Principles of Econometrics: Theory and Applications (Classroom Companion: Economics)

This textbook teaches the basics of econometrics and focuses on the acquisition of methods and skills that are essential for any student to succeed in their studies, as well as for any practitioner interested in applying econometric techniques. Employing a pedagogical and easy-to-follow style, the book puts into practice the various concepts presented, such as statistics, tests, and methods, among others. Numerous examples and empirical applications using existing econometric and statistical software are given after each theoretical presentation. The book addresses students at the undergraduate and graduate levels in economics and management, as well as students of engineering and business schools. It will further appeal to professionals and practitioners of econometrics, such as economists and researchers in companies and institutions, who will find practical solutions to the different problems they are confronted with. Preface About This Book Contents About the Author 1 Introductory Developments 1.1 What Is Econometrics? Some Introductory Examples 1.1.1 Answers to Many Questions 1.1.2 The Example of Consumption and Income 1.1.3 The Answers to the Other Questions Asked 1.2 Model and Variable 1.2.1 The Concept of Model 1.2.2 Different Types of Data 1.2.3 Explained Variable/Explanatory Variable 1.2.4 Error Term 1.3 Statistics Reminders 1.3.1 Mean 1.3.2 Variance, Standard Deviation, and Covariance 1.3.3 Linear Correlation Coefficient 1.3.4 Empirical Application 1.4 A Brief Introduction to the Concept of Stationarity 1.4.1 Stationarity in the Mean 1.4.2 Stationarity in the Variance 1.4.3 Empirical Application: A Study of the Nikkei Index 1.5 Databases and Software 1.5.1 Databases 1.5.2 Econometric Software Conclusion The Gist of the Chapter Further Reading 2 The Simple Regression Model 2.1 General 2.1.1 The Linearity Assumption Linearity in the Variables Linearity in the Parameters Linear Model 2.1.2 Specification of the Simple Regression Model and Properties of the Error Term The Nullity of the Mean Error The Absence of Autocorrelation in Errors The Homoskedasticity of Errors The Normality of Errors 2.1.3 Summary: Specification of the Simple Regression Model 2.2 The Ordinary Least Squares (OLS) Method 2.2.1 Objective and Reminder of Hypotheses 2.2.2 The OLS Principle 2.2.3 The OLS Estimators Searching for Estimators Example: The Phillips Curve and the Natural Unemployment Rate A Cross-Sectional Example: The Consumption-Income Relationship Summary and Properties 2.2.4 Properties of OLS Estimators Linear Estimators Unbiased Estimators Consistent and Minimum Variance Estimators 2.2.5 OLS Estimator of the Variance of the Error Term Finding the Estimator of the Error Variance Estimation of the Variances of the OLS Estimators 2.2.6 Empirical Application 2.3 Tests on the Regression Parameters 2.3.1 Determining the Distributions Followed by the OLS Estimators 2.3.2 Tests on the Regression Coefficients Test on α Test on β Test on σ2 2.3.3 Empirical Application 2.4 Analysis of Variance and Coefficient of Determination 2.4.1 Analysis of Variance (ANOVA) 2.4.2 Coefficient of Determination 2.4.3 Analysis of Variance and Significance Test of the Coefficient β 2.4.4 Empirical Application 2.5 Prediction 2.6 Some Extensions of the Simple Regression Model 2.6.1 Log-Linear Model 2.6.2 Semi-Log Model 2.6.3 Reciprocal Model 2.6.4 Log-Inverse or Log-Reciprocal Model Conclusion The Gist of the Chapter Further Reading Appendix 2.1: Demonstrations Appendix 2.1.1: Demonstration of the Linearity of the OLS Estimators Appendix 2.1.2: Demonstration of the Unbiasedness Property of the OLS Estimators Appendix 2.1.3: Demonstration of the Consistency and Minimum Variance Property of the OLS Estimators Appendix 2.1.4: Calculation of the Estimator of the Variance of the Error Term Appendix 2.1.5: Calculation of the Standard Deviation of the Forecast Error and Prediction Interval Appendix 2.2: Normal Distribution and Normality Test Appendix 2.3: The Maximum Likelihood Method 3 The Multiple Regression Model 3.1 Writing the Model in Matrix Form 3.2 The OLS Estimators 3.2.1 Assumptions of the Multiple Regression Model Hypothesis 1: The Matrix X Is Nonrandom Hypothesis 2: The Matrix X Is of Full Rank Hypothesis 3: The Expectation of the Error Term Is Zero Hypothesis 4: Homoskedasticity and the Absence of Autocorrelation of Errors Hypothesis 5: Normality of Errors 3.2.2 Estimation of Coefficients 3.2.3 Properties of OLS Estimators Linearity of the Estimator Unbiased Estimator Variance-Covariance Matrix of Coefficients Minimum Variance Estimator 3.2.4 Error Variance Estimation 3.2.5 Example Determination of OLS Estimators Practical Calculation 3.3 Tests on the Regression Coefficients 3.3.1 Distribution of Estimators 3.3.2 Tests on a Regression Coefficient 3.3.3 Significance Tests of Several Coefficients Test on a Particular Regression Coefficient Test of Equality of Coefficients Significance Test for All Coefficients Significance Test of a Subset of Coefficients Synthesis 3.4 Analysis of Variance (ANOVA) and Adjusted Coefficient of Determination 3.4.1 Analysis-of-Variance Equation Case of Centered Variables Case of Noncentered Variables 3.4.2 Coefficient of Determination 3.4.3 Adjusted Coefficient of Determination 3.4.4 Partial Correlation Coefficient 3.4.5 Example Analysis-of-Variance Equation: Case of Centered Variables Analysis-of-Variance Equation: Case of Noncentered Variables Tests on the Regression Coefficients Calculation of the Partial Correlation Coefficients 3.5 Some Examples of Cross-Sectional Applications 3.5.1 Determinants of Crime 3.5.2 Health Econometrics 3.5.3 Inequalities and Financial Openness 3.5.4 Inequality and Voting Behavior 3.6 Prediction 3.6.1 Determination of Predicted Value and Prediction Interval 3.6.2 Example 3.7 Model Comparison Criteria 3.7.1 Explanatory Power/Predictive Power of a Model 3.7.2 Coefficient of Determination and Adjusted Coefficient of Determination 3.7.3 Information Criteria Akaike Information Criterion ( AIC) Schwarz Information Criterion (SIC) Hannan-Quinn Information Criterion (HQ) 3.7.4 The Mallows Criterion 3.8 Empirical Application 3.8.1 Practical Calculation of the OLS Estimators 3.8.2 Software Estimation Conclusion The Gist of the Chapter Further Reading Appendix 3.1: Elements of Matrix Algebra General Main Matrix Operations Equality Transposition Addition and Subtraction Matrix Multiplication and Scalar Product Idempotent Matrix Rank, Trace, Determinant, and Inverse Matrix Rank of a Matrix Trace of a Matrix Determinant of a Matrix Inverse Matrix Appendix 3.2: Demonstrations Appendix 3.2.1: Demonstration of the Minimum Variance Property of OLS Estimators Appendix 3.2.2: Calculation of the Error Variance Appendix 3.2.3: Significance Tests of Several Coefficients 4 Heteroskedasticity and Autocorrelation of Errors 4.1 The Generalized Least Squares (GLS) Estimators 4.1.1 Properties of OLS Estimators in the Presence of Autocorrelation and/or Heteroskedasticity 4.1.2 The Generalized Least Squares (GLS) Method 4.1.3 Estimation of the Variance of the Errors 4.2 Heteroskedasticity of Errors 4.2.1 The Sources of Heteroskedasticity 4.2.2 Estimation When There Is Heteroskedasticity 4.2.3 Detecting Heteroskedasticity The Goldfeld and Quandt Test (1965) The Glejser Test (1969) The Breusch-Pagan Test (1979) The White Test (1980) ARCH Test 4.2.4 Estimation Procedures When There Is Heteroskedasticity The White Estimator of the Variance-Covariance Matrix The Newey and West Estimator of the Variance-Covariance Matrix Hypotheses About the Form of Heteroskedasticity Note on the Logarithmic Transformation 4.2.5 Empirical Application The Goldfeld and Quandt Test The Glejser Test The Breusch-Pagan Test The White Test ARCH Test Heteroskedasticity-Corrected Estimations 4.3 Autocorrelation of Errors 4.3.1 Sources of Autocorrelation 4.3.2 Estimation When There Is Autocorrelation 4.3.3 Detecting Autocorrelation The Geary Test (1970) The Durbin and Watson Test (1950, 1951) The Durbin Test (1970) The Breusch-Godfrey Test The Box-Pierce (1970) and Ljung-Box (1978) Tests 4.3.4 Estimation Procedures in the Presence of Error Autocorrelation Case Where the Variance of the Error Term Is Known: General Principle of GLS Case Where the Variance of the Error Term Is Unknown: Pseudo GLS Methods 4.3.5 Prediction in the Presence of Error Autocorrelation 4.3.6 Empirical Application Conclusion The Gist of the Chapter Further Reading 5 Problems with Explanatory Variables 5.1 Random Explanatory Variables and the Instrumental Variables Method 5.1.1 Instrumental Variables Estimator 5.1.2 The Hausman1978 Specification Test 5.1.3 Application Example: Measurement Error 5.2 Multicollinearity and Variable Selection 5.2.1 Presentation of the Problem 5.2.2 The Effects of Multicollinearity 5.2.3 Detecting Multicollinearity Correlation Between Explanatory Variables The Klein Test (1962) The Farrar and Glauber Test (1967) The Eigenvalue Method Variance Inflation Factors Empirical Application 5.2.4 Solutions to Multicollinearity Use of Preliminary Estimates The Ridge Regression Other Techniques 5.2.5 Variable Selection Methods The Method of All Possible Regressions Backward Elimination of Explanatory Variables Forward Selection of Explanatory Variables The Stepwise Method Empirical Application 5.3 Structural Changes and Indicator Variables 5.3.1 The Constrained Least Squares Method 5.3.2 The Introduction of Indicator Variables Definition Introductory Examples Model Containing Only Indicator Variables Model Containing Indicator and Usual Explanatory Variables Interactions Use of Indicator Variables for Deseasonalization Empirical Application 5.3.3 Coefficient Stability Tests Rolling Regressions and Recursive Residuals The Chow Test (1960) Empirical Application Conclusion The Gist of the Chapter Further Reading Appendix: Demonstration of the Formula for Constrained Least Squares Estimators 6 Distributed Lag Models 6.1 Why Introduce Lags? Some Examples 6.2 General Formulation and Definitions of DistributedLag Models 6.3 Determination of the Number of Lags and Estimation 6.3.1 Determination of the Number of Lags 6.3.2 The Question of Estimating Distributed Lag Models 6.4 Finite Distributed Lag Models: Almon Lag Models 6.5 Infinite Distributed Lag Models 6.5.1 The Koyck Approach The Koyck Transformation Estimation: The Instrumental Variables Method The Partial Adjustment Model The Adaptive Expectations Model 6.5.2 The Pascal Approach 6.6 Autoregressive Distributed Lag Models 6.6.1 Writing the ARDL Model 6.6.2 Calculation of ARDL Model Weights 6.7 Empirical Application Conclusion The Gist of the Chapter Further Reading 7 An Introduction to Time Series Models 7.1 Some Definitions 7.1.1 Time Series 7.1.2 Second-Order Stationarity 7.1.3 Autocovariance Function, Autocorrelation Function, and Partial Autocorrelation Function 7.2 Stationarity: Autocorrelation Function and Unit Root Test 7.2.1 Study of the Autocorrelation Function 7.2.2 TS and DS Processes Characteristics of TS Processes Characteristics of DS Processes 7.2.3 The Dickey-Fuller Test Simple Dickey-Fuller (DF) Test Augmented Dickey-Fuller (ADF) Test Sequential Testing Strategy Empirical Application 7.3 ARMA Processes 7.3.1 Definitions Autoregressive Processes Moving-Average Processes Autoregressive Moving-Average Processes: ARMA(p,q) 7.3.2 The Box and Jenkins Methodology Step 1: Identification of ARMA Processes Step 2: Estimation of ARMA Processes Step 3: Validation of ARMA Processes Step 4: Prediction of ARMA Processes 7.3.3 Empirical Application Step 1: Identification Step 2: Estimation Step 3: Validation 7.4 Extension to the Multivariate Case: VAR Processes 7.4.1 Writing the Model Introductory Example General Formulation 7.4.2 Estimation of the Parameters of a VAR(p) Process and Validation 7.4.3 Forecasting VAR Processes 7.4.4 Granger Causality 7.4.5 Empirical Application 7.5 Cointegration and Error-Correction Models 7.5.1 The Problem of Spurious Regressions 7.5.2 The Concept of Cointegration 7.5.3 Error-Correction Models 7.5.4 Estimation of Error-Correction Models and Cointegration Tests: The EngleandGranger1987 Approach Two-Step Estimation Method Dickey-Fuller Test of No Cointegration Example: The Relationship Between Prices and Dividends 7.5.5 Empirical Application Conclusion The Gist of the Chapter Further Reading 8 Simultaneous Equations Models 8.1 The Analytical Framework 8.1.1 Introductory Example 8.1.2 General Form of Simultaneous Equations Models 8.2 The Identification Problem 8.2.1 Problem Description 8.2.2 Rank and Order Conditions for Identification Restrictions Conditions for Identification 8.3 Estimation Methods 8.3.1 Indirect Least Squares 8.3.2 Two-Stage Least Squares 8.3.3 Full-Information Methods 8.4 Specification Test 8.5 Empirical Application 8.5.1 Writing the Model 8.5.2 Conditions for Identification 8.5.3 Data 8.5.4 Model Estimation OLS Estimation Equation by Equation Two-Stage Least Squares Estimation Three-Stage Least Squares Estimation Full-Information Maximum Likelihood Estimation Conclusion The Gist of the Chapter Further Reading Appendix: Statistical Tables Standard Normal Distribution Student t Distribution: Critical Values of t Chi-Squared Distribution: Critical Values of c Fisher–Snedecor Distribution: Critical Values of F Durbin–Watson Critical Values References Index