after a "sufficiently long period of search," are employed in the market; pw is the mean and a' the variance of their common wageoffer distribution; ,uwo is the mean and a2wo the variance of the home price of time W' in the group; and 0 is the group's labor-force participation rate. Then the search theory used by Gronau implies that:
170 citations