Introductury Econometrics: A Modern Approach

Brief Contents
Contents
Chapter 1: The Nature of Econometrics and Economic Data
	1-1 What Is Econometrics?
	1-2 Steps in Empirical Economic Analysis
	1-3 The Structure of Economic Data
		1-3a Cross-Sectional Data
		1-3b Time Series Data
		1-3c Pooled Cross Sections
		1-3d Panel or Longitudinal Data
		1-3e A Comment on Data Structures
	1-4 Causality, Ceteris Paribus, and Counterfactual Reasoning
	Summary
	Key Terms
	Problems
	Computer Exercises
Part 1: Regression Analysis with ­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
			2-2a A Note on Terminology
		2-3 Properties of OLS on Any Sample of Data
			2-3a Fitted Values and Residuals
			2-3b Algebraic Properties of OLS Statistics
			2-3c Goodness-of-Fit
		2-4 Units of Measurement and Functional Form
			2-4a The Effects of Changing Units of Measurement on OLS Statistics
			2-4b Incorporating Nonlinearities in Simple Regression
			2-4c The Meaning of “Linear” Regression
		2-5 Expected Values and Variances of the OLS Estimators
			2-5a Unbiasedness of OLS
			2-5b Variances of the OLS Estimators
			2-5c Estimating the Error Variance
		2-6 Regression through the Origin and Regression on a Constant
		2-7 Regression on a Binary Explanatory Variable
			2-7a Counterfactual Outcomes, Causality, and Policy Analysis
		Summary
		Key Terms
		Problems
		Computer Exercises
	Chapter 3: Multiple Regression Analysis: Estimation
		3-1 Motivation for Multiple Regression
			3-1a The Model with Two Independent Variables
			3-1b The Model with k Independent Variables
		3-2 Mechanics and Interpretation of Ordinary Least Squares
			3-2a Obtaining the OLS Estimates
			3-2b Interpreting the OLS Regression Equation
			3-2c On the Meaning of “Holding Other Factors Fixed” in Multiple Regression
			3-2d Changing More Than One Independent Variable Simultaneously
			3-2e OLS Fitted Values and Residuals
			3-2f A “Partialling Out” Interpretation of Multiple Regression
			3-2g Comparison of Simple and Multiple Regression Estimates
			3-2h Goodness-of-Fit
			3-2i Regression through the Origin
		3-3 The Expected Value of the OLS Estimators
			3-3a Including Irrelevant Variables in a Regression Model
			3-3b Omitted Variable Bias: The Simple Case
			3-3c Omitted Variable Bias: More General Cases
		3-4 The Variance of the OLS Estimators
			3-4a The Components of the OLS Variances: Multicollinearity
			3-4b Variances in Misspecified Models
			3-4c Estimating s2: Standard Errors of the OLS Estimators
		3-5 Efficiency of OLS: The Gauss-Markov Theorem
		3-6 Some Comments on the Language of Multiple Regression Analysis
		3-7 Several Scenarios for Applying Multiple Regression
			3-7a Prediction
			3-7b Efficient Markets
			3-7c Measuring the Tradeoff between Two Variables
			3-7d Testing for Ceteris Paribus Group Differences
			3-7e Potential Outcomes, Treatment Effects, and Policy Analysis
		Summary
		Key Terms
		Problems
		Computer Exercises
	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
			4-2a Testing against One-Sided Alternatives
			4-2b Two-Sided Alternatives
			4-2c Testing Other Hypotheses about bj
			4-2d Computing p-Values for t Tests
			4-2e A Reminder on the Language of Classical Hypothesis Testing
			4-2f Economic, 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 F Test
			4-5a Testing Exclusion Restrictions
			4-5b Relationship between F and t Statistics
			4-5c The R-Squared Form of the F Statistic
			4-5d Computing p-values for F Tests
			4-5e The F Statistic for Overall Significance of a Regression
			4-5f Testing General Linear Restrictions
		4-6 Reporting Regression Results
		4-7 Revisiting Causal Effects and Policy Analysis
		Summary
		Key Terms
		Problems
		Computer Exercises
	Chapter 5: Multiple Regression Analysis: OLS Asymptotics
		5-1 Consistency
			5-1a Deriving the Inconsistency in OLS
		5-2 Asymptotic Normality and Large Sample Inference
			5-2a Other Large Sample Tests: The Lagrange Multiplier Statistic
		5-3 Asymptotic Efficiency of OLS
		Summary
		Key Terms
		Problems
		Computer Exercises
	Chapter 6: Multiple Regression Analysis: Further Issues
		6-1 Effects of Data Scaling on OLS Statistics
			6-1a Beta Coefficients
		6-2 More on Functional Form
			6-2a More on Using Logarithmic Functional Forms
			6-2b Models with Quadratics
			6-2c Models with Interaction Terms
			6-2d Computing Average Partial Effects
		6-3 More on Goodness-of-Fit and Selection of Regressors
			6-3a Adjusted R-Squared
			6-3b Using Adjusted R-Squared to Choose between Nonnested Models
			6-3c Controlling for Too Many Factors in Regression Analysis
			6-3d Adding Regressors to Reduce the Error Variance
		6-4 Prediction and Residual Analysis
			6.4 a Confidence Intervals for Predictions
			6-4b Residual Analysis
			6-4c Predicting y When log(y) Is the Dependent Variable
			6-4d Predicting y When the Dependent Variable Is log(y)
		Summary
		Key Terms
		Problems
		Computer Exercises
	Chapter 7: Multiple Regression Analysis with Qualitative Information
		7-1 Describing Qualitative Information
		7-2 A Single Dummy Independent Variable
			7-2a Interpreting Coefficients on Dummy Explanatory Variables When the Dependent Variable Is log(y)
		7-3 Using Dummy Variables for Multiple Categories
			7-3a Incorporating Ordinal Information by Using Dummy Variables
		7-4 Interactions Involving Dummy Variables
			7-4a Interactions among Dummy Variables
			7-4b Allowing for Different Slopes
			7-4c 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
			7-6a Program Evaluation and Unrestricted Regression Adjustment
		7-7 Interpreting Regression Results with Discrete Dependent Variables
		Summary
		Key Terms
		Problems
		Computer Exercises
	Chapter 8: Heteroskedasticity
		8-1 Consequences of Heteroskedasticity for OLS
		8-2 Heteroskedasticity-Robust Inference after OLS Estimation
			8-2a Computing Heteroskedasticity-Robust LM Tests
		8-3 Testing for Heteroskedasticity
			8-3a The White Test for Heteroskedasticity
		8-4 Weighted Least Squares Estimation
			8-4a The Heteroskedasticity Is Known up to a Multiplicative Constant
			8-4b The Heteroskedasticity Function Must Be Estimated: Feasible GLS
			8-4c What If the Assumed Heteroskedasticity Function Is Wrong?
			8-4d Prediction and Prediction Intervals with Heteroskedasticity
		8-5 The Linear Probability Model Revisited
		Summary
		Key Terms
		Problems
		Computer Exercises
	Chapter 9: More on Specification and Data Issues
		9-1 Functional Form Misspecification
			9-1a RESET as a General Test for Functional Form Misspecification
			9-1b Tests against Nonnested Alternatives
		9-2 Using Proxy Variables for Unobserved Explanatory Variables
			9-2a Using Lagged Dependent Variables as Proxy Variables
			9-2b A Different Slant on Multiple Regression
			9-2c Potential Outcomes and Proxy Variables
		9-3 Models with Random Slopes
		9-4 Properties of OLS under Measurement Error
			9-4a Measurement Error in the Dependent Variable
			9-4b Measurement Error in an Explanatory Variable
		9-5 Missing Data, Nonrandom Samples, and Outlying Observations
			9-5a Missing Data
			9-5b Nonrandom Samples
			9-5c Outliers and Influential Observations
		9-6 Least Absolute Deviations Estimation
		Summary
		Key Terms
		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
			10-2a Static Models
			10-2b Finite Distributed Lag Models
			10-2c A Convention about the Time Index
		10-3 Finite Sample Properties of OLS under Classical Assumptions
			10-3a Unbiasedness of OLS
			10-3b The Variances of the OLS Estimators and the Gauss-Markov Theorem
			10-3c Inference under the Classical Linear Model Assumptions
		10-4 Functional Form, Dummy Variables, and Index Numbers
		10-5 Trends and Seasonality
			10-5a Characterizing Trending Time Series
			10-5b Using Trending Variables in Regression Analysis
			10-5c A Detrending Interpretation of Regressions with a Time Trend
			10-5d Computing R-Squared When the Dependent Variable Is Trending
			10-5e Seasonality
		Summary
		Key Terms
		Problems
		Computer Exercises
	Chapter 11: Further Issues in Using OLS with Time Series Data
		11-1 Stationary and Weakly Dependent Time Series
			11-1a Stationary and Nonstationary Time Series
			11-1b Weakly Dependent Time Series
		11-2 Asymptotic Properties of OLS
		11-3 Using Highly Persistent Time Series in Regression Analysis
			11-3a Highly Persistent Time Series
			11-3b Transformations on Highly Persistent Time Series
			11-3c Deciding Whether a Time Series Is I(1)
		11-4 Dynamically Complete Models and the Absence of Serial Correlation
		11-5 The Homoskedasticity Assumption for Time Series Models
		Summary
		Key Terms
		Problems
		Computer Exercises
	Chapter 12: Serial Correlation and Heteroskedasticity in Time Series Regressions
		12-1 Properties of OLS with Serially Correlated Errors
			12-1a Unbiasedness and Consistency
			12-1b Efficiency and Inference
			12-1c Goodness-of-Fit
			12-1d Serial Correlation in the Presence of Lagged Dependent Variables
		12-2 Serial Correlation–Robust Inference after OLS
		12-3 Testing for Serial Correlation
			12-3a A t Test for AR(1) Serial Correlation with Strictly Exogenous Regressors
			12-3b The Durbin-Watson Test under Classical Assumptions
			12-3c Testing for AR(1) Serial Correlation without Strictly Exogenous Regressors
			12-3d Testing for Higher-Order Serial Correlation
		12-4 Correcting for Serial Correlation with Strictly Exogenous Regressors
			12-4a Obtaining the Best Linear Unbiased Estimator in the AR(1) Model
			12-4b Feasible GLS Estimation with AR(1) Errors
			12-4c Comparing OLS and FGLS
			12-4d Correcting for Higher-Order Serial Correlation
			12-4e What if the Serial Correlation Model Is Wrong?
		12-5 Differencing and Serial Correlation
		12-6 Heteroskedasticity in Time Series Regressions
			12-6a Heteroskedasticity-Robust Statistics
			12-6b Testing for Heteroskedasticity
			12-6c Autoregressive Conditional Heteroskedasticity
			12-6d Heteroskedasticity and Serial Correlation in Regression Models
		Summary
		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
			13-1a The Chow Test for Structural Change across Time
		13-2 Policy Analysis with Pooled Cross Sections
			13-2a Adding an Additional Control Group
			13-2b A General Framework for Policy Analysis with Pooled Cross Sections
		13-3 Two-Period Panel Data Analysis
			13-3a Organizing Panel Data
		13-4 Policy Analysis with Two-Period Panel Data
		13-5 Differencing with More Than Two Time Periods
			13-5a Potential Pitfalls in First Differencing Panel Data
		Summary
		Key Terms
		Problems
		Computer Exercises
	Chapter 14: Advanced Panel Data Methods
		14-1 Fixed Effects Estimation
			14-1a The Dummy Variable Regression
			14-1b Fixed Effects or First Differencing?
			14-1c Fixed Effects with Unbalanced Panels
		14-2 Random Effects Models
			14-2a Random Effects or Pooled OLS?
			14-2b Random Effects or Fixed Effects?
		14-3 The Correlated Random Effects Approach
			14-3a Unbalanced Panels
		14-4 General Policy Analysis with Panel Data
			14-4a Advanced Considerations with Policy Analysis
		14-5 Applying Panel Data Methods to Other Data Structures
		Summary
		Key Terms
		Problems
		Computer Exercises
	Chapter 15: Instrumental Variables Estimation and Two-Stage Least Squares
		15-1 Motivation: Omitted Variables in a Simple Regression Model
			15-1a Statistical Inference with the IV Estimator
			15-1b Properties of IV with a Poor Instrumental Variable
			15-1c Computing R-Squared after IV Estimation
		15-2 IV Estimation of the Multiple Regression Model
		15-3 Two-Stage Least Squares
			15-3a A Single Endogenous Explanatory Variable
			15-3b Multicollinearity and 2SLS
			15-3c Detecting Weak Instruments
			15-3d Multiple Endogenous Explanatory Variables
			15-3e Testing Multiple Hypotheses after 2SLS Estimation
		15-4 IV Solutions to Errors-in-Variables Problems
		15-5 Testing for Endogeneity and Testing Overidentifying Restrictions
			15-5a Testing for Endogeneity
			15-5b 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 Panel Data
		Summary
		Key Terms
		Problems
		Computer Exercises
	Chapter 16: Simultaneous Equations Models
		16-1 The Nature of Simultaneous Equations Models
		16-2 Simultaneity Bias in OLS
		16-3 Identifying and Estimating a Structural Equation
			16-3a Identification in a Two-Equation System
			16-3b Estimation by 2SLS
		16-4 Systems with More Than Two Equations
			16-4a Identification in Systems with Three or More Equations
			16-4b Estimation
		16-5 Simultaneous Equations Models with Time Series
		16-6 Simultaneous Equations Models with Panel Data
		Summary
		Key Terms
		Problems
		Computer Exercises
	Chapter 17: Limited Dependent Variable Models and Sample Selection Corrections
		17-1 Logit and Probit Models for Binary Response
			17-1a Specifying Logit and Probit Models
			17-1b Maximum Likelihood Estimation of Logit and Probit Models
			17-1c Testing Multiple Hypotheses
			17-1d Interpreting the Logit and Probit Estimates
		17-2 The Tobit Model for Corner Solution Responses
			17-2a Interpreting the Tobit Estimates
			17-2b Specification Issues in Tobit Models
		17-3 The Poisson Regression Model
		17-4 Censored and Truncated Regression Models
			17-4a Censored Regression Models
			17-4b Truncated Regression Models
		17-5 Sample Selection Corrections
			17-5a When Is OLS on the Selected Sample Consistent?
			17-5b Incidental Truncation
		Summary
		Key Terms
		Problems
		Computer Exercises
	Chapter 18: Advanced Time Series Topics
		18-1 Infinite Distributed Lag Models
			18-1a The Geometric (or Koyck) Distributed Lag Model
			18-1b Rational Distributed Lag Models
		18-2 Testing for Unit Roots
		18-3 Spurious Regression
		18-4 Cointegration and Error Correction Models
			18-4a Cointegration
			18-4b Error Correction Models
		18-5 Forecasting
			18-5a Types of Regression Models Used for Forecasting
			18-5b One-Step-Ahead Forecasting
			18-5c Comparing One-Step-Ahead Forecasts
			18-5d Multiple-Step-Ahead Forecasts
			18-5e Forecasting Trending, Seasonal, and Integrated 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 Collection
			19-3a Deciding on the Appropriate Data Set
			19-3b Entering and Storing Your Data
			19-3c Inspecting, Cleaning, and Summarizing Your Data
		19-4 Econometric Analysis
		19-5 Writing an Empirical Paper
			19-5a Introduction
			19-5b Conceptual (or Theoretical) Framework
			19-5c Econometric Models and Estimation Methods
			19-5d The Data
			19-5e Results
			19.5f Conclusions
			19-5g Style Hints
		Summary
		Key Terms
		Sample Empirical Projects
		List of Journals
		Data Sources
Math Refresher A Basic Mathematical Tools
	A-1 The Summation Operator and Descriptive Statistics
	A-2 Properties of Linear Functions
	A-3 Proportions and Percentages
	A-4 Some Special Functions and Their Properties
		A-4a Quadratic Functions
		A-4b The Natural Logarithm
		A-4c The Exponential Function
	A-5 Differential Calculus
		Summary
		Key Terms
		Problems
Math Refresher B Fundamentals of Probability
	B-1 Random Variables and Their Probability Distributions
		B-1a Discrete Random Variables
		B-1b Continuous Random Variables
	B-2 Joint Distributions, Conditional Distributions, and Independence
		B-2a Joint Distributions and Independence
		B-2b Conditional Distributions
	B-3 Features of Probability Distributions
		B-3a A Measure of Central Tendency: The Expected Value
		B-3b Properties of Expected Values
		B-3c Another Measure of Central Tendency: The Median
		B-3d Measures of Variability: Variance and Standard Deviation
		B-3e Variance
		B-3f Standard Deviation
		B-3g Standardizing a Random Variable
		B-3h Skewness and Kurtosis
	B-4 Features of Joint and Conditional Distributions
		B-4a Measures of Association: Covariance and Correlation
		B-4b Covariance
		B-4c Correlation Coefficient
		B-4d Variance of Sums of Random Variables
		B-4e Conditional Expectation
		B-4f Properties of Conditional Expectation
		B-4g Conditional Variance
	B-5 The Normal and Related Distributions
		B-5a The Normal Distribution
		B-5b The Standard Normal Distribution
		B-5c Additional Properties of the Normal Distribution
		B-5d The Chi-Square Distribution
		B-5e The t Distribution
		B-5f The F Distribution
	Summary
	Key Terms
	Problems
Math Refresher C Fundamentals of Mathematical Statistics
	C-1 Populations, Parameters, and Random Sampling
		C-1a Sampling
	C-2 Finite Sample Properties of Estimators
		C-2a Estimators and Estimates
		C-2b Unbiasedness
		C-2c The Sampling Variance of Estimators
		C-2d Efficiency
	C-3 Asymptotic or Large Sample Properties of Estimators
		C-3a Consistency
		C-3b Asymptotic Normality
	C-4 General Approaches to Parameter Estimation
		C-4a Method of Moments
		C-4b Maximum Likelihood
		C-4c Least Squares
	C-5 Interval Estimation and Confidence Intervals
		C-5a The Nature of Interval Estimation
		C-5b Confidence Intervals for the Mean from a Normally Distributed Population
		C-5c A Simple Rule of Thumb for a 95% Confidence Interval
		C-5d Asymptotic Confidence Intervals for Nonnormal Populations
	C-6 Hypothesis Testing
		C-6a Fundamentals of Hypothesis Testing
		C-6b Testing Hypotheses about the Mean in a Normal Population
		C-6c Asymptotic Tests for Nonnormal Populations
		C-6d Computing and Using p-Values
		C-6e The Relationship between Confidence Intervals and Hypothesis Testing
		C-6f Practical versus Statistical Significance
	C-7 Remarks on Notation
	Summary
	Key Terms
	Problems
Advanced Treatment D Summary of Matrix Algebra
	D-1 Basic Definitions
	D-2 Matrix Operations
		D-2a Matrix Addition
		D-2b Scalar Multiplication
		D-2c Matrix Multiplication
		D-2d Transpose
		D-2e Partitioned Matrix Multiplication
		D-2f Trace
		D-2g Inverse
	D-3 Linear Independence and Rank of a Matrix
	D-4 Quadratic Forms and Positive Definite Matrices
	D-5 Idempotent Matrices
	D-6 Differentiation of Linear and Quadratic Forms
	D-7 Moments and Distributions of Random Vectors
		D-7a Expected Value
		D-7b Variance-Covariance Matrix
		D-7c Multivariate Normal Distribution
		D-7d Chi-Square Distribution
		D-7e t Distribution
		D-7f F Distribution
	Summary
	Key Terms
	Problems
Advanced Treatment E The Linear Regression Model in Matrix Form
	E-1 The Model and Ordinary Least Squares Estimation
		E-1a The Frisch-Waugh Theorem
	E-2 Finite Sample Properties of OLS
	E-3 Statistical Inference
	E-4 Some Asymptotic Analysis
		E-4a Wald Statistics for Testing Multiple Hypotheses
	Summary
	Key Terms
	Problems
Answers to Going Further Questions
Statistical Tables
References
Glossary
Index