In nonparametric and high-dimensional statistical models, the classical Gauss-Fisher-Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics.

Who decides how official statistics are produced? Do politicians have control or are key decisions left to statisticians in independent statistical agencies? Interviews with statisticians in Australia, Canada, Sweden, the UK and the USA were conducted to get insider perspectives on the nature of decision making in government statistical administration. While the popular adage suggests there are 'lies, damned lies and statistics', this research shows that official statistics in liberal democracies are far from mistruths; they are consistently insulated from direct political interference. Yet, a range of subtle pressures and tensions exist that governments and statisticians must manage. The power over statistics is distributed differently in different countries, and this book explains why. Differences in decision-making powers across countries are the result of shifting pressures politicians and statisticians face to be credible, and the different national contexts that provide distinctive institutional settings for the production of government numbers.

Factor models have become the most successful tool in the analysis and forecasting of high-dimensional time series. This monograph provides an extensive account of the so-called General Dynamic Factor Model methods. The topics covered include: asymptotic representation problems, estimation, forecasting, identification of the number of factors, identification of structural shocks, volatility analysis, and applications to macroeconomic and financial data.

Computable general equilibrium (CGE) models play an important role in supporting public-policy making on such issues as trade, climate change and taxation. This significantly revised volume, keeping pace with the next-generation standard CGE model, is the only undergraduate-level introduction of its kind. The volume utilizes a graphical approach to explain the economic theory underlying a CGE model, and provides results from simple, small-scale CGE models to illustrate the links between theory and model outcomes. Its eleven hands-on exercises introduce modelling techniques that are applied to real-world economic problems. Students learn how to integrate their separate fields of economic study into a comprehensive, general equilibrium perspective as they develop their skills as producers or consumers of CGE-based analysis.

As one of the first texts to take a behavioral approach to macroeconomic expectations, this book introduces a new way of doing economics. Roetheli uses cognitive psychology in a bottom-up method of modeling macroeconomic expectations. His research is based on laboratory experiments and historical data, which he extends to real-world situations. Pattern extrapolation is shown to be the key to understanding expectations of inflation and income. The quantitative model of expectations is used to analyze the course of inflation and nominal interest rates in a range of countries and historical periods. The model of expected income is applied to the analysis of business cycle phenomena such as the great recession in the United States. Data and spreadsheets are provided for readers to do their own computations of macroeconomic expectations. This book offers new perspectives in many areas of macro and financial economics.

This is the perfect (and essential) supplement for all econometrics classes--from a rigorous first undergraduate course, to a first master's, to a PhD course.
Explains what is going on in textbooks full of proofs and formulas
Offers intuition, skepticism, insights, humor, and practical advice (dos and don'ts)
Contains new chapters that cover instrumental variables and computational considerations
Includes additional information on GMM, nonparametrics, and an introduction to wavelets

For all its elaborate theories and models, economics always reduces to comparisons. Should we build A rather than B? Will I be better off if I eat D rather than C? How much will it cost me to produce F instead of E? At root, the ultimate goal of economics is simple: assessing the alternatives and finding the best possible outcome. This basic mathematical concept underlies all introductions to the field of economics, yet as advanced students progress through the discipline, they often lose track of this foundational idea when presented with real-world complications and uncertainty. In Competitive Agents in Certain and Uncertain Markets, Robert G. Chambers develops an integrated analytic framework for treating consumer, producer, and market equilibrium analyses as special cases of a generic optimization problem. He builds on lessons learned by all beginning students of economics to show how basic concepts can still be applied even in complex and highly uncertain conditions. Drawing from optimization theory, Chambers demonstrates how the same unified mathematical framework applies to both stochastic and non-stochastic decision settings. The book borrows from both convex and variational analysis and gives special emphasis to differentiability, conjugacy theory, and Fenchel's Duality Theorem. Throughout, Chambers includes practical examples, problems, and exercises to make abstract material accessible. Bringing together essential theoretical tools for understanding decision-making under uncertainty, Competitive Agents in Certain and Uncertain Markets provides a unified framework for analyzing a broad range of microeconomic decisions. This book will be an invaluable resource for advanced graduate students and scholars of microeconomic theory.

Nanak Kakwani and Hyun Hwa Son make use of social welfare functions to derive indicators of development relevant to specific social objectives, such as poverty- and inequality-reduction. Arguing that the measurement of development cannot be value-free, the authors assert that if indicators of development are to have policy relevance, they must be assessed on the basis of the social objectives in question. This study develops indicators that are sensitive to both the level and the distribution of individuals' capabilities. The idea of the social welfare function, defined in income space, is extended to the concept of the social well-being function, defined in capability space. Through empirical analysis from selected developing countries, with a particular focus on Brazil, the authors shape techniques appropriate to the analysis of development in different dimensions. The focus of this evidence-based policy analysis is to evaluate alternative policies affecting the capacities of people to enjoy a better life.

* A useful guide to financial product modeling and to minimizing business risk and uncertainty * Looks at wide range of financial assets and markets and correlates them with enterprises' profitability * Introduces advanced and novel machine learning techniques in finance such as Support Vector Machine, Neural Networks, Random Forest, K-Nearest Neighbors, Extreme Learning Machine, Deep Learning Approaches and applies them to analyze finance data sets * Real world applicable examples to further understanding

If you know a little bit about financial mathematics but don't yet know a lot about programming, then C++ for Financial Mathematics is for you. C++ is an essential skill for many jobs in quantitative finance, but learning it can be a daunting prospect. This book gathers together everything you need to know to price derivatives in C++ without unnecessary complexities or technicalities. It leads the reader step-by-step from programming novice to writing a sophisticated and flexible financial mathematics library. At every step, each new idea is motivated and illustrated with concrete financial examples. As employers understand, there is more to programming than knowing a computer language. As well as covering the core language features of C++, this book teaches the skills needed to write truly high quality software. These include topics such as unit tests, debugging, design patterns and data structures. The book teaches everything you need to know to solve realistic financial problems in C++. It can be used for self-study or as a textbook for an advanced undergraduate or master's level course.

Space is a crucial variable in any economic activity. Spatial Economics is the branch of economics that explicitly aims to incorporate the space dimension in the analysis of economic phenomena. From its beginning in the last century, Spatial Economics has contributed to the understanding of the economy by developing plenty of theoretical models as well as econometric techniques having the "space" as a core dimension of the analysis.This edited volume addresses the complex issue of Spatial Economics from an applied point of view. This volume is part of a more complex project including another edited volume (Spatial Economics Volume I: Theory) collecting original papers which address Spatial Economics from a theoretical perspective.

This book offers a useful combination of probabilistic and statistical tools for analyzing nonlinear time series. Key features of the book include a study of the extremal behavior of nonlinear time series and a comprehensive list of nonlinear models that address different aspects of nonlinearity. Several inferential methods, including quasi likelihood methods, sequential Markov Chain Monte Carlo Methods and particle filters, are also included so as to provide an overall view of the available tools for parameter estimation for nonlinear models. A chapter on integer time series models based on several thinning operations, which brings together all recent advances made in this area, is also included.

Readers should have attended a prior course on linear time series, and a good grasp of simulation-based inferential methods is recommended. This book offers a valuable resource for second-year graduate students and researchers in statistics and other scientific areas who need a basic understanding of nonlinear time series.

Space is a crucial variable in any economic activity. Spatial Economics is the branch of economics that explicitly aims to incorporate the space dimension in the analysis of economic phenomena. From its beginning in the last century, Spatial Economics has contributed to the understanding of the economy by developing plenty of theoretical models as well as econometric techniques having the "space" as a core dimension of the analysis. This edited volume addresses the complex issue of Spatial Economics from a theoretical point of view. This volume is part of a more complex project including another edited volume (Spatial Economics Volume II: Applications) collecting original papers which address Spatial Economics from an applied perspective.

This book examines whether continuous-time models in frictionless financial economies can be well approximated by discrete-time models. It specifically looks to answer the question: in what sense and to what extent does the famous Black-Scholes-Merton (BSM) continuous-time model of financial markets idealize more realistic discrete-time models of those markets? While it is well known that the BSM model is an idealization of discrete-time economies where the stock price process is driven by a binomial random walk, it is less known that the BSM model idealizes discrete-time economies whose stock price process is driven by more general random walks. Starting with the basic foundations of discrete-time and continuous-time models, David M. Kreps takes the reader through to this important insight with the goal of lowering the entry barrier for many mainstream financial economists, thus bringing less-technical readers to a better understanding of the connections between BSM and nearby discrete-economies.

This book examines whether continuous-time models in frictionless financial economies can be well approximated by discrete-time models. It specifically looks to answer the question: in what sense and to what extent does the famous Black-Scholes-Merton (BSM) continuous-time model of financial markets idealize more realistic discrete-time models of those markets? While it is well known that the BSM model is an idealization of discrete-time economies where the stock price process is driven by a binomial random walk, it is less known that the BSM model idealizes discrete-time economies whose stock price process is driven by more general random walks. Starting with the basic foundations of discrete-time and continuous-time models, David M. Kreps takes the reader through to this important insight with the goal of lowering the entry barrier for many mainstream financial economists, thus bringing less-technical readers to a better understanding of the connections between BSM and nearby discrete-economies.

How to Divide When There Isn't Enough develops a rigorous yet accessible presentation of the state-of-the-art for the adjudication of conflicting claims and the theory of taxation. It covers all aspects one may wish to know about claims problems: the most important rules, the most important axioms, and how these two sets are related. More generally, it also serves as an introduction to the modern theory of economic design, which in the last twenty years has revolutionized many areas of economics, generating a wide range of applicable allocations rules that have improved people's lives in many ways. In developing the theory, the book employs a variety of techniques that will appeal to both experts and non-experts. Compiling decades of research into a single framework, William Thomson provides numerous applications that will open a large number of avenues for future research.

Focusing on Bayesian approaches and computations using analytic and simulation-based methods for inference, Time Series: Modeling, Computation, and Inference, Second Edition integrates mainstream approaches for time series modeling with significant recent developments in methodology and applications of time series analysis. It encompasses a graduate-level account of Bayesian time series modeling, analysis and forecasting, a broad range of references to state-of-the-art approaches to univariate and multivariate time series analysis, and contacts research frontiers in multivariate time series modeling and forecasting. It presents overviews of several classes of models and related methodology for inference, statistical computation for model fitting and assessment, and forecasting. It explores the connections between time- and frequency-domain approaches and develop various models and analyses using Bayesian formulations and computation, including use of computations based on Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods. It illustrates the models and methods with examples and case studies from a variety of fields, including signal processing, biomedicine, environmental science, and finance. Along with core models and methods, the book represents state-of-the art approaches to analysis and forecasting in challenging time series problems. It also demonstrates the growth of time series analysis into new application areas in recent years, and contacts recent and relevant modeling developments and research challenges. New in the second edition: Expanded on aspects of core model theory and methodology. Multiple new examples and exercises. Detailed development of dynamic factor models. Updated discussion and connections with recent and current research frontiers.

Modern economies are full of uncertainties and risk. Economics studies resource allocations in an uncertain market environment. As a generally applicable quantitative analytic tool for uncertain events, probability and statistics have been playing an important role in economic research. Econometrics is statistical analysis of economic and financial data. In the past four decades or so, economics has witnessed a so-called 'empirical revolution' in its research paradigm, and as the main methodology in empirical studies in economics, econometrics has been playing an important role. It has become an indispensable part of training in modern economics, business and management.This book develops a coherent set of econometric theory, methods and tools for economic models. It is written as a textbook for graduate students in economics, business, management, statistics, applied mathematics, and related fields. It can also be used as a reference book on econometric theory by scholars who may be interested in both theoretical and applied econometrics.

The "Theory of Macrojustice", introduced by S.-C. Kolm, is a stimulating contribution to the debate on the macroeconomic income distribution. The solution called "Equal Labour Income Equalisation" (ELIE) is the result of a three stages construction: collective agreement on the scheme of labour income redistribution, collective agreement on the degree of equalisation to be chosen in that framework, individual freedom to exploit his--her personal productive capicities (the source of labour income and the sole basis for taxation). This book is organised as a discussion around four complementary themes: philosophical aspects of macrojustice, economic analysis of macrojustice, combination of ELIE with other targeted tranfers, econometric evaluations of ELIE.

From the 1980s onward, income inequality increased in many advanced countries. It is very difficult to account for the rise in income inequality using the standard labour supply/demand explanation. Fiscal redistribution has become less effective in compensating increasing inequalities since the 1990s. Some of the basic features of redistribution can be explained through the optimal tax framework developed by J. A. Mirrlees in 1971. This Element surveys some of the earlier results in linear and nonlinear taxation and produces some new numerical results. Given the key role of capital income in the overall income inequality, it also considers the optimal taxation of capital income. It examines empirically the relationship between the extent of redistribution and the components of the Mirrlees framework. The redistributive role of factors such as publicly provided private goods, public employment, endogenous wages in the overlapping generations model and income uncertainty are analysed.

Bayesian econometric methods have enjoyed an increase in popularity in recent years. Econometricians, empirical economists, and policymakers are increasingly making use of Bayesian methods. This handbook is a single source for researchers and policymakers wanting to learn about Bayesian methods in specialized fields, and for graduate students seeking to make the final step from textbook learning to the research frontier. It contains contributions by leading Bayesians on the latest developments in their specific fields of expertise. The volume provides broad coverage of the application of Bayesian econometrics in the major fields of economics and related disciplines, including macroeconomics, microeconomics, finance, and marketing. It reviews the state of the art in Bayesian econometric methodology, with chapters on posterior simulation and Markov chain Monte Carlo methods, Bayesian nonparametric techniques, and the specialized tools used by Bayesian time series econometricians such as state space models and particle filtering. It also includes chapters on Bayesian principles and methodology.

In recent years, interest in rigorous impact evaluation has grown tremendously in policy-making, economics, public health, social sciences and international relations. Evidence-based policy-making has become a recurring theme in public policy, alongside greater demands for accountability in public policies and public spending, and requests for independent and rigorous impact evaluations for policy evidence. Froelich and Sperlich offer a comprehensive and up-to-date approach to quantitative impact evaluation analysis, also known as causal inference or treatment effect analysis, illustrating the main approaches for identification and estimation: experimental studies, randomization inference and randomized control trials (RCTs), matching and propensity score matching and weighting, instrumental variable estimation, difference-in-differences, regression discontinuity designs, quantile treatment effects, and evaluation of dynamic treatments. The book is designed for economics graduate courses but can also serve as a manual for professionals in research institutes, governments, and international organizations, evaluating the impact of a wide range of public policies in health, environment, transport and economic development.

Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including: Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does calibration make sense? This manual covers the practicalities of modeling local volatility, stochastic volatility, local-stochastic volatility, and multi-asset stochastic volatility. In the course of this exploration, the author, Risk's 2009 Quant of the Year and a leading contributor to volatility modeling, draws on his experience as head quant in Societe Generale's equity derivatives division. Clear and straightforward, the book takes readers through various modeling challenges, all originating in actual trading/hedging issues, with a focus on the practical consequences of modeling choices.