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

The brms package implements Bayesian multilevel models in R using the probabilistic programming language Stan. A wide range of distributions and link functions are supported, allowing users to fit - among others - linear, robust linear, binomial, Poisson, survival, ordinal, zero-inflated, hurdle, and even non-linear models all in a multilevel context. Further modeling options include autocorrelation of the response variable, user defined covariance structures, censored data, as well as meta-analytic standard errors. Prior specifications are flexible and explicitly encourage users to apply prior distributions that actually reflect their beliefs. In addition, model fit can easily be assessed and compared with the Watanabe-Akaike information criterion and leave-one-out cross-validation.

brms: An R Package for Bayesian Multilevel Models Using Stan

A unidimensional latent trait model for responses scored in two or more ordered categories is developed. This “Partial Credit” model is a member of the family of latent trait models which share the property of parameter separability and so permit “specifically objective” comparisons of persons and items. The model can be viewed as an extension of Andrich's Rating Scale model to situations in which ordered response alternatives are free to vary in number and structure from item to item. The difference between the parameters in this model and the “category boundaries” in Samejima's Graded Response model is demonstrated. An unconditional maximum likelihood procedure for estimating the model parameters is developed.

A Rasch Model for Partial Credit Scoring.

This paper focuses on developing and adapting statistical models of counts (nonnegative integers) in the context of panel data and using them to analyze the relationship between patents and R & D expenditures. Since a variety of other economic data come in the form of repeated counts of some individual actions or events, the methodology should have wide applications. The statistical models we develop are applications and generalizations of the Poisson distribution. Two important issues are (i) Given the panel nature of our data, how can we allow for separate persistent individual (fixed or random) effects? (ii) How does one introduce the equivalent of disturbances-in-the-equation into the analysis of Poisson and other discrete probability functions? The first problem is solved by conditioning on the total sum of outcomes over the observed years, while the second problem is solved by introducing an additional source of randomness, allowing the Poisson parameter to be itself randomly distributed, and compounding the two distributions. Lastly, we develop a test statistic for the presence of serial correlation when fixed effects estimators are used in nonlinear conditional models.

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Econometric Models for Count Data with an Application to the Patents-R&D Relationship

Conventional analyses of single spell duration models control for unobservables using a random effect estimator with the distribution of unobservables selected by ad hoc criteria. Both theoretical and empirical examples indicate that estimates of structural parameters obtained from conventional procedures are very sensitive to the choice of mixing distribution. Conventional procedures overparameterize duration models. We develop a consistent nonparametric maximum likelihood estimator for the distribution of unobservables and a computational strategy for implementing it. For a sample of unemployed workers our estimator produces estimates in concordance with standard search theory while conventional estimators do not. ECONOMIC THEORIES of search unemployment (Lippman and McCall [34]; Flinn and Heckman [14]), job turnover (Jovanovic [25]), mortality (Harris [17]), labor supply (Heckman and Willis [23]) and marital instability (Becker [3]) produce structural distributions for durations of occupancy of states. These theories generate qualitative predictions about the effects of changes in parameters on these structural distributions, and occasionally predict their functional forms.2 In order to test economic theories about durations and recover structural parameters, it is necessary to account for population variation in observed and unobserved variables unless it is assumed a priori that individuals are homogeneous.3 In every microeconomic study in which the hypothesis of heterogeneity is subject to test, it is not rejected. Temporally persistent unobserved components are an empirically important fact of life in microeconomic data (Heckman [19]). Since the appearance of papers by Silcock [39] and Blumen, Kogan, and McCarthy [5], social scientists have been aware that failure to adequately control for population heterogeneity can produce severe bias in structural estimates of duration models. Serious empirical analysts attempt to control for these unob

https://www.jstor.org/stable/pdfplus/1911491.pdf

A method for minimizing the impact of distributional assumptions in econometric models for duration data

The problem of obtaining consistent estimates for structural parameters in the presence of infinitely many incidental parameters was discussed first by Neyman and Scott (1948). In this paper a maximum-likelihood method based on the conditional distribution given minimal sufficient statistics for the incidental parameters is suggested. It is proved that conditional maximumlikelihood estimates in the regular case are consistent and asymptotically normally distributed with a simple asymptotic variance. The efficiency problem of this new estimator is discussed in particular with respect to some situations with ancillary information.

Asymptotic Properties of Conditional Maximum-Likelihood Estimators

The Rasch model is an item analysis model with logistic item characteristic curves of equal slope,i.e. with constant item discriminating powers. The proposed goodness of fit test is based on a comparison between difficulties estimated from different scoregroups and over-all estimates. Based on the within scoregroup estimates and the over-all estimates of item difficulties a conditional likelihood ratio is formed. It is shown that—2 times the logarithm of this ratio isx
 2-distributed when the Rasch model is true. The power of the proposed goodness of fit test is discussed for alternative models with logistic item characteristic curves, but unequal discriminating items from a scholastic aptitude test.

A goodness of fit test for the Rasch model.

For questionnaires with two answer categories, it has been proven in complete generality that if a minimal sufficient statistic exists for the individual parameter and if it is the same statistic for all values of the item parameters, then the raw score (or the number of correct answers) is the minimal sufficient statistic. It follows that the model must by of the Rasch type with logistic item characteristic curves and equal item-discriminating powers. This paper extends these results to multiple choice questionnaires. It is shown that the minimal sufficient statistic for the individual parameter is a function of the so-called score vector. It is also shown that the so-called equidistant scoring is the only scoring of a questionnaire that allows for a real valued sufficient statistic that is independent of the item parameters, if a certain ordering property for the sufficient statistic holds.

Sufficient Statistics and Latent Trait Models.

Discrete Statistical Models with Social Science Applications.

According to the preface, this is the first book of a series of two. The second book will deal with continuous statistical models. The main subjects of the present book are based on three developments: (1) the theory of exponential families, (2) the theory of log-linear models, and (3) the theory of logistic models in psychometrics. More specifically, some of the models dealt with are loglinear models for contingency tables, latent trait models, Markov chains, and the Bradley-Terry model for paired comparisons. Each chapter contains a large number of examples and exercises. Solutions to the exercises are, however, not given. Before presenting general conclusion about the book, each chapter will be reviewed separately. Overview The first chapter (Statistical Models; 8 pages) gives an introduction to the use of statistical models in the social sciences. Examples from a variety of social disciplines, including medicine, are given. The intention of chapter 2 (Preliminary Theory; 44 pages) is to refresh the reader’s knowledge of probability theory and statistics, which are applied in the rest of the book. The given survey of subjects serves this goal well, except for the treatment of statistical optimality theory. Optimality concepts are introduced; but they are hardly, if ever, used in the rest of the book. A more serious drawback of the

Erling B. Andersen

Papers

Asymptotic Properties of Conditional Maximum-Likelihood Estimators

A goodness of fit test for the Rasch model.

Sufficient Statistics and Latent Trait Models.

Discrete Statistical Models with Social Science Applications.

Discrete statistical models with social science applications