A Guide to Modern Econometrics

Preface.1 Introduction.1.1 About Econometrics.1.2 The Structure of this Book.1.3 Illustrations and Exercises.2 An Introduction to Linear Regression.2.1 Ordinary Least Squares as an Algebraic Tool.2.1.1 Ordinary Least Squares.2.1.2 Simple Linear Regression.2.1.3 Example: Individual Wages.2.1.4 Matrix Notation.2.2 The Linear Regression Model.2.3 Small Sample Properties of the OLS Estimator.2.3.1 The Gauss-Markov Assumptions.2.3.2 Properties of the OLS Estimator.2.3.3 Example: Individual Wages (Continued).2.4 Goodness-of-fit.2.5 Hypothesis Testing.2.5.1 A Simple t-test.2.5.2 Example: Individual Wages (Continued).2.5.3 Testing One Linear Restriction.2.5.4 A Joint Test of Significance of Regression Coefficients.2.5.5 Example: Individual Wages (Continued).2.5.6 The General Case.2.5.7 Size, Power and p-Values.2.6 Asymptotic Properties of the OLS Estimator.2.6.1 Consistency.2.6.2 Asymptotic Normality.2.6.3 Small Samples and Asymptotic Theory.2.7 Illustration: The Capital Asset Pricing Model.2.7.1 The CAPM as a Regression Model.2.7.2 Estimating and Testing the CAPM.2.8 Multicollinearity.2.8.1 Example: Individual Wages (Continued).2.9 Prediction.Exercises.3 Interpreting and Comparing Regression Models.3.1 Interpreting the Linear Model.3.2 Selecting the Set of Regressors.3.2.1 Misspecifying the Set of Regressors.3.2.2 Selecting Regressors.3.2.3 Comparing Non-nested Models.3.3 Misspecifying the Functional Form.3.3.1 Nonlinear Models.3.3.2 Testing the Functional Form.3.3.3 Testing for a Structural Break.3.4 Illustration: Explaining House Prices.3.5 Illustration: Explaining Individual Wages.3.5.1 Linear Models.3.5.2 Loglinear Models.3.5.3 The Effects of Gender.3.5.4 Some Words of Warning.Exercises.4 Heteroskedasticity and Autocorrelation.4.1 Consequences for the OLS Estimator.4.2 Deriving an Alternative Estimator.4.3 Heteroskedasticity.4.3.1 Introduction.4.3.2 Estimator Properties and Hypothesis Testing.4.3.3 When the Variances are Unknown.4.3.4 Heteroskedasticity-consistent Standard Errors for OLS.4.3.5 A Model with Two Unknown Variances.4.3.6 Multiplicative Heteroskedasticity.4.4 Testing for Heteroskedasticity.4.4.1 Testing Equality of Two Unknown Variances.4.4.2 Testing for Multiplicative Heteroskedasticity.4.4.3 The Breusch-Pagan Test.4.4.4 The White Test.4.4.5 Which Test?4.5 Illustration: Explaining Labour Demand.4.6 Autocorrelation.4.6.1 First Order Autocorrelation.4.6.2 Unknown rho.4.7 Testing for First Order Autocorrelation.4.7.1 Asymptotic Tests.4.7.2 The Durbin-Watson Test.4.8 Illustration: The Demand for Ice Cream.4.9 Alternative Autocorrelation Patterns.4.9.1 Higher Order Autocorrelation.4.9.2 Moving Average Errors.4.10 What to do When you Find Autocorrelation?4.10.1 Misspecification.4.10.2 Heteroskedasticity-and-autocorrelation-consistent Standard Errors for OLS.4.11 Illustration: Risk Premia in Foreign Exchange Markets.4.11.1 Notation.4.11.2 Tests for Risk Premia in the One-month Market.4.11.3 Tests for Risk Premia Using Overlapping Samples.Exercises.5 Endogeneity, Instrumental Variables and GMM.5.1 A Review of the Properties of the OLS Estimator.5.2 Cases Where the OLS Estimator Cannot be Saved.5.2.1 Autocorrelation with a Lagged Dependent Variable.5.2.2 An Example with Measurement Error.5.2.3 Simultaneity: the Keynesian Model.5.3 The Instrumental Variables Estimator.5.3.1 Estimation with a Single Endogenous Regressor and a Single Instrument.5.3.2 Back to the Keynesian Model.5.3.3 Back to the Measurement Error Problem.5.3.4 Multiple Endogenous Regressors.5.4 Illustration: Estimating the Returns to Schooling.5.5 The Generalized Instrumental Variables Estimator.5.5.1 Multiple Endogenous Regressors with an Arbitrary Number of Instruments.5.5.2 Two-stage Least Squares and the Keynesian Model Again.5.5.3 Specification Tests.5.5.4 Weak Instruments.5.6 The Generalized Method of Moments.5.6.1 Example.5.6.2 The Generalized Method of Moments.5.6.3 Some Simple Examples.5.7 Illustration: Estimating Intertemporal Asset Pricing Models.5.8 Concluding Remarks.Exercises.6 Maximum Likelihood Estimation and Specification Tests.6.1 An Introduction to Maximum Likelihood.6.1.1 Some Examples.6.1.2 General Properties.6.1.3 An Example (Continued).6.1.4 The Normal Linear Regression Model.6.2 Specification Tests.6.2.1 Three Test Principles.6.2.2 Lagrange Multiplier Tests.6.2.3 An Example (Continued).6.3 Tests in the Normal Linear Regression Model.6.3.1 Testing for Omitted Variables.6.3.2 Testing for Heteroskedasticity.6.3.3 Testing for Autocorrelation.6.4 Quasi-maximum Likelihood and Moment Conditions Tests.6.4.1 Quasi-maximum Likelihood.6.4.2 Conditional Moment Tests.6.4.3 Testing for Normality.Exercises.7 Models with Limited Dependent Variables.7.1 Binary Choice Models.7.1.1 Using Linear Regression?7.1.2 Introducing Binary Choice Models.7.1.3 An Underlying Latent Model.7.1.4 Estimation.7.1.5 Goodness-of-fit.7.1.6 Illustration: the Impact of Unemployment Benefits on Recipiency.7.1.7 Specification Tests in Binary Choice Models.7.1.8 Relaxing Some Assumptions in Binary Choice Models.7.2 Multi-response Models.7.2.1 Ordered Response Models.7.2.2 About Normalization.7.2.3 Illustration: Willingness to Pay for Natural Areas.7.2.4 Multinomial Models.7.3 Models for Count Data.7.3.1 The Poisson and Negative Binomial Models.7.3.2 Illustration: Patents and R&D Expenditures.7.4 Tobit Models.7.4.1 The Standard Tobit Model.7.4.2 Estimation.7.4.3 Illustration: Expenditures on Alcohol and Tobacco (Part 1).7.4.4 Specification Tests in the Tobit Model.7.5 Extensions of Tobit Models.7.5.1 The Tobit II Model.7.5.2 Estimation.7.5.3 Further Extensions.7.5.4 Illustration: Expenditures on Alcohol and Tobacco (Part 2).7.6 Sample Selection Bias.7.6.1 The Nature of the Selection Problem.7.6.2 Semi-parametric Estimation of the Sample Selection Model.7.7 Estimating Treatment Effects.7.8 Duration Models.7.8.1 Hazard Rates and Survival Functions.7.8.2 Samples and Model Estimation.7.8.3 Illustration: Duration of Bank Relationships.Exercises.8 Univariate Time Series Models.8.1 Introduction.8.1.1 Some Examples.8.1.2 Stationarity and the Autocorrelation Function.8.2 General ARMA Processes.8.2.1 Formulating ARMA Processes.8.2.2 Invertibility of Lag Polynomials.8.2.3 Common Roots.8.3 Stationarity and Unit Roots.8.4 Testing for Unit Roots.8.4.1 Testing for Unit Roots in a First Order Autoregressive Model.8.4.2 Testing for Unit Roots in Higher Order Autoregressive Models.8.4.3 Extensions.8.4.4 Illustration: Annual Price/Earnings Ratio.8.5 Illustration: Long-run Purchasing Power Parity (Part 1).8.6 Estimation of ARMA Models.8.6.1 Least Squares.8.6.2 Maximum Likelihood.8.7 Choosing a Model.8.7.1 The Autocorrelation Function.8.7.2 The Partial Autocorrelation Function.8.7.3 Diagnostic Checking.8.7.4 Criteria for Model Selection.8.7.5 Illustration: Modelling the Price/Earnings Ratio.8.8 Predicting with ARMA Models.8.8.1 The Optimal Predictor.8.8.2 Prediction Accuracy.8.9 Illustration: The Expectations Theory of the Term Structure.8.10 Autoregressive Conditional Heteroskedasticity.8.10.1 ARCH and GARCH Models.8.10.2 Estimation and Prediction.8.10.3 Illustration: Volatility in Daily Exchange Rates.8.11 What about Multivariate Models?Exercises.9 Multivariate Time Series Models.9.1 Dynamic Models with Stationary Variables.9.2 Models with Nonstationary Variables.9.2.1 Spurious Regressions.9.2.2 Cointegration.9.2.3 Cointegration and Error-correction Mechanisms.9.3 Illustration: Long-run Purchasing Power Parity (Part 2).9.4 Vector Autoregressive Models.9.5 Cointegration: the Multivariate Case.9.5.1 Cointegration in a VAR.9.5.2 Example: Cointegration in a Bivariate VAR.9.5.3 Testing for Cointegration.9.5.4 Illustration: Long-run Purchasing Power Parity (Part 3).9.6 Illustration: Money Demand and Inflation.9.7 Concluding Remarks.Exercises.10 Models Based on Panel Data.10.1 Advantages of Panel Data.10.1.1 Efficiency of Parameter Estimators.10.1.2 Identification of Parameters.10.2 The Static Linear Model.10.2.1 The Fixed Effects Model.10.2.2 The Random Effects Model.10.2.3 Fixed Effects or Random Effects?10.2.4 Goodness-of-fit.10.2.5 Alternative Instrumental Variables Estimators.10.2.6 Robust Inference.10.2.7 Testing for Heteroskedasticity and Autocorrelation.10.3 Illustration: Explaining Individual Wages.10.4 Dynamic Linear Models.10.4.1 An Autoregressive Panel Data Model.10.4.2 Dynamic Models with Exogenous Variables.10.5 Illustration: Wage Elasticities of Labour Demand.10.6 Nonstationarity, Unit Roots and Cointegration.10.6.1 Panel Data Unit Root Tests.10.6.2 Panel Data Cointegration Tests.10.7 Models with Limited Dependent Variables.10.7.1 Binary Choice Models.10.7.2 The Fixed Effects Logit Model.10.7.3 The Random Effects Probit Model.10.7.4 Tobit Models.10.7.5 Dynamics and the Problem of Initial Conditions.10.7.6 Semi-parametric Alternatives.10.8 Incomplete Panels and Selection Bias.10.8.1 Estimation with Randomly Missing Data.10.8.2 Selection Bias and Some Simple Tests.10.8.3 Estimation with Nonrandomly Missing Data.Exercises.A Vectors and Matrices.A.1 Terminology.A.2 Matrix Manipulations.A.3 Properties of Matrices and Vectors.A.4 Inverse Matrices.A.5 Idempotent Matrices.A.6 Eigenvalues and Eigenvectors.A.7 Differentiation.A.8 Some Least Squares Manipulations.B Statistical and Distribution Theory.B.1 Discrete Random Variables.B.2 Continuous Random Variables.B.3 Expectations and Moments.B.4 Multivariate Distributions.B.5 Conditional Distributions.B.6 The Normal Distribution.B.7 Related Distributions.Bibliography.Index.