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Table of Contents
Introduction
About This Book
Foolish Assumptions
Icons Used in This Book
Beyond the Book
Where to Go from Here
Part I: Getting Started with Econometrics
Chapter 1: Econometrics: The Economist’s Approach to Statistical Analysis
Evaluating Economic Relationships
Using economic theory to describe outcomes and make predictions
Relying on sensible assumptions
Applying Statistical Methods to Economic Problems
Recognizing the importance of data type, frequency, and aggregation
Avoiding the data-mining trap
Incorporating quantitative and qualitative information
Using Econometric Software: An Introduction to STATA
Getting acquainted with STATA
Creating new variables
Estimating, testing, and predicting
Chapter 2: Getting the Hang of Probability
Reviewing Random Variables and Probability Distributions
Looking at all possibilities: Probability density function (PDF)
Summing up the probabilities: Cumulative density function (CDF)
Putting variable information together: Bivariate or joint probability density
Predicting the future using what you know: Conditional probability density
Understanding Summary Characteristics of Random Variables
Making generalizations with expected value or mean
Measuring variance and standard deviation
Looking at relationships with covariance and correlation
Chapter 3: Making Inferences and Testing Hypotheses
Getting to Know Your Data with Descriptive Statistics
Calculating parameters and estimators
Determining whether an estimator is good
Laying the Groundwork of Prediction with the Normal and Standard Normal Distributions
Recognizing usual variables: Normal distribution
Putting variables on the same scale: Standard normal distribution (Z)
Working with Parts of the Population: Sampling Distributions
Simulating and using the central limit theorem
Defining the chi-squared (χ2), t, and F distributions
Making Inferences and Testing Hypotheses with Probability Distributions
Performing a hypothesis test
The confidence interval approach
The test of significance approach
Part II: Building the Classical Linear Regression Model
Chapter 4: Understanding the Objectives of Regression Analysis
Making a Case for Causality
Getting Acquainted with the Population Regression Function (PRF)
Setting up the PRF model
Walking through an example
Collecting and Organizing Data for Regression Analysis
Taking a snapshot: Cross-sectional data
Looking at the past to explain the present: Time-series data
Combining the dimensions of space and time: Panel or longitudinal data
Joining multiple snapshots: Pooled cross-sectional data
Chapter 5: Going Beyond Ordinary with the Ordinary Least Squares Technique
Defining and Justifying the Least Squares Principle
Estimating the Regression Function and the Residuals
Obtaining Estimates of the Regression Parameters
Finding the formulas necessary to produce optimal coefficient values
Calculating the estimated regression coefficients
Interpreting Regression Coefficients
Seeing what regression coefficients have to say
Standardizing regression coefficients
Measuring Goodness of Fit
Decomposing variance
Measuring proportion of variance with R2
Adjusting the goodness of fit in multiple regression
Evaluating fit versus quality
Chapter 6: Assumptions of OLS Estimation and the Gauss-Markov Theorem
Characterizing the OLS Assumptions
Linearity in parameters and additive error
Random sampling and variability
Imperfect linear relationships among the independent variables
Error term has a zero conditional mean; correct specification
Error term has a constant variance
Correlation of error observations is zero
Relying on the CLRM Assumptions: The Gauss-Markov Theorem
Proving the Gauss-Markov theorem
Summarizing the Gauss-Markov theorem
Chapter 7: The Normality Assumption and Inference with OLS
Describing the Role of the Normality Assumption
The error term and the sampling distribution of OLS coefficients
Revisiting the standard normal distribution
Deriving a chi-squared distribution from the random error
OLS standard errors and the t-distribution
Testing the Significance of Individual Regression Coefficients
Picking an approach
Choosing the level of significance and p-values
Analyzing Variance to Determine Overall or Joint Significance
Normality, variance, and the F distribution
The reported F-statistic from OLS
Slope coefficients and the relationship between t and F
Joint significance for subsets of variables
Applying Forecast Error to OLS Predictions
Mean prediction and forecast error
Variance of mean prediction
All predictions are not the same: The prediction confidence interval
Part III: Working with the Classical Regression Model
Chapter 8: Functional Form, Specification, and Structural Stability
Employing Alternative Functions
Quadratic function: Best for finding minimums and maximums
Cubic functions: Good for inflexion
Inverse function: Limiting the value of the dependent variable
Giving Linearity to Nonlinear Models
Working both sides to keep elasticity constant: The log-log model
Making investments and calculating rates of return: The log-linear model
Decreasing the change of the dependent variable: The linear-log model
Checking for Misspecification
Too many or too few: Selecting independent variables
Sensitivity isn’t a virtue: Examining misspecification with results stability
Chapter 9: Regression with Dummy Explanatory Variables
Numbers Please! Quantifying Qualitative Information
Defining a dummy variable when you have only two possible characteristics
Juggling multiple characteristics with dummy variables
Finding Average Differences by Using a Dummy Variable
Specification
Interpretation
Combining Quantitative and Qualitative Data in the Regression Model
Specification
Interpretation
Interacting Quantitative and Qualitative Variables
Specification
Interpretation
Interacting Two (or More) Qualitative Characteristics
Specification
Interpretation
Segregate and Integrate: Testing for Significance
Revisiting the F-test for joint significance
Revisiting the Chow test
Part IV: Violations of Classical Regression Model Assumptions
Chapter 10: Multicollinearity
Distinguishing between the Types of Multicollinearity
Pinpointing perfect multicollinearity
Zeroing in on high multicollinearity
Rules of Thumb for Identifying Multicollinearity
Pairwise correlation coefficients
Auxiliary regression and the variance inflation factor (VIF)
Knowing When and How to Resolve Multicollinearity Issues
Get more data
Use a new model
Expel the problem variable(s)
Chapter 11: Heteroskedasticity
Distinguishing between Homoskedastic and Heteroskedastic Disturbances
Homoskedastic error versus heteroskedastic error
The consequences of heteroskedasticity
Detecting Heteroskedasticity with Residual Analysis
Examining the residuals in graph form
Brushing up on the Breusch-Pagan test
Getting acquainted with the White test
Trying out the Goldfeld-Quandt test
Conducting the Park test
Correcting Your Regression Model for the Presence of Heteroskedasticity
Weighted least squares (WLS)
Robust standard errors (also known as White-corrected standard errors)
Chapter 12: Autocorrelation
Examining Patterns of Autocorrelation
Positive versus negative autocorrelation
Misspecification and autocorrelation
Illustrating the Effect of Autoregressive Errors
Analyzing Residuals to Test for Autocorrelation
Taking the visual route: Graphical inspection of residuals
Using the normal distribution to identify residual sequences: The run test
Detecting autocorrelation of an AR(1) process: The Durbin-Watson test
Detecting autocorrelation of an AR(q) process: The Breusch-Godfrey test
Remedying Harmful Autocorrelation
Feasible generalized least squares (FGLS)
Serial correlation robust standard errors
Part V: Discrete and Restricted Dependent Variables in Econometrics
Chapter 13: Qualitative Dependent Variables
Modeling Discrete Outcomes with the Linear Probability Model (LPM)
Estimating LPM with OLS
Interpreting your results
Presenting the Three Main LPM Problems
Non-normality of the error term
Heteroskedasticity
Unbounded predicted probabilities
Specifying Appropriate Nonlinear Functions: The Probit and Logit Models
Working from the standard normal CDF: The probit model
Basing off of the logistic CDF: The logit model
Using Maximum Likelihood (ML) Estimation
Constructing the likelihood function
The log transformation and ML estimates
Interpreting Probit and Logit Estimates
Probit coefficients
Logit coefficients
Chapter 14: Limited Dependent Variable Models
The Nitty-Gritty of Limited Dependent Variables
Censored dependent variables
Truncated dependent variables
Modifying Regression Analysis for Limited Dependent Variables
Tobin’s Tobit
Truncated regression
Oh, what the heck if I self select? Heckman’s selection bias correction
Part VI: Extending the Basic Econometric Model
Chapter 15: Static and Dynamic Models
Using Contemporaneous and Lagged Variables in Regression Analysis
Examining problems with dynamic models
Testing and correcting for autocorrelation in dynamic models
Projecting Time Trends with OLS
Spurious correlation and time series
Detrending time-series data
Using OLS for Seasonal Adjustments
Estimating seasonality effects
Deseasonalizing time-series data
Chapter 16: Diving into Pooled Cross-Section Analysis
Adding a Dynamic Time Element to the Mix
Examining intercepts and/or slopes that change over time
Incorporating time dummy variables
Using Experiments to Estimate Policy Effects with Pooled Cross Sections
Benefitting from random assignment: A true experiment
Working with predetermined subject groups: A natural (or quasi) experiment
Chapter 17: Panel Econometrics
Estimating the Uniqueness of Each Individual Unit
First difference (FD) transformation
Dummy variable (DV) regression
Fixed effects (FE) estimator
Increasing the Efficiency of Estimation with Random Effects
The composite error term and assumptions of random effects model
The random effects (RE) estimator
Testing Efficiency against Consistency with the Hausman Test
Part VII: The Part of Tens
Chapter 18: Ten Components of a Good Econometrics Research Project
Introducing Your Topic and Posing the Primary Question of Interest
Discussing the Relevance and Importance of Your Topic
Reviewing the Existing Literature
Describing the Conceptual or Theoretical Framework
Explaining Your Econometric Model
Discussing the Estimation Method(s)
Providing a Detailed Description of Your Data
Constructing Tables and Graphs to Display Your Results
Interpreting the Reported Results
Summarizing What You Learned
Chapter 19: Ten Common Mistakes in Applied Econometrics
Failing to Use Your Common Sense and Knowledge of Economic Theory
Asking the Wrong Questions First
Ignoring the Work and Contributions of Others
Failing to Familiarize Yourself with the Data
Making It Too Complicated
Being Inflexible to Real-World Complications
Looking the Other Way When You See Bizarre Results
Obsessing over Measures of Fit and Statistical Significance
Forgetting about Economic Significance
Assuming Your Results Are Robust
Appendix: Statistical Tables
Cheat Sheet
Econometrics For Dummies®
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About the Author
Roberto Pedace is an associate professor of economics at Scripps College in Claremont, California. Prior to joining the faculty at Scripps College, he held positions at Claremont Graduate University, the University of Redlands, Claremont McKenna College, and the U.S. Census Bureau. He holds a PhD in economics from the University of California, Riverside.
Roberto regularly teaches courses in the areas of statistics, microeconomics, labor economics, and econometrics. While at the University of Redlands, he was nominated for both the Innovative Teaching Award and the Outstanding Teaching Award. At Scripps College, he was recognized for his scholarly achievements by winning the Mary W. Johnson Faculty Achievement Award in Scholarship.
Roberto’s academic research interests are in the area of labor and personnel economics. His work addresses a variety of important public policy issues, including the effects of immigration on domestic labor markets and the impact of minimum wages on job training and unemployment. He also examines salary determination and personnel decisions in markets for professional athletes. His published work appears in the Southern Economic Journal, the Journal of Sports Economics, Contemporary Economic Policy, Industrial Relations, and other outlets.
Roberto is also a soccer fanatic. He’s been playing soccer since the age of 5, paid for most of his undergraduate education with a soccer scholarship, and had a short semi-professional stint in the USISL (now known as the United Soccer League). He continues to participate in leagues and tournaments but now mostly enjoys sitting on the sidelines watching his children play soccer.
Dedication
To my wife, Cynthia, for supporting me emotionally and being a wonderful mother to our children. To my children, Vincent and Emily, for brightening up my days.
Author’s Acknowledgments
None of this would have been possible if my professors hadn’t motivated me and given me a solid foundation in economics. My undergraduate adviser at California State University, San Bernardino, Thomas Pierce, opened my eyes to the world of economics and gave me wonderful advice in preparation for graduate school. I was fortunate to have taken several courses from Nancy Rose and Mayo Toruño, who helped me see economics in a different light when standard theory just wasn’t helping me understand certain aspects of the world. Kazim Konyar was the first to introduce me to the realm of econometrics and helped me understand how it could be a powerful complement to economic theory. At the University of California, Riverside, Aman Ullah’s uncanny ability to make advanced econometric theory comprehensible to a first-year graduate student solidified my interest in the topic. Finally, in his labor economics course and as my dissertation adviser, David Fairris taught me the art of using econometrics to address important economic policy issues.
Many of my econometrics students deserve special gratitude. Several of them stand out: Lora Brill, Megan Cornell, Guadalupe De La Cruz, Matthew Lang, Chandler Lutz, India Mullady, and Stephanie Rohn. Some became friends, a few colleagues, and a couple coauthors, but all inspired me to think of effective approaches to making econometrics accessible, useful, and interesting.
I thank Sean Flynn, my friend and colleague, for believing that I’d be the best person to write this book and Linda Roghaar, my literary agent, for listening to Sean and having faith in my ability to complete the project.
The folks at Wiley have also been incredibly supportive. In particular, I’d like to thank Jennifer Tebbe, my project editor, for working with me every step of the way and keeping me motivated to stay on track with my deadlines. No matter how long the tunnel, she always helped me see the light at the end. Erin Calligan Mooney, my acquisitions editor at Wiley, also helped me get through my sample chapter and ensured that it would meet the standards of others on the editorial team. My copy editor, Caitie Copple, and technical reviewers, Ariel Belasen and Nicole Bissessar, were ideal for this project. Their “eagle eyes” were instrumental in finding my mistakes and improving the finished product.
My research assistant, Anne Miles, gathered data for some of the examples I use in the book and assisted with the imaging of figures and graphs. Her turnaround time was amazing, and I’ll be forever grateful for all the hard work she provided on this project. I also want to thank my friend and colleague, Latika Chaudhary, for responding immediately to an urgent request for a sample of panel data.
Last, but not least, I’d like to thank my family and friends for being patient with me while I wrote this book. I know that sometimes I wasn’t myself and that I’ll need to make up for lost time.
Publisher’s Acknowledgments
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