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Fundamentals of Applied Econometrics 

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Comment from the Stata technical groupFundamentals of Applied Econometrics by Richard A. Ashley is an elementary introduction to econometrics focused on the linear regression model. Because it uses no matrix algebra, the book can be used as the main text in a one or twosemester undergraduate econometrics course or a master’slevel methods course in the social sciences. The book is also recommended for junior analysts in industry and government who need a reference book to guide them along while doing empirical work. The book is divided into three parts and begins with a refresher on the basics of statistics and hypothesis testing. The core of the book is centered on linear regression, beginning with the simple bivariate regression model with independent errors. Later chapters then introduce multiple regression, stochastic regressors and endogeneity, and regression with timeseries data. Three full chapters are devoted to diagnostics and to testing model specification. The third part of the book, which could form the basis of a secondsemester course when supplemented with other materials, discusses panel data, forecasting time series, and binarychoice models. Most of the numerical examples in the book are produced using Stata, as are all the graphs. Stata datasets for all examples and exercises are available at the publisher’s website. Throughout the book are what the author calls “Active Learning Exercises,” longer problems that guide readers through the analysis of real datasets and help them get a “handson” feel for doing econometrics. 

Table of contentsView 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” ALE 1b: Investigating the Slope Graphically Using a Scatterplot ALE 1c: Examining Some Disturbing Variations on Dollar & Kraay’s Model ALE 1d: The Pitfalls of Making Scatterplots with Trended TimeSeries Data 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 ALE 2b: Central Limit Theorem Simulators on the Web 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 Ybar 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 Leadin to Next Chapter Exercises ALE 3a: Investigating the Consistency of the Sample Mean and Sample Variance Using ComputerGenerated Data ALE 3b: Estimating Means and Variances Regarding the Standard & Poor's SP500 Stock Index Chapter 4 STATISTICAL INFERENCE ON THE MEAN OF A NORMALLY DISTRIBUTED RANDOM VARIABLE
4.1 Introduction
4.2 Standardizing the distribution of Ybar 4.3 Confidence Intervals for μ When σ^{2} Is Known 4.4 Hypothesis Testing when σ^{2} Is Known 4.5 Using S^{2} to Estimate σ^{2} (and Introducing the ChiSquared Distribution) 4.6 Inference Results on μ When σ^{2} is Unknown (and Introducing the Student's t Distribution) 4.7 Application: StateLevel 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 σ^{2} across the Sample 4.10 Some General Comments on Diagnostic Checking 4.11 Closing Comments Exercises ALE 4a: Investigating the Sensitivity of Hypothesis Test pValues to Departures from the NIID (μ, σ^{2}) Assumption Using ComputerGenerated Data ALE 4b: Individual Income Data from the Panel Study on Income Dynamics (PSID) — Does BirthMonth Matter? 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, U_{i} 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 ALE 5b: Verifying αhat^{*}_{ols} and βhat^{*}_{ols} over a Very Small Data Set ALE 5c: Extracting and Downloading CPS Data from the Census Bureau Web Site ALE 5d: Verifying that βhat^{*}_{ols} on a Dummy Variable Equals the Difference in the Sample Means Appendix 5.1: βhat^{*}_{ols} When x_{i} 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 βhat as a Linear Estimator and the Least Squares Weights 6.4 The Sampling Distribution of βhat 6.5 Properties of βhat: Consistency 6.6 Properties of βhat: Best Linear Unbiasedness 6.7 Summary Exercises ALE 6a: Outliers and Other Perhaps Overly Influential Observations: Investigating the Sensitivity of βhat to an Outlier Using ComputerGenerated Data ALE 6b: Investigating the Consistency of βhat Using ComputerGenerated 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 σ^{2} Given 7.4 Estimates versus Estimators and the Role of the Model Assumptions 7.5 Testing a Hypothesis about β with σ^{2} Given 7.6 Estimating σ^{2} 7.7 Properties of S^{2} 7.8 A Statistic for β Not Involving σ^{2} 7.9 A 95% Confidence Interval for β with σ^{2} Unknown 7.10 Testing a Hypothesis about β with σ^{2} 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 U_{i}~NIID(O, σ^{2}) Assumption Using ComputerGenerated Data ALE 7b: Distorted Inference in TimeSeries Regressions with Serially Correlated Model Errors: An Investigation Using ComputerGenerated Data Appendix 7.1: Proof That S^{2} Is Independent of βhat Chapter 8 THE BIVARIATE REGRESSION MODEL: R^{2} AND PREDICTION
8.1 Introduction
8.2 Quantifying How Well the Model Fits the Data 8.3 Prediction as a Tool for Model Variation 8.4 Predicting Y_{N+1} given x_{N+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 βhat_{ols,1}...βhat_{ols,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? ALE 9b: Observing and Interpreting the Symptoms of Multicollinearity ALE 9c: The Market Value of a Bathroom in Georgia 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
CROSSSECTIONAL DATA CASE
10.1 Introduction
10.2 The Fitting Errors as LargeSample Estimates of the Model Errors, U_{1}...U_{N} 10.3 Reasons for Checking the Normality of the Model Errors, U_{1}...U_{N} 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 Approximates for the Model Errors ALE 10b: Does Output Per Person Depend on Human Capital? (A Test of the Augmented Solow Model of Growth) ALE 10c: Is Trade Good or Bad for the Environment? (First Pass) Chapter 11 STOCHASTIC REGRESSORS AND ENDOGENEITY
11.1 Introduction
11.2 Unbiasedness of the OLS Slope Estimator with a Stochastic Regressor Independent 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 βhat^{OLS} in the Bivariate Regression Model ALE 11b: Bootstrap Analysis of the Convergence of the Asymptotic Sampling Distributions for Multiple Regression Model Parameter Estimators 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 TwoStage 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 ALE 12b: Is Trade Good or Bad for the Environment? (Completion) ALE 12c: The Impact of Military Service on the Smoking Behavior of Veterans ALE 12d: The Effect of MeasurementError Contamination on OLS Regression Estimates and the Durbin/Bartlett IV Estimators 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 TIMESERIES DATA CASE (PART A)
13.1 An Introduction to TimeSeries Data, with a "Road Map" for this
Chapter
13.2 The Bivariate TimeSeries Regression Model with Fixed Regressors but Serially Correlated Model Errors, U_{1} ... U_{T} 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 TimeSeries 13.5 The Consistency of φhat_{1}^{OLS} as an Estimator of φ_{1} 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 φhat_{1}^{OLS} in the AR(1) Model Chapter 14 DIAGNOSTICALLY CHECKING AND RESPECIFYING THE MULTIPLE REGRESSION
MODEL: THE TIMESERIES DATA CASE (PART B)
14.1 Introduction: Generalizing the Results to Multiple TimeSeries
14.2 The Dynamic Multiple Regression Model 14.3 I(1) or “Random Walk” TimeSeries 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 SubIndex of the Monthly U.S. Consumer Price Index ALE 14b: Estimating Taylor Rules for How the U.S. Fed Sets Interest Rates 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 FirstDifferences Model 16.3 Summary Exercises ALE 16a: Assessing the Impact of 4H Participation on the Standardized Test Scores of Florida Schoolchildren ALE 16b: Using Panel Data Methods to Reanalyze Data from a Public Goods Experiment Chapter 17 A CONCISE INTRODUCTION TO TIMESERIES ANALYSIS AND FORECASTING
(PART A)
17.1 Introduction: The Difference between TimeSeries Analysis
and TimeSeries Econometrics
17.2 Optimal Forecasts: The Primacy of the ConditionalMean Forecast and When It Is Better to Use a Biased Forecast 17.3 The Crucial Assumption (Stationarity) and the Fundamental Tools: The TimePlot and the Sample Correlogram 17.4 A Polynomial in the Lag Operator and Its Inverse: The Key to Understanding and Manipulating Linear TimeSeries 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 LargeScale Macroeconometric Model ALE 17b: Modeling U.S. GNP Chapter 18 A CONCISE INTRODUCTION TO TIMESERIES ANALYSIS AND FORECASTING
(PART B)
18.1 Integrated — ARIMA(p,d,q) — Models and “Trend like”
Behavior
18.2 A Univariate Application: Modeling the Monthly U.S. Treasury Bill Rate 18.3 Seasonal TimeSeries Data and ARMA Deseasonalization of the U.S. Total Nonfarm Payroll TimeSeries 18.4 Multivariate TimeSeries Models 18.5 PostSample Model Forecast Evaluation and Testing for GrangerCausation 18.6 Modeling Nonlinear Serial Dependence in a TimeSeries 18.7 Additional Topics in Forecasting Exercises ALE 18a: Modeling the South Korean Won–U.S. Dollar Exchange Rate ALE 18b: Modeling the Daily Returns to Ford Motor Company Stock Chapter 19 PARAMETER ESTIMATION BEYOND CURVEFITTING: MLE (WITH AN APPLICATION
TO BINARYCHOICE 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 BinaryChoice 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 PenaltyWeights 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

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