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Preface | |
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Introduction | |
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About Econometrics | |
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The Structure of this Book | |
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Illustrations and Exercises | |
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An Introduction to Linear Regression | |
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Ordinary Least Squares as An Algebraic Tool | |
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Ordinary Least Squares | |
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Simple Linear Regression | |
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Example: Individual Wages | |
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Matrix Notation | |
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The Linear Regression Model | |
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Small Sample Properties of the OLS Estimator | |
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The Gauss--Markov Assumptions | |
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Properties of the OLS Estimator | |
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Example: Individual Wages (Continued) | |
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Goodness-of-fit | |
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Hypothesis Testing | |
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A Simple t-test | |
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Example: Individual Wages (Continued) | |
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Testing One Linear Restriction | |
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A Joint Test of Significance of Regression Coefficients | |
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Example: Individual Wages (Continued) | |
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The General Case | |
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Size, Power and p-values | |
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Asymptotic Properties of the OLS Estimator | |
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Consistency | |
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Asymptotic Normality | |
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Illustration: the Capital Asset Pricing Model | |
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The CAPM as a Regression Model | |
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Estimating and Testing the CAPM | |
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Multicollinearity | |
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Example: Individual Wages (Continued) | |
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Prediction | |
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Exercises | |
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Interpreting and Comparing Regression Models | |
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Interpreting the Linear Model | |
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Selecting the Set of Regressors | |
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Misspecifying the Set of Regressors | |
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Selecting Regressors | |
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Comparing Non-nested Models | |
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Misspecifying the Functional Form | |
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Nonlinear Models | |
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Testing the Functional Form | |
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Illustration: Explaining House Prices | |
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Illustration: Explaining Individual Wages | |
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Linear Models | |
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Loglinear Models | |
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The Effects of Gender | |
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Some Words of warning | |
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Exercises | |
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Heteroskedasticity and Autocorrelation | |
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Consequences for the OLS Estimator | |
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Deriving an Alternative Estimator | |
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Heteroskedasticity | |
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Introduction | |
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Estimator Properties and Hypothesis Testing | |
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When the Variances are Unknown | |
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Heteroskedasticity-consistent Standard Errors for OLS | |
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A Model with Two Unknown Variances | |
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Multiplicative Heteroskedasticity | |
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Testing for Heteroskedasticity | |
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Testing Equality of Two Unknown Variances | |
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Testing for Multiplicative Heteroskedasticity | |
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The Breusch--Pagan Test | |
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The White Test | |
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Which Test? | |
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Illustration: Explaining Labour Demand | |
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Autocorrelation | |
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First Order Autocorrelation | |
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Unknown [rho] | |
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Testing for First Order Autocorrelation | |
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Asymptotic Tests | |
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The Durbin--Watson Test | |
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Illustration: The Demand for Ice Cream | |
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Alternative Autocorrelation Patterns | |
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Higher Order Autocorrelation | |
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Moving Average Errors | |
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What to do When you Find Autocorrelation? | |
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Misspecification | |
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Heteroskedasticity-and-autocorrelation-consistent Standard Errors for OLS | |
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Illustration: Risk Premia in Foreign Exchange Markets | |
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Notation | |
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Tests for Risk Premia in the One-month Market | |
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Tests for Risk Premia using Overlapping Samples | |
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Exercises | |
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Endogeneity, Instrumental Variables and GMM | |
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A Review of the Properties of the OLS Estimator | |
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Cases Where the OLS Estimator Cannot be Saved | |
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Autocorrelation with a Lagged Dependent Variable | |
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An Example with Measurement Error | |
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Simultaneity: the Keynesian Model | |
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The Instrumental Variables Estimator | |
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Estimation with a Single Endogenous Regressor and a Single Instrument | |
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Back to the Keynesian Model | |
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Back to the Measurement Error Problem | |
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Multiple Endogenous Regressors | |
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Illustration: Estimating the Returns to Schooling | |
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The Generalized Instrumental Variables Estimator | |
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Multiple Endogenous Regressors with an Arbitrary Number of Instruments | |
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Two-stage Least Squares and the Keynesian Model Again | |
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The Generalized Method of Moments | |
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Example | |
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The Generalized Method of Moments | |
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Some Simple Examples | |
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Illustration: Estimating Intertemporal Asset Pricing Models | |
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Concluding Remarks | |
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Exercises | |
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Maximum Likelihood Estimation and Specification Tests | |
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An Introduction to Maximum Likelihood | |
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Some Examples | |
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General Properties | |
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An Example (Continued) | |
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The Normal Linear Regression Model | |
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Specification Tests | |
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Three Test Principles | |
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Lagrange Multiplier Tests | |
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An Example (Continued) | |
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Tests in the Normal Linear Regression Model | |
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Testing for Omitted Variables | |
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Testing for Heteroskedasticity | |
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Testing for Autocorrelation | |
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Quasi-maximum Likelihood and Moment Conditions Tests | |
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Quasi-maximum Likelihood | |
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Conditional Moment Tests | |
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Testing for Normality | |
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Exercises | |
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Models with Limited Dependent Variables | |
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Binary Choice Models | |
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Using Linear Regession? | |
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Introducing Binary Choice Models | |
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An Underlying Latent Model | |
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Estimation | |
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Goodness-of-fit | |
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Illustration: the Impact of Unemployment Benefits on Recipiency | |
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Specification Tests in Binary Choice Models | |
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Relaxing Some Assumptions in Binary Choice Models | |
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Multi-response Models | |
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Ordered Response Models | |
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About Normalization | |
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Illustration: Willingness to Pay for Natural Areas | |
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Multinomial Models | |
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Tobit Models | |
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The Standard Tobit Model | |
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Estimation | |
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Illustration: Expenditures on Alcohol and Tobacco (Part 1) | |
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Specification Tests in the Tobit Model | |
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Extensions of Tobit Models | |
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The Tobit II Model | |
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Estimation | |
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Further Extensions | |
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Illustration: Expenditures on Alcohol and Tobacco (Part 2) | |
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Sample Selection Bias | |
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The Nature of the Selection Problem | |
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Semi-parametric Estimation of the Sample Selection Model | |
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Exercises | |
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Univariate Time Series Models | |
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Introduction | |
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Some Examples | |
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Stationarity and the Autocorrelation Function | |
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General ARMA Processes | |
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Formulating ARMA Processes | |
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Invertibility of Lag Polynomials | |
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Common Roots | |
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Stationarity and Unit Roots | |
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Testing for Unit Roots | |
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Testing for Unit Roots in a First Order Autoregressive Model | |
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Testing for Unit Roots in Higher Order Autoregressive Models | |
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Illustration: Quarterly Disposable Income | |
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Illustration: Long-run Purchasing Power Parity (Part 1) | |
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Estimation of ARMA Models | |
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Least Squares | |
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Maximum Likelihood | |
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Choosing a Model | |
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The Autocorrelation Function | |
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The Partial Autocorrelation Function | |
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Diagnostic Checking | |
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Criteria for Model Selection | |
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Illustration: Modelling Quarterly Disposable Income | |
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Predicting with ARMA Models | |
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The Optimal Predictor | |
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Prediction Accuracy | |
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Illustration: The Expectations Theory of the Term Structure | |
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Autoregressive Conditional Heteroskedasticity | |
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ARCH and GARCH Models | |
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Estimation and Prediction | |
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Illustration: Volatility in Daily Exchange Rates | |
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What about Multivariate Models? | |
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Exercises | |
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Multivariate Time Series Models | |
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Dynamic Models with Stationary Variables | |
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Models with Nonstationary Variables | |
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Spurious Regressions | |
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Cointegration | |
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Cointegration and Error-correction Mechanisms | |
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Illustration: Long-run Purchasing Power Parity (Part 2) | |
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Vector Autoregressive Models | |
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Cointegration: The Multivariate Case | |
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Cointegration in a VAR | |
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Example: Cointegration in a Bivariate VAR | |
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Testing for Cointegration | |
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Illustration: Long-run Purchasing Power Parity (Part 3) | |
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Illustration: Money Demand and Inflation | |
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Concluding Remarks | |
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Exercises | |
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Models Based on Panel Data | |
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Advantages of Panel Data | |
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Efficiency of Parameter Estimators | |
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Identification of Parameters | |
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The Static Linear Model | |
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The Fixed Effects Model | |
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The Random Effects Model | |
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Fixed Effects or Random Effects? | |
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Goodness-of-fit | |
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Alternative Instrumental Variables Estimators | |
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Alternative Error Structures | |
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Testing for Heteroskedasticity and Autocorrelation | |
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Illustration: Explaining Individual Wages | |
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Dynamic Linear Models | |
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An Autoregressive Panel Data Model | |
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Dynamic Models with Exogenous Variables | |
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Unit Roots and Cointegration | |
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Illustration: Wage Elasticities of Labour Demand | |
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Models with Limited Dependent Variables | |
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Binary Choice Models | |
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The Fixed Effects Logit Model | |
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The Random Effects Probit Model | |
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Tobit Models | |
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Dynamics and the Problem of Initial Conditions | |
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Incomplete Panels and Selection Bias | |
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Estimation with Randomly Missing Data | |
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Selection Bias and Some Simple Tests | |
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Estimation with Nonrandomly Missing Data | |
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Exercises | |
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Vectors and Matrices | |
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Terminology | |
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Matrix Manipulations | |
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Properties of Matrices and Vectors | |
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Inverse Matrices | |
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Idempotent Matrices | |
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Eigenvalues and Eigenvectors | |
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Differentiation | |
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Some Least Squares Manipulations | |
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Statistical and Distribution Theory | |
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Discrete Random Variables | |
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Continuous Random Variables | |
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Expectations and Moments | |
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Multivariate Distributions | |
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Conditional Distributions | |
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The Normal Distribution | |
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Related Distributions | |
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Bibliography | |
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Index | |