Introductory Econometrics: Using Monte Carlo Simulation with Microsoft Excel

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
The Purpose of This Book......Page 19
Our Goals......Page 20
Content and Level of Presentation......Page 23
Conclusion......Page 24
References......Page 25
0.1 Conventions and Organization of Files......Page 27
0.2 Preparing and Working with Microsoft Excel......Page 29
Excel Versions and Your Version......Page 30
Properly Configuring Excel......Page 31
Troubleshooting......Page 34
1.1 Definition of Econometrics......Page 36
Workbook: Cig.xls......Page 37
Summary......Page 53
1.3 Conclusion......Page 54
1.4 Exercises......Page 55
References......Page 56
Part 1: Description......Page 57
Workbook: Correlation.xls......Page 59
Univariate Analysis: Average, SD, and Histogram......Page 60
Bivariate Analysis: The Scatter Diagram (or Plot)
and Correlation Coefficient......Page 61
Summary......Page 64
The Correlation Coefficient as a Poor Descriptor of the Data......Page 66
Association Is Not Causation......Page 69
Workbooks: EcolCorr.xls; EcolCorrCPS.xls......Page 70
A Hypothetical Example......Page 71
An Actual Example......Page 74
2.5 Conclusion......Page 76
References......Page 77
Workbooks: IndianaFTWorkers.xls; Histogram.xla(Excel add-in)......Page 79
Workbook: IndianaFTWorkers.xls......Page 85
A New Data Set......Page 91
3.5 Conclusion......Page 95
3.6 Exercises......Page 96
References......Page 97
Workbook: Reg.xls......Page 98
The Residual......Page 100
Minimizing the SSR Using Excel’s Solver......Page 103
Another View of the Least Squares Optimization Problem......Page 104
Summary......Page 107
Notation......Page 108
Workbook: Reg.xls......Page 110
4.6 Exercises......Page 116
The Optimization Problem in Abstract Notation......Page 117
Workbooks: DoubleCompression.xls; EastNorthCentralFTWorkers.xls......Page 121
First Compression......Page 122
Second Compression......Page 124
Yearly Earnings Regressed on Education......Page 125
Regression versus the SD Line......Page 127
Summary......Page 129
Workbook: TwoRegressionLines.xls......Page 130
Workbook: OLSFormula.xls......Page 133
The Sample Average......Page 134
The Regression Line......Page 137
Summary......Page 139
Residual Output......Page 140
The Root-Mean-Squared Error (RMSE)......Page 142
Calculating the RMSE......Page 143
Example: Wabash College SAT Scores......Page 144
Workbook: RSquared.xls......Page 148
The Logic of R2 :The Guessing Game......Page 149
Computing R2......Page 150
Summary......Page 151
Example 1: The Anscombe Data......Page 152
Example 2: Nonlinearity in the Real World......Page 153
Example 3: A New Pattern in the Residuals......Page 155
Example 4: Heteroskedasticity in Earnings Data......Page 157
Summary......Page 159
5.9 Exercises......Page 161
Appendix: Proof that the Sample Average is a Least
Squares Estimator......Page 162
6.1 Introduction......Page 164
Workbook: Galileo.xls......Page 165
Workbook: IMRGDPFunForm.xls......Page 170
Human Capital Theory......Page 174
The Earnings Function in Practice......Page 179
6.5 Elasticity......Page 181
Reviewing the Concept of Elasticity......Page 182
Elasticity with Different Functional Forms......Page 184
6.6 Conclusion......Page 185
References......Page 186
Workbook: FuncFormCatalog.xls......Page 187
7.1 Introduction......Page 190
Terminology and Visualization......Page 191
Example: The Demand for Heating Oil......Page 194
Univariate, Bivariate, and Multivariate Least Squares Regressions......Page 196
Workbook: MultiReg.xls......Page 200
Bivariate Cases......Page 201
Price......Page 202
Ways to Deal with Confounding......Page 203
Controlling for Confounding: Smaller, More Homogenous Groups......Page 204
Controlling for Confounding: Multiple Regression......Page 208
Summary......Page 209
Workbook: Multicollinearity.xls......Page 210
A Heating Oil Example......Page 211
Near-Perfect Multicollinearity......Page 215
7.5 Conclusion......Page 217
7.6 Exercises......Page 218
Using Calculus and Algebra to Obtain the OLS Formulas......Page 220
The Omitted Variable Rule Relating Bivariate and Multiple Regression Coefficients......Page 222
Summary......Page 223
8.1 Introduction......Page 224
Workbook: Female.xls......Page 225
Using Dummy Variables in a Regression......Page 226
Summary......Page 227
Workbook: Female.xls......Page 228
Workbook: Female.xls......Page 231
Workbook: Female.xls......Page 234
Summary......Page 236
8.6 Conclusion......Page 237
References......Page 238
Part 2: Inference......Page 239
9.1 Introduction......Page 241
Workbook: RNGTheory.xls......Page 242
Workbook: RNGPractice.xls......Page 246
Workbook: MonteCarlo.xls......Page 251
Summary......Page 257
Workbooks: MonteCarlo.xls; MCSim.xla (Excel add-in);
MCSimSolver.xla (Excel add-in)......Page 258
Summary......Page 260
9.6 Conclusion......Page 261
References......Page 262
10.1 Introduction......Page 264
10.2 Introducing Box Models for Chance Processes......Page 265
Summary......Page 267
Making a Coin-Flip Box Model......Page 268
Monte Carlo Simulation of the Coin-Flip Box Model......Page 270
Summary......Page 275
Workbook: PresidentialHeights.xls......Page 277
Workbook: PValue.xla (Excel add-in)......Page 283
Summary......Page 287
Workbook: Consistency.xls......Page 288
Summary......Page 290
Introducing the Expectations Operator E ( )......Page 291
The Algebra of Expectations......Page 296
Summary......Page 302
10.9 Exercises......Page 303
Appendix: The Normal Approximation......Page 304
11.1 Introduction......Page 307
11.2 Introducing the Problem......Page 309
The Idea of Measurement Error......Page 310
11.3 The Measurement Box Model......Page 311
A Box Model for Measurement Error......Page 312
The Measurement Box Model in a Picture......Page 313
The Measurement Box Model in Equation Form......Page 314
Workbook: Measure.xls......Page 316
Monte Carlo Simulation......Page 317
Summary......Page 318
Workbook: Measure.xls......Page 319
Summary......Page 321
Workbook: HookesLaw.xls......Page 322
Summary......Page 326
11.8 Exercises......Page 327
References......Page 328
12.2 Two Boxes......Page 329
A Two Box Model for Comparing Populations......Page 330
Summary......Page 331
Setting Up The Two Box Model......Page 332
Monte Carlo Simulation......Page 334
Workbook: CPS90Workers.xls......Page 335
The Data......Page 336
Setting Up the Box Model......Page 337
Constructing the Test Statistic and Interpreting the Results......Page 338
A Brief Note on Confounding......Page 339
12.5 Conclusion......Page 340
References......Page 341
Workbook: Skiing.xls......Page 342
The Measurement Box Model......Page 343
A New DGP to Describe Observed Ski Times......Page 345
Comparing Box Models......Page 347
Workbook: Skiing.xls......Page 348
Monte Carlo Simulation......Page 352
Why Can We Assume That the Average of the Error Box Is Zero?......Page 353
The CEM in Words and Pictures......Page 354
Requirements of the CEM......Page 356
Summary......Page 357
13.5 Conclusion......Page 358
13.6 Exercises......Page 359
References......Page 360
14.1 Introduction......Page 361
Estimating the Population Average......Page 362
Digression on Linearity......Page 366
The Sample Average Is the Least Squares Estimator......Page 367
Workbook: GaussMarkovUnivariate.xls......Page 368
Eliminating Biased Estimators from Contention......Page 369
Choosing a Winner......Page 371
Gauss–Markov with 10 Observations......Page 373
Gauss–Markov with n Observations......Page 377
Workbook: GaussMarkovBivariate.xls......Page 378
The DGP Follows the CEM......Page 379
The OLS Estimator of the Slope Is a Linear Estimator......Page 380
The OLS Estimator of the Slope Is an Unbiased Estimator......Page 383
Other Linear, Unbiased Estimators......Page 384
Workbook: GaussMarkovBivariate.xls......Page 387
Workbooks: GaussMarkovUnivariate.xls; GaussMarkovBivariate.xls......Page 392
Estimating the Population Average......Page 393
Estimating......Page 396
14.8 Conclusion......Page 400
14.9 Exercises......Page 401
References......Page 402
Workbook: SEb1OLS.xls......Page 404
Univariate CEM: Estimating the Population Average......Page 405
Bivariate CEM: Estimating the Slope (B1)......Page 406
Implementing the SE of the OLS Sample Slope Formula......Page 407
The SEs in the Multivariate CEM......Page 408
Workbook: SEb1OLS.xls......Page 409
RMSE Estimates SD......Page 410
The SE of the OLS Sample Slope in Practice......Page 412
Workbook: SEb1OLS.xls......Page 413
Summary......Page 414
Workbook: EstimatingSDErrors.xls......Page 418
The Estimated SE Is a Biased, But Consistent Estimator of the Exact SE......Page 422
Summary......Page 423
Workbook: SEForecast.xls......Page 424
The SE of Forecasted Y......Page 428
The SE of the Forecast Error......Page 430
Multivariate Forecasting......Page 431
Monte Carlo Simulation......Page 432
15.7 Conclusion......Page 434
15.8 Exercises......Page 435
References......Page 436
16.1 Introduction......Page 437
Workbook: LinestRandomVariables.xls......Page 438
The Distribution of the Errors......Page 439
The Distribution of LINEST Random Variables......Page 445
Summary......Page 446
Workbook: ConfidenceIntervals.xls......Page 447
Confidence Intervals in Action......Page 448
Confidence Intervals for b1 – Known Box......Page 451
Confidence Interval for b1 – Unknown Box......Page 452
Summary......Page 455
Workbook: HypothesisTest.xls......Page 456
Workbooks: ZandTTests.xls; ConfidenceIntervals.xls......Page 460
The t-Distribution and Confidence Intervals......Page 467
Summary......Page 468
Workbook: CigDataInference.xls......Page 469
An Alternative Functional Form......Page 474
Summary......Page 475
Workbook: SemiLogEarningsFn.xls......Page 476
References......Page 477
An Example of a Test Involving More than One Parameter......Page 479
Organization......Page 481
Three Examples......Page 482
Workbook: ChiSquareDist.xls......Page 484
Summary......Page 486
Workbook: FDist.xls......Page 487
The General Idea Behind the F-Test......Page 488
Applying the F-Test to the Galileo Example......Page 489
Summary......Page 493
Workbook: FDistFoodStamps.xls......Page 494
Monte Carlo Evidence......Page 498
The Relationship between F- and T-Statistics......Page 499
Workbook: FDistEarningsFn.xls......Page 501
Workbook: CorrelatedEstimates.xls......Page 504
The Joint Confidence Region......Page 510
Summary......Page 512
Workbook: MyMonteCarlo.xls......Page 513
References......Page 514
18.1 Introduction......Page 516
18.2 Why Omitted Variable Bias Is Important......Page 517
Summary......Page 518
Workbook: SkiingOVB.xls......Page 519
A Fictional Example......Page 520
Summary......Page 523
Workbook: ComputerUse1997.xls......Page 524
Summary......Page 527
Workbook: ComputerUse1997.xls......Page 528
Summary......Page 531
18.7 Exercises......Page 532
References......Page 533
19.1 Introduction......Page 534
Workbook: Het.xls......Page 536
Comparing the Precision of the Three Sample Averages......Page 541
Analytic Computation of the SEs of the Sample Averages......Page 542
Workbook: Het.xls......Page 544
A Measurement Error Example: Hooke’s Law Revisited......Page 545
More General Heteroskedasticity in the Bivariate Setting......Page 548
Theoretical Reasons to Worry about Heteroskedasticity......Page 553
Diagnosing Heteroskedasticity in the Data......Page 554
The B–P Sampling Distribution......Page 556
Workbooks: HetRobustSE.xls; OLSRegression.xla (Excel add-in in the
Basic Tools folder)......Page 559
The OLS Regression Add-In......Page 566
Workbook: HetGLS.xls......Page 568
The Univariate Case: Finding the Optimal Estimator......Page 569
The Transformation for Regression Models......Page 570
Workbook: WagesOct97.xls......Page 575
Summary......Page 580
19.8 Conclusion......Page 581
19.9 Exercises......Page 582
References......Page 583
20.1 Introduction......Page 584
Workbook: AutoCorr.xls......Page 586
The Naming Scheme......Page 587
The AR (1) Model of Autocorrelation......Page 588
The AR (1) Process in Action......Page 589
The Data Generation Process......Page 592
Three Econometric Consequences of Autocorrelation......Page 593
A Monte Carlo Simulation of the Consequences of Positive,
First-Order Autocorrelation......Page 594
Summary......Page 600
Eyeballing the Residuals......Page 602
Testing for Autocorrelation via the Sample Estimate of p......Page 604
Testing for Autocorrelation via the Durbin–Watson d statistic......Page 608
Summary......Page 613
The Algebra behind GLS......Page 614
An Example of GLS Estimation......Page 617
Evaluating the GLS Estimator......Page 618
Feasible Generalized Least Squares......Page 622
Summary......Page 625
The Highlights of Autocorrelation......Page 626
Two Real-World Examples......Page 627
Workbooks: Misspecification.xls; FreeThrowAutoCorr.xls......Page 628
References......Page 629
21.1 Introduction......Page 630
Linear Trend......Page 631
Log-Linear (Exponential) Trend......Page 633
Example: U.S. Real GDP, 1947–2003......Page 635
Trends and Spurious Regression......Page 637
Dummy Variables in Time Series......Page 639
Example: Coal Mine Safety......Page 640
Workbooks: SeasonalTheory.xls; SeasonalPractice.xls......Page 643
Comparing Graphs......Page 645
Seasonal Adjustment Theory......Page 646
Seasonal Adjustment in Practice......Page 648
Seasonal Adjustment: To Do or Not To Do?......Page 649
Workbook: Stationarity.xls......Page 650
Random Walks......Page 657
Workbooks: Stationarity.xls; Spurious.xls......Page 659
Partial Adjustment Models......Page 664
Short- and Long-Run Impacts in Partial Adjustment Models......Page 666
Workbooks: MoneyDemand.xls; LaggedDepVar.xls......Page 671
Detecting First-Order Autocorrelation When There Is a
Lagged Dependent Variable......Page 675
Workbooks: AnnualGDP.xls; ForecastingGDP.xls......Page 678
Summary......Page 683
21.10 Conclusion......Page 684
21.11 Exercises......Page 685
References......Page 687
22.1 Introduction......Page 689
More Examples of Dummy Dependent Variables......Page 690
Organization......Page 691
Workbook: Raid.xls......Page 692
Workbook: CampCont.xls......Page 695
Workbooks: Raid.xls; CampCont.xls......Page 697
Workbooks: CampCont.xls; LPMMonteCarlo.xls......Page 700
Using the Linear Probability Model (LPM)......Page 702
2. LPM Is an Unbounded Functional Form......Page 704
Summary......Page 705
Workbooks: NLLSFit.xls; NLLSMCSim.xls......Page 706
Why Nonlinear Least Squares?......Page 707
Which S Shape?......Page 708
If the Normal’s S Shape Can Be Altered, How Is a
Particular S Shape Determined?......Page 710
Using Excel’s Solver to Fit the S Shape......Page 713
Monte Carlo Simulation......Page 714
Workbooks: NLLSFit.xls; DDV.xla (Excel add-in)......Page 716
Interpreting the Estimates......Page 717
LPM versus NLLS with a Probit DGP......Page 720
The Research Question......Page 721
Mortgage Discrimination as a Dummy Dependent Variable Model......Page 723
Using the DDV.xla Add-in on a Sample......Page 726
Understanding the SE and Sampling Distribution via Monte Carlo Simulation......Page 728
Mortgage Discrimination in the Real World......Page 729
22.9 Conclusion......Page 732
22.10 References......Page 733
23.1 Introduction......Page 735
Workbook: PercentageBootstrap.xls......Page 736
Workbook: PairedXYBootstrap.xls......Page 739
Workbooks: PairedXYBootstrap.xls; Bookstrap.xla (Excel add-in)......Page 744
Workbook: BootstrapR2.xls......Page 747
23.6 Conclusion......Page 752
References......Page 754
24.1 Introduction......Page 756
Workbook: SimEq.xls......Page 757
Workbook: SimEq.xls......Page 761
Workbook: SimEq.xls......Page 767
24.5 Conclusion......Page 771
24.6 Exercises......Page 772
References......Page 773
Glossary......Page 775
Index......Page 787