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The advent of electronic computing permits the empirical analysis of economic models of far greater subtlety and rigour than before, when many interesting ideas were not followed up because the calculations involved made this impracticable. The estimation and testing of these more intricate models is usually based on the method of Maximum Likelihood, which is a well-established branch of mathematical statistics. Its use in econometrics has led to the development of a number of special techniques; the specific conditions of econometric research moreover demand certain changes in the interpretation of the basic argument. This book is a self-contained introduction to this field. It consists of three parts. The first deals with general features of Maximum Likelihood methods; the second with linear and nonlinear regression; and the third with discrete choice and related micro-economic models. Readers should already be familiar with elementary statistical theory, with applied econometric research papers, or with the literature on the mathematical basis of Maximum Likelihood theory. They can also try their hand at some advanced econometric research of their own

The economics and statistics literature using computer simulation based methods has grown enormously over the past decades. Maximum Simulated Likelihood is a statistical tool useful for incorporating individual differences (called heterogeneity in the econometrics literature) and variations into a statistical analysis. Problems that can be intractable with traditional methods are solved using computer simulation integrated with classical methods. Instead of assuming that everyone responds to stimuli in the same way, allowances are made for the possibility that different decision makers will respond in different ways. The techniques can be applied to problems of individual choice, such as the choice of a transportation model, or choice among health care options, as well as to the problem of making financial and macroeconomic predictions. Contributors to the volume discuss alternative simulation methods that permit faster and more accurate inference, as well as applications of established methods.

The economics and statistics literature using computer simulation based methods has grown enormously over the past decades. Maximum Simulated Likelihood is a statistical tool useful for incorporating individual differences (called heterogeneity in the econometrics literature) and variations into a statistical analysis. Problems that can be intractable with traditional methods are solved using computer simulation integrated with classical methods. Instead of assuming that everyone responds to stimuli in the same way, allowances are made for the possibility that different decision makers will respond in different ways. The techniques can be applied to problems of individual choice, such as the choice of a transportation model, or choice among health care options, as well as to the problem of making financial and macroeconomic predictions. Contributors to the volume discuss alternative simulation methods that permit faster and more accurate inference, as well as applications of established methods.

This volume provides a practical introduction to the method of maximum likelihood as used in social science research. Ward and Ahlquist focus on applied computation in R and use real social science data from actual, published research. Unique among books at this level, it develops simulation-based tools for model evaluation and selection alongside statistical inference. The book covers standard models for categorical data as well as counts, duration data, and strategies for dealing with data missingness. By working through examples, math, and code, the authors build an understanding about the contexts in which maximum likelihood methods are useful and develop skills in translating mathematical statements into executable computer code. Readers will not only be taught to use likelihood-based tools and generate meaningful interpretations, but they will also acquire a solid foundation for continued study of more advanced statistical techniques

Based on a course in the theory of statistics this text concentrates on what can be achieved using the likelihood/Fisherian method of taking account of uncertainty when studying a statistical problem. It takes the concept ot the likelihood as providing the best methods for unifying the demands of statistical modelling and the theory of inference. Every likelihood concept is illustrated by realistic examples, which are not compromised by computational problems. Examples range from asimile comparison of two accident rates, to complex studies that require generalised linear or semiparametric mode

Econometric Modeling provides a new and stimulating introduction to econometrics, focusing on modeling. The key issue confronting empirical economics is to establish sustainable relationships that are both supported by data and interpretable from economic theory. The unified likelihood-based approach of this book gives students the required statistical foundations of estimation and inference, and leads to a thorough understanding of econometric techniques. David Hendry and Bent Nielsen introduce modeling for a range of situations, including binary data sets, multiple regression, and cointegrated systems. In each setting, a statistical model is constructed to explain the observed variation in the data, with estimation and inference based on the likelihood function. Substantive issues are always addressed, showing how both statistical and economic assumptions can be tested and empirical results interpreted. Important empirical problems such as structural breaks, forecasting, and model selection are covered, and Monte Carlo simulation is explained and applied. Econometric Modeling is a self-contained introduction for advanced undergraduate or graduate students. Throughout, data illustrate and motivate the approach, and are available for computer-based teaching. Technical issues from probability theory and statistical theory are introduced only as needed. Nevertheless, the approach is rigorous, emphasizing the coherent formulation, estimation, and evaluation of econometric models relevant for empirical research

This paper provides high-dimensional and flexible importance sampling procedures for the likelihood evaluation of dynamic latent variable models involving finite or infinite mixtures leading to possibly heavy tailed and/or multi-modal target densities. Our approach is based upon the efficient importance sampling (EIS) approach of Richard and Zhang (2007) and exploits the mixture structure of the model when constructing importance sampling distributions as mixture of distributions. The proposed mixture EIS procedures are illustrated with ML estimation of a student-t state space model for realized volatilities and a stochastic volatility model with leverage effects and jumps for asset returns. -- Dynamic latent variable model ; Importance sampling ; Marginalized likelihood ; Mixture ; Monte Carlo ; Realized Volatility ; Stochastic volatility

Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Preface -- List of Figures -- List of Tables -- 1: Introduction -- 1.1 Motivating example: mapping river-blindness in Africa -- 1.2 Empirical or mechanistic models -- 1.3 What is in this book? -- 2: Regression modelling for spatially referenced data -- 2.1 Linear regression models -- 2.1.1 Malnutrition in Ghana -- 2.2 Generalised linear models -- 2.2.1 Logistic Binomial regression: river-blindness in Liberia -- 2.2.2 Log-linear Poisson regression: abundance of Anopheles Gambiae mosquitoes in Southern Cameroon -- 2.3 Questioning the assumption of independence -- 2.3.1 Testing for residual spatial correlation: the empirical variogram -- 3: Theory -- 3.1 Gaussian processes -- 3.2 Families of spatial correlation functions -- 3.2.1 The exponential family -- 3.2.2 The Matérn family -- 3.2.3 The spherical family -- 3.2.4 The theoretical variogram and the nugget variance -- 3.3 Statistical inference -- 3.3.1 Likelihood-based inference -- 3.4 Bayesian Inference -- 3.5 Predictive inference -- 3.6 Approximations to Gaussian processes -- 3.6.1 Low-rank approximations -- 3.6.2 Gaussian Markov random field approximations via stochastic partial differential equations -- 4: The linear geostatistical model -- 4.1 Model formulation -- 4.2 Inference -- 4.2.1 Likelihood-based inference -- 4.2.1.1 Maximum likelihood estimation -- 4.2.2 Bayesian inference -- 4.2.3 Trans-Gaussian models -- 4.3 Model validation -- 4.3.1 Scenario 1: omission of the nugget effect -- 4.3.2 Scenario 2: miss-specification of the smoothness parameter -- 4.3.3 Scenario 3: non-Gaussian data -- 4.4 Spatial prediction -- 4.5 Applications -- 4.5.1 Heavy metal monitoring in Galicia -- 4.5.2 Malnutrition in Ghana (continued) -- 4.5.2.1 Spatial predictions for the target population.

This book examines the consequences of misspecifications ranging from the fundamental to the nonexistent for the interpretation of likelihood-based methods of statistical estimation and interference. Professor White first explores the underlying motivation for maximum-likelihood estimation, treats the interpretation of the maximum-likelihood estimator (MLE) for misspecified probability models, and gives the conditions under which parameters of interest can be consistently estimated despite misspecification, and the consequences of misspecification, for hypothesis testing in estimating the asymptotic covariance matrix of the parameters. Although the theory presented in the book is motivated by econometric problems, its applicability is by no means restricted to economics. Subject to defined limitations, the theory applies to any scientific context in which statistical analysis is conducted using approximate models

Maximum likelihood estimation is a general method for estimating the parameters of econometric models from observed data. The principle of maximum likelihood plays a central role in the exposition of this book, since a number of estimators used in econometrics can be derived within this framework. Examples include ordinary least squares, generalized least squares and full-information maximum likelihood. In deriving the maximum likelihood estimator, a key concept is the joint probability density function (pdf) of the observed random variables, yt. Maximum likelihood estimation requires that the following conditions are satisfied. (1) The form of the joint pdf of yt is known. (2) The specification of the moments of the joint pdf are known. (3) The joint pdf can be evaluated for all values of the parameters, 9. Parts ONE and TWO of this book deal with models in which all these conditions are satisfied. Part THREE investigates models in which these conditions are not satisfied and considers four important cases. First, if the distribution of yt is misspecified, resulting in both conditions 1 and 2 being violated, estimation is by quasi-maximum likelihood (Chapter 9). Second, if condition 1 is not satisfied, a generalized method of moments estimator (Chapter 10) is required. Third, if condition 2 is not satisfied, estimation relies on nonparametric methods (Chapter 11). Fourth, if condition 3 is violated, simulation-based estimation methods are used (Chapter 12). 1.2 Motivating Examples To highlight the role of probability distributions in maximum likelihood estimation, this section emphasizes the link between observed sample data and 4 The Maximum Likelihood Principle the probability distribution from which they are drawn.

Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- Authors -- 1: Linear Models -- Simple Linear Regression -- Estimating Regression Models with Ordinary Least Squares -- Distributional Assumptions Underlying Regression -- Coefficient of Determination -- Inference for Regression Parameters -- Multiple Regression -- Example of Simple Linear Regression by Hand -- Regression in R -- Interaction Terms in Regression -- Categorical Independent Variables -- Checking Regression Assumptions with R -- Summary -- 2: An Introduction to Multilevel Data Structure -- Nested Data and Cluster Sampling Designs -- Intraclass Correlation -- Pitfalls of Ignoring Multilevel Data Structure -- Multilevel Linear Models -- Random Intercept -- Random Slopes -- Centering -- Basics of Parameter Estimation with MLMs -- Maximum Likelihood Estimation -- Restricted Maximum Likelihood Estimation -- Assumptions Underlying MLMs -- Overview of Two-Level MLMs -- Overview of Three-Level MLMs -- Overview of Longitudinal Designs and Their Relationship to MLMs -- Summary -- 3: Fitting Two-Level Models in R -- Simple (Intercept-Only) Multilevel Models -- Interactions and Cross-Level Interactions Using R -- Random Coefficients Models using R -- Centering Predictors -- Additional Options -- Parameter Estimation Method -- Estimation Controls -- Comparing Model Fit -- lme4 and Hypothesis Testing -- Summary -- Note -- 4: Three-Level and Higher Models -- Defining Simple Three-Level Models Using the lme4 Package -- Defining Simple Models with More than Three Levels in the lme4 Package -- Random Coefficients Models with Three or More Levels in the lme4 Package -- Summary -- Note -- 5: Longitudinal Data Analysis Using Multilevel Models -- The Multilevel Longitudinal Framework -- Person Period Data Structure -- Fitting Longitudinal Models Using the lme4 Package.

The second edition of this book contains several new recipes illustrating how do-files, ado-files, and Mata functions can be used to solve programming problems. Several recipes have also been updated to reflect new features in Stata added between versions 10 and 14. The discussion of maximum-likelihood function evaluators has been significantly expanded in this edition. The new topics covered in this edition include factor variables and operatores; use of margins, marginsplot, and suest; Mata-based likelihood function evaluators; and associative arrays. (Preface)

This book provides a new approach to the identification and the estimation of structural VAR models. The role of deterministic variables and the connection with the concept of cointegration is discussed at length. The book also provides criteria to select among alternative structures. In addition, the asymptotic distributions of the structural estimates of impulse response functions and forecast error variance decomposition coefficients are obtained and used to construct asymptotically based confidence intervals around the maximum likelihood estimates. Moreover, the book contains a critical evaluation of the problem of non-fundamental representations and of their relevance on the interpretability of the results of structural VAR analysis. Finally, the book contains applied examples

Front Cover -- Spatial Econometrics -- Copyright -- Contents -- List of Empirical Illustrations -- List of Figures -- List of Tables -- Preface -- Acknowledgements -- 1 Spatial Models: Basic Issues -- 1.1 Illustrations Involving Spatial Interactions -- 1.2 Concept of a Neighbor and the Weighting Matrix -- 1.3 Some Different Ways to Specify Spatial Weighting Matrices -- 1.4 Typical Weighting Matrices in Computer Studies -- Suggested Problems -- 2 Specification and Estimation -- 2.1 The General Model -- 2.1.1 Triangular Arrays -- 2.1.2 Geršgorin's Theorem and Weighting Matrices -- 2.1.3 Normalization to Ensure a Continuous Parameter Space -- 2.1.4 An Important Condition in Large Sample Analysis -- 2.2 Estimation: Various Special Cases -- 2.2.1 Estimation When ρ1=ρ2=0 -- 2.2.2 Estimation When ρ1=0 and ρ20 -- 2.2.2.1 Maximum Likelihood Estimation: ρ1=0, ρ20 -- 2.2.3 Assumptions of the General Model -- 2.2.4 A Generalized Moments Estimator of ρ2 -- 2.3 IV Estimation of the General Model -- 2.4 Maximum Likelihood Estimation of the General Model -- 2.5 An Identi cation Fallacy -- 2.6 Time Series Procedures Do Not Always Carry Over -- Appendix A2 Proofs for Chapter 2 -- Suggested Problems -- 3 Spillover Effects in Spatial Models -- 3.1 Effects Emanating From a Given Unit -- 3.2 Emanating Effects of a Uniform Worsening of Fundamentals -- 3.3 Vulnerability of a Given Unit to Spillovers -- Suggested Problems -- 4 Predictors in Spatial Models -- 4.1 Preliminaries on Expectations -- 4.2 Information Sets and Predictors of the Dependent Variable -- 4.3 Mean Squared Errors of the Predictors -- Suggested Problems -- 5 Problems in Estimating Weighting Matrices -- 5.1 The Spatial Model -- 5.2 Shortcomings of Selection Based on R2 -- 5.3 An Extension to Nonlinear Spatial Models -- 5.4 R2 Selection in the Multiple Panel Case -- Suggested Problems.

Cover -- Half Title -- Title Page -- Copyright Page -- Contents -- Preface -- Acknowledgments -- Authors -- Chapter 1 Introduction -- 1.1 Backgroundon Animal Movement -- 1.1.1 Population Dynamics -- 1.1.2 Spatial Redistribution -- 1.1.3 Home Ranges, Territories, and Groups -- 1.1.4 Group Movement and Dynamics -- 1.1.5 Informed Dispersal and Prospecting -- 1.1.6 Memory -- 1.1.7 Individual Condition -- 1.1.8 Energy Balance -- 1.1.9 Food Provision -- 1.1.10 Encounter Rates and Patterns -- 1.2 Telemetry Data -- 1.3 Notation -- 1.4 Statistical Concepts -- 1.5 Additional Reading -- Chapter 2 Statistics for Spatial Data -- 2.1 Point Processes -- 2.1.1 Homogeneous SPPs -- 2.1.2 Density Estimation -- 2.1.3 Parametric Models -- 2.2 Continuous Spatial Processes -- 2.2.1 Modeling and Parameter Estimation -- 2.2.2 Prediction -- 2.2.3 Restricted Maximum Likelihood -- 2.2.4 Bayesian Geostatistics -- 2.3 Discrete Spatial Processes -- 2.3.1 Descriptive Statistics -- 2.3.2 Models for Discrete Spatial Processes -- 2.4 Spatial Confounding -- 2.5 Dimension Reduction Methods -- 2.5.1 Reducing Necessary Calculations -- 2.5.2 Reduced-Rank Models -- 2.5.3 Predictive Processes -- 2.6 Additional Reading -- Chapter 3 Statistics for Temporal Data -- 3.1 Univariate Time Series -- 3.1.1 Descriptive Statistics -- 3.1.2 Models for Univariate Temporal Data -- 3.1.2.1 Autoregressive Models -- 3.1.2.2 Moving Average Models -- 3.1.2.3 Backshift Notation -- 3.1.2.4 Differencing in Time Series Models -- 3.1.2.5 Fitting Time Series Models -- 3.1.3 Forecasting -- 3.1.4 Additional Univariate Time Series Notes -- 3.1.5 Temporally Varying Coefficient Models -- 3.1.6 Temporal Point Processes -- 3.2 Multivariate Time Series -- 3.2.1 Vector Autoregressive Models -- 3.2.2 Implementation -- 3.3 Hierarchical Time Series Models -- 3.3.1 Measurement Error -- 3.3.2 Hidden Markov Models