# Introductory Econometrics: A Modern Approach

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## Efnisyfirlit

• 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

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# Introductory Econometrics: A Modern Approach

Vörumerki: Cengage
Vörunúmer: 9781337671330
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