Preface v List of Examples xxi 1 An Introduction to Econometrics 1 1.1 Why Study Econometrics? 1 1.2 What Is Econometrics About? 2 1.2.1 Some Examples 3 1.3 The Econometric Model 4 1.3.1 Causality and Prediction 5 1.
4 How Are Data Generated? 5 1.4.1 Experimental Data 6 1.4.2 Quasi-Experimental Data 6 1.4.3 Nonexperimental Data 7 1.5 Economic Data Types 7 1.
5.1 Time-Series Data 7 1.5.2 Cross-Section Data 8 1.5.3 Panel or Longitudinal Data 9 1.6 The Research Process 9 1.7 Writing an Empirical Research Paper 11 1.
7.1 Writing a Research Proposal 11 1.7.2 A Format for Writing a Research Report 11 1.8 Sources of Economic Data 13 1.8.1 Links to Economic Data on the Internet 13 1.8.
2 Interpreting Economic Data 14 1.8.3 Obtaining the Data 14 Probability Primer 15 P.1 Random Variables 16 P.2 Probability Distributions 17 P.3 Joint, Marginal, and Conditional Probabilities 20 P.3.1 Marginal Distributions 20 P.
3.2 Conditional Probability 21 P.3.3 Statistical Independence 21 P.4 A Digression: Summation Notation 22 P.5 Properties of Probability Distributions 23 P.5.1 Expected Value of a Random Variable 24 P.
5.2 Conditional Expectation 25 P.5.3 Rules for Expected Values 25 P.5.4 Variance of a Random Variable 26 P.5.5 Expected Values of Several Random Variables 27 P.
5.6 Covariance Between Two Random Variables 27 P.6 Conditioning 29 P.6.1 Conditional Expectation 30 P.6.2 Conditional Variance 31 P.6.
3 Iterated Expectations 32 P.6.4 Variance Decomposition 33 P.6.5 Covariance Decomposition 34 P.7 The Normal Distribution 34 P.7.1 The Bivariate Normal Distribution 37 P.
8 Exercises 39 2 The Simple Linear Regression Model 46 2.1 An Economic Model 47 2.2 An Econometric Model 49 2.2.1 Data Generating Process 51 2.2.2 The Random Error and Strict Exogeneity 52 2.2.
3 The Regression Function 53 2.2.4 Random Error Variation 54 2.2.5 Variation in x 56 2.2.6 Error Normality 56 2.2.
7 Generalizing the Exogeneity Assumption 56 2.2.8 Error Correlation 57 2.2.9 Summarizing the Assumptions 58 2.3 Estimating the Regression Parameters 59 2.3.1 The Least Squares Principle 61 2.
3.2 Other Economic Models 65 2.4 Assessing the Least Squares Estimators 66 2.4.1 The Estimator b2 67 2.4.2 The Expected Values of b1 and b2 68 2.4.
3 Sampling Variation 69 2.4.4 The Variances and Covariance of b1 and b2 69 2.5 The Gauss-Markov Theorem 72 2.6 The Probability Distributions of the Least Squares Estimators 73 2.7 Estimating the Variance of the Error Term 74 2.7.1 Estimating the Variances and Covariance of the Least Squares Estimators 74 2.
7.2 Interpreting the Standard Errors 76 2.8 Estimating Nonlinear Relationships 77 2.8.1 Quadratic Functions 77 2.8.2 Using a Quadratic Model 77 2.8.
3 A Log-Linear Function 79 2.8.4 Using a Log-Linear Model 80 2.8.5 Choosing a Functional Form 82 2.9 Regression with Indicator Variables 82 2.10 The Independent Variable 84 2.10.
1 Random and Independent x 84 2.10.2 Random and Strictly Exogenous x 86 2.10.3 Random Sampling 87 2.11 Exercises 89 2.11.1 Problems 89 2.
11.2 Computer Exercises 93 Appendix 2A Derivation of the Least Squares Estimates 98 Appendix 2B Deviation from the Mean Form of b2 99 Appendix 2C b2 Is a Linear Estimator 100 Appendix 2D Derivation of Theoretical Expression for b2 100 Appendix 2E Deriving the Conditional Variance of b2 100 Appendix 2F Proof of the Gauss-Markov Theorem 102 Appendix 2G Proofs of Results Introduced in Section 2.10 103 2G.1 The Implications of Strict Exogeneity 103 2G.2 The Random and Independent x Case 103 2G.3 The Random and Strictly Exogenous x Case 105 2G.4 Random Sampling 106 Appendix 2H Monte Carlo Simulation 106 2H.1 The Regression Function 106 2H.
2 The Random Error 107 2H.3 Theoretically True Values 107 2H.4 Creating a Sample of Data 108 2H.5 Monte Carlo Objectives 109 2H.6 Monte Carlo Results 109 2H.7 Random-x Monte Carlo Results 110 3 Interval Estimation and Hypothesis Testing 112 3.1 Interval Estimation 113 3.1.
1 The t-Distribution 113 3.1.2 Obtaining Interval Estimates 115 3.1.3 The Sampling Context 116 3.2 Hypothesis Tests 118 3.2.1 The Null Hypothesis 118 3.
2.2 The Alternative Hypothesis 118 3.2.3 The Test Statistic 119 3.2.4 The Rejection Region 119 3.2.5 A Conclusion 120 3.
3 Rejection Regions for Specific Alternatives 120 3.3.1 One-Tail Tests with Alternative ''''Greater Than'''' (>) 120 3.3.2 One-Tail Tests with Alternative ''''Less Than'''' (<) 121 3.3.3 Two-Tail Tests with Alternative ''''Not Equal To'''' (â ) 122 3.4 Examples of Hypothesis Tests 123 3.
5 The p-Value 126 3.6 Linear Combinations of Parameters 129 3.6.1 Testing a Linear Combination of Parameters 131 3.7 Exercises 133 3.7.1 Problems 133 3.7.
2 Computer Exercises 139 Appendix 3A Derivation of the t-Distribution 144 Appendix 3B Distribution of the t-Statistic under H1 145 Appendix 3C Monte Carlo Simulation 147 3C.1 Sampling Properties of Interval Estimators 148 3C.2 Sampling Properties of Hypothesis Tests 149 3C.3 Choosing the Number of Monte Carlo Samples 149 3C.4 Random-x Monte Carlo Results 150 4 Prediction, Goodness-of-Fit, and Modeling Issues 152 4.1 Least Squares Prediction 153 4.2 Measuring Goodness-of-Fit 156 4.2.
1 Correlation Analysis 158 4.2.2 Correlation Analysis and R2 158 4.3 Modeling Issues 160 4.3.1 The Effects of Scaling the Data 160 4.3.2 Choosing a Functional Form 161 4.
3.3 A Linear-Log Food Expenditure Model 163 4.3.4 Using Diagnostic Residual Plots 165 4.3.5 Are the Regression Errors Normally Distributed? 167 4.3.6 Identifying Influential Observations 169 4.
4 Polynomial Models 171 4.4.1 Quadratic and Cubic Equations 171 4.5 Log-Linear Models 173 4.5.1 Prediction in the Log-Linear Model 175 4.5.2 A Generalized R2 Measure 176 4.
5.3 Prediction Intervals in the Log-Linear Model 177 4.6 Log-Log Models 177 4.7 Exercises 179 4.7.1 Problems 179 4.7.2 Computer Exercises 185 Appendix 4A Development of a Prediction Interval 192 Appendix 4B The Sum of Squares Decomposition 193 Appendix 4C Mean Squared Error: Estimation and Prediction 193 5 The Multiple Regression Model 196 5.
1 Introduction 197 5.1.1 The Economic Model 197 5.1.2 The Econometric Model 198 5.1.3 The General Model 202 5.1.
4 Assumptions of the Multiple Regression Model 203 5.2 Estimating the Parameters of the Multiple Regression Model 205 5.2.1 Least Squares Estimation Procedure 205 5.2.2 Estimating the Error Variance Ï2 207 5.2.3 Measuring Goodness-of-Fit 208 5.
2.4 Frisch-Waugh-Lovell (FWL) Theorem 209 5.3 Finite Sample Properties of the Least Squares Estimator 211 5.3.1 The Variances and Covariances of the Least Squares Estimators 212 5.3.2 The Distribution of the Least Squares Estimators 214 5.4 Interval Estimation 216 5.
4.1 Interval Estimation for a Single Coefficient 216 5.4.2 Interval Estimation for a Linear Combination of Coefficients 217 5.5 Hypothesis Testing 218 5.5.1 Testing the Significance of a Single Coefficient 219 5.5.
2 One-Tail Hypothesis Testing for a Single Coefficient 220 5.5.3 Hypothesis Testing for a Linear Combination of Coefficients 221 5.6 Nonlinear Relationships 222 5.7 Large Sample Properties of the Least Squares Estimator 227 5.7.1 Consistency 227 5.7.
2 Asymptotic Normality 229 5.7.3 Relaxing Assumptions 230 5.7.4 Inference for a Nonlinear Function of Coefficients 232 5.8 Exercises 234 5.8.1 Problems 234 5.
8.2 Computer Exercises 240 Appendix 5A Derivation of Least Squares Estimators 247 Appendix 5B The Delta Method 248 5B.1 Nonlinear Function of a Single Parameter 248 5B.2 Nonlinear Function of Two Parameters 249 Appendix 5C Monte Carlo Simulation 250 5C.1 Least Squares Estimation with Chi-Square Errors 250 5C.2 Monte Carlo Simulation of the Delta Method 252 Appendix 5D Bootstrapping 254 5D.1 Resampling 255 5D.2 Bootstrap Bias Estimate 256 5D.
3 Bootstrap Standard Error 256 5D.4 Bootstrap Percentile Interval Estimate 257 5D.5 Asymptotic Refinement 258 6 Further Inference in the Multiple Regression Model 260 6.1 Testing Joint Hypotheses: The F-test 261 6.1.1 Testing the Significance of the Model 264 6.1.2 The Relationship Between t- and F-Tests 265 6.
1.3 More General F-Tests 267 6.1.4 Using Computer Software 268 6.1.5 Large Sample Tests 269 6.2 The Use of Nonsample Information 271 6.3 Model Specification 273 6.
3.1 Causality versus Prediction 273 6.3.2 Omitted Variables 275 6.3.3 Irrelevant Variables 277 6.3.4 Control Variables 278 6.
3.5 Choosing a Model 280 6.3.6 RESET 281 6.4 Prediction 282.