Econometric Theory and Methods

1 Econometric Theory and MethodsRussell DavidsonDepartment of EconomicsMcGill UniversityJames G. MacKinnonDepartment of EconomicsQueen s University at KingstonCopyrightc 2021 by Russell Davidson and James G. MacKinnonOxford University Press, New YorkISBN 0-19-512372-7 Oxford University Press, New YorkISBN 0-19-512372-7 This book was originally published by Oxford University Pressin late 2003 with a 2004 date. By agreement with OUP,the rights reverted to the authors in 2004 by Oxford University Press, 2021 by Russell Davidson and James G. MacKinnonISBN 0-19-512372-7, 2004 xxxContentsPrefaceixData, Solutions, and Correctionsxviii1 Regression Distributions, Densities, and The Specification of Regression Matrix Method-of-Moments Notes on the Exercises382 The Geometry of Linear The Geometry of Vector The Geometry of OLS The Frisch-Waugh-Lovell Applications of the FWL Influential Observations and Final Exercises823 The Statistical Properties of Ordinary Least Are OLS Parameter Estimators Unbiased?

2 Are OLS Parameter Estimators Consistent? The Covariance Matrix of the OLS Parameter Efficiency of the OLS Residuals and Error Misspecification of Linear Regression Measures of Goodness of Final Exercises1184 Hypothesis Testing in Linear Regression Basic Some Common Exact Tests in the Classical Normal Linear Large-Sample Tests in Linear Regression Simulation-Based The Power of Hypothesis Final Exercises1725 Confidence Exact and Asymptotic Confidence Bootstrap Confidence Confidence Heteroskedasticity-Consistent Covariance The Delta Final Exercises2096 Nonlinear Method-of-Moments Estimators for Nonlinear Nonlinear Least Computing NLS The Gauss -Newton One-Step Hypothesis

3 Heteroskedasticity-Robust Final Exercises2537 Generalized Least Squares and Related The GLS Computing GLS Feasible Generalized Least Autoregressive and Moving-Average Testing for Serial Estimating Models with Autoregressive Specification Testing and Serial Models for Panel Final Exercises3068 Instrumental Variables Correlation Between Error Terms and Instrumental Variables Finite-Sample Properties of IV Hypothesis Testing Overidentifying Durbin-Wu-Hausman Bootstrap IV estimation of Nonlinear Final Exercises3479 The Generalized Method of GMM Estimators for Linear Regression HAC Covariance Matrix Tests Based on the GMM Criterion GMM Estimators for Nonlinear The Method of Simulated Final Exercises39410 The Method of maximum Basic Concepts of maximum likelihood Asymptotic Properties of ML The Covariance Matrix of the ML Hypothesis The Asymptotic Theory of the Three Classical ML estimation of Models with Autoregressive Transformations of the Dependent Final Exercises44411 Discrete and Limited Dependent Binary Response Models: Binary Response Models.

4 Models for More Than Two Discrete Models for Count Models for Censored and Truncated Sample Duration Final Exercises49512 Multivariate Seemingly Unrelated Linear Systems of Nonlinear Linear Simultaneous Equations maximum likelihood Nonlinear Simultaneous Equations Final Appendix: Detailed Results on FIML and Exercises55013 Methods for Stationary Time -Series Autoregressive and Moving-Average Estimating AR, MA, and ARMA Single-Equation Dynamic Autoregressive Conditional Vector Final Exercises59914 Unit Roots and Random Walks and Unit Unit Root Serial Correlation and Unit Root Testing for Final Exercises64415 Testing the Specification of Econometric Specification Tests Based on Artificial Nonnested Hypothesis Model Selection Based on Information Nonparametric Final Appendix.

5 Test Regressors in Artificial Exercises695 References702 Author Index722 Subject Index726 PrefaceThis book is the second graduate-level econometrics textbook that we havewritten. Our first one, estimation and Inference in Econometrics, appearedeleven years ago and has been quite successful. Why then did we choose towrite this book instead of a second edition of the first one? Although it wouldhave been quicker and easier to write a second edition, there were severalcompelling reasons that drove us to write an entirely new seems unavoidable that the second edition of a book is longer than and Inference in Econometricsis by no means , it contains too much material even for most two-course book is significantly shorter. The entire book can be taught in a two-course sequence, as we explain below in detail, and a substantial fraction ofit can be taught in a single course, possibly at a somewhat lower subject of econometrics has evolved as rapidly in the last ten years as itdid in the ten years prior to that.

6 This means not only that there are manynew things that students of econometrics should learn, but also that thereare new and perhaps better ways of understanding older material. Althoughmany parts ofEstimation and Inference in Econometricshave held up well,we would have had to reorganize and rewrite it radically if we were to producea second edition that we could be truly happy reason for preferring to write a new book is that the level of ourearlier one, especially in several key chapters in the first half, is too high forthe first graduate courses at many institutions. With hindsight, this was amistake. One of our goals in writing this book has been to start at a moremodest level and work up from there gradually as the book proceeds.

7 Someof the earlier chapters do contain some fairly advanced material, but much ofit is confined to exercises, and the rest is in sections and subsections that canbe skipped without serious loss of of This BookCheap personal computers were already a fact of life around 1990. Since then,computers have become vastly more powerful and even less expensive. It isno surprise that econometrics, always a computer-intensive discipline, shouldhave been profoundly affected by the development of computers. Ten yearsago, one could have predicted that they would make the practice of econo-metrics a lot easier, and of course that is what has happened. What was lesspredictable is that the ability to perform simulations easily and quickly wouldchange many of the directions of Econometric Theory as well as econometricpractice.

8 The use of the computer in econometrics, especially for simulation,has blossomed so quickly that no textbook like this one can reasonably avoida serious discussion of Methods greatly enhance the asymptotic Theory that hasbeen at the heart of econometrics for many decades. Problems that are in-tractable analytically are often simple to handle by simulation, and a widevariety of new techniques that exploit this fact has been proposed duringthe last ten years. Of these techniques, the one that seems most generalin its application is the bootstrap, and we make a point of introducing thisimportant topic early on. Other Methods can do things that the bootstrapcannot, and we discuss some of these more briefly in later chapters. We arehappy to confess that we have ourselves learned a great deal by exploringnew simulation-based Methods while preparing this book, and we are nowenthusiastic in our use of these have for many years been advocates of the use of artificial regressions formany purposes in econometrics.

9 They are useful not only for simplifying manynumerical procedures but also for providing better theoretical best-known, and no doubt the most widely used, artificial regression isthe Gauss-Newton regression. We use it as a model for a host of other artificialregressions, some of which were developed expressly for this functions and estimating equations are topics that are not terriblyfamiliar to most econometricians. We ourselves became aware of them only inthe mid-1990s, when V. P. Godambe, of the University of Waterloo, proddedus to look more closely at a theme that he had himself pioneered back in the1960s. In this book, these concepts are not introduced until Chapter 9, butthey are present implicitly in the earlier chapters, usually in the guise of themethod of moments.

10 Once introduced, estimating equations make it mucheasier to explore the Theory of the generalized method of moments than themethods conventionally used in econometrics. Some of the more advancedtopics that we treat in the last third of the book are also greatly simplifiedby an approach based on estimating chapter has a substantial number of exercises. We put a great deal ofeffort into posing and solving these, and we made numerous changes to thetext itself as a result of doing so. There are several types of exercises, intendedfor different purposes. Some of the exercises are empirical, designed to givestudents the opportunity to become familiar with a variety of practical econo-metric Methods . Others involve simulation, including some that ask studentsto conduct small Monte Carlo experiments.