| |

| |

Preface | |

| |

| |

Introduction | |

| |

| |

About Econometrics | |

| |

| |

The Structure of this Book | |

| |

| |

Illustrations and Exercises | |

| |

| |

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 t-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 | |

| |

| |

Asymptotic Properties of the OLS Estimator | |

| |

| |

Consistency | |

| |

| |

Asymptotic Normality | |

| |

| |

Illustration: the Capital Asset Pricing Model | |

| |

| |

The CAPM as a Regression Model | |

| |

| |

Estimating and Testing the CAPM | |

| |

| |

Multicollinearity | |

| |

| |

Example: Individual Wages (Continued) | |

| |

| |

Prediction | |

| |

| |

Exercises | |

| |

| |

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 | |

| |

| |

Illustration: Explaining House Prices | |

| |

| |

Illustration: Explaining Individual Wages | |

| |

| |

Linear Models | |

| |

| |

Loglinear Models | |

| |

| |

The Effects of Gender | |

| |

| |

Some Words of warning | |

| |

| |

Exercises | |

| |

| |

Heteroskedasticity and Autocorrelation | |

| |

| |

Consequences for the OLS Estimator | |

| |

| |

Deriving an Alternative Estimator | |

| |

| |

Heteroskedasticity | |

| |

| |

Introduction | |

| |

| |

Estimator Properties and Hypothesis Testing | |

| |

| |

When the Variances are Unknown | |

| |

| |

Heteroskedasticity-consistent Standard Errors for OLS | |

| |

| |

A Model with Two Unknown Variances | |

| |

| |

Multiplicative Heteroskedasticity | |

| |

| |

Testing for Heteroskedasticity | |

| |

| |

Testing Equality of Two Unknown Variances | |

| |

| |

Testing for Multiplicative Heteroskedasticity | |

| |

| |

The Breusch--Pagan Test | |

| |

| |

The White Test | |

| |

| |

Which Test? | |

| |

| |

Illustration: Explaining Labour Demand | |

| |

| |

Autocorrelation | |

| |

| |

First Order Autocorrelation | |

| |

| |

Unknown [rho] | |

| |

| |

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 One-month Market | |

| |

| |

Tests for Risk Premia using Overlapping Samples | |

| |

| |

Exercises | |

| |

| |

Endogeneity, 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 | |

| |

| |

An Example with Measurement Error | |

| |

| |

Simultaneity: the Keynesian Model | |

| |

| |

The Instrumental Variables Estimator | |

| |

| |

Estimation with a Single Endogenous Regressor and a Single Instrument | |

| |

| |

Back to the Keynesian Model | |

| |

| |

Back to the Measurement Error Problem | |

| |

| |

Multiple Endogenous Regressors | |

| |

| |

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 | |

| |

| |

The Generalized Method of Moments | |

| |

| |

Example | |

| |

| |

The Generalized Method of Moments | |

| |

| |

Some Simple Examples | |

| |

| |

Illustration: Estimating Intertemporal Asset Pricing Models | |

| |

| |

Concluding Remarks | |

| |

| |

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 | |

| |

| |

Exercises | |

| |

| |

Models with Limited Dependent Variables | |

| |

| |

Binary Choice Models | |

| |

| |

Using Linear Regession? | |

| |

| |

Introducing Binary Choice Models | |

| |

| |

An Underlying Latent Model | |

| |

| |

Estimation | |

| |

| |

Goodness-of-fit | |

| |

| |

Illustration: the Impact of Unemployment Benefits on Recipiency | |

| |

| |

Specification Tests in Binary Choice Models | |

| |

| |

Relaxing Some Assumptions in Binary Choice Models | |

| |

| |

Multi-response Models | |

| |

| |

Ordered Response Models | |

| |

| |

About Normalization | |

| |

| |

Illustration: Willingness to Pay for Natural Areas | |

| |

| |

Multinomial Models | |

| |

| |

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 | |

| |

| |

Exercises | |

| |

| |

Univariate Time Series Models | |

| |

| |

Introduction | |

| |

| |

Some Examples | |

| |

| |

Stationarity and the Autocorrelation Function | |

| |

| |

General ARMA Processes | |

| |

| |

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 | |

| |

| |

Illustration: Quarterly Disposable Income | |

| |

| |

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: Modelling Quarterly Disposable Income | |

| |

| |

Predicting with ARMA Models | |

| |

| |

The Optimal Predictor | |

| |

| |

Prediction Accuracy | |

| |

| |

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? | |

| |

| |

Exercises | |

| |

| |

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 | |

| |

| |

Illustration: Long-run Purchasing Power Parity (Part 3) | |

| |

| |

Illustration: Money Demand and Inflation | |

| |

| |

Concluding Remarks | |

| |

| |

Exercises | |

| |

| |

Models Based on Panel Data | |

| |

| |

Advantages of Panel Data | |

| |

| |

Efficiency of Parameter Estimators | |

| |

| |

Identification of Parameters | |

| |

| |

The Static Linear Model | |

| |

| |

The Fixed Effects Model | |

| |

| |

The Random Effects Model | |

| |

| |

Fixed Effects or Random Effects? | |

| |

| |

Goodness-of-fit | |

| |

| |

Alternative Instrumental Variables Estimators | |

| |

| |

Alternative Error Structures | |

| |

| |

Testing for Heteroskedasticity and Autocorrelation | |

| |

| |

Illustration: Explaining Individual Wages | |

| |

| |

Dynamic Linear Models | |

| |

| |

An Autoregressive Panel Data Model | |

| |

| |

Dynamic Models with Exogenous Variables | |

| |

| |

Unit Roots and Cointegration | |

| |

| |

Illustration: Wage Elasticities of Labour Demand | |

| |

| |

Models with Limited Dependent Variables | |

| |

| |

Binary Choice Models | |

| |

| |

The Fixed Effects Logit Model | |

| |

| |

The Random Effects Probit Model | |

| |

| |

Tobit Models | |

| |

| |

Dynamics and the Problem of Initial Conditions | |

| |

| |

Incomplete Panels and Selection Bias | |

| |

| |

Estimation with Randomly Missing Data | |

| |

| |

Selection Bias and Some Simple Tests | |

| |

| |

Estimation with Nonrandomly Missing Data | |

| |

| |

Exercises | |

| |

| |

Vectors and Matrices | |

| |

| |

Terminology | |

| |

| |

Matrix Manipulations | |

| |

| |

Properties of Matrices and Vectors | |

| |

| |

Inverse Matrices | |

| |

| |

Idempotent Matrices | |

| |

| |

Eigenvalues and Eigenvectors | |

| |

| |

Differentiation | |

| |

| |

Some Least Squares Manipulations | |

| |

| |

Statistical and Distribution Theory | |

| |

| |

Discrete Random Variables | |

| |

| |

Continuous Random Variables | |

| |

| |

Expectations and Moments | |

| |

| |

Multivariate Distributions | |

| |

| |

Conditional Distributions | |

| |

| |

The Normal Distribution | |

| |

| |

Related Distributions | |

| |

| |

Bibliography | |

| |

| |

Index | |