Exam (elaborations) TEST BANK FOR Microeconometrics Methods and Applic

Exam (elaborations) TEST BANK FOR Microeconometrics Methods and Applic This book provides a detailed treatment of microeconometric analysis, the analysis of individuallevel data on the economic behavior of individuals or firms. This usually entails regression methods applied to cross-section and panel data. The book aims to provide the practitioner with a comprehensive coverage of statistical methods and their application in modern applied microeconometrics research. These methods include nonlinear modelling, inference under minimal distributional assumptions, identifying and measuring causation rather than mere association, and correcting from departures from simple random sampling. Many of these features are of relevance to individual-level data analysis throughout the social sciences. The ambitious agenda has determined the characteristics of this book. First, although oriented to the practitioner the book is relatively advanced in places. A cookbook approach is inadequate as when two or more complications occur simultaneously, a common situation, the practitioner must know enough to be able to adapt available methods. Second, the book provides considerable coverage of practical data problems, see especially the last three chapters. Third, the book includes substantial empirical examples in many chapters, to illustrate some of the methods covered. Finally, the book is unusually long. Despite this length we have been space-constrained. We had intended to include even more empirical examples. And abbreviated presentations will at times fail to recognize the accomplishments of researchers who have made substantive contributions. The book assumes a basic understanding of the linear regression model with matrix algebra. It is written at the mathematical level of the first-year economics Ph.D. sequence, comparable to Greene (2003). We have two types of readers in mind. First, the book can be used as a course text for a microeconometrics course, typically taught in the second-year of the Ph.D., or for data-oriented microeconomics field courses such as labor economics, public economics and industrial organization. Second, the book can be used as a reference work for graduate students and applied researchers who despite training in microeconometrics will inevitably have gaps that they wish to fill. For instructors using this book as an econometrics course text it is best to introduce the basic nonlinear cross-section and linear panel data models as early as possible, initially skipping many of the methods chapters. The key methods chapter (chapter 5) covers maximum likelihood and nonlinear least squares estimation. ML and NLS provide adequate background for the most commonly-used nonlinear cross-section models (chapters 14-17, 20), basic linear panel data models (chapter 21) and treatment evaluation methods (chapter 25). Generalized method of moments estimation (chapter 6) is needed especially for advanced linear panel data methods (chapter 22). For readers using this book as a reference work, the chapters have been written to be as selfcontained as possible. The notable exception is that some command of general estimation results in chapter 5, and occasionally chapter 6, will be necessary. Most models chapters are structured to begin with a discussion and example that is accessible to a wide audience. The web-site computer programs used in this book, and related materials useful for instructional purposes. This project has been long and arduous, and at times seemingly without an end. Its completion has been greatly aided by our colleagues, friends, and graduate students. We would like to thank especially the following for reading and commenting on specific chapters: Bijan Borah, Kurt Brännäs, Pian Chen, Tim Cogley, Parthe Deb, David Drukker, Massimiliano De Santis, Jeff Gill, 11 Tue Gorgens, Shiferaw Gurmu, Lu Ji, Oscar Jorda, Roger Koenker, Chenghui Li, Tong Li, Doug Miller, Murat Munkin, Jim Prieger, Ahmed Rahmen, Sunil Sapra, Haruki Seitani, Yacheng Sun, Xiaoyong Zheng, and David Zimmer. We thank Rajeev Dehejia, Bronwyn Hall, Cathy Kling, Jeffrey Kling, Will Manning, Brian McCall and Jim Ziliak for making their data available for empirical illustrations. We thank our respective departments for facilitating our collaboration, and for the production and distribution of the draft manuscript at various stages. We benefitted from the comments of two anonymous reviewers. Guidance, advice and encouragement from our CUP editor, Scott Pariss, has been invaluable. Our interest in econometrics owes much to the training and environments we encountered as students and in the initial stages of our academic careers. The first author thanks The Australian National University, Stanford University, especially Takeshi Amemiya and Tom MaCurdy, and The Ohio State University. The second author thanks the London School of Economics and The Australian National University. Our interest in writing a book oriented to the practitioner owes much to our exposure to the research of graduate students and colleagues at our respective institutions, UC-Davis and IUBloomington. Finally, we would like to thank our families for their patience and understanding without which completion of this project would not have been possible. A. Colin Cameron Davis, California Pravin K. Trivedi Bloomington, Indiana 12 TABLE OF CONTENTS I: PRELIMINARIES 1. Overview 2. Causal and Noncausal Models 3. Microeconomic Data Structures II: CORE METHODS 4. Linear models 5. ML and NLS estimation 6. GMM and Systems Estimation 7. Hypothesis Tests 8. Specification Tests and Model Selection 9. Semiparametric Methods 10. Numerical Optimization III: SIMULATIONBASED METHODS 11. Bootstrap Methods 12. Simulation-based Methods 13. Bayesian Methods IV: CROSS-SECTION DATA MODELS 14. Binary Outcome Models 15. Multinomial Models 16. Tobit and Selection Models 17. Transition Data: Survival Analysis 18. Mixture Models and Unobserved Heterogeneity 19. Models of Multiple Hazards 20. Count Data Models V: PANEL DATA MODELS 21. Linear Panel Models: Basics 22. Linear Panel Models: Extensions 23. Nonlinear Panel Models VI: FURTHER TOPICS 24. Stratified and Clustered Samples 25. Treatment Evaluation 26. Measurement Error Models 27. Missing Data and Imputation APPENDICES A. Asymptotic Theory B. Making Pseudo-Random Draws 13 PART 1 (chapters 1-3) Part 1 covers the essential components of microeconometric analysis -- an economic specification, a statistical model and a data set. Chapter 1 discusses the distinctive aspects of microeconometrics, and provides an outline of the book. It emphasizes that discreteness of data, and nonlinearity and heterogeneity of behavioral relationships are key aspects of disaggregated microeconometric models. It concludes by presenting the notation and conventions used throughout the book. Chapters 2 and 3 set the scene for the remainder of the book by introducing the reader to key model and data concepts that shape the analyses of later chapters. A key distinction in econometrics is between essentially descriptive models and data summaries at various levels of statistical sophistication and models that go beyond associations and attempt to estimate causal parameters. The classic definitions of causality in econometrics derive from the Cowles Commission simultaneous equations models that draw sharp distinctions between exogenous and endogenous variables, and between structure and reduced form parameters. Although reduced form models are very useful for prediction, knowledge of structural or causal parameters is essential for policy analyses. Identification of structural parameters within the simultaneous equations framework poses numerous conceptual and practical difficulties. An alternative approach based on the potential outcome model, also attempts to identify causal parameters but it does so by posing limited questions within a more manageable framework. Chapter 2 attempts to provide an overview of the fundamental issues that arise in these alternative frameworks. Readers who initially find this material challenging should return to this chapter later after gaining greater familiarity with specific models covered later in the book. The empirical researcher’s ability to identify causal parameters depends not only on the statistical tools and models but also on the type of data available. An experimental framework provides a standard for establishing causal connections. However, observational, not experimental, data form the basis of much of econometric inference. Chapter 3 surveys the pros and cons of three main types of data available: observational data, data from social experiments, and those from natural experiments. The potential as well as the difficulties of conducting causal inference based on each type of data are reviewed. PART 2 (chapters 4-10) Part 2 presents the core methods – least squares, method of moments, and maximum likelihood -- of estimation and inference in nonlinear regression models that are central in microeconometrics. Both the traditional topics as well as more modern topics like quantile regression, sequential estimation, empirical likelihood, bootstrap, and semi- and nonparametric regression are covered. In general the discussion is at a level intended to provide enough background and detail to enable the practitioner to read and comprehend articles in the leading econometrics journals. We presume prior familiarity with linear regression analysis. Chapter 4 begins with the linear regression model. It then covers at an introductory level quantile regression, which models distributional features other than the conditional mean. It provides a lengthy expository treatment of instrumental variables estimation, a major semiparametric method 14 of causal inference. Chapter 5 presents the most commonly-used estimation methods for nonlinear models, beginning with the quite general topic of m-estimation, before specialization to maximum likelihood and nonlinear least squares regression. Chapter 6 provides a comprehensive treatment of generalized method of moments, which is a quite general estimation framework, applicable both in linear and nonlinear, and single- and multi-equation settings. The chapter emphasizes the special case of instrumental variables estimation. Chapter 7 covers both the classical and bootstrap approaches to hypothesis testing, while Chapter 8 presents relatively more modern methods of model selection and specification analysis. .Because of their importance the bootstrap methods also get a more detailed stand-alone treatment in Chapter 11. As much as possible testing methods are presented in a unified manner in these chapters, but specific applications occur throughout the book Chapter 9 is a stand-alone chapter that presents nonparametric and semiparametric estimation methods that place a flexible structure on the econometric model. Chapter 10 presents the computational methods used to compute the nonlinear estimators presented in chapters 5 and 6. This material becomes especially relevant to the practitioner if an estimator is not automatically computed by an econometrics package. PART 3 (chapters 11-13) Part 1 emphasized that: (1) Microeconometric models are often nonlinear; (2) they are frequently estimated using large and heterogeneous data sets; and (3) the data often come from surveys that are complex and subject to a variety of sampling biases. A realistic depiction of the economic phenomena in such settings often requires the use of models that are difficult to estimate and analyze. Advances in computing hardware and software now make it feasible to tackle such tasks. Part 3 presents modern, computer-intensive, simulation-based methods of inference that mitigate some of these difficulties. The background required to cover this material varies somewhat with the chapter but the essential base is least squares and maximum likelihood estimation. Chapter 11 presents bootstrap methods for statistical inference. These methods have the attraction of providing a simple way to obtain standard errors when the formulae from asymptotic theory are complex, as is the case for some two-step estimators. Furthermore, if implemented appropriately, a bootstrap can lead to a more refined asymptotic theory that may then lead to better statistical inference in small samples. Chapter 12 presents simulation-based estimation methods. These methods permit estimation in situations where standard computational methods may not permit calculation of an estimator, because of the presence of an integral over a probability distribution for which there is no closedform solution. Chapter 13 surveys Bayesian methods that provide an approach to estimation and inference that is quite different from the classical approach used in other chapters of this book. Despite this different approach, the Bayesian toolkit can also be adopted to permit classical estimation and inference for problems that are otherwise intractable 15 PART 4 (chapters 14-20) Part 4, consisting of chapters 14 to 20, covers the core nonlinear limited dependent variable models for cross-section data, defined by the range of values taken by the dependent variable. Topics covered include models for binary and multinomial data, duration data and count data. The complications of censoring, truncation and sample selection are also studied. Chapters 14-15 cover models for binary and multinomial data that are standard in the analysis of discrete choice and outcomes. Maximum likelihood methods are dominant. Different parameterizations for the conditional probabilities in these models lead to different models, notably logit and probit models, which are well-established Recent literature has focused on less restrictive modeling with more flexible functional forms for conditional probabilities and on accommodating individual unobserved heterogeneity. These objectives motivate the use of semiparametric methods and simulation-based estimation methods. Censoring, truncation or sample selection generate empirically several important classes of models that are analyzed in Chapter 16. The long-established Tobit model is central to this literature, but its estimation and inference rely on strong distributional assumptions to permit consistent estimation. We also examine the newer semiparametric methods require weaker assumptions. Chapters 17-19 consider duration models in which the focus is on either the determinants of spell lengths, such as length of an unemployment spell, or on modeling the hazard rate of transitions from one initial state to another. The relative importance of state dependence and unobserved heterogeneity as determinants of the average length of spell is a central issue, whose resolution raises fundamental questions about alternative modeling approaches. The analysis covers both discrete and continuous time models, and both parametric and semiparametric formulations, including the standard models like the exponential, the Weibull, and the proportional hazards model. Chapter 18 covers formulation and interpretation of richer models that incorporate unobserved heterogeneity. Chapter 19 deals with models with several types of events using the competing risks formulation and models of multiple spells. Chapter 20 covers the analysis of event count of the kind very common in health economics. There are many strong connections and parallels between count data models and duration models because of their common foundation in stochastic processes. We analyze the widely-used Poisson and negative binomial regression models, together with important variants such as the two-part or hurdle model, zero-inflated models, latent class models, and endogenous regressor models, all of which accommodate different facets of the event processes. PART 5 (chapters 21-23) Cross section models have certain inherent limitations. They are predominantly equilibrium models that generally do not shed light on intertemporal dependence of events. They also cannot satisfactorily resolve fundamental issues about the sources of persistence in behavior. Such persistence may be behavioral, i.e. arising from true state dependence, or it may be spurious, being an artifact of the inability to control for heterogeneous behavior in the population. Because panel data, also called longitudinal data, contain periodically repeated observations of the same subjects, they have a large potential for resolving issues that cross section models cannot satisfactorily handle. Chapters 21 through 23 present methods for panel data. We progress systematically from 16 linear models for continuous data in Chapter 21 to nonlinear panel data models for limited dependent variables in Chapter 23. Both fixed effects and random effects models are considered. A persistent theme through these three chapters is the importance of using robust methods of inference. Chapter 21, which reviews the key general results for linear panel data regression models, can be read easily by those with a good grasp of linear regression; it does not require the material covered in Parts 2 to 4. We recommend that even those who are interested in more advanced material should quickly peruse through the contents of this chapter first to gain familiarity with key concepts and definitions. Chapter 22 covers important extensions of Chapter 21, especially to dynamic panels which allow for Markovian dependence structure of current variables. The analysis is in the GMM framework that is currently favored by many practitioners in this area. The analysis here is at times intricate, involving many issues of detail. A strong grasp of GMM will be helpful in absorbing the main results of this chapter. The results of Chapters 21 and 22 do not extend to nonlinear panel models of Chapter 23 in a general and unified fashion. There are relatively fewer general results for limited dependent variable panel models. Despite this, in Chapter 23 we begin by presenting an analysis of some general issues and approaches. Later sections can be treated as panel data extensions of the counterpart cross section models in Part 4. these analyze four categories of models for binary, count , censored, and duration data, respectively. These should be accessible to a suitably prepared reader familiar with the parallel cross section models. PART 6 (chapters 24-27) Frequently in empirical work data present not one but multiple complications that the analysis must simultaneously deal with. Examples of such complications include departures from simple random sampling, clustering of observations, measurement errors, and missing data. When they occur, individually or jointly, and in the context of any of the models developed in Parts 4 and 5, identification of parameters of interest will be compromised. Three chapters in Part 6 – Chapters 24, 26, and 27 – analyze the consequences of such complications and then present methods that attempt to overcome the consequences. The methods are illustrated using examples taken from the earlier parts of the book. This features gives points of connection between Part 6 and the rest of the book. Chapter 24, which deals with features of data from complex surveys, complements various topics covered Chapters 3, 5, and 16. Chapter 26 which deals with measurement errors complements topics in Chapter 4, 14, and 20. Chapter 27 is a stand-alone chapter on missing data and multiple imputation, but its use of the EM algorithm and Gibbs sampler also gives it points of contact with Chapters 10 and 13, respectively. Chapter 25 deals with the important topic of treatment evaluation. Treatment is a broad term that refers to the impact of one variable, e.g. schooling, on some outcome variable, e.g. income. Treatment variables may be exogenously assigned, or may be endogenously chosen. The topic of treatment evaluation concerns the identifiability of the impact of treatment on outcome, as measured by either the marginal effects or certain functions of marginal effect. A variety of methods are used including instrumental variables regression and propensity score matching. The problem of treatment evaluation can arise in the context of any model considered in parts 4 and 5. This chapter 17 may also be read on its own, but it does presume familiarity with many other topics covered in the book, including instrumental variables and selection models, which is why it is placed in the last part. 18 GUIDE FOR INSTRUCTORS AND OTHER READERS The book assumes a basic understanding of the linear regression model with matrix algebra. It is written at the mathematical level of the first-year economics Ph.D. sequence, comparable to Greene (2000). While some of the material in this book is covered in a first-year sequence, most of the material in this book appears in second year econometrics Ph.D. courses or in data-oriented microeconomics field courses such as labor economics, public economics or industrial organization. This book is intended to be used as both an econometrics text and as an adjunct for such field courses. More generally, the book is intended to be useful as a reference work for applied researchers in economics, in related social sciences such as sociology and political science, and in epidemiology. The models chapters have been written to be as self-contained as possible, to minimize the amount of background material in the methods chapters that needs to be read. For the specific models presented in parts four and five (chapters 14-23) it will generally be sufficient to read the relevant chapter in isolation, except that some command of the general estimation results in chapter 5 and in some cases chapter 6 will be necessary. Most chapters are structured to begin with a discussion and example that is accessible to a wide audience. For instructors using this book as a course text it is best to introduce the basic nonlinear crosssection and linear panel data models as early as possible, skipping many of the methods chapters. The most commonly-used nonlinear cross-section models are presented in chapters 14-16, and require knowledge of maximum likelihood and least squares estimation, presented in chapter five. Chapter twenty-one on linear panel data models requires even less preparation, essentially just chapter four. Table 1.2 provides an outline for a one-quarter second-year graduate course taught at the University of California - Davis, immediately following the required first-year statistics and econometrics sequence. A quarter provides sufficient time to cover the basic results given in the first half of the chapters in this outline. With additional time one can go into further detail or cover a subset of chapters eleven to thirteen on computationally-intensive estimation methods (simulation-based estimation, the bootstrap which is also briefly presented in chapter seven and Bayesian methods); additional cross-section models (durations and counts) presented in chapters seventeen to twenty; and additional panel data models (linear model extensions and nonlinear models) given in chapters twenty-two and twenty-three. Outline of a twenty-lecture ten-week course: Lectures Chapter Topic 1-3 4 Review of linear models and asymptotic theory 4-7 5 Estimation: M-estimation, ML and NLS 8 10 Estimation: Numerical Optimization 9-11 14,15 Models: Binary and multinomial 12-14 16 Models: Censored and Truncated 15 6 Estimation: GMM 16 7 Testing: Hypothesis Tests 17-19 21 Models: Basic Linear Panel 20 9 Estimation: Semiparametric At Indiana University - Bloomington, a fifteen-week semester long field course in microeconometrics is based on material in most of Parts 4 and 5 (chapters 14-23). The prerequisite courses for this course cover material similar to the material in Part 2 (chapters 4-10). 19 Some exercises are provided at the end of each chapter after the first three introductory chapters. These exercises are usually learning-by-doing exercises, some are purely methodological while others entail analysis of generated or actual data. The level of difficulty of the questions is mostly related to the level of difficulty of the topic. Detailed programs and data for all the data applications (using either actual data or generated data) will be made available at the book website. 20 ADVANCE REVIEWS "This book presents an elegant and accessible treatment of the broad range of rapidly expanding topics currently being studied by microeconometricians. Thoughtful, intuitive, and careful in laying out central concepts of sophisticated econometric methodologies, it is not only an excellent textbook for students, but also an invaluable reference text for practitioners and researchers." - Cheng Hsiao, University of Southern California "I wish "Microeconometrics" was available when I was a student! Here, in one place -- and in clear and readable prose -- you can find all of the tools that are necessary to do cutting-edge applied economic analysis, and with many helpful examples." - Alan Krueger, Princeton University "Cameron and Trivedi have written a remarkably thorough and up-to-date treatment of microeconometric methods. This is not a superficial cookbook; the early chapters carefully lay the theoretical foundations on which the authors build their discussion of methods for discrete and limited dependent variables and for analysis of longitudinal data. A distinctive feature of the book is its attention to cutting-edge topics like semiparametric regression, bootstrap methods, simulationbased estimation, and empirical likelihood estimation. A highly valuable book." - Gary Solon, University of Michigan "The empirical analysis of micro data is more widespread than ever before. The book by Cameron and Trivedi contains a superb treatment of all the methods that economists like to apply to such data. What is more, it fully integrates a number of exciting new methods that have become applicable due to recent advances in computer technology. The text is in perfect balance between econometric theory and empirical intuition, and it contains many insightful examples." - Gerard J. van den Berg, Free University, Amsterdam, The Netherlands 21 PROGRAMS: I. INTRODUCTION (chapters 1-3) No programs. PROGRAMS: II. CORE METHODS (chapters 4-10) Section Pages Example Program and Output Data [* means generated] 4.5.3 84-5 Robust Standard Errors for OLS, WLS and GLS * 4.6.4 88-90 Quantile and Median Regression or 4.8.8 102-3 Instrumental Variables Regression * 4.9.6 110-2 IV Application with Weak Instruments DATA and DATA 5.9.2-3 159-63 Exponential: MLE using ml command * 5.9.2-3 159-63 Exponential: NLS using nl command