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Principles of Econometrics, 3rd Edition
Comments from the Stata technical groupPrinciples of Econometrics, Third Edition, by R. Carter Hill, William E. Griffiths, and Guay C. Lim is an introductory book for undergraduate econometrics. This book exemplifies learning by doing and gets the reader working through examples as fast as possible with a minimum of theory. Although designed to be the textbook in a principles of econometrics course, the style and coverage make it useful background reading in higher level courses. This book covers a broad area of econometrics. Appendices provide quick reviews of the required mathematical, probability, and elementary-statistics tools. The first six chapters cover estimation and inference in linear models, without using matrix algebra. The next three chapters cover nonlinear least squares, heteroskedasticity, and simple dynamic models. Chapters 10 and 11 cover the method-of-moments approach to least squares and instrumental-variables estimators and their application in simultaneous-equation models. Chapters 12, 13, and 14 provide nice introductions to the advanced time-series topics of modeling nonstationary series, multiple time series, and time series with time-varying volatility. Chapters 15 and 16 introduce two advanced topics in microeconometrics: panel-data models and models for qualitative and limited dependent variables. Chapter 17 provides an introduction to writing empirical papers. The numerous, nicely discussed examples in this book make the hands-on approach work well. The level of abstraction is held to a minimum, and instruction proceeds by interpreting examples. The many excellent exercises will help interested readers gain experience in and understanding about the methods discussed in the text. Table of contents1 An Introduction to Econometrics
1.1 Why Study Econometrics?
1.2 What is Econometrics about?
1.2.1 Some examples
1.3 The Econometric Model 1.4 How Do We Obtain Data?
1.4.1 Experimental Data
1.5 Statistical Inference 1.4.2 Nonexperimental Data 1.6 A Research Format 2 The Simple Linear Regression Model
2.1 An Economic Model
2.2 An Econometric Model
2.2.1 Introducing the Error Term
2.3 Estimating the Regression Parameters
2.3.1 The Least Squares Principle
2.4 Assessing the Least Squares Estimators
2.3.2 Estimates for the Food Expenditure Function 2.3.3 Interpreting the Estimates
2.3.3a Elasticities
2.3.4 Other Economic Models
2.3.3b Prediction 2.3.3c Computer Output
2.4.1 The Estimator b2
2.5 The Gauss–Markov Theorem 2.4.2 The Expected Values of b1 and b2 2.4.3 Repeated Sampling 2.3.4 The Variances and Covariances of b1 and b2 2.6 The Probability Distributions of the Least Squares Estimators 2.7 Estimating the Variance of the Error Term
2.7.1 Estimating the Variances and Covariances of the Least Squares Estimators
2.8 Exercises 2.7.2 Calculations for the Food Expenditure Data
2.8.1 Problems
Appendix 2A Derivation of the least Squares Estimates 2.8.2 Computer Exercises Appendix 2B Deviation from the Mean Form of b2 Appendix 2C b2 is a Linear Estimator Appendix 2D Derivation of Theoretical Expression for b2 Appendix 2E Deriving the Variance of b2 Appendix 2F Proof of the Gauss–Markov Theorem 3 Interval Estimation and Hypothesis Testing
Learning Objectives
Keywords 3.1 Interval Estimation
3.1.1 The t-distribution
3.2 Hypothesis Tests
3.1.2 Obtaining Interval Estimates 3.1.3 An Illustration 3.1.4 The Repeated Sampling Context
3.2.1 The Null Hypothesis
3.3 Rejection Regions for Specific Alternatives 3.2.2 The Alternative Hypothesis 3.2.3 The Test Statistic 3.2.4 The Rejection Region 3.2.5 A Conclusion
3.3.1 One-Tail Tests with Alternative “Greater Than” (>)
3.4 Examples of Hypothesis Tests
3.3.2 One-Tail Tests with Alternative “Less Than” (<) 3.3.3 Two-Tail Tests with Alternative “Not Equal To” (≠)
3.4.1 Right-Tail Tests
3.5 The p-value
3.4.1a One-Tail Test of Significance
3.4.2 Left-Tail Tests 3.4.1b One-Tail Test of an Economic Hypothesis 3.4.3 Two-Tail Tests
3.4.3a Two-Tail Test of an Economic Hypothesis
3.4.3b Two-Tail Test of Significance
3.5.1 p-value for a Right-Tail Test
3.6 Exercises
3.5.2 p-value for a Left-Tail Test 3.5.3 p-value for a Two-Tail Test 3.5.4 p-value for a Two-Tail Test of Significance
3.6.1 Problems
Appendix 3A Derivation of the t-Distribution 3.6.2 Computer Exercises Appendix 3B Distribution of the t-Statistic under H1 4 Prediction, Goodness of Fit and Modeling Issues
Learning Objectives
Keywords 4.1 Least Squares Prediction
4.1.1 Prediction in the Food Expenditure Model
4.2 Measuring Goodness-of-Fit
4.2.1 Correlation Analysis
4.3 Modeling Issues
4.2.2 Correlation Analysis and R2 4.2.3 The Food Expenditure Example 4.2.4 Reporting the Results
4.3.1 The Effects of Scaling the Data
4.4 Log-Linear Models
4.3.2 Choosing a Functional Form 4.3.3 The Food Expenditure Model 4.3.4 Are the Regression Errors Normally Distributed 4.3.5 Another Empirical Example
4.4.1 A Growth Model
4.5 Exercises
4.4.2 A Wage Equation 4.4.3 Prediction in the Log-Linear Model 4.4.4 A Generalized R2 Measure 4.4.5 Prediction Intervals in the Log-Linear Model
4.5.1 Problems
Appendix 4A Development of a Prediction Interval 4.5.2 Computer Exercises Appendix 4B The Sum of Squares Decomposition Appendix 4C The Log-Normal Distribution 5 The Multiple Regression Model
Learning Objectives
Keywords 5.1 Introduction
5.1.1 The Economic Model
5.2 Estimating the Parameters of the Multiple Regression Model 5.1.2 The Econometric Model
5.1.2a The General Model
5.1.2b The Assumptions of the Model
5.2.1 Least Squares Estimation Procedure
5.3 Sampling Properties of the Least Squares Estimator
5.2.2 Least Squares Estimates Using Hamburger Chain Data 5.2.3 Estimation of the Error Variance σ2
5.3.1 The Variances and Covariances of the Least Squares Estimators
5.4 Interval Estimation 5.3.2 The Properties of the Least Squares Estimators Assuming Normally Distributed Errors 5.5 Hypothesis Testing for a Single Coefficient
5.5.1 Testing the Significance of a Single Coefficient
5.6 Measuring Goodness-of-Fit 5.5.2 One-tail Hypothesis Testing for a Single Coefficient
5.5.2a Testing for Elastic Demand
5.5.2b Testing for Advertising Effectiveness
5.6.1 Reporting the Regression Results
5.7 Exercises
5.7.1 Problems
Appendix 5A Derivation of Least Squares Estimators
5.7.2 Computer Exercises 6 Further Inference in the Multiple Regression Model
Learning Objectives
Keywords 6.1 The F-test
6.1.1 The Relationship Between t- and F-Tests
6.2 Testing the Significance of a Model 6.3 An Extended Model 6.4 Testing Some Economic Hypotheses
6.4.1 The Significance of Advertising
6.5 The Use of Nonsample Information 6.4.2 The Optimal Level of Advertising
6.4.2a A One-Tail Test with More than One Parameter
6.4.3 Using Computer Software 6.6 Model Specification
6.6.1 Omitted Variables
6.7 Poor Data, Collinearity, and Insignificance
6.6.2 Irrelevant Variables 6.6.3 Choosing the Model
6.6.3a The RESET Test
6.7.1 The Consequences of Collinearity
6.8 Prediction 6.7.2 An Example 6.7.3 Choosing the Model 6.9 Exercises
6.9.1 Problems
Appendix 6A Chi-Square and F-Tests: More Details 6.9.2 Computer Exercises Appendix 6B Omitted-Variable Bias: A Proof 7 Nonlinear Relationships
Learning Objectives
Keywords 7.1 Polynomials
7.1.1 Cost and Product Curves
7.2 Dummy Variables
7.1.2 A Wage Equation
7.2.1 Intercept Dummy Variables
7.3 Applying Dummy Variables
7.2.1a Choosing the Reference Group
7.2.2 Slope Dummy Variables 7.2.3 An Example: The University Effect on House Prices
7.3.1 Interactions between Qualitative Factors
7.4 Interactions Between Continuous Variables 7.3.2 Qualitative Factors with Several Categories 7.3.3 Testing the Equivalence of Two Regressions 7.3.4 Controlling for Time
7.3.4a Seasonal Dummies
7.3.4b Annual Dummies 7.3.4c Regime Effects 7.5 Log-Linear Models
7.5.1 Dummy Variables
7.6 Exercises
7.5.1a A Rough Calculation
7.5.2 Interaction and Quadratic Terms
7.5.1b An Exact Calculation
7.6.1 Problems
Appendix 7A Details of Log-Linear Model Interpretation
7.6.2 Computer Exercises 8 Heteroskedasticity
Learning Objectives
Keywords 8.1 The Nature of Heteroskedasticity 8.2 Using the Least Squares Estimator 8.3 The Generalized Least Squares Estimator
8.3.1 Transforming The Model
8.4 Detecting Heteroskedasticity 8.3.2 Estimating the Variance Function 8.3.3 A Heteroskedastic Partition
8.4.1 Residual Plots
8.5 Exercises
8.4.2 The Goldfeld–Quandt Test 8.4.3 Testing the Variance Function
8.4.3a The White Test
8.4.3b Testing the Food Expenditure Example
8.5.1 Problems
Appendix 8A Properties of the Least Squares Estimator 8.5.2 Computer Exercises Appendix 8B Variance Function Tests for Heteroskedasticity 9 Dynamic Models, Autocorrelation and Forecasting
Learning Objectives
Keywords 9.1 Introduction 9.2 Lags in the Error Term: Autocorrelation
9.2.1 Area Response Model for Sugar Cane
9.3 Estimating an AR(1) Error Model 9.2.2 First Order Autoregressive Errors
9.3.1 Least Squares Estimation
9.4 Testing for Autocorrelation
9.3.2 Nonlinear Least Squares Estimation
9.3.2a Generalized Least Squares Estimation
9.3.3 Estimating a More General Model
9.4.1 Residual Correlogram
9.5 An Introduction to Forecasting: Autoregressive Models 9.4.2 A Lagrange Multiplier Test 9.4.3 Recapping and Looking Forward 9.6 Finite Distributed Lags 9.7 Autoregressive Distributed Lag Models 9.8 Exercises
9.8.1 Problems
Appendix 9A Generalized Least Squares Estimation 9.8.2 Computer Exercises Appendix 9B The Durbin–Watson Bounds Test
9B.1 The Durbin–Watson Bounds Test
Appendix 9C Deriving ARDL Lag Weights
9C.1 The Geometric Lag
Appendix 9D Forecasting: Exponential Smoothing
9C.2 Lag Weights for More General ARDL Models 10 Random Regressors and Moment Based Estimation
Learning Objectives
Keywords 10.1 Linear Regression with Random x’s
10.1.1 The small Sample Properties of the Least Squares Estimator
10.2 Cases in Which x and e are Correlated
10.1.2 Asymptotic Properties of the Least Squares Estimator: x Not Random 10.1.3 Asymptotic Properties of the Least Squares Estimator: x Random 10.1.4 Why Least Squares Fails
10.2.1 Measurement Error
10.3 Estimators Based on the Method of Moments
10.2.2 Omitted Variables 10.2.3 Simultaneous Equations Bias 10.2.4 Lagged Dependent Variable Models with Serial Correlation
10.3.1 Method of Moments Estimation of a Popular Mean and Variance
10.4 Specification Tests
10.3.2 Method of Moments Estimation in the Simple Linear Regression Model 10.3.3 Instrumental Variables Estimating in the Simple Linear Regression Model
10.3.3a The Importance of Using Strong Instruments
10.3.4 Instrumental Variables Estimation with Surplus Instruments
10.3.3b An Illustration Using Simulated Data 10.3.3c An Illustration Using a Wage Equation
10.3.4a An Illustration using Simulated Data
10.3.5 Instrumental Variables Estimation in a General Model
10.3.4b An Illustration Using a Wage Equation
10.3.5a Hypothesis Testing with Instrumental Variables Estimates
10.3.5b Goodness-of-Fit with Instrumental Variables Estimates
10.4.1 The Hausman Test for Endogeneity
10.5 Exercises
10.4.2 Testing for Weak Instruments 10.4.3 Testing Instrument Validity 10.4.4 Numerical Examples Using Simulated Data
10.4.4a The Hausman Test
10.4.5 Specification Tests for the Wage Equation
10.4.4b Test for Weak Instruments 10.4.4c Testing Surplus Moment Conditions
10.5.1 Problems
Appendix 10A Conditional and Iterated Expectations
10.5.2 Computer Exercises
10A.1 Conditional Expectations
Appendix 10B The Inconsistency of Least Squares 10A.2 Iterated Expectations 10A.3 Regression Model Applications Appendix 10C The Consistency of the IV Estimator Appendix 10D The Logic of the Hausman Test 11 Simultaneous Equations Models
Learning Objectives
Keywords 11.1 A Supply and Demand Model 11.2 The Reduced Form Equations 11.3 The Failure of Least Squares 11.4 The Identification Problem 11.5 Two-Stage Least Squares Estimation
11.5.1 The General Two-Stage Least Squares Estimation Procedure
11.6 An Example of Two-Stage Least Squares Estimation 11.5.2 The Properties of the Two-Stage Least Squares Estimator
11.6.1 Identification
11.7 Supply and Demand at the Fulton Fish Market
11.6.2 The Reduced Form Equations 11.6.3 The Structural Equations
11.7.1 Identification
11.8 Exercises
11.7.2 The Reduced Form Equations 11.7.3 Two-Stage Least Squares Estimation of Fish Demand
11.8.1 Problems
Appendix 11A An Algebraic Explanation of the Failure of Least Squares
11.8.2 Computer Exercises 12 Nonstationary Time Series Data and Cointegration
Learning Objectives
Keywords 12.1 Stationary and Nonstationary Variables
12.1.1 The First-Order Autoregressive Model
12.2 Spurious Regressions 12.1.2 Random Walk Models 12.3 Unit Root Tests for Stationarity
12.3.1 Dickey–Fuller Test 1 (No Constant and No Trend)
12.4 Cointegration
12.3.2 Dickey–Fuller Test 2 (With Constant But No Trend) 12.3.3 Dickey–Fuller Test 3 (With Constant and With Trend) 12.3.4 The Dickey–Fuller Testing Procedure 12.3.5 The Dickey–Fuller Tests: An Example 12.3.6 Order of Integration
12.4.1 An Example of a Cointegration Test
12.5 Regression When There is No Cointegration
12.5.1 First Difference Stationary
12.6 Exercises
12.5.2 Trend Stationary
12.6.1 Problems
12.6.2 Computer Exercises 13 Vector Error Correction and Vector Autoregressive Models: An Introduction to Macroeconometrics
Learning Objectives
Keywords 13.1 VEC and VAR Models 13.2 Estimating a Vector Error Correction Model
13.2.1 Example
13.3 Estimating a VAR Model 13.4 Impulse Responses and Variance Decompositions
13.4.1 Impulse Response Functions
13.5 Exercises
13.4.1a The Univariate Case
13.4.2 Forecast Error Variance Decompositions
13.4.1b The Bivariate Case
13.4.2a Univariate Analysis
13.4.2b Bivariate Analysis 13.4.2c The General Case
13.5.1 Problems
Appendix 13A The Identification Problem
13.5.2 Computer Exercises 14 Time-Varying Volatility and ARCH Models: An Introduction to Financial Econometrics
Learning Objectives
Keywords 14.1 The ARCH Model
14.1.1 Conditional and Unconditional Forecasts
14.2 Time-Varying Volatility 14.3 Testing, Estimating and Forecasting
14.3.1 Testing for ARCH Effects
14.4 Extensions
14.3.2 Estimating ARCH Models 14.3.3 Forecasting Volatility
14.4.1 The GARCH Model—Generalized ARCH
14.5 Exercises
14.4.2 Allowing for an Asymmetric Effect 14.4.3 GARCH-in-Mean and Time-Varying Risk Premium
14.5.1 Problems
14.5.2 Computer Exercises 15 Panel Data Models
Learning Objectives
Keywords 15.1 Grunfeld’s Investment Data 15.2 Sets of Regression Equations 15.3 Seemingly Unrelated Regressions
15.3.1 Separate or Joint Estimation?
15.4 The Fixed Effects Model
15.3.2 Testing Cross-Equation Hypotheses
15.4.1 A Dummy Variable Model
15.5 The Random Effects Model
15.4.2 The Fixed Effects Estimator 15.4.3 Fixed Effects Estimation Using a Microeconomic Panel
15.5.1 Error Term Assumptions
15.6 Exercises
15.5.2 Testing for Random Effects 15.5.3 Estimation of the Random Effects Model 15.5.4 An Example Using the NLS Data 15.5.5 Comparing Fixed and Random Effects Estimators
15.5.5a Endogeneity in the Random Effects Model
15.5.5b The Fixed Estimator in a Random Effects Model 15.5.5c A Hausman Test
15.6.1 Problems
Appendix 15A Estimation of Error Components
15.6.2 Computer Exercises 16 Qualitative and Limited Dependent Variable Models
Learning Objectives
Keywords 16.1 Models with Binary Dependent Variables
16.1.1 The Linear Probability Model
16.2 The Logit Model for Binary Choice 16.1.2 The Probit Model 16.1.3 Interpretation of the Probit Model 16.1.4 Maximum Likelihood Estimation of the Probit Model 16.1.5 An Example 16.3 Multinomial Logit
16.3.1 Multinomial Logit Choice Probabilities
16.4 Conditional Logit
16.3.2 Maximum Likelihood Estimation 16.3.3 Post-Estimation Analysis
16.4.1 Conditional Logit Choice Probabilities
16.5 Ordered Choice Models
16.4.2 Post-Estimation Analysis 16.4.3 An Example
16.5.1 Ordinal Probit Choice Probabilities
16.6 Models for Count Data
16.5.2 Estimation and Interpretation 16.5.3 An Example
16.6.1 Maximum Likelihood Estimation
16.7 Limited Dependent Variables
16.6.2 Interpretation in the Poisson Regression Model 16.6.3 An Example
16.7.1 Censored Data
16.8 Exercises
16.7.2 A Monte Carlo Experiment 16.7.3 Maximum Likelihood Estimation 16.7.4 Tobit Model Interpretation 16.7.5 An Example 16.7.6 Sample Selection
16.7.6a The Econometric Model
16.7.6b Heckit Example: Wages of Married Women 17 Writing an Empirical Research Report, and Sources of Economic Data
17.1 Selecting a Topic for an Economics Project
17.1.1 Choosing a Topic
17.2 A Format for Writing a Research Report 17.1.2 Writing an Abstract 17.3 Sources of Economic Data
17.3.1 Links to Economic Data on the Internet
17.4 Exercises
17.3.2 Traditional Sources of Economic Data 17.3.3 Interpreting Economic Data Appendix A Review of Math Essentials
Learning Objectives
Keywords A.1 Summation A.2 Some Basics
A.2.1 Numbers
A.3 Linear Relationships
A.2.2 Exponents A.2.3 Scientific Notation A.2.4 Logarithms and the Number e
A.3.1 Elasticity
A.4 Nonlinear Relationships
A.4.1 Quadratic Function
A.5 Exercises
A.4.2 Cubic Function A.4.3 Reciprocal Function A.4.4 Log-Log Function A.4.5 Log-Linear Function A.4.6 Approximating Logarithms A.4.7 Approximating Logarithms in the Log-Linear Model A.4.8 Linear-Log Function Appendix B Review of Probability Concepts
Learning Objectives
Keywords B.1 Random Variables B.2 Probability Distributions B.3 Joint, Marginal, and Conditional Probability Distributions
B.3.1 Marginal Distributions
B.4 Properties of Probability Distributions
B.3.2 Conditional Probability B.3.3 A Simple Experiment
B.4.1 Mean, Median, and Mode
B.5 Some Important Probability Distributions
B.4.2 Expected Values of Functions of a Random Variable B.4.3 Expected Values of Several Random Variables B.4.4 The Simple Experiment Again
B.5.1 The Normal Distribution
B.6 Exercises
B.5.2 The Chi-Square Distribution B.5.3 The t-Distribution 8.5.4 The F-Distribution Appendix C Review of Statistical Inference
Learning Objectives
Keywords C.1 A Sample of Data C.2 An Econometric Model C.3 Estimating the Mean of a Population
C.3.1 The Expected Value of Y
C.4 Estimating the Population Variance and Other Moment
C.3.2 The Variance of Y C.3.3 The Sampling Distribution of Y C.3.4 The Central Limit Theorem C.3.5 Best Linear Unbiased Estimation
C.4.1 Estimating the Population Variance
C.5 Interval Estimation
C.4.2 Estimating Higher Moments C.4.3 The Hip Data C.4.4 Using the Estimates
C.5.1 Interval Estimation: σZ2 Known
C.6 Hypothesis Tests About a Population Mean
C.5.2 A Simulation C.5.3 Interval Estimation: σZ2 Unknown C.5.4 A Simulation (continued) C.5.5 Interval Estimation Using the Hip Data
C.6.1 Components of Hypothesis Tests
C.7 Some Other Useful Tests
C.6.1a The Null Hypothesis
C.6.2 One-Tail Tests with Alternative “Greater Than” (>)C.6.1b The Alternative Hypothesis C.6.1c The Test Statistic C.6.1d The Rejection Region C.6.1e A Conclusion C.6.3 One-Tail Tests with Alternative “Less Than&rsdquo; (<) C.6.4 Two-Tail Tests with Alternative “Not Equal To” (≠) C.6.5 Example of a One-Tail Test Using the Hip Data C.6.6 Example of a Two-Tail Test Using Hip Data C.6.7 The p-Value C.6.8 A Comment on Stating Null and Alternative Hypotheses C.6.9 Type I and Type II Errors C.6.10 A Relationship Between Hypothesis Testing and Confidence Intervals
C.7.1 Testing the Population Variance
C.8 Introduction to Maximum Likelihood Estimation
C.7.2 Testing the Equality of Two Population Means C.7.3 Testing the Ratio of Two Population Variances C.7.4 Testing the Normality of a Population
C.8.1 Inference with Maximum Likelihood Estimators
C.9 Algebraic Supplements (Optimal)
C.8.2 The Variance of the Maximum Likelihood Estimator C.8.3 The Distribution of the Sample Proportion C.8.4 Asymptotic Test Procedures
C.8.4a The Likelihood Ratio (LR) Test
C.8.4b The Wald Test C.8.4c The Lagrange Multiplier (LM) Test
C.9.1 Derivation of Least Squares Estimator
C.10 Exercises
C.9.2 Best Linear Unbiased Estimation Appendix D Solutions to Selected Exercises
Appendix E Tables
Table 1 Cumulative Probabilities for the Standard Normal Distribution
Table 2 Percentiles for the t-Distribution Table 3 Percentiles for the Chi-square Distribution Table 4 95th Percentile for the F-Distribution Table 5 99th Percentile for the F-Distribution Index
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