Loading
9845 views
Basic Econometrics, Gujarati, 5th edition (Online book)
Page 1
1–6
Table of Contents
« Back to eTextbook- Preface, xvi
- Acknowledgments, xix
- Introduction, 1
- I.1. What Is Econometrics?, 1
- I.2. Why a Separate Discipline?, 2
- I.3. Methodology of Econometrics, 2
- 1. Statement of Theory or Hypothesis, 3
- 2. Specification of the Mathematical Model of Consumption, 3
- 3. Specification of the Econometric Model of Consumption, 4
- 4. Obtaining Data, 5
- 5. Estimation of the Econometric Model, 5
- 6. Hypothesis Testing, 7
- 7. Forecasting or Prediction, 8
- 8. Use of the Model for Control or Policy Purposes, 9
- Choosing among Competing Models, 9
- I.4. Types of Econometrics, 10
- I.5. Mathematical and Statistical Prerequisites, 11
- I.6. The Role of the Computer, 11
- I.7. Suggestions for Further Reading, 12
- Part ONE. SINGLE-EQUATION REGRESSION MODELS, 13
- Chapter 1. The Nature of Regression Analysis, 15
- 1.1. Historical Origin of the Term Regression, 15
- 1.2. The Modern Interpretation of Regression, 15
- Examples, 16
- 1.3. Statistical versus Deterministic Relationships, 19
- 1.4. Regression versus Causation, 19
- 1.5. Regression versus Correlation, 20
- 1.6. Terminology and Notation, 21
- 1.7. The Nature and Sources of Data for Economic Analysis, 22
- Types of Data, 22
- The Sources of Data, 25
- The Accuracy of Data, 27
- A Note on the Measurement Scales of Variables, 27
- Summary and Conclusions, 28
- Exercises, 29
- Chapter 2. Two-Variable Regression Analysis: Some Basic Ideas, 34
- 2.1. A Hypothetical Example, 34
- 2.2. The Concept of Population Regression Function (PRF), 37
- 2.3. The Meaning of the Term Linear, 38
- Linearity in the Variables, 38
- Linearity in the Parameters, 38
- 2.4. Stochastic Specification of PRF, 39
- 2.5. The Significance of the Stochastic Disturbance Term, 41
- 2.6. The Sample Regression Function (SRF), 42
- 2.7. Illustrative Examples, 45
- Summary and Conclusions, 48
- Exercises, 48
- Chapter 3. Two-Variable Regression Model: The Problem of Estimation, 55
- 3.1. The Method of Ordinary Least Squares, 55
- 3.2. The Classical Linear Regression Model: The Assumptions Underlying the Method of Least Squares, 61
- A Word about These Assumptions, 68
- 3.3. Precision or Standard Errors of Least-Squares Estimates, 69
- 3.4. Properties of Least-Squares Estimators: The Gauss–Markov Theorem, 71
- 3.5. The Coefficient of Determination r2: A Measure of “Goodness of Fit”, 73
- 3.6. A Numerical Example, 78
- 3.7. Illustrative Examples, 81
- 3.8. A Note on Monte Carlo Experiments, 83
- Summary and Conclusions, 84
- Exercises, 85
- Appendix 3A, 92
- 3A.1. Derivation of Least-Squares Estimates, 92
- 3A.2. Linearity and Unbiasedness Properties of Least-Squares Estimators, 92
- 3A.3. Variances and Standard Errors of Least-Squares Estimators, 93
- 3A.4. Covariance Between β1 and β2, 93
- 3A.5. The Least-Squares Estimator of σ2, 93
- 3A.6. Minimum-Variance Property of Least-Squares Estimators, 95
- 3A.7. Consistency of Least-Squares Estimators, 96
- Chapter 4. Classical Normal Linear Regression Model (CNLRM), 97
- 4.1. The Probability Distribution of Disturbances ui, 97
- 4.2. The Normality Assumption for ui, 98
- Why the Normality Assumption?, 99
- 4.3. Properties of OLS Estimators under the Normality Assumption, 100
- 4.4. The Method of Maximum Likelihood (ML), 102
- Summary and Conclusions, 102
- Appendix 4A, 103
- 4A.1. Maximum Likelihood Estimation of Two-Variable Regression Model, 103
- 4A.2. Maximum Likelihood Estimation of Food Expenditure in India, 105
- Appendix 4A Exercises, 105
- Chapter 5. Two-Variable Regression: Interval Estimation and Hypothesis Testing, 107
- 5.1. Statistical Prerequisites, 107
- 5.2. Interval Estimation: Some Basic Ideas, 108
- 5.3. Confidence Intervals for Regression Coefficients β1 and β2, 109
- Confidence Interval for β2, 109
- Confidence Interval for β1 and β2 Simultaneously, 111
- 5.4. Confidence Interval for σ2, 111
- 5.5. Hypothesis Testing: General Comments, 113
- 5.6. Hypothesis Testing: The Confidence-Interval Approach, 113
- Two-Sided or Two-Tail Test, 113
- One-Sided or One-Tail Test, 115
- 5.7. Hypothesis Testing: The Test-of-Significance Approach, 115
- Testing the Significance of Regression Coefficients: The t Test, 115
- Testing the Significance of σ2: The χ2 Test, 118
- 5.8. Hypothesis Testing: Some Practical Aspects, 119
- The Meaning of “Accepting” or “Rejecting” a Hypothesis, 119
- The “Zero” Null Hypothesis and the “2-t” Rule of Thumb, 120
- Forming the Null and Alternative Hypotheses, 121
- Choosing α, the Level of Significance, 121
- The Exact Level of Significance: The p Value, 122
- Statistical Significance versus Practical Significance, 123
- The Choice between Confidence-Interval and Test-of-Significance Approaches to Hypothesis Testing, 124
- 5.9. Regression Analysis and Analysis of Variance, 124
- 5.10. Application of Regression Analysis: The Problem of Prediction, 126
- Mean Prediction, 127
- Individual Prediction, 128
- 5.11. Reporting the Results of Regression Analysis, 129
- 5.12. Evaluating the Results of Regression Analysis, 130
- Normality Tests, 130
- Other Tests of Model Adequacy, 132
- Summary and Conclusions, 134
- Exercises, 135
- Appendix 5A, 143
- 5A.1. Probability Distributions Related to the Normal Distribution, 143
- 5A.2. Derivation of Equation (5.3.2), 145
- 5A.3. Derivation of Equation (5.9.1), 145
- 5A.4. Derivations of Equations (5.10.2) and (5.10.6), 145
- Variance of Mean Prediction, 145
- Variance of Individual Prediction, 146
- Chapter 6. Extensions of the Two-Variable Linear Regression Model, 147
- 6.1. Regression through the Origin, 147
- r2 for Regression-through-Origin Model, 150
- 6.2. Scaling and Units of Measurement, 154
- A Word about Interpretation, 157
- 6.3. Regression on Standardized Variables, 157
- 6.4. Functional Forms of Regression Models, 159
- 6.5. How to Measure Elasticity: The Log-Linear Model, 159
- 6.6. Semilog Models: Log–Lin and Lin–Log Models, 162
- How to Measure the Growth Rate: The Log–Lin Model, 162
- The Lin–Log Model, 164
- 6.7. Reciprocal Models, 166
- Log Hyperbola or Logarithmic Reciprocal Model, 172
- 6.8. Choice of Functional Form, 172
- 6.9. A Note on the Nature of the Stochastic Error Term: Additive versus Multiplicative Stochastic Error Term, 174
- Summary and Conclusions, 175
- Exercises, 176
- Appendix 6A, 182
- 6A.1. Derivation of Least-Squares Estimators for Regression through the Origin, 182
- 6A.2. Proof that a Standardized Variable Has Zero Mean and Unit Variance, 183
- 6A.3. Logarithms, 184
- 6A.4. Growth Rate Formulas, 186
- 6A.5. Box-Cox Regression Model, 187
- Chapter 7. Multiple Regression Analysis: The Problem of Estimation, 188
- 7.1. The Three-Variable Model: Notation and Assumptions, 188
- 7.2. Interpretation of Multiple Regression Equation, 191
- 7.3. The Meaning of Partial Regression Coefficients, 191
- 7.4. OLS and ML Estimation of the Partial Regression Coefficients, 192
- OLS Estimators, 192
- Variances and Standard Errors of OLS Estimators, 194
- Properties of OLS Estimators, 195
- Maximum Likelihood Estimators, 196
- 7.5. The Multiple Coefficient of Determination R2 and the Multiple Coefficient of Correlation R, 196
- 7.6. An Illustrative Example, 198
- Regression on Standardized Variables, 199
- Impact on the Dependent Variable of a Unit Change in More than One Regressor, 199
- 7.7. Simple Regression in the Context of Multiple Regression: Introduction to Specification Bias, 200
- 7.8. R2 and the Adjusted R2, 201
- Comparing Two R2 Values, 203
- Allocating R2 among Regressors, 206
- The “Game'' of Maximizing R̄2, 206
- 7.9. The Cobb–Douglas Production Function: More on Functional Form, 207
- 7.10. Polynomial Regression Models, 210
- 7.11. Partial Correlation Coefficients, 213
- Explanation of Simple and Partial Correlation Coefficients, 213
- Interpretation of Simple and Partial Correlation Coefficients, 214
- Summary and Conclusions, 215
- Exercises, 216
- Appendix 7A, 227
- 7A.1. Derivation of OLS Estimators Given in Equations (7.4.3) to (7.4.5), 227
- 7A.2. Equality between the Coefficients of PGNP in Equations (7.3.5) and (7.6.2), 229
- 7A.3. Derivation of Equation (7.4.19), 229
- 7A.4. Maximum Likelihood Estimation of the Multiple Regression Model, 230
- 7A.5. EViews Output of the Cobb–Douglas Production Function in Equation (7.9.4), 231
- Chapter 8. Multiple Regression Analysis: The Problem of Inference, 233
- 8.1. The Normality Assumption Once Again, 233
- 8.2. Hypothesis Testing in Multiple Regression: General Comments, 234
- 8.3. Hypothesis Testing about Individual Regression Coefficients, 235
- 8.4. Testing the Overall Significance of the Sample Regression, 237
- The Analysis of Variance Approach to Testing the Overall Significance of an Observed Multiple Regression: The F Test, 238
- Testing the Overall Significance of a Multiple Regression: The F Test, 240
- An Important Relationship between R2 and F, 241
- Testing the Overall Significance of a Multiple Regression in Terms of R2, 242
- The “Incremental” or “Marginal” Contribution of an Explanatory Variable, 243
- 8.5. Testing the Equality of Two Regression Coefficients, 246
- 8.6. Restricted Least Squares: Testing Linear Equality Restrictions, 248
- The t-Test Approach, 249
- The F-Test Approach: Restricted Least Squares, 249
- General F Testing, 252
- 8.7. Testing for Structural or Parameter Stability of Regression Models: The Chow Test, 254
- 8.8. Prediction with Multiple Regression, 259
- 8.9. The Troika of Hypothesis Tests: The Likelihood Ratio (LR), Wald (W), and Lagrange Multiplier (LM) Tests, 259
- 8.10. Testing the Functional Form of Regression: Choosing between Linear and Log–Linear Regression Models, 260
- Summary and Conclusions, 262
- Exercises, 262
- Appendix 8A: Likelihood Ratio (LR) Test, 274
- Chapter 9. Dummy Variable Regression Models, 277
- 9.1. The Nature of Dummy Variables, 277
- 9.2. ANOVA Models, 278
- Caution in the Use of Dummy Variables, 281
- 9.3. ANOVA Models with Two Qualitative Variables, 283
- 9.4. Regression with a Mixture of Quantitative and Qualitative Regressors: The ANCOVA Models, 283
- 9.5. The Dummy Variable Alternative to the Chow Test, 285
- 9.6. Interaction Effects Using Dummy Variables, 288
- 9.7. The Use of Dummy Variables in Seasonal Analysis, 290
- 9.8. Piecewise Linear Regression, 295
- 9.9. Panel Data Regression Models, 297
- 9.10. Some Technical Aspects of the Dummy Variable Technique, 297
- The Interpretation of Dummy Variables in Semilogarithmic Regressions, 297
- Dummy Variables and Heteroscedasticity, 298
- Dummy Variables and Autocorrelation, 299
- What Happens If the Dependent Variable Is a Dummy Variable?, 299
- 9.11. Topics for Further Study, 300
- 9.12. A Concluding Example, 300
- Summary and Conclusions, 304
- Exercises, 305
- Appendix 9A: Semilogarithmic Regression with Dummy Regressor, 314
- Part TWO. RELAXING THE ASSUMPTIONS OF THE CLASSICAL MODEL, 315
- Chapter 10. Multicollinearity: What Happens If the Regressors Are Correlated?, 320
- 10.1. The Nature of Multicollinearity, 321
- 10.2. Estimation in the Presence of Perfect Multicollinearity, 324
- 10.3. Estimation in the Presence of “High” but “Imperfect” Multicollinearity, 325
- 10.4. Multicollinearity: Much Ado about Nothing? Theoretical Consequences of Multicollinearity, 326
- 10.5. Practical Consequences of Multicollinearity, 327
- Large Variances and Covariances of OLS Estimators, 328
- Wider Confidence Intervals, 330
- “Insignificant” t Ratios, 330
- A High R2 but Few Significant t Ratios, 331
- Sensitivity of OLS Estimators and Their Standard Errors to Small Changes in Data, 331
- Consequences of Micronumerosity, 332
- 10.6. An Illustrative Example, 332
- 10.7. Detection of Multicollinearity, 337
- 10.8. Remedial Measures, 342
- Do Nothing, 342
- Rule-of-Thumb Procedures, 342
- 10.9. Is Multicollinearity Necessarily Bad? Maybe Not, If the Objective Is Prediction Only, 347
- 10.10. An Extended Example: The Longley Data, 347
- Summary and Conclusions, 350
- Exercises, 351
- Chapter 11. Heteroscedasticity: What Happens If the Error Variance Is Nonconstant?, 365
- 11.1. The Nature of Heteroscedasticity, 365
- 11.2. OLS Estimation in the Presence of Heteroscedasticity, 370
- 11.3. The Method of Generalized Least Squares (GLS), 371
- Difference between OLS and GLS, 373
- 11.4. Consequences of Using OLS in the Presence of Heteroscedasticity, 374
- OLS Estimation Allowing for Heteroscedasticity, 374
- OLS Estimation Disregarding Heteroscedasticity, 374
- A Technical Note, 376
- 11.5. Detection of Heteroscedasticity, 376
- Informal Methods, 376
- Formal Methods, 378
- 11.6. Remedial Measures, 389
- When σ2i Is Known: The Method of Weighted Least Squares, 389
- When σ2i Is Not Known, 391
- 11.7. Concluding Examples, 395
- 11.8. A Caution about Overreacting to Heteroscedasticity, 400
- Summary and Conclusions, 400
- Exercises, 401
- Appendix 11A, 409
- 11A.1. Proof of Equation (11.2.2), 409
- 11A.2. The Method of Weighted Least Squares, 409
- 11A.3. Proof that E(σ̂2) ≠ σ2 in the Presence of Heteroscedasticity, 410
- 11A.4. White's Robust Standard Errors, 411
- Chapter 12. Autocorrelation: What Happens If the Error Terms Are Correlated?, 412
- 12.1. The Nature of the Problem, 413
- 12.2. OLS Estimation in the Presence of Autocorrelation, 418
- 12.3. The BLUE Estimator in the Presence of Autocorrelation, 422
- 12.4. Consequences of Using OLS in the Presence of Autocorrelation, 423
- OLS Estimation Allowing for Autocorrelation, 423
- OLS Estimation Disregarding Autocorrelation, 423
- 12.5. Relationship between Wages and Productivity in the Business Sector of the United States, 1960–2005, 428
- 12.6. Detecting Autocorrelation, 429
- I. Graphical Method, 429
- II. The Runs Test, 431
- III. Durbin–Watson d Test, 434
- IV. A General Test of Autocorrelation: The Breusch–Godfrey (BG) Test, 438
- Why So Many Tests of Autocorrelation?, 440
- 12.7. What to Do When You Find Autocorrelation: Remedial Measures, 440
- 12.8. Model Mis-Specification versus Pure Autocorrelation, 441
- 12.9. Correcting for (Pure) Autocorrelation: The Method of Generalized Least Squares (GLS), 442
- When ρ Is Known, 442
- When ρ Is Not Known, 443
- 12.10. The Newey–West Method of Correcting the OLS Standard Errors, 447
- 12.11. OLS versus FGLS and HAC, 448
- 12.12. Additional Aspects of Autocorrelation, 449
- Dummy Variables and Autocorrelation, 449
- ARCH and GARCH Models, 449
- Coexistence of Autocorrelation and Heteroscedasticity, 450
- 12.13. A Concluding Example, 450
- Summary and Conclusions, 452
- Exercises, 453
- Appendix 12A, 466
- 12A.1. Proof that the Error Term vt in Equation (12.1.11) Is Autocorrelated, 466
- 12A.2. Proof of Equations (12.2.3), (12.2.4), and (12.2.5), 466
- Chapter 13. Econometric Modeling: Model Specification and Diagnostic Testing, 467
- 13.1. Model Selection Criteria, 468
- 13.2. Types of Specification Errors, 468
- 13.3. Consequences of Model Specification Errors, 470
- Underfitting a Model (Omitting a Relevant Variable), 471
- Inclusion of an Irrelevant Variable (Overfitting a Model), 473
- 13.4. Tests of Specification Errors, 474
- Detecting the Presence of Unnecessary Variables (Overfitting a Model), 475
- Tests for Omitted Variables and Incorrect Functional Form, 477
- 13.5. Errors of Measurement, 482
- Errors of Measurement in the Dependent Variable Y, 482
- Errors of Measurement in the Explanatory Variable X, 483
- 13.6. Incorrect Specification of the Stochastic Error Term, 486
- 13.7. Nested versus Non-Nested Models, 487
- 13.8. Tests of Non-Nested Hypotheses, 488
- The Discrimination Approach, 488
- The Discerning Approach, 488
- 13.9. Model Selection Criteria, 493
- The R2 Criterion, 493
- Adjusted R2, 493
- Akaike's Information Criterion (AIC), 494
- Schwarz's Information Criterion (SIC), 494
- Mallows's Cp Criterion, 494
- A Word of Caution about Model Selection Criteria, 495
- Forecast Chi-Square (χ2), 496
- 13.10. Additional Topics in Econometric Modeling, 496
- Outliers, Leverage, and Influence, 496
- Recursive Least Squares, 498
- Chow's Prediction Failure Test, 498
- Missing Data, 499
- 13.11. Concluding Examples, 500
- 1. A Model of Hourly Wage Determination, 500
- 2. Real Consumption Function for the United States, 1947–2000, 505
- 13.12. Non-Normal Errors and Stochastic Regressors, 509
- 1. What Happens If the Error Term Is Not Normally Distributed?, 509
- 2. Stochastic Explanatory Variables, 510
- 13.13. A Word to the Practitioner, 511
- Summary and Conclusions, 512
- Exercises, 513
- Appendix 13A, 519
- 13A.1. The Proof that E(b12) = β2 + β3b32 [Equation (13.3.3)], 519
- 13A.2. The Consequences of Including an Irrelevant Variable: The Unbiasedness Property, 520
- 13A.3. The Proof of Equation (13.5.10), 521
- 13A.4. The Proof of Equation (13.6.2), 522
- Part THREE. TOPICS IN ECONOMETRICS, 523
- Chapter 14. Nonlinear Regression Models, 525
- 14.1. Intrinsically Linear and Intrinsically Nonlinear Regression Models, 525
- 14.2. Estimation of Linear and Nonlinear Regression Models, 527
- 14.3. Estimating Nonlinear Regression Models: The Trial-and-Error Method, 527
- 14.4. Approaches to Estimating Nonlinear Regression Models, 529
- Direct Search or Trial-and-Error or Derivative-Free Method, 529
- Direct Optimization, 529
- Iterative Linearization Method, 530
- 14.5. Illustrative Examples, 530
- Summary and Conclusions, 535
- Exercises, 535
- Appendix 14A, 537
- 14A.1. Derivation of Equations (14.2.4) and (14.2.5), 537
- 14A.2. The Linearization Method, 537
- 14A.3. Linear Approximation of the Exponential Function Given in Equation (14.2.2), 538
- Chapter 15. Qualitative Response Regression Models, 541
- 15.1. The Nature of Qualitative Response Models, 541
- 15.2. The Linear Probability Model (LPM), 543
- Non-Normality of the Disturbances ui, 544
- Heteroscedastic Variances of the Disturbances, 544
- Nonfulfillment of 0 ≤ E(Yi | Xi) ≤ 1, 545
- Questionable Value of R2 as a Measure of Goodness of Fit, 546
- 15.3. Applications of LPM, 549
- 15.4. Alternatives to LPM, 552
- 15.5. The Logit Model, 553
- 15.6. Estimation of the Logit Model, 555
- Data at the Individual Level, 556
- Grouped or Replicated Data, 556
- 15.7. The Grouped Logit (Glogit) Model: A Numerical Example, 558
- Interpretation of the Estimated Logit Model, 558
- 15.8. The Logit Model for Ungrouped or Individual Data, 561
- 15.9. The Probit Model, 566
- Probit Estimation with Grouped Data: gprobit, 567
- The Probit Model for Ungrouped or Individual Data, 570
- The Marginal Effect of a Unit Change in the Value of a Regressor in the Various Regression Models, 571
- 15.10. Logit and Probit Models, 571
- 15.11. The Tobit Model, 574
- Illustration of the Tobit Model: Ray Fair's Model of Extramarital Affairs, 575
- 15.12. Modeling Count Data: The Poisson Regression Model, 576
- 15.13. Further Topics in Qualitative Response Regression Models, 579
- Ordinal Logit and Probit Models, 580
- Multinomial Logit and Probit Models, 580
- Duration Models, 580
- Summary and Conclusions, 581
- Exercises, 582
- Appendix 15A, 589
- 15A.1. Maximum Likelihood Estimation of the Logit and Probit Models for Individual (Ungrouped) Data, 589
- Chapter 16. Panel Data Regression Models, 591
- 16.1. Why Panel Data?, 592
- 16.2. Panel Data: An Illustrative Example, 593
- 16.3. Pooled OLS Regression or Constant Coefficients Model, 594
- 16.4. The Fixed Effect Least-Squares Dummy Variable (LSDV) Model, 596
- A Caution in the Use of the Fixed Effect LSDV Model, 598
- 16.5. The Fixed-Effect Within-Group (WG) Estimator, 599
- 16.6. The Random Effects Model (REM), 602
- Breusch and Pagan Lagrange Multiplier Test, 605
- 16.7. Properties of Various Estimators, 605
- 16.8. Fixed Effects versus Random Effects Model: Some Guidelines, 606
- 16.9. Panel Data Regressions: Some Concluding Comments, 607
- 16.10. Some Illustrative Examples, 607
- Summary and Conclusions, 612
- Exercises, 613
- Chapter 17. Dynamic Econometric Models: Autoregressive and Distributed-Lag Models, 617
- 17.1. The Role of “Time,'' or “Lag,'' in Economics, 618
- 17.2. The Reasons for Lags, 622
- 17.3. Estimation of Distributed-Lag Models, 623
- Ad Hoc Estimation of Distributed-Lag Models, 623
- 17.4. The Koyck Approach to Distributed-Lag Models, 624
- The Median Lag, 627
- The Mean Lag, 627
- 17.5. Rationalization of the Koyck Model: The Adaptive Expectations Model, 629
- 17.6. Another Rationalization of the Koyck Model: The Stock Adjustment, or Partial Adjustment, Model, 632
- 17.7. Combination of Adaptive Expectations and Partial Adjustment Models, 634
- 17.8. Estimation of Autoregressive Models, 634
- 17.9. The Method of Instrumental Variables (IV), 636
- 17.10. Detecting Autocorrelation in Autoregressive Models: Durbin h Test, 637
- 17.11. A Numerical Example: The Demand for Money in Canada, 1979–I to 1988–IV, 639
- 17.12. Illustrative Examples, 642
- 17.13. The Almon Approach to Distributed-Lag Models: The Almon or Polynomial Distributed Lag (PDL), 645
- 17.14. Causality in Economics: The Granger Causality Test, 652
- The Granger Test, 653
- A Note on Causality and Exogeneity, 657
- Summary and Conclusions, 658
- Exercises, 659
- Appendix 17A, 669
- 17A.1. The Sargan Test for the Validity of Instruments, 669
- Part FOUR. SIMULTANEOUS-EQUATION MODELS AND TIME SERIES ECONOMETRICS, 671
- Chapter 18. Simultaneous-Equation Models, 673
- 18.1. The Nature of Simultaneous-Equation Models, 673
- 18.2. Examples of Simultaneous-Equation Models, 674
- 18.3. The Simultaneous-Equation Bias: Inconsistency of OLS Estimators, 679
- 18.4. The Simultaneous-Equation Bias: A Numerical Example, 682
- Summary and Conclusions, 684
- Exercises, 684
- Chapter 19. The Identification Problem, 689
- 19.1. Notations and Definitions, 689
- 19.2. The Identification Problem, 692
- Underidentification, 692
- Just, or Exact, Identification, 694
- Overidentification, 697
- 19.3. Rules for Identification, 699
- The Order Condition of Identifiability, 699
- The Rank Condition of Identifiability, 700
- 19.4. A Test of Simultaneity, 703
- Hausman Specification Test, 703
- 19.5. Tests for Exogeneity, 705
- Summary and Conclusions, 706
- Exercises, 706
- Chapter 20. Simultaneous-Equation Methods, 711
- 20.1. Approaches to Estimation, 711
- 20.2. Recursive Models and Ordinary Least Squares, 712
- 20.3. Estimation of a Just Identified Equation: The Method of Indirect Least Squares (ILS), 715
- An Illustrative Example, 715
- Properties of ILS Estimators, 718
- 20.4. Estimation of an Overidentified Equation: The Method of Two-Stage Least Squares (2SLS), 718
- 20.5. 2SLS: A Numerical Example, 721
- 20.6. Illustrative Examples, 724
- Summary and Conclusions, 730
- Exercises, 730
- Appendix 20A, 735
- 20A.1. Bias in the Indirect Least-Squares Estimators, 735
- 20A.2. Estimation of Standard Errors of 2SLS Estimators, 736
- Chapter 21. Time Series Econometrics: Some Basic Concepts, 737
- 21.1. A Look at Selected U.S. Economic Time Series, 738
- 21.2. Key Concepts, 739
- 21.3. Stochastic Processes, 740
- Stationary Stochastic Processes, 740
- Nonstationary Stochastic Processes, 741
- 21.4. Unit Root Stochastic Process, 744
- 21.5. Trend Stationary (TS) and Difference Stationary (DS) Stochastic Processes, 745
- 21.6. Integrated Stochastic Processes, 746
- Properties of Integrated Series, 747
- 21.7. The Phenomenon of Spurious Regression, 747
- 21.8. Tests of Stationarity, 748
- 1. Graphical Analysis, 749
- 2. Autocorrelation Function (ACF) and Correlogram, 749
- Statistical Significance of Autocorrelation Coefficients, 753
- 21.9. The Unit Root Test, 754
- The Augmented Dickey–Fuller (ADF) Test, 757
- Testing the Significance of More than One Coefficient: The F Test, 758
- The Phillips–Perron (PP) Unit Root Tests, 758
- Testing for Structural Changes, 758
- A Critique of the Unit Root Tests, 759
- 21.10. Transforming Nonstationary Time Series, 760
- Difference-Stationary Processes, 760
- Trend-Stationary Processes, 761
- 21.11. Cointegration: Regression of a Unit Root Time Series on Another Unit Root Time Series, 762
- Testing for Cointegration, 763
- Cointegration and Error Correction Mechanism (ECM), 764
- 21.12. Some Economic Applications, 765
- Summary and Conclusions, 768
- Exercises, 769
- Chapter 22. Time Series Econometrics: Forecasting, 773
- 22.1. Approaches to Economic Forecasting, 773
- Exponential Smoothing Methods, 774
- Single-Equation Regression Models, 774
- Simultaneous-Equation Regression Models, 774
- ARIMA Models, 774
- VAR Models, 775
- 22.2. AR, MA, and ARIMA Modeling of Time Series Data, 775
- An Autoregressive (AR) Process, 775
- A Moving Average (MA) Process, 776
- An Autoregressive and Moving Average (ARMA) Process, 776
- An Autoregressive Integrated Moving Average (ARIMA) Process, 776
- 22.3. The Box–Jenkins (BJ) Methodology, 777
- 22.4. Identification, 778
- 22.5. Estimation of the ARIMA Model, 782
- 22.6. Diagnostic Checking, 782
- 22.7. Forecasting, 782
- 22.8. Further Aspects of the BJ Methodology, 784
- 22.9. Vector Autoregression (VAR), 784
- Estimation or VAR, 785
- Forecasting with VAR, 786
- VAR and Causality, 787
- Some Problems with VAR Modeling, 788
- An Application of VAR: A VAR Model of the Texas Economy, 789
- 22.10. Measuring Volatility in Financial Time Series: The ARCH and GARCH Models, 791
- What to Do If ARCH Is Present, 795
- A Word on the Durbin–Watson d and the ARCH Effect, 796
- A Note on the GARCH Model, 796
- 22.11. Concluding Examples, 796
- Summary and Conclusions, 798
- Exercises, 799
- Appendix A. A Review of Some Statistical Concepts, 801
- A.1. Summation and Product Operators, 801
- A.2. Sample Space, Sample Points, and Events, 802
- A.3. Probability and Random Variables, 802
- Probability, 802
- Random Variables, 803
- A.4. Probability Density Function (PDF), 803
- Probability Density Function of a Discrete Random Variable, 803
- Probability Density Function of a Continuous Random Variable, 804
- Joint Probability Density Functions, 805
- Marginal Probability Density Function, 805
- Statistical Independence, 806
- A.5. Characteristics of Probability Distributions, 808
- Expected Value, 808
- Properties of Expected Values, 809
- Variance, 810
- Properties of Variance, 811
- Covariance, 811
- Properties of Covariance, 812
- Correlation Coefficient, 812
- Conditional Expectation and Conditional Variance, 813
- Properties of Conditional Expectation and Conditional Variance, 814
- Higher Moments of Probability Distributions, 815
- A.6. Some Important Theoretical Probability Distributions, 816
- Normal Distribution, 816
- The χ2 (Chi-Square) Distribution, 819
- Student's t Distribution, 820
- The F Distribution, 821
- The Bernoulli Binomial Distribution, 822
- Binomial Distribution, 822
- The Poisson Distribution, 823
- A.7. Statistical Inference: Estimation, 823
- Point Estimation, 823
- Interval Estimation, 824
- Methods of Estimation, 825
- Small-Sample Properties, 826
- Large-Sample Properties, 828
- A.8. Statistical Inference: Hypothesis Testing, 831
- The Confidence Interval Approach, 832
- The Test of Significance Approach, 836
- References, 837
- Appendix B. Rudiments of Matrix Algebra, 838
- B.1. Definitions, 838
- Matrix, 838
- Column Vector, 838
- Row Vector, 839
- Transposition, 839
- Submatrix, 839
- B.2. Types of Matrices, 839
- Square Matrix, 839
- Diagonal Matrix, 839
- Scalar Matrix, 840
- Identity, or Unit, Matrix, 840
- Symmetric Matrix, 840
- Null Matrix, 840
- Null Vector, 840
- Equal Matrices, 840
- B.3. Matrix Operations, 840
- Matrix Addition, 840
- Matrix Subtraction, 841
- Scalar Multiplication, 841
- Matrix Multiplication, 841
- Properties of Matrix Multiplication, 842
- Matrix Transposition, 843
- Matrix Inversion, 843
- B.4. Determinants, 843
- Evaluation of a Determinant, 844
- Properties of Determinants, 844
- Rank of a Matrix, 845
- Minor, 846
- Cofactor, 846
- B.5. Finding the Inverse of a Square Matrix, 847
- B.6. Matrix Differentiation, 848
- References, 848
- Appendix C. The Matrix Approach to Linear Regression Model, 849
- C.1. The k-Variable Linear Regression Model, 849
- C.2. Assumptions of the Classical Linear Regression Model in Matrix Notation, 851
- C.3. OLS Estimation, 853
- An Illustration, 855
- Variance-Covariance Matrix of, 856
- Properties of OLS Vector, 858
- C.4. The Coefficient of Determination R2 in Matrix Notation, 858
- C.5. The Correlation Matrix, 859
- C.6. Hypothesis Testing about Individual Regression Coefficients in Matrix Notation, 859
- C.7. Testing the Overall Significance of Regression: Analysis of Variance in Matrix Notation, 860
- C.8. Testing Linear Restrictions: General F Testing Using Matrix Notation, 861
- C.9. Prediction Using Multiple Regression: Matrix Formulation, 861
- Mean Prediction, 861
- Variance of Mean Prediction, 862
- Individual Prediction, 862
- Variance of Individual Prediction, 862
- C.10. Summary of the Matrix Approach: An Illustrative Example, 863
- C.11. Generalized Least Squares (GLS), 867
- C.12. Summary and Conclusions, 868
- Exercises, 869
- Appendix CA, 874
- CA.1. Derivation of k Normal or Simultaneous Equations, 874
- CA.2. Matrix Derivation of Normal Equations, 875
- CA.3. Variance–Covariance Matrix of β̂, 875
- CA.4. BLUE Property of OLS Estimators, 875
- Appendix D. Statistical Tables, 877
- Appendix E. Computer Output of EViews, MINITAB, Excel, and STATA, 894
- E.1. EViews, 894
- E.2. MINITAB, 896
- E.3. Excel, 897
- E.4. STATA, 898
- E.5. Concluding Comments, 898
- References, 899
- Appendix F. Economic Data on the World Wide Web, 900
- Selected Bibliography, 902
- Name Index, 905
- Subject Index, 909
thanks and Jazak Allah for uploading the link for the book.
Wa iyyak.
You're welcome!
Hi there,
Thanks for the book, but i was hoping to
have full acces to the whole book in pdf.
Thanks a lot anyways
Here are some books related to Econometrics, as well as Gujarati 4th ed.:
http://avaxsearch.com/avaxhome_search?q=basic+econometrics&commit=Go
You're welcome
thanks a lot!
Page 1
1–6
