Basic econometrics:
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Boston [u.a.]
McGraw-Hill
2009
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| Edition: | 5. ed., internat. ed. |
| Series: | The McGraw-Hill series economics
Higher education |
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| ISBN: | 0071276254 9780071276252 |
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| 100 | 1 | |a Gujarati, Damodar N. |e Verfasser |0 (DE-588)129300462 |4 aut | |
| 245 | 1 | 0 | |a Basic econometrics |c Damodar N. Gujarati ; Dawn C. Porter |
| 250 | |a 5. ed., internat. ed. | ||
| 264 | 1 | |a Boston [u.a.] |b McGraw-Hill |c 2009 | |
| 300 | |a XX, 922 S. |b graph. Darst. | ||
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| adam_text | Titel: Basic econometrics
Autor: Gujarati, Damodar N.
Jahr: 2009
Preface xvi
Acknowledgments xix
Introduction 1
1.1 What Is Econometrics? 1
1.2 Why a Separate Discipline? 2
1.3 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
1.4 Types of Econometrics 10
1.5 Mathematical and Statistical Prerequisites 11
1.6 The Role of the Computer 11
1.7 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
ofVariables 27
vi
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
3 A.I 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 $ and /§2 93
3A.5 The Least-Squares Estimator of a2 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 «,- 97
4.2 The Normality Assumption for «,- 98
JF/zy ?Ae 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 fa and fa 109
Confidence Interval for fa 109
Confidence Interval for fa and fa
Simultaneously 111
5.4 Confidence Interval for a2 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 1 IS
5.7 Hypothesis Testing:
The Test-of-Significance Approach 115
Testing the Significance of Regression
Coefficients: The t Test 115
Testing the Significance of a2: The x2 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
ofThumb 120
Forming the Null and Alternative
Hypotheses 121
Choosing a, the Level of Significance 121
The Exact Level of Significance:
Thep 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 5 A 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
r 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 6 A 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 MaximizingR2 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 7 A 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 ofR2 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
ofOLS 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 ofMicronumerosiiy 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 3 73
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 3 76
Formal Methods 378
11.6 Remedial Measures 389
When a Is Known: The Method of Weighted
Least Squares 389
When a2. 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
11 A.I Proof of Equation (11.2.2) 409
11 A.2 The Method of Weighted Least
Squares 409
11 A.3 Proof that E(a2) ^o2 in the Presence
of Heteroscedasticity 410
11 A.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
/. Graphical Method 429
II. The Runs Test 431
HI. 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 p Is Known 442
When p Is Not Known 443
MAO 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
ARCHand GARCHModels 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) 4 75
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 (x2) 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(bn) = ft + fob32
[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 u, 544
Heteroscedastic Variances
of the Disturbances 544
Nonfulfillment ofO E(Yt Xt) 1 545
Questionable Value ofR2 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: gpmbit 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
15 A.I 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
LSDVModel 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, 1979-1 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 74 7
21.7 The Phenomenon of Spurious
Regression 747
21.8 Tests of Stationarity 748
/. 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-Stationaiy 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 ARJMA 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.I 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 x2 (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.I The £-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 offi 856
Properties of OLS Vector J3 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
CIO Summary of the Matrix Approach: An
Illustrative Example 863
C.11 Generalized Least Squares (GLS) 867
C.I 2 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 p 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.I 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
|
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| id | DE-604.BV035304162 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:30:51Z |
| institution | BVB |
| isbn | 0071276254 9780071276252 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017108978 |
| oclc_num | 226356768 |
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| physical | XX, 922 S. graph. Darst. |
| publishDate | 2009 |
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| publisher | McGraw-Hill |
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| series2 | The McGraw-Hill series economics Higher education |
| spelling | Gujarati, Damodar N. Verfasser (DE-588)129300462 aut Basic econometrics Damodar N. Gujarati ; Dawn C. Porter 5. ed., internat. ed. Boston [u.a.] McGraw-Hill 2009 XX, 922 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier The McGraw-Hill series economics Higher education Hier auch später erschienene, unveränderte Nachdrucke Ökonometrie (DE-588)4132280-0 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Ökonometrie (DE-588)4132280-0 s DE-604 Porter, Dawn C. Verfasser (DE-588)1231308087 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017108978&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gujarati, Damodar N. Porter, Dawn C. Basic econometrics Ökonometrie (DE-588)4132280-0 gnd |
| subject_GND | (DE-588)4132280-0 (DE-588)4151278-9 |
| title | Basic econometrics |
| title_auth | Basic econometrics |
| title_exact_search | Basic econometrics |
| title_full | Basic econometrics Damodar N. Gujarati ; Dawn C. Porter |
| title_fullStr | Basic econometrics Damodar N. Gujarati ; Dawn C. Porter |
| title_full_unstemmed | Basic econometrics Damodar N. Gujarati ; Dawn C. Porter |
| title_short | Basic econometrics |
| title_sort | basic econometrics |
| topic | Ökonometrie (DE-588)4132280-0 gnd |
| topic_facet | Ökonometrie Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017108978&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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