A Guide to Modern Econometric:

Transcription

1 A Guide to Modern Econometric: 4th edition Marno Verbeek Rotterdam School of Management, Erasmus University, Rotterdam B )WILEY A John Wiley & Sons, Ltd., Publication

2 Contents Preface xiii 1 Introduction About Econometrics The Structure of this Book Illustrations and Exercises 4 2 An Introduction to Linear Regression Ordinary Least Squares as an Algebraic Tool Ordinary Least Squares Simple Linear Regression Example: Individual Wages Matrix Notation The Linear Regression Model Small Sample Properties of the OLS Estimator The Gauss-Markov Assumptions Properties of the OLS Estimator Example: Individual Wages (Continued) Goodness-of-fit Hypothesis Testing A Simple/-Test Example: Individual Wages (Continued) Testing One Linear Restriction A Joint Test of Significance of Regression Coefficients Example: Individual Wages (Continued) The General Case Size, Power and p-values 31

3 vi CONTENTS 2.6 Asymptotic Properties of the OLS Estimator Consistency Asymptotic Normality Small Samples and Asymptotic Theory Illustration: The Capital Asset Pricing Model The CAPM as a Regression Model Estimating and Testing the CAPM The World's Largest Hedge Fund Multicollinearity Example: Individual Wages (Continued) Missing Data, Outliers and Influential Observations Outliers and Influential Observations Robust Estimation Methods 49 v Missing Observations Prediction 52 Wrap-up 53 Exercises 54 3 Interpreting and Comparing Regression Models Interpreting the Linear Model Selecting the Set of Regressors Misspecifying the Set of Regressors Selecting Regressors Comparing Non-nested Models Misspecifying the Functional Form Nonlinear Models Testing the Functional Form Testing for a Structural Break Illustration: Explaining House Prices Illustration: Predicting Stock Index Returns Model Selection Forecast Evaluation Illustration: Explaining Individual Wages Linear Models Loglinear Models The Effects of Gender Some Words of Warning 89 Wrap-up 90 Exercises 90 4 Heteroskedasticity and Autocorrelation Consequences for the OLS Estimator Deriving an Alternative Estimator Heteroskedasticity Introduction Estimator Properties and Hypothesis Testing When the Variances are Unknown 101

4 CONTENTS vii Heteroskedasticity-consistent Standard Errors for OLS Multiplicative Heteroskedasticity Weighted Least Squares with Arbitrary Weights Testing for Heteroskedasticity Testing for Multiplicative Heteroskedasticity The Breusch-Pagan Test The White Test Which Test? Illustration: Explaining Labour Demand Autocorrelation First-order Autocorrelation Unknown p Testing for First-order Autocorrelation Asymptotic Tests The Durbin-Watson Test Illustration: The Demand for Ice Cream Alternative Autocorrelation Patterns Higher-order Autocorrelation Moving Average Errors What to do When you Find Autocorrelation? Misspecification Heteroskedasticity-and-autocorrelation-consistent Standard Errors for OLS Illustration: Risk Premia in Foreign Exchange Markets Notation Tests for Risk Premia in the 1 Month Market Tests for Risk Premia Using Overlapping Samples 132 Wrap-up 134 Exercises Endogenous Regressors, Instrumental Variables and GMM A Review of the Properties of the OLS Estimator Cases Where the OLS Estimator Cannot be Saved Autocorrelation with a Lagged Dependent Variable 141 ] Measurement Error in an Explanatory Variable 142! Endogeneity and Omitted Variable Bias Simultaneity and Reverse Causality The Instrumental Variables Estimator 148 i Estimation with a Single Endogenous Regressor I and a Single Instrument Back to the Keynesian model Back to the Measurement Error Problem Multiple Endogenous Regressors 153

5 viii CONTENTS 5.4 Illustration: Estimating the Returns to Schooling The Generalized Instrumental Variables Estimator Multiple Endogenous Regressors with an Arbitrary Number of Instruments Two-stage Least Squares and the Keynesian Model Again Specification Tests Weak Instruments The Generalized Method of Moments Example > The Generalized Method of Moments Some Simple Examples Weak Identification 171 \ 5.7 Illustration: Estimating Intertemporal Asset Pricing Models 171 Wrap-up 175 Exercises Maximum Likelihood Estimation and Specification Tests An Introduction to Maximum Likelihood Some Examples General Properties An Example (Continued) The Normal Linear Regression Model Specification Tests Three Test Principles Lagrange Multiplier Tests An Example (Continued) Tests in the Normal Linear Regression Model Testing for Omitted Variables Testing for Heteroskedasticity Testing for Autocorrelation Quasi-maximum Likelihood and Moment Conditions Tests Quasi-maximum Likelihood Conditional Moment Tests Testing for Normality 202 Wrap-up 203 Exercises Models with Limited Dependent Variables Binary Choice Models Using Linear Regression? Introducing Binary Choice Models An Underlying Latent Model Estimation 211

6 CONTENTS Goodness-of-fit Illustration:!The Impact of Unemployment Benefits on Recipiency Specification Tests in Binary Choice Models Relaxing Some Assumptions in Binary Choice Models Multiresponse Models Ordered Response Models About Normalization Illustration: Explaining Firms' Credit Ratings Illustration: Willingness to Pay for Natural Areas Multinomial Models Models for Count Data The Poisson and Negative Binomial Models Illustration: Patents and R&D Expenditures Tobit Models The Standard Tobit Model Estimation Illustration: Expenditures on Alcohol and Tobacco (Part 1) Specification Tests in the Tobit Model Extensions of Tobit Models The Tobit II Model Estimation Further Extensions Illustration: Expenditures on Alcohol and Tobacco (Part 2) Sample Selection Bias The Nature of the Selection Problem Semi-parametric Estimation of the Sample-Selection Model Estimating Treatment Effects Regression-based Estimators Alternative Approaches Duration Models Hazard Rates and Survival Functions Samples and Model Estimation Illustration: Duration of Bank Relationships 273 Wrap-up 274 Exercises 274 Univariate Time Series Models Introduction Some Examples Stationarity and the Autocorrelation Function General ARMA Processes 284

7 CONTENTS Formulating ARMA Processes Invertibility of Lag Polynomials Common Roots Stationarity and Unit Roots Testing for Unit Roots Testing for Unit Roots in a First-order Autoregressive Model Testing for Unit Roots in Higher-order Autoregressive Models Extensions Illustration: Stock Prices and Earnings Illustration: Long-run Purchasing Power Parity (Part 1) Estimation of ARMA Models Least Squares Maximum Likelihood Choosing a Model The Autocorrelation Function The Partial Autocorrelation Function Diagnostic Checking Criteria for Model Selection Illustration: The Persistence of Inflation Predicting with ARMA Models The Optimal Predictor Prediction Accuracy Evaluating predictions Illustration: The Expectations Theory of the Term Structure Autoregressive Conditional Heteroskedasticity ARCH and GARCH Models Estimation and Prediction Illustration: Volatility in Daily Exchange Rates What about Multivariate Models? 333 Wrap-up 333 Exercises 334 Multivariate Time Series Models Dynamic Models with Stationary Variables Models with Nonstationary Variables Spurious Regressions Cointegration Cointegration and Error-correction Mechanisms Illustration: Long-run Purchasing Power Parity (Part 2) Vector Autoregressive Models Cointegration: the Multivariate Case Cointegration in a VAR Example: Cointegration in a Bivariate VAR Testing for Cointegration 358

8 CONTENTS xi Illustration: Long-run Purchasing Power Parity (Part 3) Illustration: Money Demand and Inflation 362 Wrap-up 368 '. Exercises 369 ] 10 Models Based on Panel Date 372 : 10.1 Introduction to Panel Data Modelling 373 i Efficiency of Parameter Estimators 374 I Identification of Parameters 375 I 10.2 The Static Linear Model 376 ; The Fixed Effects Model 377 j The First-difference Estimator 379 ' % The Random Effects Model 381 i Fixed Effects or Random Effects? 384 ' Goodness-of-fit Alternative Instrumental Variables Estimators Robust Inference 389 ; Testing for Heteroskedasticity and Autocorrelation 391 j The Fama-MacBeth Approach 392 j 10.3 Illustration: Explaining Individual Wages 394 j 10.4 Dynamic Linear Models 396 j An Autoregressive Panel Data Model 396 ] Dynamic Models with Exogenous Variables 401 i Too Many Instruments 403 i 10.5 Illustration: Explaining Capital Structure 405 j 10.6 Panel Time Series Heterogeneity First Generation Panel Unit Root Tests Second Generation Panel Unit Root Tests Panel Cointegration Tests Models with Limited Dependent Variables Binary Choice Models The Fixed Effects Logit Model The Random Sffects Probit Model Tobit Models Dynamics and the Problem of Initial Conditions Semi-parametric Alternatives Incomplete Panels and Selection Bias Estimation with Randomly Missing Data Selection Bias and Some Simple Tests Estimation with Nonrandomly Missing Data Pseudo Panels and Repeated Cross-sections The Fixed Effects Model An Instrumental Variables Interpretation 433

9 xii CONTENTS Dynamic Models 434 Wrap-up 435 Exercises 436 A Vectors and Matrices 441 A.I Terminology 441 A.2 Matrix Manipulations 442 A.3 Properties of Matrices and Vectors 443 A.4 Inverse Matrices i 444 A.5 Idempotent Matrices. 445 A.6 Eigenvalues and Eigenvectors 445 A.7 Differentiation 446 A.8 Some Least Squares Manipulations 447 B Statistical and Distribution Theory 449 B.I Discrete Random Variables 449 B.2 Continuous Random Variables 450 B.3 Expectations and Moments 451 B.4 Multivariate Distributions 452 B.5 Conditional Distributions 453 B.6 The Normal Distribution 454 B.7 Related Distributions 457 Bibliography 459 Index 477