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.

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Econometric Analysis of Cross Section and Panel Data

Regressions explaining the wage rates of white males, black males, and white females are used to analyze the white-black wage differential among men and the male-female wage differential among whites A distinction is drawn between reduced form and structural wage equations, and both are estimated They are shown to have very different implications for analyzing the white-black and male-female wage differentials When the two sets of estimates are synthesized, they jointly imply that 70 percent of the overall race differential and 100 percent of the overall sex differential are ultimately attributable to discrimination of various sorts

https://www.jstor.org/stable/pdfplus/144855.pdf

Wage Discrimination: Reduced Form and Structural Estimates

It is argued that P-values and the tests based upon them give unsatisfactory results, especially in large samples. It is shown that, in regression, when there are many candidate independent variables, standard variable selection procedures can give very misleading results. Also, by selecting a single model, they ignore model uncertainty and so underestimate the uncertainty about quantities of interest. The Bayesian approach to hypothesis testing, model selection, and accounting for model uncertainty is presented. Implementing this is straightforward through the use of the simple and accurate BIC approximation, and it can be done using the output from standard software. Specific results are presented for most of the types of model commonly used in sociology. It is shown that this approach overcomes the difficulties with P-values and standard model selection procedures based on them. It also allows easy comparison of nonnested models, and permits the quantification of the evidence for a null hypothesis of interest, such as a convergence theory or a hypothesis about societal norms.

https://www.jstor.org/stable/pdfplus/271063.pdf

Bayesian Model Selection in Social Research

Higher education as a filter

SUMMARY A general class of regression models for ordinal data is developed and discussed. These models utilize the ordinal nature of the data by describing various modes of stochastic ordering and this eliminates the need for assigning scores or otherwise assuming cardinality instead of ordinality. Two models in particular, the proportional odds and the proportional hazards models are likely to be most useful in practice because of the simplicity of their interpretation. These linear models are shown to be multivariate extensions of generalized linear models. Extensions to non-linear models are discussed and it is shown that even here the method of iteratively reweighted least squares converges to the maximum likelihood estimate, a property which greatly simplifies the necessary computation. Applications are discussed with the aid of examples.

https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1980.tb01109.x

Regression Models for Ordinal Data

Walton, John 1966a "Substance and artifact: the current status of research on community power structure." American Journal of Sociology 71 (January) :430-8. 1966b "Discipline, method and community power: a note on the sociology of knowledge." American Sociological Review 31 (October): 684-99. 1967 "The vertical axis of community organization and the structure of power." Southwestern Social Science Quarterly 48 (December) :353-68. Wolfinger, Raymond E. 1962 "Reputation and reality in the study of community power." American Sociological Review 25 (October) :636-44.

Some Methodological Issues in Cohort Analysis of Archival Data

Current estimates of the contribution of education to economic growth have been questioned because they ignore the interaction of education with ability. Whether the neglect of ability differences in the analyses of the income-education relationship results in estimates that are too high was considered in an earlier paper by one of the authors (Griliches 1970), and a negative answer was conjectured. In this paper, we pursue this question a bit further, using a new and larger body of data. Unfortunately, a definitive answer to this question is hampered both by the vagueness and elasticity of "education" and "ability" as analytical concepts and by the lack of data on early (preschooling) intelligence. The data examined in this paper are based on a 1964 sample of U.S. military veterans. The variables measured include scores on a mental ability test, indicators of parental status, region of residence while growing up, school years completed before service, and school years completed during or after service. These have allowed us to inquire into the separate effects of parental background, intelligence, and schooling. The basic problem and analytical framework can be set out very simply. Let income be a linear function of education and ability, or, Y a + P1E + P(2G + u, where Y is income, E is education, G is ability,

Education, Income, and Ability

A hierarchical logistic regression model is proposed for studying data with group structure and a binary response variable. The group structure is defined by the presence of micro observations embedded within contexts (macro observations), and the specification is at both of these levels. At the first (micro) level, the usual logistic regression model is defined for each context. The same regressors are used in each context, but the micro regression coefficients are free to vary over contexts. At the second level, the micro coefficients are treated as functions of macro regressors. An empirical Bayes estimation procedure is proposed for estimating the micro and macro coefficients. Explicit formulas are provided that are computationally feasible for large-scale data analyses; these include an algorithm for finding the maximum likelihood estimates of the covariance components representing within— and between—macro-equation error variability. The methodology is applied to World Fertility Survey data...

The Hierarchical Logistic Regression Model for Multilevel Analysis

A general linear multilevel model and its estimation are described and illustrated empirically. The specification of a multilevel linear model within the covariance component framework was rendered. This model is appropriate for a wide range of applications in contextual analysis because it allows for macro as well as micro errors. Then an estimation procedure the restricted maximum likelihood/Bayes (REML/Bayes) was proposed and described for this multilevel model. Finally an extended empirical example was presented with the primary purpose of illustrating the use of the statistical methodology in conjunction with a meaningful substantive problem not to carry out a critical test of the underlying substantive theory and not to demonstrate the general superiority of the proposed estimation procedure. The example suggests that the REML/Bayes estimation procedure may be appropriate inasmuch as the results extracted with REML/Bayes are more consistent with theoretical anticipations than those extracted with ordinary least squares or estimated generalized least squares. The methodology presented by no means exhausts the subject of multilevel estimation. There is a need for estimation procedures to handle discrete micro response variables systems of micro-structural equations and other generalizations. Work is currently proceeding on some of these extensions of the multilevel linear model as the goal of sound estimation procedures for generalized multilevel models is worthwhile and by no means esoteric. It may be hard for researchers to find contextual effects unless they use efficient and appropriate estimation techniques.

Contextual analysis through the multilevel linear model.

In many regions of Asia and Africa, consanguineous marriages currently account for approximately 20 to 50% of all unions, and preliminary observations indicate that migrants from these areas continue to contract marriages with close relatives when resident in North America and Western Europe. Consanguinity is associated with increased gross fertility, due at least in part to younger maternal age at first livebirth. Morbidity and mortality also may be elevated, resulting in comparable numbers of surviving offspring in consanguineous and nonconsanguineous families. With advances in medicine and public health, genetic disorders will account for an increased proportion of disease worldwide. Predictably, this burden will fall more heavily on countries and communities in which consanguinity is strongly favored, as the result of the expression of deleterious recessive genes. However, studies conducted in such populations indicate that the adverse effects associated with inbreeding are experienced by a minority of families.

https://science.sciencemag.org/content/sci/252/5007/789.full.pdf

William M. Mason

Papers

Some Methodological Issues in Cohort Analysis of Archival Data

Education, Income, and Ability

The Hierarchical Logistic Regression Model for Multilevel Analysis

Contextual analysis through the multilevel linear model.

Reproductive behavior and health in consanguineous marriages.