Detailed Contents
List of Exhibits Abbreviations Guide to the Book
1
1
xvi xix xxi
Introduction
1
Econometrics Purpose of the book Characteristic features of the book Target audience and required background knowledge Brief contents of the book Study advice Teaching suggestions Some possible course structures
1 2 3 4 4 5 6 8
Review of Statistics
1.1 Descriptive statistics 1.1.1 Data graphs 1.1.2 Sample statistics
1.2 Random variables 1.2.1 1.2.2 1.2.3 1.2.4
Single random variables Joint random variables Probability distributions Normal random samples
1.3 Parameter estimation 1.3.1 Estimation methods 1.3.2 Statistical properties 1.3.3 Asymptotic properties
1.4 Tests of hypotheses 1.4.1 Size and power 1.4.2 Tests for mean and variance 1.4.3 Interval estimates and the bootstrap
11 12 12 16
20 20 23 29 35 38 38 42 47 55 55 59 63
x
Detailed Contents
Summary, further reading, and keywords Exercises
68 71
2
75
Simple Regression
2.1 Least squares 2.1.1 2.1.2 2.1.3 2.1.4
Scatter diagrams Least squares Residuals and R2 Illustration: Bank Wages
2.2 Accuracy of least squares 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5
Data generating processes Examples of regression models Seven assumptions Statistical properties Efficiency
2.3 Significance tests 2.3.1 The t-test 2.3.2 Examples 2.3.3 Use under less strict conditions
2.4 Prediction 2.4.1 Point predictions and prediction intervals 2.4.2 Examples
76 76 79 82 84 87 87 91 92 94 97 99 99 101 103 105 105 107
Summary, further reading, and keywords Exercises
111 113
3
Multiple Regression
117
3.1 Least squares in matrix form
118 118 120 123 125 127 129 131
3.1.1 3.1.2 3.1.3 3.1.4 3.1.5 3.1.6 3.1.7
Introduction Least squares Geometric interpretation Statistical properties Estimating the disturbance variance Coefficient of determination Illustration: Bank Wages
3.2 Adding or deleting variables 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5
Restricted and unrestricted models Interpretation of regression coefficients Omitting variables Consequences of redundant variables Partial regression
134 135 139 142 143 145
Detailed Contents
3.3 The accuracy of estimates 3.3.1 3.3.2 3.3.3 3.3.4
The t-test Illustration: Bank Wages Multicollinearity Illustration: Bank Wages
3.4 The F-test 3.4.1 3.4.2 3.4.3 3.4.4
The F-test in different forms Illustration: Bank Wages Chow forecast test Illustration: Bank Wages
152 152 154 156 159 161 161 166 169 174
Summary, further reading, and keywords Exercises
178 180
4
187
Non-Linear Methods
4.1 Asymptotic analysis 4.1.1 4.1.2 4.1.3 4.1.4 4.1.5
Introduction Stochastic regressors Consistency Asymptotic normality Simulation examples
4.2 Non-linear regression 4.2.1 4.2.2 4.2.3 4.2.4 4.2.5
Motivation Non-linear least squares Non-linear optimization The Lagrange Multiplier test Illustration: Coffee Sales
4.3 Maximum likelihood 4.3.1 4.3.2 4.3.3 4.3.4 4.3.5 4.3.6 4.3.7 4.3.8 4.3.9
Motivation Maximum likelihood estimation Asymptotic properties The Likelihood Ratio test The Wald test The Lagrange Multiplier test LM-test in the linear model Remarks on tests Two examples
4.4 Generalized method of moments 4.4.1 4.4.2 4.4.3 4.4.4
Motivation GMM estimation GMM standard errors Quasi-maximum likelihood
188 188 191 193 196 198 202 202 205 209 212 218 222 222 224 228 230 232 235 238 240 243 250 250 252 255 259
xi
xii
Detailed Contents
4.4.5 GMM in simple regression 4.4.6 Illustration: Stock Market Returns
260 262
Summary, further reading, and keywords Exercises
266 268
5
273
Diagnostic Tests and Model Adjustments
5.1 Introduction
274
5.2 Functional form and explanatory variables
277 277 285 289 296 302
5.2.1 5.2.2 5.2.3 5.2.4 5.2.5
The number of explanatory variables Non-linear functional forms Non-parametric estimation Data transformations Summary
5.3 Varying parameters 5.3.1 5.3.2 5.3.3 5.3.4
The use of dummy variables Recursive least squares Tests for varying parameters Summary
5.4 Heteroskedasticity 5.4.1 5.4.2 5.4.3 5.4.4 5.4.5 5.4.6
Introduction Properties of OLS and White standard errors Weighted least squares Estimation by maximum likelihood and feasible WLS Tests for homoskedasticity Summary
5.5 Serial correlation 5.5.1 5.5.2 5.5.3 5.5.4 5.5.5
Introduction Properties of OLS Tests for serial correlation Model adjustments Summary
5.6 Disturbance distribution 5.6.1 5.6.2 5.6.3 5.6.4 5.6.5
Introduction Regression diagnostics Test for normality Robust estimation Summary
5.7 Endogenous regressors and instrumental variables 5.7.1 5.7.2 5.7.3 5.7.4
Instrumental variables and two-stage least squares Statistical properties of IV estimators Tests for exogeneity and validity of instruments Summary
303 303 310 313 318 320 320 324 327 334 343 352 354 354 358 361 368 376 378 378 379 386 388 394 396 396 404 409 418
Detailed Contents
5.8 Illustration: Salaries of top managers
419
Summary, further reading, and keywords Exercises
424 427
6
437
Qualitative and Limited Dependent Variables
6.1 Binary response 6.1.1 6.1.2 6.1.3 6.1.4 6.1.5 6.1.6
Model formulation Probit and logit models Estimation and evaluation Diagnostics Model for grouped data Summary
6.2 Multinomial data 6.2.1 6.2.2 6.2.3 6.2.4
Unordered response Multinomial and conditional logit Ordered response Summary
6.3 Limited dependent variables 6.3.1 6.3.2 6.3.3 6.3.4 6.3.5
Truncated samples Censored data Models for selection and treatment effects Duration models Summary
438 438 443 447 452 459 461 463 463 466 474 480 482 482 490 500 511 521
Summary, further reading, and keywords Exercises
523 525
7
531
Time Series and Dynamic Models
7.1 Models for stationary time series 7.1.1 7.1.2 7.1.3 7.1.4 7.1.5 7.1.6 7.1.7
Introduction Stationary processes Autoregressive models ARMA models Autocorrelations and partial autocorrelations Forecasting Summary
7.2 Model estimation and selection 7.2.1 The modelling process 7.2.2 Parameter estimation 7.2.3 Model selection
532 532 535 538 542 545 550 553 555 555 558 563
xiii
xiv
Detailed Contents
7.2.4 Diagnostic tests 7.2.5 Summary
7.3 Trends and seasonals 7.3.1 7.3.2 7.3.3 7.3.4 7.3.5
Trend models Trend estimation and forecasting Unit root tests Seasonality Summary
7.4 Non-linearities and time-varying volatility 7.4.1 7.4.2 7.4.3 7.4.4 7.4.5
Outliers Time-varying parameters GARCH models for clustered volatility Estimation and diagnostic tests of GARCH models Summary
7.5 Regression models with lags 7.5.1 7.5.2 7.5.3 7.5.4
Autoregressive models with distributed lags Estimation, testing, and forecasting Regression of variables with trends Summary
7.6 Vector autoregressive models 7.6.1 7.6.2 7.6.3 7.6.4
Stationary vector autoregressions Estimation and diagnostic tests of stationary VAR models Trends and cointegration Summary
7.7 Other multiple equation models 7.7.1 7.7.2 7.7.3 7.7.4 7.7.5
Introduction Seemingly unrelated regression model Panel data Simultaneous equation model Summary
567 576 578 578 585 592 604 611 612 612 616 620 626 636 637 637 640 647 654 656 656 661 667 681 682 682 684 692 700 709
Summary, further reading, and keywords Exercises
710 713
Appendix A. Matrix Methods
723
A.1 A.2 A.3 A.4 A.5 A.6 A.7
Summations Vectors and matrices Matrix addition and multiplication Transpose, trace, and inverse Determinant, rank, and eigenvalues Positive (semi)deďŹ nite matrices and projections Optimization of a function of several variables
723 725 727 729 731 736 738
Detailed Contents
A.8 Concentration and the Lagrange method
743
Exercise
746
Appendix B. Data Sets List of Data Sets
Index
747 748
773
xv
List of Exhibits
0.1 0.2 0.3
Econometrics as an interdisciplinary field Econometric modelling Book structure
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14
Student Learning (Example 1.1) Student Learning (Example 1.2) Student Learning (Example 1.3) Student Learning (Example 1.4) Student Learning (Example 1.5) Student Learning (Example 1.6) Normal distribution 2 -distribution t-distribution F-distribution Bias and variance Normal Random Sample (Example 1.9) Consistency Simulated Normal Random Sample (Example 1.10) 1.15 Simulated Normal Random Sample (Example 1.11) 1.16 P-value 1.17 Student Learning (Example 1.13) 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 2.15
Stock Market Returns (Example 2.1) Bank Wages (Example 2.2) Coffee Sales (Example 2.3) Scatter diagram with fitted line Bank Wages (Section 2.1.4) Bank Wages (Section 2.1.4) Simulated Regression Data (Example 2.4) Simulated Regression Data (Example 2.4) Accuracy of least squares Simulated Regression Data (Example 2.8) Bank Wages (Example 2.9) Quantiles of distributions of t-statistics Prediction error Simulated Regression Data (Example 2.10) Bank Wages (Example 2.11)
2 3 8 13 14 15 17 19 28 30 32 33 34 44 47 48 54 58 61 66 77 78 79 80 85 86 89 90 97 101 103 103 106 108 109
3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18 3.19
Scatter diagrams of Bank Wage data Least squares Least squares Geometric picture of R2 Bank Wages (Section 3.1.7) Direct and indirect effects Bank Wages (Example 3.1) Bank Wages (Example 3.2) Bias and efficiency Bank Wages (Example 3.3) Bank Wages (Example 3.3) Bank Wages (Section 3.3.2) Bank Wages (Section 3.3.4) P-value Geometry of F-test Bank Wages (Section 3.4.2) Prediction Bank Wages (Section 3.4.4) Bank Wages (Section 3.4.4)
119 124 124 130 132 134 138 141 145 149 150 155 160 162 163 167 170 175 176
4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19
Bank Wages (Example 4.1) Inconsistency Simulation Example (Section 4.1.5) Simulation Example (Section 4.1.5) Coffee Sales (Example 4.2) Food Expenditure (Example 4.3) Newton–Raphson Lagrange multiplier Coffee Sales (Section 4.2.5) Coffee Sales (Section 4.2.5) Stock Market Returns (Example 4.4) Maximum likelihood Likelihood Ratio test Wald test Lagrange Multiplier test Comparison of tests F- and 2 -distributions Stock Market Returns (Example 4.5) Coffee Sales (Example 4.6)
190 195 198 200 203 204 210 214 219 220 224 225 231 233 236 241 242 245 248
List of Exhibits
4.20 Stock Market Returns (Example 4.7) 4.21 Stock Market Returns (Section 4.4.6) 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13 5.14 5.15 5.16 5.17 5.18 5.19 5.20 5.21 5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 5.30 5.31 5.32 5.33 5.34 5.35 5.36 5.37 5.38 5.39 5.40 5.41 5.42 5.43 5.44
The empirical cycle in econometric modelling Bank Wages (Example 5.1) Bank Wages (Example 5.1) Bank Wages (Example 5.2) Tricube weights Simulated Data from a Non-Linear Model (Example 5.3) Bank Wages (Example 5.4) Bank Wages (Example 5.5) Bank Wages (Example 5.5) Fashion Sales (Example 5.6) Fashion Sales (Example 5.6) Coffee Sales (Example 5.7) Bank Wages (Example 5.8) Bank Wages (Example 5.9) Bank Wages (Example 5.9) Bank Wages (Example 5.10) Interest and Bond Rates (Example 5.11) Bank Wages; Interest and Bond Rates (Example 5.12) Bank Wages (Example 5.13) Bank Wages (Example 5.13) Interest and Bond Rates (Example 5.14) Bank Wages (Example 5.15) Interest and Bond Rates (Example 5.16) Bank Wages (Example 5.17) Bank Wages (Example 5.17) Interest and Bond Rates (Example 5.18) Interest and Bond Rates (Example 5.18) Interest and Bond Rates (Example 5.19) Food Expenditure (Example 5.20) Interest and Bond Rates (Example 5.21) Interest and Bond Rates (Example 5.22) Food Expenditure (Example 5.23) Interest and Bond Rates (Example 5.24) Food Expenditure (Example 5.25) Industrial Production (Example 5.26) Industrial Production (Example 5.26) Outliers and OLS Stock Market Returns (Example 5.27) Stock Market Returns (Example 5.27) Stock Market Returns (Example 5.28) Simulated Data of Normal and Student t(2) Distribution (Example 5.29) Three estimation criteria Interest and Bond Rates (Example 5.30) Motor Gasoline Consumption (Example 5.31)
251 264
276 283 284 287 291 294 295 299 300 306 307 309 312 317 318 322 323 326 331 332 333 338 341 347 349 350 351 355 358 360 366 367 371 373 375 376 382 385 386 388 389 391 401 403
5.45 Motor Gasoline Consumption (Example 5.31) 5.46 Interest and Bond Rates (Example 5.32) 5.47 Interest and Bond Rates (Example 5.33) 5.48 Motor Gasoline Consumption (Example 5.34) 5.49 Salaries of Top Managers (Example 5.35) 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 6.13 6.14 6.15 6.16 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 7.18 7.19 7.20 7.21
xvii
404 408 415 417 420
Probability models Normal and logistic densities Direct Marketing for Financial Product (Example 6.2) Direct Marketing for Financial Product (Example 6.3) Bank Wages (Example 6.4) Ordered response Bank Wages (Example 6.5) Truncated data Direct Marketing for Financial Product (Example 6.6) Censored data Direct Marketing for Financial Product (Example 6.7) Student Learning (Example 6.8) Student Learning (Example 6.8) Duration data Hazard rates Duration of Strikes (Example 6.9)
440 444
Industrial Production (Example 7.1) Dow-Jones Index (Example 7.2) Simulated AR Time Series (Example 7.3) Simulated MA and ARMA Time Series (Example 7.4) Simulated Times Series (Example 7.5) Simulated Time Series (Example 7.6) Steps in modelling Industrial Production (Example 7.7) Industrial Production (Example 7.8) Industrial Production (Example 7.10) Industrial Production (Example 7.11) Industrial Production (Example 7.11) Simulated Series with Trends (Example 7.12) Industrial Production (Example 7.13) Industrial Production (Example 7.13) Unit root tests Industrial Production (Example 7.14) Dow-Jones Index (Example 7.15) Industrial Production (Example 7.16) Industrial Production (Example 7.16) Industrial Production (Example 7.17)
533 534 542
451 458 472 476 478 484 489 491 498 508 509 512 514 517
545 549 553 555 557 563 566 573 575 584 591 592 595 601 603 609 610 615
xviii
List of Exhibits
7.22 Industrial Production (Example 7.18) 7.23 Simulated ARCH and GARCH Time Series (Example 7.19) 7.24 Industrial Production (Example 7.20) 7.25 Dow-Jones Index (Example 7.21) 7.26 Interest and Bond Rates (Example 7.22) 7.27 Mortality and Marriages (Example 7.23) 7.28 Simulated Random Walk Data (Example 7.24) 7.29 Interest and Bond Rates (Example 7.25) 7.30 Interest and Bond Rates (Example 7.26) 7.31 Cointegration tests 7.32 Interest and Bond Rates (Example 7.27) 7.33 Treasury Bill Rates (Example 7.28)
619 624 630 632 645 648
7.34 7.35 7.36 7.37
Primary Metal Industries (Example 7.29) Primary Metal Industries (Example 7.29) Primary Metal Industries (Example 7.30) Simulated Macroeconomic Consumption and Income (Example 7.31) 7.38 Interest and Bond Rates (Example 7.32) A.1
650 653 665 672 676 679
A.2 A.3
Simulated Data on Student Learning (Example A.1) Simulated Data on Student Learning (Example A.7) Simulated Data on Student Learning (Example A.11)
689 690 698 703 708
724 735 742