Introduction to Econometrics, 2nd Edition

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Brief Contents
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PART ONE: INTRODUCTION AND REVIEW
Chapter 1 Economic Questions and Data
Chapter 2 Review of Probability
Chapter 3 Review of Statistics

PART TWO: FUNDAMENTALS OF REGRESSION ANALYSIS
Chapter 4 Linear Regression with One Regressor
Chapter 5 Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals
Chapter 6 Linear Regression with Multiple Regressors
Chapter 7 Hypothesis Tests and Confidence Intervals in Multiple Regression
Chapter 8 Nonlinear Regression Functions
Chapter 9 Assessing Studies Based on Multiple Regression

PART THREE: FURTHER TOPICS IN REGRESSION ANALYSIS
Chapter 10 Regression with Panel Data
Chapter 11 Regression with a Binary Dependent Variable
Chapter 12 Instrumental Variables Regression
Chapter 13 Experiments and Quasi-Experiments

PART FOUR: REGRESSION ANALYSIS OF ECONOMIC TIME SERIES DATA
Chapter 14 Introduction to Time Series Regression and Forecasting
Chapter 15 Estimation of Dynamic Causal Effects
Chapter 16 Additional Topics in Time Series Regression

PART FIVE: THE ECONOMETRIC THEORY OF REGRESSION ANALYSIS
Chapter 17 The Theory of Linear Regression with One Regressor
Chapter 18 The Theory of Multiple Regression
Appendix: Statistical Tables 

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Table of contents
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Preface
Part One Introduction and Review
Chapter 1 Economic Questions and Data
1.1 Economic Questions We Examine
Question #1: Does Reducing Class Size Improve Elementary School Education?
Question #2: Is There Racial Discrimination in the Market for Home Loans?
Question #3: How Much Do Cigarette Taxes Reduce Smoking?
Question #4: What Will the Rate of Inflation Be Next Year?
Quantitative Questions, Quantitative Answers
1.2 Causal Effects and Idealized Experiments
Estimation of Causal Effects
Forecasting and Causality
1.3 Data: Sources and Types
Experimental versus Observational Data
Cross-Sectional Data
Time Series Data
Panel Data

Chapter 2 Review of Probability
2.1 Random Variables and Probability Distributions
Probabilities, the Sample Space, and Random Variables
Probability Distribution of a Discrete Random Variable
Probability Distribution of a Continuous Random Variable
2.2 Expected Values, Mean, and Variance
The Expected Value of a Random Variable
The Standard Deviation and Variance
Mean and Variance of a Linear Function of a Random Variable
Other Measures of the Shape of Distribution
2.3 Two Random Variables
Joint and Marginal Distributions
Conditional Distributions
Independence
Covariance and Correlation
The Mean and Variance of Sums of Random Variables
2.4 The Normal, Chi-Squared, Student t, and F Distributions
The Normal Distribution
The Chi-Squared Distribution
The Student t Distribution
The F Distribution
2.5 Random Sampling and the Distribution of the Sample Average
Random Sampling
The Sampling Distribution of the Sample Average
2.6 Large-Sample Approximations to Sampling Distributions
The Law of Large Numbers and Consistency
The Central Limit Theorem
Appendix 2.1   Derivation of Results in Key Concept 2.3

Chapter 3  Review of Statistics
3.1 Estimation of the Population Mean
Estimators and Their Properties
Properties of Y-bar
The Importance of Random Sampling
3.2 Hypothesis Tests Concerning the Population Mean
Null and Alternative Hypotheses
The p-Value
Calculating the p-Value When sigmaY Is Known
The Sample Variance, Sample Standard Deviation, and Standard Error
Calculating the p-Value When sigmaY Is Unknown
The t-Statistic
Hypothesis Testing with a Prespecified Significance Level
One-Sided Alternatives
3.3 Confidence Intervals for the Population Mean
3.4 Comparing Means from Different Populations
Hypothesis Tests for the Difference Between Two Means
Confidence Intervals for the Difference Between Two Population Means
3.5 Differences-of-Means Estimation of Causal Effects Using Experimental Data
The Causal Effect as a Difference of Conditional Expectations
Estimation of the Causal Effect Using Differences of Means
3.6 Using the t-Statistic When the Sample Size Is Small
The t-Statistic and the Student t Distribution
Use of the Student t Distribution in Practice
3.7 Scatterplots, the Sample Covariance, and the Sample Correlation
Scatterplots
Sample Covariance and Correlation
Appendix 3.1   The U.S. Current Population Survey
Appendix 3.2   Two Proofs That Y-bar Is the Least Squares Estimator of muY
Appendix 3.3   A Proof That the Sample Variance Is Consistent
Part Two Fundamentals of Regression Analysis
Chapter 4 Linear Regression with One Regressor
4.1 The Linear Regression Model
4.2 Estimating the Coefficients of the Linear Regression Model
The Ordinary Least Squares Estimator
OLS Estimates of the Relationship Between Test Scores and the Student-Teacher Ratio
Why Use the OLS Estimator?
4.3 Measures of Fit
The R2
The Standard Error of the Regression
Application to the Test Score Data
4.4 The Least Squares Assumptions
Assumption #1: The Conditional Distribution of ui Given Xi Has a Mean of Zero
Assumption #2: (Xi, Yi) i = 1, ..., n Are Independently and Identically Distributed
Assumption #3: Large Outliers are Unlikely
Use of the Lease Squares Assumptions
4.5 The Sampling Distribution of the OLS Estimators
The Sampling Distribution of the OLS Estimators
4.6 Conclusion
Appendix 4.1   The California Test Score Data Set
Appendix 4.2   Derivation of the OLS Estimators
Appendix 4.3   Sampling Distribution of the OLS Estimator

Chapter 5 Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals
5.1 Testing Hypotheses About One of the Regression Coefficients
Two-Sided Hypotheses Concerning beta1
One-Sided Hypotheses Concerning beta1
Testing Hypotheses About the Intercept beta0
5.2 Confidence Intervals for a Regression Coefficient
5.3 Regression When X Is a Binary Variable
Interpretation of the Regression Coefficients
5.4 Heteroskedasticity and Homoskedasticity
What Are Heteroskedasticity and Homoskedasticity?
Mathematical Implications of Homoskedasticity
What Does This Mean in Practice?
5.5 The Theoretical Foundations of Ordinary Least Squares
Linear Conditionally Unbiased Estimators and the Gauss–Markov Theorem
Regression Estimators Other Than OLS
5.6 Using the t-Statistic in Regression When the Sample Size Is Small
The t-Statistic and the Student t Distribution
Use of the Student t Distribution in Practice
5.7 Conclusion
Appendix 5.1   Formulas for OLS Standard Errors
Appendix 5.2   The Gauss–Markov Conditions and a Proof of the Gauss–Markov Theorem

Chapter 6 Linear Regression with Multiple Regressors
6.1 Omitted Variable Bias
Definition of Omitted Variable Bias
A Formula for Omitted Variable Bias
Addressing Omitted Variable Bias by Dividing the Data into Groups
6.2 The Multiple Regression Model
The Population Regression Line
The Population Multiple Regression Model
6.3 The OLS Estimator in Multiple Regression
The OLS Estimator
Application to Test Scores and the Student-Teacher Ratio
6.4 Measures of Fit in Multiple Regression
The Standard Error of the Regression (SER)
The R2
The “Adjusted R2”
Application to Test Scores
6.5 The Least Squares Assumptions in Multiple Regression
Assumption #1: The Conditional Distribution of ui Given X1i, X2i, ..., Xki Has a Mean of Zero
Assumption #2: (X1i, X2i, ..., Xki, Yi)i=1, ..., n Are i.i.d.
Assumption #3: Large Outliers are Unlikely
Assumption #4: No Perfect Multicollinearity
6.6 The Distribution of the OLS Estimators in Multiple Regression
6.7 Multicollinearity
Examples of Perfect Multicollinearity
Imperfect Multicollinearity
6.8 Conclusion
Appendix 6.1   Derivation of Equation (6.1)
Appendix 6.2   Distribution of the OLS Estimators When There Are Two Regressors and Homoskedastic Errors

Chapter 7  Hypothesis Tests and Confidence Intervals in Multiple Regression
7.1 Hypothesis Tests and Confidence Intervals for a Single Coefficient
Standard Errors for the OLS Estimators
Hypothesis Tests for a Single Coefficient
Confidence Intervals for a Single Coefficient
Application to Test Scores and the Student-Teacher Ratio
7.2 Tests of Joint Hypotheses
Testing Hypotheses on Two or More Coefficients
The F-Statistic
Application to Test Scores and the Student-Teacher Ratio
The Homoskedasticity-Only F-Statistic
7.3 Testing Single Restrictions Involving Multiple Coefficients
7.4 Confidence Sets for Multiple Coefficients
7.5 Model Specification for Multiple Regression
Omitted Variable Bias in Multiple Regression
Model Specification in Theory and Practice
Interpreting the R2 and the Adjusted R2 in Practice
7.6 Analysis of the Test Score Data Set
7.7 Conclusion
Appendix 7.1   The Bonferroni Test of a Joint Hypothesis

Chapter 8  Nonlinear Regression Functions
8.1 A General Strategy for Modeling Nonlinear Regression Functions
Test Scores and District Income
The Effect on Y of a Change in X in Nonlinear Specifications
A General Approach to Modeling Nonlinearities Using Multiple Regression
8.2 Nonlinear Functions of a Single Independent Variable
Polynomials
Logarithms
Polynomial and Logarithmic Models of Test Scores and District Income
8.3 Interactions Between Independent Variables
Interactions Between Two Binary Variables
Interactions Between a Continuous and a Binary Variable
Interactions Between Two Continuous Variables
8.4 Nonlinear Effects on Test Scores of the Student-Teacher Ratio
Discussion of Regression Results
Summary of Findings
8.5 Conclusion
Appendix 8.1   Regression Functions That Are Nonlinear in the Parameters

Chapter 9  Assessing Studies Based on Multiple Regression
9.1 Internal and External Validity
Threats to Internal Validity
Threats to External Validity
9.2 Threats to Internal Validity of Multiple Regression Analysis

Omitted Variable Bias
Misspecification of the Functional Form of the Regression Function
Errors-in-Variables
Sample Selection
Simultaneous Causality
Sources of Inconsistency of OLS Standard Errors
9.3 Internal and External Validity When the Regression is Used for Forecasting
Using Regression Models for Forecasting
Assessing the Validity of Regression Models for Forecasting
9.4 Example: Test Scores and Class Size
External Validity
Internal Validity
Discussion and Implications
9.5 Conclusion
Appendix 9.1   The Massachusetts Elementary School Testing Data

Part Three Further Topics in Regression Analysis

Chapter 10  Regression with Panel Data
10.1 Panel Data
Example: Traffic Deaths and Alcohol Taxes
10.2 Panel Data with Two Time Periods: \"Before and After\" Comparisons
10.3 Fixed Effects Regression
The Fixed Effects Regression Model
Estimation and Inference
Application to Traffic Deaths
10.4 Regression with Time Fixed Effects
Time Effects Only
Both Entity and Time Fixed Effects
10.5 The Fixed Effects Regression Assumptions and Standard Errors for Fixed Effects Regression
The Fixed Effects Regression Assumptions
Standard Errors for Fixed Effects Regression
10.6 Drunk Driving Laws and Traffic Deaths
10.7 Conclusion
Appendix 10.1   The State Traffic Fatality Data Set
Appendix 10.2   Standard Errors for Fixed Effects Regression with Serially Correlated Errors

Chapter 11  Regression with a Binary Dependent Variable
11.1 Binary Dependent Variables and the Linear Probability Model
Binary Dependent Variables
The Linear Probability Model
11.2 Probit and Logit Regression
Probit Regression
Logit Regression
Comparing the Linear Probability, Probit, and Logit Models
11.3 Estimation and Inference in the Logit and Probit Models
Nonlinear Least Squares Estimation
Maximum Likelihood Estimation
Measures of Fit
11.4 Application to the Boston HMDA Data
11.5 Summary
Appendix 11.1   The Boston HMDA Data Set
Appendix 11.2   Maximum Likelihood Estimation
Appendix 11.3 Other Limited Dependent Variable Models

Chapter 12  Instrumental Variables Regression
12.1 The IV Estimator with a Single Regressor and a Single Instrument
The IV Model and Assumptions
The Two Stage Least Squares Estimator
Why Does IV Regression Work?
The Sampling Distribution of the TSLS Estimator
Application to the Demand for Cigarettes
12.2 The General IV Regression Model
TSLS in the General IV Model
Instrument Relevance and Exogeneity in the General IV Model
The IV Regression Assumptions and Sampling Distribution of the TSLS Estimator
Inference Using the TSLS Estimator
Application to the Demand for Cigarettes
12.3 Checking Instrument Validity
Assumption #1: Instrument Relevance
Assumption #2: Instrument Exogeneity
12.4 Application to the Demand for Cigarettes
12.5 Where Do Valid Instruments Come From?
Three Examples
12.6 Conclusion
Appendix 12.1 The Cigarette Consumption Panel Data Set
Appendix 12.2 Derivation of the Formula for the TSLS Estimator in Equation (12.4)
Appendix 12.3 Large-Sample Distribution of the TSLS Estimator
Appendix 12.4 Large-Sample Distribution of the TSLS Estimator When the Instrument Is Not Valid
Appendix 12.5 Instrumental Variables Analysis with Weak Instruments

Chapter 13  Experiments and Quasi-Experiments
13.1 Idealized Experiments and Causal Effects
Ideal Randomized Controlled Experiments
The Differences Estimator
13.2 Potential Problems with Experiments in Practice
Threats to Internal Validity
Threats to External Validity
13.3 Regression Estimators of Causal Effects Using Experimental Data
The Differences Estimator with Additional Regressors
The Differences-in-Differences Estimator
Estimation of Causal Effects for Different Groups
Estimation When There Is Partial Compliance
Testing for Randomization
13.4 Experimental Estimates of the Effect of Class Size Reductions
Experimental Design
Analysis of the STAR Data
Comparison of the Observational and Experimental Estimates of Class Size Effects
13.5 Quasi-Experiments
Examples
Econometric Methods for Analyzing Quasi-Experiments
13.6 Potential Problems with Quasi-Experiments
Threats to Internal Validity
Threats to External Validity
13.7 Experimental and Quasi-Experimental Estimates in Heterogeneous Populations
Population Heterogeneity: Whose Causal Effect?
OLS with Heterogeneous Causal Effects
IV Regression with Heterogeneous Causal Effects
13.8 Conclusion
Appendix 13.1   The Project STAR Data Set
Appendix 13.2   Extension of the Differences-in-Differences Estimator to Multiple Time Periods
Appendix 13.3   Conditional Mean Independence
Appendix 13.4   IV Estimation When the Causal Effect Across Individuals
Part Four Regression Analysis of Economic Time Series Data
Chapter 14 Introduction to Time Series Regression and Forecasting
14.1 Using Regression to Time Series Regression and Forecasting
14.2 Introduction to Time Series Data and Serial Correlation
The Rates of Inflation and Unemployment in the United States
Lags, First Differences, Logarithms, and Growth Rates
Autocorrelation
Other Examples of Economic Time Series
14.3 Autoregressions
The First Order Autoregressive Model
The pth Order Autoregressive Model
14.4 Time Series Regression with Additional Predictors and the Autoregressive Distributed Lag Model
Forecasting Changes in the Inflation Rate Using Past Unemployment Rates
Stationarity
Time Series Regression with Multiple Predictors
Forecast Uncertainty and Forecast Intervals
14.5 Lag Length Selection Using Information Criteria
Determining the Order of an Autoregression
Lag Length Selection in Time Series Regression with Multiple Predictors
14.6 Nonstationarity I: Trends
What Is a Trend?
Problems Caused by Stochastic Trends
Detecting Stochastic Trends: Testing for a Unit AR Root
Avoiding the Problems Caused by Stochastic Trends
14.7 Nonstationarity II: Breaks
What Is a Break?
Testing for Breaks
Pseudo Out-of-Sample Forecasting
Avoiding the Problems Caused by Breaks
14.8 Conclusion
Appendix 14.1   Time Series Data Used in Chapter 12
Appendix 14.2   Stationarity in the AR(1) Model
Appendix 14.3   Lag Operator Notation
Appendix 14.4   ARMA Models
Appendix 14.5   Consistency of the BIC Lag Length Estimator
Chapter 15  Estimation of Dynamic Causal Effects
15.1 An Initial Taste of the Orange Juice Data
15.2 Dynamic Causal Effects
Causal Effects and Time Series Data
Two Types of Exogeneity
15.3 Estimation of Dynamic Causal Effects with Exogenous Regressors
The Distributed Lag Model Assumptions
Autocorrelated ut, Standard Errors, and Inference
Dynamic Multipliers and Cumulative Dynamic Multipliers
15.4 Heteroskedasticity- and Autocorrelation-Consistent Standard Errors
Distribution of the OLS Estimator with Autocorrelated Errors
HAC Standard Errors
15.5 Estimation of Dynamic Causal Effects with Strictly Exogenous Regressors
The Distributed Lab Model with AR(1) Errors
OLS Estimation of the ADL Model
GLS Estimation
The Distributed Lag Model with Additional Lags and AR(p) Errors
15.6 Orange Juice Prices and Cold Weather
15.7 Is Exogeneity Plausible? Some Examples
U.S. Income and Australian Exports
Oil Prices and Inflation
Monetary Policy and Inflation
The Phillips Curve
15.8 Conclusion
Appendix 15.1   The Orange Juice Data Set
Appendix 15.2   The ADL Model and Generalized Least Squares in Lag Operator Notation
Chapter 16  Additional Topics in Time Series Regression
16.1 Vector Autoregressions
The VAR Model
A VAR Model of the Rates of Inflation and Unemployment
16.2 Multiperiod Forecasts
Iterated Multiperiod Forecasts
Direct Multiperiod Forecasts
Which Method Should You Use?
16.3 Orders of Integration and the DF-GLS Unit Root Test
Other Models of Trends and Orders of Integration
The DF-GLS Test for a Unit Root
Why Do Unit Root Tests Have Non-normal Distributions?
16.4 Cointegration
Cointegration and Error Correction
How Can You Tell Whether Two Variables Are Cointegrated?
Estimation of Cointegrating Coefficients
Extension to Multiple Cointegrated Variables
Application to Interest Rates
16.5 Volatility Clustering and Autoregressive Conditional Heteroskedasticity
Volatility Clustering
Autoregressive Conditional Heteroskedasticity
Application to Stock Price Volatility
16.6 Conclusion
Appendix 16.1   U.S. Financial Data Used in Chapter 16
Part Five The Econometric Theory of Regression Analysis
Chapter 17  The Theory of Linear Regression with One Regressor
17.1 The Extended Least Squares Assumptions and the OLS Estimator
The Extended Least Squares Assumptions
The OLS Estimator
17.2 Fundamentals of Asymptotic Distribution Theory
Convergence in Probability and the Law of Large Numbers
The Central Limit Theorem and Convergence in Distribution
Slutsky’s Theorem and the Continuous Mapping Theorem
Application to the t-Statistic Based on the Sample Mean
17.3 Asymptotic Distribution of the OLS Estimator and t-Statistic
Consistency and Asymptotic Normality of the OLS Estimators
Consistency of Heteroskedasticity-Robust Standard Errors
Asymptotic Normality of the Heteroskedasticity-Robust t-Statistic
17.4 Exact Sampling Distributions When the Errors Are Normally Distributed
Distribution of B1 with Normal Errors
Distribution of the Homoskedasticity-only t-Statistic
17.5 Weighted Least Squares
WLS with Known Heteroskedasticity
WLS with Heteroskedasticity of Known Functional Form
Heteroskedasticity-Robust Standard Errors or WLS?
Appendix 17.1   The Normal and Related Distributions and Moments of Continuous Random Variables
Appendix 17.2   Two Inequalities
Chapter 18  The Theory of Multiple Regression
18.1 The Linear Multiple Regression Model and OLS Estimator in Matrix Form
The Multiple Regression Model in Matrix Notation
The Extended Least Squares Assumptions
The OLS Estimator
18.2 Asymptotic Distribution of the OLS Estimator and t-Statistic
The Multivariate Central Limit Theorem
Asymptotic Normality of B
Heteroskedasticity-Robust Standard Errors
Confidence Intervals for Predicted Effects
Asymptotic Distribution of the t-Statistic
18.3 Tests of Joint Hypotheses
Joint Hypotheses in Matrix Notation
Asymptotic Distribution of the F-Statistic
Confidence Sets for Multiple Coefficients
18.4 Distribution of Regression Statistics with Normal Errors
Matrix Representations of OLS Regression Statistics
Distribution of B with Normal Errors
Distribution of s2û
Homoskedasticity-Only Standard Errors
Distribution of the t-Statistic
Distribution of the F-Statistic
18.5 Efficiency of the OLS Estimator with Homoskedastic Errors
The Gauss–Markov Conditions for Multiple Regression
Linear Conditionally Unbiased Estimators
The Gauss–Markov Theorem for Multiple Regression
18.6 Generalized Least Squares
The GLS Assumptions
GLS When omega Is Known
GLS When omega Contains Unknown Parameters
The Zero Conditional Unknown Parameters
18.7 Instrumental Variables and Generalized Method of Moments Estimation
The IV Estimator in Matrix Form
Asymptotic Distribution of the TSLS Estimator
Properties of the TSLS When the Errors are Homoskedastic
Generalized Method of Moments Estimation in Linear Models
Appendix 18.1   Summary of Matrix Algebra
Appendix 18.2   Multivariate Distributions
Appendix 18.3   Derivation of the Asymptotic Distribution of B
Appendix 18.4   Derivations of Exact Distributions of OLS Test Statistics with Normal Errors
Appendix 18.5   Proof of the Gauss–Markov Theorem for Multiple Regression
Appendix 18.5   Proof of Selected Results for IV and GMM Estimation
Appendix
References
Answers to \"Review the Concepts\" Questions
Glossary
Index

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