Fundamentals of Applied Econometrics

Copyright
Brief Contents
Table of Contents
What’s Different about This Book
Working with Data in the “Active Learning Exercises”
Acknowledgments
Notation
Part I: INTRODUCTION AND STATISTICS REVIEW
	Chapter 1: INTRODUCTION
		1.1 Preliminaries
		1.2 Example: Is Growth Good for the Poor?
		1.3 What’s to Come
		ALE 1a: An Econometrics “Time Capsule”
	Chapter 2: A REVIEW OF PROBABILITY THEORY
		2.1 Introduction
		2.2 Random Variables
		2.3 Discrete Random Variables
		2.4 Continuous Random Variables
		2.5 Some Initial Results on Expectations
		2.6 Some Results on Variances
		2.7 A Pair of Random Variables
		2.8 The Linearity Property of Expectations
		2.9 Statistical Independence
		2.10 Normally Distributed Random Variables
		2.11 Three Special Properties of Normally Distributed Variables
		2.12 Distribution of a Linear Combination of Normally Distributed Random Variables
		2.13 Conclusion
		Exercises
		ALE 2a: The Normal Distribution
		Appendix 2.1: The Conditional Mean of a Random Variable
		Appendix 2.2: Proof of the Linearity Property for the Expectation of a Weighted Sum of Two Discretely Distributed Random Variables
	Chapter 3: ESTIMATING THE MEAN OF A NORMALLY DISTRIBUTED RANDOM VARIABLE
		3.1 Introduction
		3.2 Estimating μ by Curve Fitting
		3.3 The Sampling Distribution of Y
		3.4 Consistency – A First Pass
		3.5 Unbiasedness and the Optimal Estimator
		3.6 The Squared Error Loss Function and the Optimal Estimator
		3.7 The Feasible Optimality Properties: Efficiency and BLUness
		3.8 Summary
		3.9 Conclusions and Lead-in to Next Chapter
		Exercises
		ALE 3a: Investigating the Consistency of the Sample Mean and Sample Variance Using Computer-Generated Data
	Chapter 4: STATISTICAL INFERENCE ON THE MEAN OF A NORMALLY DISTRIBUTED RANDOM VARIABLE
		4.1 Introduction
		4.2 Standardizing the distribution of Y
		4.3 Confidence Intervals for µ When σ² Is Known
		4.4 Hypothesis Testing when σ² Is Known
		4.5 Using S² to Estimate σ² (and Introducing the Chi-Squared Distribution)
		4.6 Inference Results on µ When σ² Is Unknown (and Introducing the Student’s t Distribution)
		4.7 Application: State-Level U.S. Unemployment Rates
		4.8 Introduction to Diagnostic Checking: Testing the Constancy of µ across the Sample
		4.9 Introduction to Diagnostic Checking: Testing the Constancy of σ² across the Sample
		4.10 Some General Comments on Diagnostic Checking
		4.11 Closing Comments
		Exercises
		ALE 4a: Investigating the Sensitivity of Hypothesis Test p-Values to Departures from the NIID(µ, σ²) Assumption Using Computer-Generated Data
Part II: REGRESSION ANALYSIS
	Chapter 5: THE BIVARIATE REGRESSION MODEL: INTRODUCTION, ASSUMPTIONS, AND PARAMETER ESTIMATES
		5.1 Introduction
		5.2 The Transition from Mean Estimation to Regression: Analyzing the Variation of Per Capita Real Output across Countries
		5.3 The Bivariate Regression Model – Its Form and the “Fixed in Repeated Samples” Causality Assumption
		5.4 The Assumptions on the Model Error Term, Ui
		5.5 Least Squares Estimation of α and β
		5.6 Interpreting the Least Squares Estimates of α and β
		5.7 Bivariate Regression with a Dummy Variable: Quantifying the Impact of College Graduation on Weekly Earnings
		Exercises
		ALE 5a: Exploring the Penn World Table Data
		Appendix 5.1: β*ols When xi Is a Dummy Variable
	Chapter 6: THE BIVARIATE LINEAR REGRESSION MODEL: SAMPLING DISTRIBUTIONS AND ESTIMATOR PROPERTIES
		6.1 Introduction
		6.2 Estimates and Estimators
		6.3 β as a Linear Estimator and the Least Squares Weights
		6.4 The Sampling Distribution of β
		6.5 Properties of β: Consistency
		6.6 Properties of β: Best Linear Unbiasedness
		6.7 Summary
		Exercises
		ALE 6a: Outliers and Other Perhaps Overly Influential Observations: Investigating the Sensitivity of β to an Outlier Using Computer-Generated Data
	Chapter 7: THE BIVARIATE LINEAR REGRESSION MODEL: INFERENCE ON β
		7.1 Introduction
		7.2 A Statistic for β with a Known Distribution
		7.3 A 95% Confidence Interval for β with σ² Given
		7.4 Estimates versus Estimators and the Role of the Model Assumptions
		7.5 Testing a Hypothesis about β with σ² Given
		7.6 Estimating σ²
		7.7 Properties of S²
		7.8 A Statistic for β Not Involving σ²
		7.9 A 95% Confidence Interval for β with σ² Unknown
		7.10 Testing a Hypothesis about β with σ² Unknown
		7.11 Application: The Impact of College Graduation on Weekly Earnings (Inference Results)
		7.12 Application: Is Growth Good for the Poor?
		7.13 Summary
		Exercises
		ALE 7a: Investigating the Sensitivity of Slope Coefficient Inference to Departures from the Ui ~ NIID(0, σ²) Assumption Using Computer-Generated Data
		Appendix 7.1: Proof That S² Is Independent of β
	Chapter 8: THE BIVARIATE REGRESSION MODEL: R² AND PREDICTION
		8.1 Introduction
		8.2 Quantifying How Well the Model Fits the Data
		8.3 Prediction as a Tool for Model Validation
		8.4 Predicting YN+1 given xN+1
		Exercises
		ALE 8a: On the Folly of Trying Too Hard: A Simple Example of “Data Mining”
	Chapter 9: THE MULTIPLE REGRESSION MODEL
		9.1 Introduction
		9.2 The Multiple Regression Model
		9.3 Why the Multiple Regression Model Is Necessary and Important
		9.4 Multiple Regression Parameter Estimates via Least Squares Fitting
		9.5 Properties and Sampling Distribution of βols; 1...βols; k
		9.6 Overelaborate Multiple Regression Models
		9.7 Underelaborate Multiple Regression Models
		9.8 Application: The Curious Relationship between Marriage and Death
		9.9 Multicollinearity
		9.10 Application: The Impact of College Graduation and Gender on Weekly Earnings
		9.11 Application: Vote Fraud in Philadelphia Senatorial Elections
		Exercises
		ALE 9a: A Statistical Examination of the Florida Voting in the November 2000 Presidential Election – Did Mistaken Votes for Pat Buchanan Swing the Election from Gore to Bush?
		Appendix 9.1: Prediction Using the Multiple Regression Model
	Chapter 10: DIAGNOSTICALLY CHECKING AND RESPECIFYING THE MULTIPLE REGRESSION MODEL: DEALING WITH POTENTIAL OUTLIERS AND HETEROSCEDASTICITY IN THE CROSS-SECTIONAL DATA CASE
		10.1 Introduction
		10.2 The Fitting Errors as Large-Sample Estimates of the Model Errors, U1...UN
		10.3 Reasons for Checking the Normality of the Model Errors, U1,...UN
		10.4 Heteroscedasticity and Its Consequences
		10.5 Testing for Heteroscedasticity
		10.6 Correcting for Heteroscedasticity of Known Form
		10.7 Correcting for Heteroscedasticity of Unknown Form
		10.8 Application: Is Growth Good for the Poor? Diagnostically Checking the Dollar/Kraay (2002) Model.
		Exercises
		ALE 10a: The Fitting Errors as Approximations for the Model Errors
	Chapter 11: STOCHASTIC REGRESSORS AND ENDOGENEITY
		11.1 Introduction
		11.2 Unbiasedness of the OLS Slope Estimator with a Stochastic RegressorIndependent of the Model Error
		11.3 A Brief Introduction to Asymptotic Theory
		11.4 Asymptotic Results for the OLS Slope Estimator with a Stochastic Regressor
		11.5 Endogenous Regressors: Omitted Variables
		11.6 Endogenous Regressors: Measurement Error
		11.7 Endogenous Regressors: Joint Determination – Introduction to Simultaneous Equation Macroeconomic and Microeconomic Models
		11.8 How Large a Sample Is “Large Enough”? The Simulation Alternative
		11.9 An Example: Bootstrapping the Angrist-Krueger (1991) Model
		Exercises
		ALE 11a: Central Limit Theorem Convergence for βOLS in the Bivariate Regression Model
		Appendix 11.1: The Algebra of Probability Limits
		Appendix 11.2: Derivation of the Asymptotic Sampling Distribution of the OLS Slope Estimator
	Chapter 12: INSTRUMENTAL VARIABLES ESTIMATION
		12.1 Introduction – Why It Is Challenging to Test for Endogeneity
		12.2 Correlation versus Causation – Two Ways to Untie the Knot
		12.3 The Instrumental Variables Slope Estimator (and Proof of Its Consistency) in the Bivariate Regression Model
		12.4 Inference Using the Instrumental Variables Slope Estimator
		12.5 The Two-Stage Least Squares Estimator for the Overidentified Case
		12.6 Application: The Relationship between Education and Wages (Angrist and Krueger, 1991)
		Exercises
		ALE 12a: The Role of Institutions “Rule of Law” in Economic Growth
		Appendix 12.1: Derivation of the Asymptotic Sampling Distribution of the Instrumental Variables Slope Estimator
		Appendix 12.2: Proof That the 2SLS Composite Instrument Is Asymptotically Uncorrelated with the Model Error Term
	Chapter 13: DIAGNOSTICALLY CHECKING AND RESPECIFYING THE MULTIPLE REGRESSION MODEL: THE TIME-SERIES DATA CASE (PART A)
		13.1 An Introduction to Time-Series Data, with a “Road Map” for This Chapter
		13.2 The Bivariate Time-Series Regression Model with Fixed Regressors but Serially Correlated Model Errors, U1 ... UT
		13.3 Disastrous Parameter Inference with Correlated Model Errors: Two Cautionary Examples Based on U.S. Consumption Expenditures Data
		13.4 The AR(1) Model for Serial Dependence in a Time-Series
		13.5 The Consistency of φOLS 1 as an Estimator of φ1 in the AR(1) Model and Its Asymptotic Distribution
		13.6 Application of the AR(1) Model to the Errors of the (Detrended) U.S. Consumption Function – and a Straightforward Test for Serially Correlated Regression Errors
		13.7 Dynamic Model Respecification: An Effective Response to Serially Correlated Regression Model Errors, with an Application to the (Detrended) U.S. Consumption Function
		Exercises
		Appendix 13.1: Derivation of the Asymptotic Sampling Distribution of φOLS 1 in the AR(1) Model
	Chapter 14: DIAGNOSTICALLY CHECKING AND RESPECIFYING THE MULTIPLE REGRESSION MODEL: THE TIME-SERIES DATA CASE (PART B)
		14.1 Introduction: Generalizing the Results to Multiple Time-Series
		14.2 The Dynamic Multiple Regression Model
		14.3 I(1) or “Random Walk” Time-Series
		14.4 Capstone Example Part 1: Modeling Monthly U.S. Consumption Expenditures in Growth Rates
		14.5 Capstone Example Part 2: Modeling Monthly U.S. Consumption Expenditures in Growth Rates and Levels (Cointegrated Model)
		14.6 Capstone Example Part 3: Modeling the Level of Monthly U.S. Consumption Expenditures
		14.7 Which Is Better: To Model in Levels or to Model in Changes?
		Exercises
		ALE 14a: Analyzing the Food Price Sub-Index of the Monthly U.S. Consumer Price Index
Part III: ADDITIONAL TOPICS IN REGRESSION ANALYSIS
	Chapter 15: REGRESSION MODELING WITH PANEL DATA (PART A)
		15.1 Introduction: A Source of Large (but Likely Heterogeneous) Data Sets
		15.2 Revisiting the Chapter 5 Illustrative Example Using Data from the Penn World Table
		15.3 A Multivariate Empirical Example
		15.4 The Fixed Effects and the Between Effects Models
		15.5 The Random Effects Model
		15.6 Diagnostic Checking of an Estimated Panel Data Model
		Exercises
		Appendix 15.1: Stata Code for the Generalized Hausman Test
	Chapter 16: REGRESSION MODELING WITH PANEL DATA (PART B)
		16.1 Relaxing Strict Exogeneity: Dynamics and Lagged Dependent Variables
		16.2 Relaxing Strict Exogeneity: The First-Differences Model
		16.3 Summary
		Exercises
		ALE 16a: Assessing the Impact of 4-H Participation on the Standardized Test Scores of Florida Schoolchildren
	Chapter 17: A CONCISE INTRODUCTION TO TIME-SERIES ANALYSIS AND FORECASTING (PART A)
		17.1 Introduction: The Difference between Time-Series Analysis and Time-Series Econometrics
		17.2 Optimal Forecasts: The Primacy of the Conditional-Mean Forecast and When It Is Better to Use a Biased Forecast
		17.3 The Crucial Assumption (Stationarity) and the Fundamental Tools: The Time-Plot and the Sample Correlogram
		17.4 A Polynomial in the Lag Operator and Its Inverse: The Key to Understanding and Manipulating Linear Time-Series Models
		17.5 Identification/Estimation/Checking/Forecasting of an Invertible MA(q) Model
		17.6 Identification/Estimation/Checking/Forecasting of a Stationary AR(p) Model
		17.7 ARMA(p,q) Models and a Summary of the Box-Jenkins Modeling Algorithm
		Exercises
		ALE 17a: Conditional Forecasting Using a Large-Scale Macroeconometric Model
	Chapter 18: A CONCISE INTRODUCTION TO TIME-SERIES ANALYSIS AND FORECASTING (PART B)
		18.1 Integrated – ARIMA(p, d, q) – Models and “Trendlike” Behavior
		18.2 A Univariate Application: Modeling the Monthly U.S. Treasury Bill Rate
		18.3 Seasonal Time-Series Data and ARMA Deseasonalization of the U.S. Total Nonfarm Payroll Time-Series
		18.4 Multivariate Time-Series Models
		18.5 Post-Sample Model Forecast Evaluation and Testing for Granger-Causation
		18.6 Modeling Nonlinear Serial Dependence in a Time-Series
		18.7 Additional Topics in Forecasting
		Exercises
		ALE 18a: Modeling the South Korean Won – U.S. Dollar Exchange Rate
	Chapter 19: PARAMETER ESTIMATION BEYOND CURVE-FITTING: MLE (WITH AN APPLICATION TO BINARY-CHOICE MODELS) AND GMM (WITH AN APPLICATION TO IV REGRESSION)
		19.1 Introduction
		19.2 Maximum Likelihood Estimation of a Simple Bivariate Regression Model
		19.3 Maximum Likelihood Estimation of Binary-Choice Regression Models
		19.4 Generalized Method of Moments (GMM) Estimation
		Exercises
		ALE 19a: Probit Modeling of the Determinants of Labor Force Participation
		Appendix 19.1: GMM Estimation of β in the Bivariate Regression Model (Optimal Penalty-Weights and Sampling Distribution)
	Chapter 20: CONCLUDING COMMENTS
		20.1 The Goals of This Book
		20.2 Diagnostic Checking and Model Respecification
		20.3 The Four “Big Mistakes”
Mathematics Review
Index