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The book presents in a rigorous and thorough manner the main elements of Charles Manski's research on partial identification of probability distributions. The approach to inference that runs throughout the book is deliberately conservative and thoroughly nonparametric. There is an enormous scope for fruitful inference using data and assumptions that partially identify population parameters.
"This book addresses key aspects of this broad question, exploring and partially resolving pervasive problems of identification and statistical inference that arise when studying treatment response and making treatment choices. Charles Manski addresses the treatment-choice problem directly using Abraham Wald's statistical decision theory, taking into account the ambiguity that arises from identification problems under weak but justifiable assumptions."--BOOK JACKET.
Specially selected from The New Palgrave Dictionary of Economics 2nd edition, each article within this compendium covers the fundamental themes within the discipline and is written by a leading practitioner in the field. A handy reference tool.
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, with much debate about whether some covariate is or is not a "valid instrument" in an application of interest. There is therefore good reason to consider weaker but more credible assumptions. assumptions. To this end, we introduce monotone instrumental variable (MIV) A particularly interesting special case of an MIV assumption is monotone treatment selection (MTS). IV and MIV assumptions may be imposed alone or in combination with other assumptions. We study the identifying power of MIV assumptions in three informational settings: MIV alone; MIV combined with the classical linear response assumption; MIV combined with the monotone treatment response (MTR) assumption. We apply the results to the problem of inference on the returns to schooling. We analyze wage data reported by white male respondents to the National Longitudinal Survey of Youth (NLSY) and use the respondent's AFQT score as an MIV. We find that this MIV assumption has little identifying power when imposed alone. However combining the MIV assumption with the MTR and MTS assumptions yields fairly tight bounds on two distinct measures of the returns to schooling.
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
The author draws on examples from a range of disciplines to provide social and behavioural scientists with a toolkit for finding bounds when predicting behaviours based upon nonexperimental and experimental data.
This is the first systematic exposition of random sets theory since Matheron (1975), with full proofs, exhaustive bibliographies and literature notes Interdisciplinary connections and applications of random sets are emphasized throughout the book An extensive bibliography in the book is available on the Web at http://liinwww.ira.uka.de/bibliography/math/random.closed.sets.html, and is accompanied by a search engine
This book shows how the Bayesian approach to inference is applicable to partially identified models (PIMs) and examines the performance of Bayesian procedures in partially identified contexts. Drawing on his many years of research in this area, the author presents a thorough overview of the statistical theory, properties, and applications of PIM
This book is a full-scale exposition of Charles Manski's new methodology for analyzing empirical questions in the social sciences. He recommends that researchers first ask what can be learned from data alone, and then ask what can be learned when data are combined with credible weak assumptions. Inferences predicated on weak assumptions, he argues, can achieve wide consensus, while ones that require strong assumptions almost inevitably are subject to sharp disagreements. Building on the foundation laid in the author's Identification Problems in the Social Sciences (Harvard, 1995), the book's fifteen chapters are organized in three parts. Part I studies prediction with missing or otherwise incomplete data. Part II concerns the analysis of treatment response, which aims to predict outcomes when alternative treatment rules are applied to a population. Part III studies prediction of choice behavior. Each chapter juxtaposes developments of methodology with empirical or numerical illustrations. The book employs a simple notation and mathematical apparatus, using only basic elements of probability theory.