Introductory econometrics : using Monte Carlo simulation with Microsoft Excel /

Contents 9
Preface 19
The Purpose of This Book 19
Our Goals 20
Content and Level of Presentation 23
Conclusion 24
Acknowledgments 25
References 25
User Guide 27
0.1 Conventions and Organization of Files 27
0.2 Preparing and Working with Microsoft Excel 29
1 Introduction 36
1.1 Definition of Econometrics 36
1.2 Regression Analysis 37
1.3 Conclusion 54
1.4 Exercises 55
References 56
Part 1: Description 57
2 Correlation 59
2.1 Introduction 59
2.2 Correlation Basics 59
2.3 Correlation Dangers 66
2.4 Ecological Correlation 70
2.5 Conclusion 76
2.6 Exercises 77
References 77
3 PivotTables 79
3.1 Introduction 79
3.2 The Basic PivotTable 79
3.3 The Crosstab and Conditional Average 85
3.4 PivotTables and the Conditional Mean Function 91
3.5 Conclusion 95
3.6 Exercises 96
References 97
4 Computing the OLS Regression Line 98
4.1 Introduction 98
4.2 Fitting the Ordinary Least Squares Regression Line 98
4.3 Least Squares Formulas 108
4.4 Fitting the Regression Line in Practice 110
4.5 Conclusion 116
4.6 Exercises 116
References 117
Appendix: Deriving the Least Squares Formulas 117
5 Interpreting OLS Regression 121
5.1 Introduction 121
5.2 Regression as Double Compression 121
5.3 Galton and Two Regression Lines 130
5.4 Properties of the Sample Average and the Regression Line 133
5.5 Residuals and the Root-Mean-Square Error 140
5.6 R-Squared (R2) 148
5.7 Limitations of Data Description with Regression 152
5.8 Conclusion 161
5.9 Exercises 161
References 162
Appendix: Proof that the Sample Average is a Least Squares Estimator 162
6 Functional Form of the Regression 164
6.1 Introduction 164
6.2 Understanding Functional Form via an Econometric Fable 165
6.3 Exploring Two Other Functional Forms 170
6.4 The Earnings Function 174
6.5 Elasticity 181
6.6 Conclusion 185
6.7 Exercises 186
References 186
Appendix: A Catalog of Functional Forms 187
7 Multiple Regression 190
7.1 Introduction 190
7.2 Introducing Multiple Regression 191
7.3 Improving Description via Multiple Regression 200
7.4 Multicollinearity 210
7.5 Conclusion 217
7.6 Exercises 218
Appendix: The Multivariate Least Squares Formula and the Omitted Variable Rule 220
8 Dummy Variables 224
8.1 Introduction 224
8.2 Defining and Using Dummy Variables 225
8.3 Properties of Dummy Variables 228
8.4 Dummy Variables as Intercept Shifters 231
8.5 Dummy Variable Interaction Terms 234
8.6 Conclusion 237
8.7 Exercises 238
References 238
Part 2: Inference 239
9 Monte Carlo Simulation 241
9.1 Introduction 241
9.2 Random Number Generation Theory 242
9.3 Random Number Generation in Practice 246
9.4 Monte Carlo Simulation: An Example 251
9.5 The Monte Carlo Simulation Add-In 258
9.6 Conclusion 261
9.7 Exercises 262
References 262
10 Review of Statistical Inference 264
10.1 Introduction 264
10.2 Introducing Box Models for Chance Processes 265
10.3 The Coin-Flip Box Model 268
10.4 The Polling Box Model 277
10.5 Hypothesis Testing 283
10.6 Consistent Estimators 288
10.7 The Algebra of Expectations 291
10.8 Conclusion 303
10.9 Exercises 303
References 304
Appendix: The Normal Approximation 304
11 The Measurement Box Model 307
11.1 Introduction 307
11.2 Introducing the Problem 309
11.3 The Measurement Box Model 311
11.4 Monte Carlo Simulation 316
11.5 Applying the Box Model 319
11.6 Hooke\u2019s Law 322
11.7 Conclusion 327
11.8 Exercises 327
References 328
12 Comparing Two Populations 329
12.1 Introduction 329
12.2 Two Boxes 329
12.3 Monte Carlo Simulation of a Two Box Model 332
12.4 A Real Example: Education and Wages 335
12.5 Conclusion 340
12.6 Exercises 341
13 The Classical Econometric Model 342
13.1 Introduction 342
13.2 Introducing the CEM via a Skiing Example 342
13.3 Implementing the CEM via a Skiing Example 348
13.4 CEM Requirements 354
13.5 Conclusion 358
13.6 Exercises 359
References 360
14 The Gauss\u2013Markov Theorem 361
14.1 Introduction 361
14.2 Linear Estimators 362
14.3 Choosing an Estimator 368
14.4 Proving the Gauss-Markov Theorem in the Univariate Case 373
14.5 Linear Estimators in Regression Analysis 378
14.6 OLS is BLUE: The Gauss\u2013Markov Theorem for the Bivariate Case 387
14.7 Using the Algebra of Expectations 392
14.8 Conclusion 400
14.9 Exercises 401
References 402
15 Understanding the Standard Error 404
15.1 Introduction 404
15.2 SE Intuition 404
15.3 The Estimated SE 409
15.4 Determinants of the SE of the OLS Sample Slope 413
15.5 Estimating the SD of the Errors 418
15.6 The Standard Error of the Forecast and the Standard Error of the Forecast Error 424
15.7 Conclusion 434
15.8 Exercises 435
References 436
16 Confidence Intervals and Hypothesis Testing 437
16.1 Introduction 437
16.2 Distributions of OLS Regression Statistics 438
16.3 Understanding Confidence Intervals 447
16.4 The Logic of Hypothesis Testing 456
16.5 Z- and T-Tests 460
16.6 A Practical Example 469
16.7 Conclusion 476
16.8 Exercises 476
References 477
17 Joint Hypothesis Testing 479
17.1 Introduction 479
17.2 Restricted Regression 482
17.3 The Chi-Square Distribution 484
17.4 The F-Distribution 487
17.5 An F-Test: The Galileo Example 488
17.6 F- and T-Tests for Equality of Two Parameters 494
17.7 F-Test for Multiple Parameters 501
17.8 The Consequences of Multicollinearity 504
17.9 Conclusion 513
17.10 Exercises 513
References 514
18 Omitted Variable Bias 516
18.1 Introduction 516
18.2 Why Omitted Variable Bias Is Important 517
18.3 Omitted Variable Bias Defined and Demonstrated 519
18.4 A Real Example of Omitted Variable Bias 524
18.5. Random X\u2019s: AMore Realistic Data Generation Process 528
18.6 Conclusion 532
18.7 Exercises 532
References 533
19 Heteroskedasticity 534
19.1 Introduction 534
19.2 A Univariate Example of Heteroskedasticity 536
19.3 A Bivariate Example of Heteroskedasticity 544
19.4 Diagnosing Heteroskedasticity with the B\u2013P Test 553
19.5 Dealing with Heteroskedasticity: Robust Standard Errors 559
19.6 Correcting for Heteroskedasticity: Generalized Least Squares 568
19.7 A Real Example of Heteroskedasticity: The Earnings Function 575
19.8 Conclusion 581
19.9 Exercises 582
References 583
20 Autocorrelation 584
20.1 Introduction 584
20.2 Understanding Autocorrelation 586
20.3 Consequences of Autocorrelation 592
20.4 Diagnosing Autocorrelation 602
20.5 Correcting Autocorrelation 614
20.6 Conclusion 626
20.7 Exercises 628
References 629
21 Topics in Time Series 630
21.1 Introduction 630
21.2 Trends in Time Series Models 631
21.3 Dummy Variables in Time Series Models 639
21.4 Seasonal Adjustment 643
21.5 Stationarity 650
21.6 Weak Dependence 659
21.7 Lagged Dependent Variables 664
21.8 Money Demand 671
21.9 Comparing Forecasts Using Different Models of the DGP 678
21.10 Conclusion 684
21.11 Exercises 685
References 687
22 Dummy Dependent Variable Models 689
22.1 Introduction 689
22.2 Developing Intuition about Dummy Dependent Variable Models 692
22.3 The Campaign Contributions Example 695
22.4 A DDV Box Model 697
22.5 The Linear Probability Model (OLS with a Dummy Dependent Variable) 700
22.6 Nonlinear Least Squares Applied to Dummy Dependent Variable Models 706
22.7 Interpreting NLLS Estimates 716
22.8. Is There Mortgage Discrimination? 721
22.9 Conclusion 732
22.10 References 733
23 Bootstrap 735
23.1 Introduction 735
23.2 Bootstrapping the Sample Percentage 736
23.3 Paired XY Bootstrap 739
23.4 The Bootstrap Add-In 744
23.5 Bootstrapping R2 747
23.6 Conclusion 752
23.7 Exercises 754
References 754
24 Simultaneous Equations 756
24.1 Introduction 756
24.2 Simultaneous Equations Model Example 757
24.3 Simultaneity Bias with OLS 761
24.4 Two-Stage Least Squares 767
24.5 Conclusion 771
24.6 Exercises 772
References 773
Glossary 775
Index 787