Contents
Chapter 1 The Nature of Econometrics and Economic Data
1 What Is Econometrics?
1.2 Steps in Empirical Economic Analysis
1.3 The Structure of Economic Data
Cross-Sectionai Data
Time Series Data
Pooied Cross Sections
Panei or Longitudinal Data
A Comnent on Data Structures
1.4 Causality and the Notion of Ceteris Paribus in Econometric
Analysis
Summary
Key Terms

PART 1
REGRESSION ANALYSIS WITR CROSS-SECTIONAL DATA

Chapter 2 The Simple Regression Model
2.1 Definition of the Simple Regression Model
2.2 Deriving the Ordinary Least Squares Estimates
A Note on Terminoiogy
2.3 Mechanics of OLS
Fitted Vaiues and Residuais
Algebraic Properties of OLS Statistics
Goodness-of-Fit
2.4 Units of Measurement and Functional Form
The Effects of c/uanging Units ofMeasurement on OLS Statistics
Incorporating Nonlinearities in Simpie Regression
The Meaning of Linear" Regression
2.5 Expected Values and Variances of the OLS Estimators
Unbiasedness of OLS
Variances of the OLS Estimators
Estimating the Error Variance
2.6 Regression Through the Origin
Summary
Key Terms
Problems
Computer Exercises
Appendix 2A

Chapter 3 Multiple Regression Analysis: Estimation
3.1 Motivation for Multiple Regression
The Model with Two Independent Variables
The Model with k Independent Variables
3.2 Mechanics and Interpretation of Ordinary Least Squares
Obtaining the OLS Estimates
Interpreting the OLS Regression Equation
On the Meaning of "Holding Other Factors Fixed" in Multiple
Regression
Changing More than One Independent Variable Simultaneously
OLS Fitted Values and Residuais
A "Partialling Our" Interpretation of Multiple Regression
Comparison of Simple and Multiple Regression Estimates
Goodness-of-Fir
Regression Through the Origin
3.3 The Expected Value of the OLS Estimators
Including Irrelevant Variables in a Regression Model
Omitted Variable Bias: The Simple Case
Omitted Variable Bias: More General Cases
3.4 The Variance of the OLS Estimators
The Components of the OLS Variances: Multicollinearily
Variances in Misspeczfied Modeis
Estimating 0.2: Standard Errors of the OLS Estimators
3.5 Efficiency of OLS: The Gauss-Markov Theorem
Summary
Key Terms
Problems
Computer Exercises
Appendix 3 A

Chapter 4 Multiple Regression Analysis: Inference
4.1 Sampling Distributions of the OLS Estimators
4.2 Testing Hypotheses About a Single Population Parameter:
The t Test
Testing Against One-Sided Alternatives
Two-SidedAlternatives
Testing Other Hypotheses About B
Computing p-Values for t Tests
A Reminder on the Language of Classical Hypothesis Testing
Econornic, or Practical, versus Statistical Significance
4.3 Confidence Intervals
4.4 Testing Hypotheses About a Single Linear Combination of the Parameters
4.5 Testing Multiple Linear Restrictions: The FTest
Testing Exclusion Restrictions
Relationship Between F and t Sratistics
The R-Squared Form of the F Statistic
Computing p-Valuesjbr F Tests
The F Statistic for Overali Significance of a Regression
Testing General Linear Restrictions
4.6 Reporting Regression Results
Summary
KeyTerms
Problems
Computer Exercises

Chapter 5 Multiple Regression Analysis: OLS Asymptotics
5.1 Consistency
Deriving the Jnconsistencv ia OLS
5.2 Asymptotic Normality and Large Sample Inference
Other Large Sample Tests: The Lagrange Multiplier
Statistic
5.3 Asymptotic Efficiency of OLS
Summary
KeyTerms
Problems
Computer Exercises
Appendix 5A

Chapter 6 Multiple Regression Analysis: Further Issues
6.1 Effects of Data Scaling on OLS Statistics
Beta Coefficients
6.2 More on Functional Form
More on Using Logarithmic Functional Forrns
Modeis with Quadratics
Models with Interaction Terms
6.3 More on Goodness-of-Fit and Selection of Regressors
Adjusted R-Squared
Using Adjusted R-Squared to Choose Between IVonnested
Modeis
Controlling for Too Manv Factors in Regression Analvsis
Adding Regressors to Reduce the Error Variance
6.4 Prediction and Residual Analysis
Confidence Inrervais for Predictions
Residual Analvsis
Predicting y when log(y) Is the Dependem Variabie
Summary
KeyTerms
Problems
Computer Exercises

Chapter 7 Multiple Regression Analysis with Qualitative Information:
Binary (or Dummy) Variables
7.1 Describing Qualitative Enformation
7.2 A Single Dummy Independent Variable
Interpreting Coefficients on Dummy Explanatory Variables
when the Dependent Variable Is log(y)
7.3 Using Dummy Variables for Multiple Categories
lncorporaring Ordinal Information hy Using Dummy Variables
7.4 Interactions Involving Dummy Variables
Interacrions Among Dummy Variables
Aliowing for Dfferent Siopes
Testing for Differences in Regression Functions Across Groups
7.5 A Binary Dependent Variable: The Linear Probability Model
7.6 More on Policy Analysis and Program Evaluation
Summary
Key Terms
Problems
Computer Exercises

Chapter 8 Heteroskedasticity
8.1 Consequences of Heteroskedasticity for OLS
8.2 Heteroskedasticity-Robust Inference After OLS Estimation
Computing Heteroskedasticity-Robust LM Tests
8.3 Testing for Heteroskedasticity
The White Test for Heteroskedasticity
8.4 Weighted Least Squares Estimation
The Heteroskedasticitv Is Known up to a Multiplicative Constant
The J-Jeteroskedasticity Function Must Be Estirnated: Feasible GLS
8.5 The Linear Probability Model Revisited
Summary
Key Terras
Problems
Computer Exercises

Chapter 9 More on Specification and Data Problems
9.1 Functional Form Misspecification
RESET as a General Test for Functional Form
Misspecification
Tests Against Nonnested Alrernatives
9.2 Using Proxy Variables for Unobserved Explanatory Variables
Using Lagged Dependent Variables as Pro.rv Variables
9.3 Properties of OLS Under Measurement Error
Measurement Error in the Dependent Variable
Measurement Error in an Explanatorv Variable
9.4 Missing Data, Nonrandom Samples. and Outlying Observations
Missing Data
Nonrandom Samples
Outliers and Influential Observations
Summary
KeyTerms
Problems
Computer Exercises

PART 2
REGRESSION ANALYSIS WITH TIME SERIES DATA

Chapter 10 Basic Regression Analysis with Time Series Data
10.1 The Nature of Time Series Data
10.2 Examples of Time Series Regression Models
Static Modeis
Emite Disrributed Lag Modeis
A C'onvention abour lhe Time Index
10.3 Finite Sample Properties of OLS Under Classical Assumptions
Unbiasedness of OLS
The Variances of lhe OLS Estimators and lhe Gauss-Markov Theorem
inference under lhe Classical Linear Model Assumptions
10.4 Functional Form, Dummy Variables, and Index Numbers
10.5 Trends and Seasonality
Characterizing Trending Time Series
Using Trending Vuriables in Regression Analysis
A Detrending Interpretation ofRegressions with a Time
Trend
Computing R-Squared when The Dependem' Variable Is
Trending
Seasonalirv
Summary
KeyTerms
Problems
Computer Exercises

Chapter 11 Further Issues in Using OLS with Time Series Data
11.1 Stationary and Weakly Dependent Time Series
Stationarv and Nonstationarv Time Series
Weaklv Dependent Time Series
11.2 Asymptotic Properties of OLS
11.3 Using Highly Persistent Time Series in Regression Analysis
Highlv Persistent Time Series
Transforinations on Highlv Persistent Time Series
Deciding Whether a Time Series Is 1(1)
11.4 Dynamically Complete Modeis and the Absence of Serial Correlation
11.5 The Homoskedasticity Assumption for Time Series Modeis
Sunimary
Key Terms
Problems
Computer Exercises

Chapter 12 Serial Correlation and Heteroskedasticity in Time Series Regressions
12.1 Properties of OLS with Serially Correlated Errors
Unbiasedness and Consistency
Efficiency and Inference
Goodness-ofFit
Serial Correlation in the Presence of Lagged Dependenr Variables
12.2 Testmg for Serial Correlation
A t Testfor AR(1) Serial Correlation with Strictly Exogenous
Regressors
The Durbin-Watson Tesi under Classical Assurnptions
Testing for AR(]) Serial Correlation without Strictly Exogenous
Regressors
Testing for Higher Order Serial Correlation
12.3 Correcting for Serial Correlation with Strictly Exogenous Regressors
Obraining the Besr Linear Unbiased Estimaror in the AR(1)
Model
Feasible GLS Estimation with AR(1) Errors
Comparing OLS and FGLS
Correcring for Higher Order Serial Correlation
12.4 Differencing and Serial Correlation
12.5 Serial Correlation-Robust Inference After OLS
12.6 Heteroskedasticity in Time Series Regressions
Heteroskedasticity-Robust Statistics
Testing for Heteroskedasticitv
Auto regressive Conditional Heteroskedasticity
Heteroskedasticity and Serial Correlation in Regression
Modeis
Sunimary
Key Terms
Problems
Computer Exercises

PART 3
ADVANCED TOPICS

Chapter 13 Pooling Cross Sections Across Time. Simple Panel Data Methods
13.1 Pooling Independent Cross Sections Across Time
The Chow Test for Strucrurai Change Across Time
13.2 Policy Analysis with Pooled Cross Sections
13.3 Two-Period Panei Data Analysis Organizing Panei Data
13.4 Policy Analysis with Two-Period Panei Data
13.5 Differencing with More than Two Time Periods
Summary
Key Terms
Problems
Computer Exercises
Appendix 13A
Chapter 14 Advanced Panei Data Methods
14.1 Fixed Effects Estimation
The Dummy Variable Regression
Fixed Effects or First Dfferencing?
Fixed Effects with Unbalanced Paneis
14.2 Random Effects Modeis
Random Effects or Fixed Effects?
14.3 Applying Panei Data Methods to Other Data Structures
Summary
Key Terms
Problems
Computer Exercises
Appendix 14A
Chapter 15 Instrumental Variabies Estimation and Two Stage Least Squares
15.1 Motivation: Omitted Variables in a Simple Regression Model
Statistical Inference with the IV Estimator
Properties oJIV with a Poor Instrumental Variabie
Coinpuring R-Squared after IV Esriination
15.2 IV Estimation of the Multiple Regression Model
15.3 Two Stage Least Squares
A Single Endogenous Explanatoiy Variable
Multicoliinearitv and 2SLS
Multiple Endogenous Explanatory Variables
Testing Multiple Hypotheses after 2SLS Estimation
15.4 IV Solutions to Errors-in-Variables Problems
15.5 Testing for Endogeneity and Testing Overidentifying Restrictions
Testing for Endogeneity
Testing Overidentification Restrictions
15.6 2SLS with Heteroskedasticity
15.7 Applying 2SLS to Time Series Equations
15.8 Applying 2SLS to Pooled Cross Sections and Panei Data
Summary
KeyTerms
Problems
Computer Exercises
Appendix iSA

Chapter 16 Simultaneous Equations Modeis
16.1 The Nature of Simuitaneous Equations Modeis
16.2 Simultaneity Bias in OLS
16.3 Identifying and Estimatirig a Structural Equation
Idenhification in a Two-Equarion Ss'stem
Estimation bv 2SLS
16.4 Systems with More than Two Equations
Identification in Systems with Three or More Equations
Estimation
16.5 Simultaneous Equations Models with Time Series
16.6 Simultaneous Equations Modeis with Panei Data
Summary
Key Terms
Problems
Computer Exercises

Chapter 17 Limited Dependent Vanable Modeis and Sample Selection Corrections
17.1 Logit and Probit Modeis for Binary Response
Specifying Logit and Probit Modeis
Maximum Likelihood Estimation of Logit and Probit
Modeis
Testing Multiple Hypotheses
inrerprering fixe Logit and Probit Estimares
17.2 The Tobit Model for Comer Solution Responses
interprering the Tobit Estimules
Specification Issues in Tobit Modeis
17.3 The Poisson Regression Model
17.4 Censored and Truncated Regression Modeis
Censored Regression Modeis
Truncated Regression Models
17.5 Sample Selection Corrections
When is OLS on the Selected Sample Consistent?
Incidental Truncation
Summary
Key Terms
Problems
Computer Exercises
Appendix 17A

Chapter 18 Advanced Time Series Topics
18.1 intinite Distributed Lag Models
The Geometric (or Koyck) Distributed Lag
Rational Distributed Lag Modeis
18.2 Testing for Unit Roots
18.3 Spurious Regression
18.4 Cointegration and Error Correction Modeis
Cointegration
Error Correction Modeis
18.5 Forecasting
Types of Regression Modeis Used for Forecasting
One-Step-Ahead Forecasting
C'omparing One-Step-Ahead Forecasis
Multiple Step-Ahead-Forecasts
Forecasting Trending, Seasonal, and Inregrated Processes
Summary
Key Terms
Problems
Computer Exercises

Chapter 19 Carrying out an Empirical Project
19.1 Posing a Question
19.2 Literature Review
19.3 Data Coliection
Deciding on the Appropriate Data Se
Eniering and Storing Your Data
Jnspecting. Cleaning, and Suinmarizing Your Data
19.4 Econometric Analysis
19.5 Writing an Empirical Paper
Introduction
Conceptual (ar Theoretica!) Framework
Econo,netric Modeis and Esti,nation Methods
The Data
Results
Conclusions
Stvle Hints
Summary
Key Terms
Sample Empirical Projects
List of Journals
Data Sources

APPENDICES
Appendix A Basic Mathematical Tools
A. 1 The Surnmation Operator and Descriptive Statistics
A.2 Properties of Linear Functions
A.3 Proportions and Percentages
A.4 Some Special Functions and Their Properties
Quadratic Functions
The Natural Logarithm
The Exponential Function
A.5 Differential Calculus
Suminary
Key Terms
Problems
Appendix B Fundamentais of Probability
B.1 Random Variables and Their Probability Distributions
Discrete Random Variables
Conrinuous Random Variables
B.2 Joint Distributions. Conditional Distributions, and lndependence
Joini Distributions and independence
C'onditional Distributions
B.3 Features of Probability Distributions
A Measure of Central Tendencv: The Expected Value
Properties ofExpected Values
Another Measure of Central Tendencv: The Median
Measures of Variahilirv: Variance and Standard Deviarion
Variance
Standard Deviation
Standardizing a Random Variable
B.4 Features of Joint and Conditional Distributions
Measures ofAssociation. Covariance and Correlation
Cova riance
Correlation Coefficient
Variance of Sums of Random Variables
Conditional Expectation
Properties of Conditional Expectation
Conditional Variance
B.5 The Normal and Related Distributions
The Normal Distribution
The Standard Normal Distribution
Additional Properties of the Normal Distribution
The Chi-Square Distribution
The t Distribution
The F Distribution
Summary
Key Terms
Problems
Appendix C Fundamentais of Mathematicai Statistics
CI Populations, Parameters, and Random Sampling
Sampling
C.2 Finite Sample Properties of Estimators
Estimators and Estimates
Unbiasedness
The Sampling Variance of Estimators
Efficiency
C.3 Asymptotic or Large Sample Properties of Estimators
Consistency
Asymptotic Normaiitv
C.4 General Approaches to Parameter Estimation
Method ofMoments
Maximum Likelihood
Leasi Squares
C.5 Interval Estimation and Confidence Intervals
The Nature of Interval Estimation
Confidence intervals ftr the Mean from a Normallv Distributed
Population
A Simple Rule of Thumb fora 95% Confidence Interval
Asyrnptotic Confidence íntervals for Nonnormal
Populations
C.6 Hypothesis Testing
Fundamentais of Hypothesis Testing
Testing Hvpotheses About me Mean iii a Normal
Population
Asymptotic Tesis for Nonnormai Populations
Computing and Lising p- Values
The Relarionship Between Confidence Intervais and Hypothesis Tes/ing
Practical Versus Statistical Significance
C.7 Remarks on Notation
Summary
Key Terms
Problems
Appendix D Summary of Matrix Algebra
D.1 Basic Definitions
D.2 Matrix Operations
Matrix Addition
Scalar Multiplication
Matrix Multiplication
Transpose
Partitioned Matrix Multiplication
Trace
Inverse
D.3 Linear Independence. Rank of a Matrix
D.4 Quadratic Forms and Positive Definite Matrices
D.5 ldempotent Matrices
D.6 Differentiation of Linear and Quadratic Forms
D.7Moments and Distributions of Random Vectors
Expected Value
Variance-Covariance Matrix
Multivariate Normal Distribution
Chi-Square Distribution
t Distribution
F Distribution
Summary
Key Terms
Problems
Appendix E The Linear Regression Model in Matrix Form
E.1 The Model and Ordinary Least Squares Estimation
E.2 Finite Sample Properties of OLS
E.3 Statistical Inference
E.4 Some Asymptotic Analysis
Wald Statistics for Testing Multiple Hvporheses
Summary
Key Terms
Problems
Appendix F Answers to Chapter Questions
Appendix G Statistical Tables