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This substantial volume has two principal objectives. First it provides an overview of the statistical foundations of Simulation-based inference. This includes the summary and synthesis of the many concepts and results extant in the theoretical literature, the different classes of problems and estimators, the asymptotic properties of these estimators, as well as descriptions of the different simulators in use. Second, the volume provides empirical and operational examples of SBI methods. Often what is missing, even in existing applied papers, are operational issues. Which simulator works best for which problem and why? This volume will explicitly address the important numerical and computational issues in SBI which are not covered comprehensively in the existing literature. Examples of such issues are: comparisons with existing tractable methods, number of replications needed for robust results, choice of instruments, simulation noise and bias as well as efficiency loss in practice.
This book introduces a new generation of statistical econometrics. After linear models leading to analytical expressions for estimators, and non-linear models using numerical optimization algorithms, the availability of high- speed computing has enabled econometricians to consider econometric models without simple analytical expressions. The previous difficulties presented by the presence of integrals of large dimensions in the probability density functions or in the moments can be circumvented by a simulation-based approach. After a brief survey of classical parametric and semi-parametric non-linear estimation methods and a description of problems in which criterion functions contain integrals, the authors present a general form of the model where it is possible to simulate the observations. They then move to calibration problems and the simulated analogue of the method of moments, before considering simulated versions of maximum likelihood, pseudo-maximum likelihood, or non-linear least squares. The general principle of indirect inference is presented and is then applied to limited dependent variable models and to financial series.
This book contains an up-to-date coverage of the last twenty years advances in Bayesian inference in econometrics, with an emphasis on dynamic models. It shows how to treat Bayesian inference in non linear models, by integrating the useful developments of numerical integration techniques based on simulations (such as Markov Chain Monte Carlo methods), and the long available analytical results of Bayesian inference for linear regression models. It thus covers a broad range of rather recent models for economic time series, such as non linear models, autoregressive conditional heteroskedastic regressions, and cointegrated vector autoregressive models. It contains also an extensive chapter on unit root inference from the Bayesian viewpoint. Several examples illustrate the methods.