Introduction to Eco n o m et rics

Transcription

1 2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. Introduction to Eco n o m et rics Third Edition G.S. Maddala Formerly of Ohio State University JOHN WILEY & SONS, LTD Chichester New Weinheim Brisbane Toronto

2 Contents Foreword Preface to the Second Edition Preface to the Third Edition Obituary PART I INTRODUCTION AND THE LINEAR REGRESSION MODEL xvii XiX xxiii xxv 1 1 What is Econometrics? 1.1 What is Econometrics? 1.2 Economic and Econometric Models 1.3 The Aims and Methodology of Econometrics 1.4 What Constitutes a Test of an Economic Theory? and an Outline of the Book 2 Statistical Background and Matrix Algebra 2.1 Introduction 2.2 Probability Addition Rules of Probability Conditional Probability and the Multiplication Rule Bayes Theorem Summation and Product Operations 2.3 Random Variables and Probability Distributions Joint, Marginal, and Conditional Distributions 2.4 The Normal Probability Distribution and Related Distributions The Normal Distribution Related Distributions

3 vi CONTENTS Classical Statistical Inference Point Estimation Properties of Estimators Unbiasedness Efficiency Consistency Other Asymptotic Properties Sampling Distributions for Samples from a Normal Population Interval Estimation Testing of Hypotheses Relationship Between Confidence Interval Procedures and Tests of Hypotheses Combining Independent Tests Appendix to Chapter 2 Matrix Algebra on Matrix Algebra 3 Simple Regression 3.1 Introduction 3.2 Specification of the Relationships 3.3 The Method of Moments 3.4 The Method of Least Squares Reverse Regression 3.5 Statistical Inference in the Linear Regression Model Confidence Intervals for ß, and o2 Testing of Hypotheses Example of Comparing Test Scores from the GRE and GMAT Tests Regression with No Constant Term Analysis of Variance for the Simple Regression Model Prediction with the Simple Regression Model Prediction of Expected Values 3.8 Outliers Some s 3.9 Alternative Functional Forms for Regression Equations *3.10 Inverse Prediction in the Least Squares Regression Model *3.11 Stochastic Regressors

4 CONTENTS vii *3.12 The Regression Fallacy The Bivariate Normal Distribution Galton s Result and the Regression Fallacy A Note on the Term: Regression Appendix to Chapter 3 4 Multiple Regression 4.1 Introduction 4.2 A Model with Two Explanatory Variables The Least Squares Method 4.3 Statistical Inference in the Multiple Regression Model Formulas for the General Case of k Explanatory Variables Some s 4.4 Interpretation of the Regression Coefficients Partial Correlations and Multiple Correlation Relationships Among Simple, Partial, and Multiple Correlation Coefficients Two s Prediction in the Multiple Regression Model Analysis of Variance and Tests of Hypotheses Nested and Nonnested Hypotheses Tests for Linear Functions of Parameters Omission of Relevant Variables and Inclusion of Irrelevant Variables Omission of Relevant Variables Example 1: Demand for Food in the United States Example 2: Production Functions and Management Bias Inclusion of Irrelevant Variables Degrees of Freedom and Tests for Stability The Analysis of Variance Test Example 1: Stability of the Demand for Food Function Example 2: Stability of Production Functions Predictive Tests for Stability *4.12 The LR, W, and LM Tests

5 viii CONTENTS Appendix to Chapter 4 The Multiple Regression Model in Matrix Notation Data Sets PART II VIOLATION OF THE ASSUMPTIONS OF THE BASIC MODEL 5 Heteroskedasticity 5.1 Introduction 5.2 Detection of Heteroskedasticity Some Other Tests An Intuitive Justification for the Breusch-Pagan Test 5.3 Consequences of Heteroskedasticity Estimation of the Variance of the OLS Estimator Under Heteroskedasticity 5.4 Solutions to the Heteroskedasticity Problem 5.5 Heteroskedasticity and the Use of Deflators : The Density Gradient Model *5.6 Testing the Linear Versus Log-Linear Functional Form The Box-Cox Test The BM Test The PE Test Appendix to Chapter 5 Generalized Least Squares 6 Autocorrelation 6.1 Introduction 6.2 Durbin-Watson Test 6.3 Estimation in Levels Versus First Differences Some s 6.4 Estimation Procedures with Autocorrelated Errors Iterative Procedures Grid-Search Procedures 6.5 Effect of AR(1) Errors on OLS Estimates

6 CONTENTS ix 6.6 Some Further Comments on the DW Test The von Neumann Ratio The Berenblut-Webb Test 6.7 Tests for Serial Correlation in Models with Lagged Dependent Variables Durbin s h-test Durbin s Alternative Test A General Test for Higher-Order Serial Correlation: The LM Test Strategies When the DW Test Statistic is Significant Errors Not AR( 1) Autocorrelation Caused by Omitted Variables Serial Correlation Due to Misspecified Dynamics The Wald Test *6.10 Trends and Random Walks Spurious Trends Differencing and Long-Run Effects: The Concept of Cointegration *6.11 ARCH Models and Serial Correlation 6.12 Some Comments on the DW Test and Durbin s h-test and t-test 7 Multicollinearity 7.1 Introduction 7.2 Some s 7.3 Some Measures of Multicollinearity 7.4 Problems with Measuring Multicollinearity 7.5 Solutions to the Multicollinearity Problem: Ridge Regression 7.6 Principal Component Regression 7.7 Dropping Variables 7.8 Miscellaneous Other Solutions Using Ratios or First Differences Using Extraneous Estimates Getting More Data Appendix to Chapter 7 Linearly Dependent Explanatory Variables 8 Dummy Variables and Truncated Variables 8.1 Introduction

7 X CONTENTS 8.2 Dummy Variables for Changes in the Intercept Term Two More s 8.3 Dummy Variables for Changes in Slope Coefficients 8.4 Dummy Variables for Cross-Equation Constraints 8.5 Dummy Variables for Testing Stability of Regression Coefficients 8.6 Dummy Variables Under Heteroskedasticity and Autocorrelation 8.7 Dummy Dependent Variables The Linear Probability Model and the Linear Discriminant Function The Linear Probability Model The Linear Discriminant Function The Probit and Logit Models The Problem of Disproportionate Sampling Prediction of Effects of Changes in the Explanatory Variables Measuring Goodness of Fit Truncated Variables: The Tobit Model Some Examples Method of Estimation Limitations of the Tobit Model The Truncated Regression Model 9 Simultaneous Equations Models 9.1 Introduction 9.2 Endogenous and Exogenous Variables 9.3 The Identification Problem: Identification through Reduced Form 9.4 Necessary and Sufficient Conditions for Identification 9.5 Methods of Estimation: The Instrumental Variable Method Measuring R2 9.6 Methods of Estimation: The Two-Stage Least Squares Method Computing Standard Errors 9.7 The Question of Normalization *9.8 The Limited-Information Maximum Likelihood Method

8 CONTENTS xi *9.9 On the Use of OLS in the Estimation of Simultaneous Equations Models Working s Concept of Identification Recursive Systems Estimation of Cobb-Douglas Production Functions *9.10 Exogeneity and Causality Weak Exogeneity Superexogeneity Strong Exogeneity Granger Causality Granger Causality and Exogeneity Tests for Exogeneity 9.11 Some Problems with Instrumental Variable Methods Appendix to Chapter 9 10 Nonlinear Regressions, Models of Expectations, and Nonnormality IO. 1 Introduction 10.2 The Newton-Raphson Method 10.3 Nonlinear Least Squares The Gauss-Newton Method 10.4 Models of Expectations 10.5 Naive Models of Expectations 10.6 The Adaptive Expectations Model 10.7 Estimation with the Adaptive Expectations Model Estimation in the Autoregressive Form Estimation in the Distributed Lag Form 10.8 Two s 10.9 Expectational Variables and Adjustment Lags Partial Adjustment with Adaptive Expectations Alternative Distributed Lag Models: Polynomial Lags Finite Lags: The Polynomial Lag Choosing the Degree of the Polynomial Rational Lags IO. 13 Rational Expectations Tests for Rationality Estimation of a Demand and Supply Model Under Rational Expectations Case 1 Case 2 lllustrative Example The Serial Correlation Problem in Rational Expectations Models I I

9 xii CON TENTS Nonnormality of Errors Tests for Normality Data Transformations 11 Errors in Variables Introduction 11.2 The Classical Solution for a Single-Equation Model with One Explanatory Variable 11.3 The Single-Equation Model with Two Explanatory Variables Two Explanatory Variables: One Measured with Error Two Explanatory Variables: Both Measured with Error 11.4 Reverse Regression Instrumental Variable Methods 11.6 Proxy Variables Coefficient of the Proxy Variable 11.7 Some Other Problems The Case of Multiple Equations Correlated Errors PART 111 SPECIAL TOPICS 12 Diagnostic Checking, Model Selection, and Specification Testing 12.1 Introduction 12.2 Diagnostic Tests Based on Least Squares Residuals Tests for Omitted Variables Tests for ARCH Effects Problems with Least Squares Residuals Some Other Types of Residuals Predicted Residuals and Studentized Residuals Dummy Variable Method for Studentized Residuals BLUS Residuals Recursive Residuals 12.5 DFFITS and Bounded Influence Estimation 12.6 Model Selection Hypothesis-Testing Search Interpretive Search

10 CON TENTS xiii Simplification Search Proxy Variable Search Data Selection Search Post-Data Model Construction Hendry s Approach to Model Selection 12.7 Selection of Regressors Theil s R2 Criterion Criteria Based on Minimizing the Mean-Squared Error of Prediction Akaike s Information Criterion 12.8 Implied F-Ratios for the Various Criteria Bayes Theorem and Posterior Odds for Model Selection 12.9 Cross-Validation Hausman s Specification Error Test An Application: Testing for Errors in Variables or Exogeneity Some s An Omitted Variable Interpretation of the Hausman Test The Plosser-Schwert-White Differencing Test Tests for Nonnested Hypotheses The Davidson and MacKinnon Test The Encompassing Test A Basic Problem in Testing Nonnested Hypotheses Hypothesis Testing Versus Model Selection as a Research Strategy Appendix to Chapter Introduction to Time-Series Analysis 13.1 Introduction 13.2 Two Methods of Time-Series Analysis: Frequency Domain and Time Domain 13.3 Stationary and Nonstationary Time Series Strict Stationarity Weak Stationarity Properties of Autocorrelation Function Nonstationarity 13.4 Some Useful Models for Time Series Purely Random Process Random Walk Moving Average Process Autoregressive Process Autoregressive Moving Average Process Autoregressive Integrated Moving Average Process

11 xiv CONTENTS 13.5 Estimation of AR, MA, and ARMA Models Estimation of MA Models Estimation of ARMA Models Residuals from the ARMA Models Testing Goodness of Fit 13.6 The Box-Jenkins Approach Forecasting from Box-Jenkins Models Trend Elimination: The Traditional Method A Assessment Seasonality in the Box-Jenkins Modeling 13.7 R2 Measures in Time-Series Models Data Sets 14 Vector Autoregressions, Unit Roots, and Cointegration 14.1 Introduction 14.2 Vector Autoregressions 14.3 Problems with VAR Models in Practice 14.4 Unit Roots 14.5 Unit Root Tests Dickey-Fuller Test The Serial Correlation Problem The Low Power of Unit Root Tests The DF-GLS Test What are the Null and Alternative Hypotheses in Unit Root Tests? Tests with Stationarity as Null Confirmatory Analysis Panel Data Unit Root Tests Structural Change and Unit Roots 14.6 Cointegration 14.7 The Cointegrating Regression 14.8 Vector Autoregressions and Cointegration 14.9 Cointegration and Error Correction Models Tests for Cointegration Cointegration and Testing of the REH and MEH A Assessment of Cointegration

12 CONTENTS xv 15 Panel Data Analysis 15.1 Introduction 15.2 The LSDV or Fixed Effects Model 15.3 The Random Effects Model 15.4 Fixed Effects Versus Random Effects Hausman Test Breusch and Pagan Test 15.5 The SUR Model 15.6 Dynamic Panel Data Models 15.7 The Random Coefficient Model Large-Sample Theory 16.1 The Maximum Likelihood Method 16.2 Methods of Solving the Likelihood Equations 16.3 The Cramer-Rao Lower Bound 16.4 Large-Sample Tests Based on ML 16.5 GIVE and GMM Small-Sample Inference: Resampling Methods 17.1 Introduction 17.2 Monte Carlo Methods More Efficient Monte Carlo Methods Response Surfaces 17.3 Resampling Methods: Jackknife and Bootstrap Some s Other Issues Relating to Bootstrap 17.4 Bootstrap Confidence Intervals 17.5 Hypothesis Testing with the Bootstrap 17.6 Bootstrapping Residuals Versus Bootstrapping the Data 17.7 NonIID Errors and Nonstationary Models Heteroskedasticity and Autocorrelation Unit Root Tests Based on the Bootstrap Cointegration Tests 17.8 Miscellaneous Other Applications

13 xvi CONTENTS Appendices Appendix A: Data Sets Appendix B: Data Sets on the Web Appendix C: Computer Programs Index