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Econometrics & Statistical Methods

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This book offers a unified, comprehensive, and up-to-date treatment of analytical and numerical tools for solving dynamic economic problems. The focus is on introducing recursive methods—an important part of every economist’s set of tools—and readers will learn to apply recursive methods to a variety of dynamic economic problems. The book is notable for its combination of theoretical foundations and numerical methods. Each topic is first described in theoretical terms, with explicit definitions and rigorous proofs; numerical methods and computer codes to implement these methods follow. Drawing on the latest research, the book covers such cutting-edge topics as asset price bubbles, recursive utility, robust control, policy analysis in dynamic New Keynesian models with the zero lower bound on interest rates, and Bayesian estimation of dynamic stochastic general equilibrium (DSGE) models.

The book first introduces the theory of dynamical systems and numerical methods for solving dynamical systems, and then discusses the theory and applications of dynamic optimization. The book goes on to treat equilibrium analysis, covering a variety of core macroeconomic models, and such additional topics as recursive utility (increasingly used in finance and macroeconomics), dynamic games, and recursive contracts. The book introduces Dynare, a widely used software platform for handling a range of economic models; readers will learn to use Dynare for numerically solving DSGE models and performing Bayesian estimation of DSGE models. Mathematical appendixes present all the necessary mathematical concepts and results. Matlab codes used to solve examples are indexed and downloadable from the book’s website. A solutions manual for students is available for sale from the MIT Press; a downloadable instructor’s manual is available to qualified instructors.

Financial Modeling is now the standard text for explaining the implementation of financial models in Excel. This long-awaited fourth edition maintains the “cookbook” features and Excel dependence that have made the previous editions so popular. As in previous editions, basic and advanced models in the areas of corporate finance, portfolio management, options, and bonds are explained with detailed Excel spreadsheets. Sections on technical aspects of Excel and on the use of Visual Basic for Applications (VBA) round out the book to make Financial Modeling a complete guide for the financial modeler.

The new edition of Financial Modeling includes a number of innovations. A new section explains the principles of Monte Carlo methods and their application to portfolio management and exotic option valuation. A new chapter discusses term structure modeling, with special emphasis on the Nelson-Siegel model. The discussion of corporate valuation using pro forma models has been rounded out with the introduction of a new, simple model for corporate valuation based on accounting data and a minimal number of valuation parameters.

Praise for earlier editions
“Financial Modeling belongs on the desk of every finance professional. Its no-nonsense, hands-on approach makes it an indispensable tool.”
—Hal R. Varian, Dean, School of Information Management and Systems, University of California, Berkeley

Financial Modeling is highly recommended to readers who are interested in an introduction to basic, traditional approaches to financial modeling and analysis, as well as to those who want to learn more about applying spreadsheet software to financial analysis."
—Edward Weiss, Journal of Computational Intelligence in Finance

“Benninga has a clear writing style and uses numerous illustrations, which make this book one of the best texts on using Excel for finance that I've seen.”
—Ed McCarthy, Ticker Magazine

This book provides an innovative, integrated, and methodical approach to understanding complex financial models, integrating topics usually presented separately into a comprehensive whole. The book brings together financial models and high-level mathematics, reviewing the mathematical background necessary for understanding these models organically and in context. It begins with underlying assumptions and progresses logically through increasingly complex models to operative conclusions. Readers who have mastered the material will gain the tools needed to put theory into practice and incorporate financial models into real-life investment, financial, and business scenarios.

Modern finance’s most bothersome shortcoming is that the two basic models for building an optimal investment portfolio, Markowitz’s mean-variance model and Sharpe and Treynor’s Capital Asset Pricing Model (CAPM), fall short when we try to apply them using Excel Solver. This book explores these two models in detail, and for the first time in a textbook the Black-Litterman model for building an optimal portfolio constructed from a small number of assets (developed at Goldman Sachs) is thoroughly presented. The model’s integration of personal views and its application using Excel templates are demonstrated. The book also offers innovative presentations of the Modigliani–Miller model and the Consumption-Based Capital Asset Pricing Model (CCAPM). Problems at the end of each chapter invite the reader to put the models into immediate use. Fundamental Models in Financial Theory is suitable for classroom use or as a reference for finance practitioners.

Downloadable instructor resources available for this title: solution manual

A Self-Contained Approach

This unique introduction to econometrics provides undergraduate students with a command of regression analysis in one semester, enabling them to grasp the empirical literature and undertake serious quantitative projects of their own. It does not assume any previous exposure to probability and statistics but does discuss the concepts in these areas that are essential for econometrics. The bulk of the textbook is devoted to regression analysis, from simple to advanced topics. Students will gain an intuitive understanding of the mathematical concepts; Java applet simulations on the book’s website demonstrate how the algebraic equations are derived in the text and are designed to reinforce the important concepts.

After presenting the essentials of probability and statistics, the book covers simple regression analysis, multiple regression analysis, and advanced topics including heteroskedasticity, autocorrelation, large sample properties, instrumental variables, measurement error, omitted variables, panel data, simultaneous equations, and binary/truncated dependent variables. Two optional chapters treat additional probability and statistics topics. Each chapter offers examples, prep problems (bringing students “up to speed” at the beginning of a chapter), review questions, and exercises. An accompanying website offers students easy access to Java simulations and data sets (available in EViews, Stata, and Excel files). After a single semester spent mastering the material presented in this book, students will be prepared to take any of the many elective courses that use econometric techniques.

• Requires no background in probability and statistics
• Regression analysis focus
• “Econometrics lab” with Java applet simulations on accompanying Website

Downloadable instructor resources available for this title: solution manual, slides, and handouts

This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems.

The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective.
The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.

This text offers a comprehensive presentation of the mathematics required to tackle problems in economic analyses. To give a better understanding of the mathematical concepts, the text follows the logic of the development of mathematics rather than that of an economics course. The only prerequisite is high school algebra, but the book goes on to cover all the mathematics needed for undergraduate economics. It is also a useful reference for graduate students. After a review of the fundamentals of sets, numbers, and functions, the book covers limits and continuity, the calculus of functions of one variable, linear algebra, multivariate calculus, and dynamics. To develop the student’s problem-solving skills, the book works through a large number of examples and economic applications. This streamlined third edition offers an array of new and updated examples. Additionally, lengthier proofs and examples are provided on the book’s website. The book and the Web material are cross-referenced in the text. A student solutions manual is available, and instructors can access online instructor’s material that includes solutions and PowerPoint slides. 

Downloadable instructor resources available for this title: instuctor's manual

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.

Downloadable instructor resources available for this title: solutions to all problems in the text

A Math Tool Kit

This text offers an accessible yet rigorous development of many of the fields of mathematics necessary for success in investment and quantitative finance, covering topics applicable to portfolio theory, investment banking, option pricing, investment, and insurance risk management. The approach emphasizes the mathematical framework provided by each mathematical discipline, and the application of each framework to the solution of finance problems. It emphasizes the thought process and mathematical approach taken to develop each result instead of the memorization of formulas to be applied (or misapplied) automatically. The objective is to provide a deep level of understanding of the relevant mathematical theory and tools that can then be effectively used in practice, to teach students how to “think in mathematics” rather than simply to do mathematics by rote. Each chapter covers an area of mathematics such as mathematical logic, Euclidean and other spaces, set theory and topology, sequences and series, probability theory, and calculus, in each case presenting only material that is most important and relevant for quantitative finance. Each chapter includes finance applications that demonstrate the relevance of the material presented. Problem sets are offered on both the mathematical theory and the finance applications sections of each chapter. The logical organization of the book and the judicious selection of topics make the text customizable for a number of courses. The development is self-contained and carefully explained to support disciplined independent study as well. A solutions manual for students provides solutions to the book’s Practice Exercises; an instructor’s manual offers solutions to the Assignment Exercises as well as other materials.

Downloadable instructor resources available for this title: instructor's manual

The field of forest economics has expanded rapidly in the last two decades, and yet there exists no up-to-date textbook for advanced undergraduate-graduate level use or rigorous reference work for professionals. Economics of Forest Resources fills these gaps, offering a comprehensive technical survey of the field with special attention to recent developments regarding policy instrument choice and uncertainty. It covers all areas in which mathematical models have been used to explain forest owner and user incentives and government behavior, introducing the reader to the rigor needed to think through the consequences of policy instruments. Technically difficult concepts are presented with a unified and progressive approach; an appendix outlines the basic concepts from calculus needed to understand the models and results developed. The book first presents the historical and classic models that every student or researcher in forest economics must know, including Faustman and Hartman approaches, public goods, spatial interdependence, two period life-cycle models, and overlapping generations problems. It then discusses topics including policy instrument choice, deforestation, biodiversity conservation, and age-class based forest modeling. Finally, it surveys such advanced topics as uncertainty in two period models, catastrophic risk, stochastic control problems, deterministic optimal control, and stochastic and deterministic dynamic programming approaches. Boxes with empirical content illustrating applications of the theoretical material appear throughout. Each chapter is self-contained, allowing the reader, student, or instructor to use the text according to individual needs.

Theory and Computation

This text provides an introduction to the modern theory of economic dynamics, with emphasis on mathematical and computational techniques for modeling dynamic systems. Written to be both rigorous and engaging, the book shows how sound understanding of the underlying theory leads to effective algorithms for solving real world problems. The material makes extensive use of programming examples to illustrate ideas. These programs help bring to life the abstract concepts in the text. Background in computing and analysis is offered for readers without programming experience or upper-level mathematics. Topics covered in detail include nonlinear dynamic systems, finite-state Markov chains, stochastic dynamic programming, stochastic stability and computation of equilibria. The models are predominantly nonlinear, and the emphasis is on studying nonlinear systems in their original form, rather than by means of rudimentary approximation methods such as linearization. Much of the material is new to economics and improves on existing techniques. For graduate students and those already working in the field, Economic Dynamics will serve as an essential resource.

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