Basic Econometrics

ISBN-10: 0072478527

ISBN-13: 9780072478525

Edition: 4th 2003 (Revised)

Authors: Damodar N. Gujarati

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Book details

List price: $167.50
Edition: 4th
Copyright year: 2003
Publisher: McGraw-Hill Higher Education
Publication date: 3/18/2002
Binding: Hardcover
Size: 7.25" wide x 9.00" long x 1.50" tall
Weight: 3.784
Language: English

Damodar Gujarati has over 40 years of teaching and writing experience. As well as his bestselling textbooks he has published many articles in leading economics and statistics journals. He has Visiting Professorships at leading universities in the UK, Australia, Singapore and India.

Prefacep. xxi
Introductionp. 1
Single-Equation Regression Models
The Nature of Regression Analysisp. 15
Historical Origin of the Term "Regression"p. 15
The Modern Interpretation of Regressionp. 16
Examplesp. 16
Statistical vs. Deterministic Relationshipsp. 19
Regression vs. Causationp. 20
Regression vs. Correlationp. 21
Terminology and Notationp. 22
The Nature and Sources of Data for Econometric Analysisp. 23
Types of Datap. 23
The Sources of Datap. 24
The Accuracy of Datap. 26
Summary and Conclusionsp. 27
Exercisesp. 28
Appendix 1Ap. 29
Sources of Economic Datap. 29
Sources of Financial Datap. 31
Two-Variable Regression Analysis: Some Basic Ideasp. 32
A Hypothetical Examplep. 32
The Concept of Population Regression Function (PRF)p. 36
The Meaning of the Term "Linear"p. 36
Linearity in the Variablesp. 37
Linearity in the Parametersp. 37
Stochastic Specification of PRFp. 38
The Significance of the Stochastic Disturbance Termp. 39
The Sample Regression Function (SRF)p. 41
Summary and Conclusionsp. 45
Exercisesp. 45
Two-Variable Regression Model: The Problem of Estimationp. 52
The Method of Ordinary Least Squaresp. 52
The Classical Linear Regression Model: The Assumptions Underlying the Method of Least Squaresp. 59
How Realistic Are These Assumptions?p. 68
Precision or Standard Errors of Least-Squares Estimatesp. 69
Properties of Least-Squares Estimators: The Gauss-Markov Theoremp. 72
The Coefficient of Determination r2: A Measure of "Goodness of Fit"p. 74
A Numerical Examplep. 80
Illustrative Examplesp. 83
Coffee Consumption in the United States, 1970-1980p. 83
Keynesian Consumption Function for the United States, 1980-1991p. 84
Computer Output for the Coffee Demand Functionp. 85
A Note on Monte Carlo Experimentsp. 85
Summary and Conclusionsp. 86
Exercisesp. 87
Questionsp. 87
Problemsp. 89
Appendix 3Ap. 94
Derivation of Least-Squares Estimatesp. 94
Linearity and Unbiasedness Properties of Least-Squares Estimatorsp. 94
Variances and Standard Errors of Least-Squares Estimatorsp. 95
Covariance between B1 and B2p. 96
The Least-Squares Estimator of o2p. 96
Minimum-Variance Property of Least-Squares Estimatorsp. 97
SAS Output of the Coffee Demand Function (3.7.1)p. 99
The Normality Assumption: Classical Normal Linear Regression Model (CNLRM)p. 101
The Probability Distribution of Disturbances uip. 101
The Normality Assumptionp. 102
Properties of OLS Estimators under the Normality Assumptionp. 104
The Method of Maximum Likelihood (ML)p. 107
Probability Distributions Related to the Normal Distribution: The t, Chi-square (X2), and F Distributionsp. 107
Summary and Conclusionsp. 109
Appendix 4Ap. 110
Maximum Likelihood Estimation of Two-Variable Regression Modelp. 110
Maximum Likelihood Estimation of the Consumption-Income Examplep. 113
Appendix 4A Exercisesp. 113
Two-Variable Regression: Interval Estimation and Hypothesis Testingp. 115
Statistical Prerequisitesp. 115
Interval Estimation: Some Basic Ideasp. 116
Confidence Intervals for Regression Coefficients B1 and B2p. 117
Confidence Interval for B2p. 117
Confidence Interval for B1p. 119
Confidence Interval for B1 and B2 Simultaneouslyp. 120
Confidence Interval for o2p. 120
Hypothesis Testing: General Commentsp. 121
Hypothesis Testing: The Confidence-Interval Approachp. 122
Two-Sided or Two-Tail Testp. 122
One-Sided or One-Tail Testp. 124
Hypothesis Testing: The Test-of-Significance Approachp. 124
Testing the Significance of Regression Coefficients: The t-Testp. 124
Testing the Significance of o2: the X2 Testp. 128
Hypothesis Testing: Some Practical Aspectsp. 129
The Meaning of "Accepting" or "Rejecting" a Hypothesisp. 129
The "Zero" Null Hypothesis and the "2-t" Rule of Thumbp. 129
Forming the Null and Alternative Hypothesesp. 130
Choosing a, the Level of Significancep. 131
The Exact Level of Significance: The p Valuep. 132
Statistical Significance versus Practical Significancep. 133
The Choice between Confidence-Interval and Test-of-Significance Approaches to Hypothesis Testingp. 134
Regression Analysis and Analysis of Variancep. 134
Application of Regression Analysis: The Problem of Predictionp. 137
Mean Predictionp. 137
Individual Predictionp. 138
Reporting the Results of Regression Analysisp. 140
Evaluating the Results of Regression Analysisp. 140
Normality Testp. 141
Other Tests of Model Adequacyp. 144
Summary and Conclusionsp. 144
Exercisesp. 145
Questionsp. 145
Problemsp. 147
Appendix 5Ap. 152
Derivation of Equation (5.3.2)p. 152
Derivation of Equation (5.9.1)p. 152
Derivation of Equations (5.10.2) and (5.10.6)p. 153
Variance of Mean Predictionp. 153
Variance of Individual Predictionp. 153
Extensions of the Two-Variable Linear Regression Modelp. 155
Regression through the Originp. 155
r2 for Regression-through-Origin Model An Illustrative Example: The Characteristic Line of Portfolio Theoryp. 159
Scaling and Units of Measurementp. 161
A Numerical Example: The Relationship between GPDI and GNP, United States, 1974-1983p. 163
A Word about Interpretationp. 164
Functional Forms of Regression Modelsp. 165
How to Measure Elasticity: The Log-Linear Modelp. 165
An Illustrative Example: The Coffee Demand Function Revisitedp. 167
Semilog Models: Log-Lin and Lin-Log Modelsp. 169
How to Measure the Growth Rate: The Log-Lin Modelp. 169
The Lin-Log Modelp. 172
Reciprocal Modelsp. 173
An Illustrative Example: The Phillips Curve for the United Kingdom, 1950-1966p. 176
Summary of Functional Formsp. 176
A Note on the Nature of the Stochastic Error Term: Additive versus Multiplicative Stochastic Error Termp. 178
Summary and Conclusionsp. 179
Exercisesp. 180
Questionsp. 180
Problemsp. 183
Appendix 6Ap. 186
Derivation of Least-Squares Estimators for Regression through the Originp. 186
SAS Output of the Characteristic Line (6.1.12)p. 189
SAS Output of the United Kingdom Phillips Curve Regression (6.6.2)p. 190
Multiple Regression Analysis: The Problem of Estimationp. 191
The Three-Variable Model: Notation and Assumptionsp. 192
Interpretation of Multiple Regression Equationp. 194
The Meaning of Partial Regression Coefficientsp. 195
OLS and ML Estimation of the Partial Regression Coefficientsp. 197
OLS Estimatorsp. 197
Variances and Standard Errors of OLS Estimatorsp. 198
Properties of OLS Estimatorsp. 199
Maximum Likelihood Estimatorsp. 201
The Multiple Coefficient of Determination R2 and the Multiple Coefficient of Correlation Rp. 201
Example 7.1: The Expectations-Augmented Phillips Curve for the United States, 1970-1982p. 203
Simple Regression in the Context of Multiple Regression: Introduction to Specification Biasp. 204
R2 and the Adjusted R2p. 207
Comparing Two R2 Valuesp. 209
Example 7.2: Coffee Demand Function Revisitedp. 210
The "Game" of Maximizing R2p. 211
Partial Correlation Coefficientsp. 211
Explanation of Simple and Partial Correlation Coefficientsp. 211
Interpretation of Simple and Partial Correlation Coefficientsp. 213
Example 7.3: The Cobb-Douglas Production Function: More on Functional Formp. 214
Polynomial Regression Modelsp. 217
Example 7.4: Estimating the Total Cost Functionp. 218
Empirical Resultsp. 220
Summary and Conclusionsp. 221
Exercisesp. 221
Questionsp. 221
Problemsp. 224
Appendix 7Ap. 231
Derivation of OLS Estimators Given in Equations (7.4.3) and (7.4.5)p. 231
Equality between a1 of (7.3.5) and B2 of (7.4.7)p. 232
Derivation of Equation (7.4.19)p. 232
Maximum Likelihood Estimation of the Multiple Regression Modelp. 233
The Proof that E(b12) = B2 + B3b32 (Equation 7.7.4)p. 234
SAS Output of the Expectations-Augmented Phillips Curve (7.6.2)p. 236
SAS Output of the Cobb-Douglas Production Function (7.10.4)p. 237
Multiple Regression Analysis: The Problem of Inferencep. 238
The Normality Assumption Once Againp. 238
Example 8.1: U.S. Personal Consumption and Personal Disposal Income Relation, 1956-1970p. 239
Hypothesis Testing in Multiple Regression: General Commentsp. 242
Hypothesis Testing about Individual Partial Regression Coefficientsp. 242
Testing the Overall Significance of the Sample Regressionp. 244
The Analysis of Variance Approach to Testing the Overall Significance of an Observed Multiple Regression: The F Testp. 245
An Important Relationship between R2 and Fp. 248
The "Incremental," or "Marginal," Contribution of an Explanatory Variablep. 250
Testing the Equality of Two Regression Coefficientsp. 254
Example 8.2: The Cubic Cost Function Revisitedp. 255
Restricted Least Squares: Testing Linear Equality Restrictionsp. 256
The t Test Approachp. 256
The F Test Approach: Restricted Least Squaresp. 257
Example 8.3: The Cobb-Douglas Production Function for Taiwanese Agricultural Sector, 1958-1972p. 259
General F Testingp. 260
Comparing Two Regressions: Testing for Structural Stability of Regression Modelsp. 262
Testing the Functional Form of Regression: Choosing between Linear and Log-Linear Regression Modelsp. 265
Example 8.5: The Demand for Rosesp. 266
Prediction with Multiple Regressionp. 267
The Troika of Hypothesis Tests: The Likelihood Ratio (LR), Wald (W), and Lagrange Multiplier (LM) Testsp. 268
Summary and Conclusionsp. 269
The Road Aheadp. 269
Exercisesp. 270
Questionsp. 270
Problemsp. 273
Appendix 8Ap. 280
Likelihood Ratio (LR) Testp. 280
The Matrix Approach to Linear Regression Modelp. 282
The k-Variable Linear Regression Modelp. 282
Assumptions of the Classical Linear Regression Model in Matrix Notationp. 284
OLS Estimationp. 287
An Illustrationp. 289
Variance-Covariance Matrix of Bp. 290
Properties of OLS Vector Bp. 291
The Coefficient of Determination R2 in Matrix Notationp. 292
The Correlation Matrixp. 292
Hypothesis Testing about Individual Regression Coefficients in Matrix Notationp. 293
Testing the Overall Significance of Regression: Analysis of Variance in Matrix Notationp. 294
Testing Linear Restrictions: General F Testing Using Matrix Notationp. 295
Prediction Using Multiple Regression: Matrix Formulationp. 296
Mean Predictionp. 296
Individual Predictionp. 296
Variance of Mean Predictionp. 297
Variance of Individual Predictionp. 298
Summary of the Matrix Approach: An Illustrative Examplep. 298
Summary and Conclusionsp. 303
Exercisesp. 304
Appendix 9Ap. 309
Derivation of k Normal or Simultaneous Equationsp. 309
Matrix Derivation of Normal Equationsp. 310
Variance-Covariance Matrix of Bp. 310
Blue Property of OLS Estimatorsp. 311
Relaxing the Assumptions of the Classical Model
Multicollinearity and Micronumerosityp. 319
The Nature of Multicollinearityp. 320
Estimation in the Presence of Perfect Multicollinearityp. 323
Estimation in the Presence of "High" but "Imperfect" Multicollinearityp. 325
Multicollinearity: Much Ado about Nothing? Theoretical Consequences of Multicollinearityp. 325
Practical Consequences of Multicollinearityp. 327
Large Variances and Covariances of OLS Estimatorsp. 328
Wider Confidence Intervalsp. 329
"Insignificant" t Ratiosp. 330
A High R2 but Few Significant t Ratiosp. 330
Sensitivity of OLS Estimators and Their Standard Errors to Small Changes in Datap. 331
Consequences of Micronumerosityp. 332
An Illustrative Example: Consumption Expenditure in Relation to Income and Wealthp. 332
Detection of Multicollinearityp. 335
Remedial Measuresp. 339
Is Multicollinearity Necessarily Bad? Maybe Not If the Objective Is Prediction Onlyp. 344
Summary and Conclusionsp. 345
Exercisesp. 346
Questionsp. 346
Problemsp. 351
Heteroscedasticityp. 355
The Nature of Heteroscedasticityp. 355
OLS Estimation in the Presence of Heteroscedasticityp. 359
The Method of Generalized Least Squares (GLS)p. 362
Difference between OLS and GLSp. 364
Consequences of Using OLS in the Presence of Heteroscedasticityp. 365
OLS Estimation Allowing for Heteroscedasticityp. 365
OLS Estimation Disregarding Heteroscedasticityp. 366
Detection of Heteroscedasticityp. 367
Informal Methodsp. 368
Formal Methodsp. 369
Remedial Measuresp. 381
When oi2 Is Known: The Method of Weighted Least Squaresp. 381
When o12 Is Not Knownp. 382
A Concluding Examplep. 387
Summary and Conclusionsp. 389
Exercisesp. 390
Questionsp. 390
Problemsp. 392
Appendix 11Ap. 398
Proof of Equation (11.2.2)p. 398
The Method of Weighted Least Squaresp. 399
Autocorrelationp. 400
The Nature of the Problemp. 400
OLS Estimation in the Presence of Autocorrelationp. 406
The BLUE Estimator in the Presence of Autocorrelationp. 409
Consequences of Using OLS in the Presence of Autocorrelationp. 410
OLS Estimation Allowing for Autocorrelationp. 410
OLS Estimation Disregarding Autocorrelationp. 411
Detecting Autocorrelationp. 415
Graphical Methodp. 415
The Runs Testp. 419
Durbin-Watson d Testp. 420
Additional Tests of Autocorrelationp. 425
Remedial Measuresp. 426
When the Structure of Autocorrelation Is Knownp. 427
When p Is Not Knownp. 428
An Illustrative Example: The Relationship between Help-Wanted Index and the Unemployment Rate, United States: Comparison of the Methodsp. 433
Autoregressive Conditional Heteroscedasticity (ARCH) Modelp. 436
What to Do If ARCH Is Present?p. 438
A Word on the Durbin-Watson d Statistic and the ARCH Effectp. 438
Summary and Conclusionsp. 439
Exercisesp. 440
Questionsp. 440
Problemsp. 446
Appendix 12Ap. 449
TSP Output of United States Wages (Y)-Productivity (X) Regression, 1960-1991p. 449
Econometric Modeling I: Traditional Econometric Methodologyp. 452
The Traditional View of Econometric Modeling: Average Economic Regression (AER)p. 452
Types of Specification Errorsp. 455
Consequences of Specification Errorsp. 456
Omitting a Relevant Variable (Underfitting a Model)p. 456
Inclusion of an Irrelevant Variable (Overfitting a Model)p. 458
Tests of Specification Errorsp. 459
Detecting the Presence of Unnecessary Variablesp. 460
Tests for Omitted Variables and Incorrect Functional Formp. 461
Errors of Measurementp. 467
Errors of Measurement in the Dependent Variable Yp. 468
Errors of Measurement in the Explanatory Variable Xp. 469
An Examplep. 470
Measurement Errors in the Dependent Variable Y Onlyp. 471
Errors of Measurement in Xp. 472
Summary and Conclusionsp. 472
Exercisesp. 473
Questionsp. 473
Problemsp. 476
Appendix 13Ap. 477
The Consequences of Including an Irrelevant Variable: The Unbiasedness Propertyp. 477
Proof of (13.5.10)p. 478
Econometric Modeling II: Alternative Econometric Methodologiesp. 480
Learner's Approach to Model Selectionp. 481
Hendry's Approach to Model Selectionp. 485
Selected Diagnostic Tests: General Commentsp. 486
Tests of Nonnested Hypothesisp. 487
The Discrimination Approachp. 487
The Discerning Approachp. 488
Summary and Conclusionsp. 494
Exercisesp. 494
Questionsp. 494
Problemsp. 495
Topics in Econometrics
Regression on Dummy Variablesp. 499
The Nature of Dummy Variablesp. 499
Example 15.1: Professor's Salary by Sexp. 500
Regression on One Quantitative Variable and One Qualitative Variable with Two Classes, or Categoriesp. 502
Example 15.2: Are Inventories Sensitive to Interest Rates?p. 505
Regression on One Quantitative Variable and One Qualitative Variable with More than Two Classesp. 505
Regression on One Quantitative Variable and Two Qualitative Variablesp. 507
Example 15.3: The Economics of "Moonlighting"p. 508
Testing for Structural Stability of Regression Models: Basic Ideasp. 509
Example 15.4: Savings and Income, United Kingdom, 1946-1963p. 509
Comparing Two Regressions: The Dummy Variable Approachp. 512
Comparing Two Regressions: Further Illustrationp. 514
Example 15.5: The Behavior of Unemployment and Unfilled Vacancies: Great Britain, 1958-1971p. 514
Interaction Effectsp. 516
The Use of Dummy Variables in Seasonal Analysisp. 517
Example 15.6: Profits-Sales Behavior in U.S. Manufacturingp. 517
Piecewise Linear Regressionp. 519
Example 15.7: Total Cost in Relation to Outputp. 521
The Use of Dummy Variables in Combining Time Series and Cross-Sectional Datap. 522
Pooled Regression: Pooling Time Series and Cross-Sectional Datap. 522
Example 15.8: Investment Functions for General Motors and Westinghouse Companiesp. 524
Some Technical Aspects of Dummy Variable Techniquep. 525
The Interpretation of Dummy Variables in Semilogarithmic Regressionsp. 525
Example 15.9: Semilogarithmic Regression with Dummy Variablep. 525
Another Method of Avoiding the Dummy Variable Trapp. 526
Dummy Variables and Heteroscedasticityp. 527
Dummy Variables and Autocorrelationp. 527
Topics for Further Studyp. 528
Summary and Conclusionsp. 529
Exercisesp. 530
Questionsp. 530
Problemsp. 535
Appendix 15Ap. 538
Data Matrix for Regression (15.8.2)p. 538
Data Matrix for Regression (15.10.2)p. 539
Regression on Dummy Dependent Variable: The LPM, Logit, Probit, and Tobit Modelsp. 540
Dummy Dependent Variablep. 540
The Linear Probability Model (LPM)p. 541
Problems in Estimation of LPMp. 542
Nonnormality of the Disturbances uip. 542
Heteroscedastic Variances of the Disturbancesp. 543
Nonfulfillment of 0 [= E(Yi\X) [= 1p. 544
Questionable Value of R2 as a Measure of Goodness of Fitp. 545
LPM: A Numerical Examplep. 546
Applications of LPMp. 548
Example 16.1: Cohen-Rea-Lerman studyp. 548
Example 16.2: Predicting a Bond Ratingp. 551
Example 16.3: Predicting Bond Defaultsp. 552
Alternatives to LPMp. 552
The Logit Modelp. 554
Estimation of the Logit Modelp. 556
The Logit Model: A Numerical Examplep. 558
The Logit Model: Illustrative Examplesp. 561
Example 16.4: "An Application of Logit Analysis to Prediction of Merger Targets"p. 561
Example 16.5: Predicting a Bond Ratingp. 562
The Probit Modelp. 563
The Probit Model: A Numerical Examplep. 567
Logit versus Probitp. 567
Comparing Logit and Probit Estimatesp. 568
The Marginal Effect of a Unit Change in the Value of a Regressorp. 569
The Probit Model: Example 16.5p. 569
The Tobit Modelp. 570
Summary and Conclusionsp. 575
Exercisesp. 576
Questionsp. 576
Problemsp. 578
Dynamic Econometric Model: Autoregressive and Distributed-Lag Modelsp. 584
The Role of "Time," or "Lag," in Economicsp. 585
The Reasons for Lagsp. 589
Estimation of Distributed-Lag Modelsp. 590
Ad Hoc Estimation of Distributed-Lag Modelsp. 590
The Koyck Approach to Distributed-Lag Modelsp. 592
The Median Lagp. 595
The Mean Lagp. 595
Rationalization of the Koyck Model: The Adaptive Expectations Modelp. 596
Another Rationalization of the Koyck Model: The Stock Adjustment, or Partial Adjustment, Modelp. 599
Combination of Adaptive Expectations and Partial Adjustment Modelsp. 601
Estimation of Autoregressive Modelsp. 602
The Method of Instrumental Variables (IV)p. 604
Detecting Autocorrelation in Autoregressive Models: Durbin h Testp. 605
A Numerical Example: The Demand for Money in Indiap. 607
Illustrative Examplesp. 609
Example 17.7: The Fed and the Real Rate of Interestp. 609
Example 17.8: The Short- and Long-Run Aggregate Consumption Functions for the United States, 1946-1972p. 611
The Almon Approach to Distributed-Lag Models: The Almon or Polynomial Distributed Lag (PDL)p. 612
Causality in Economics: The Granger Testp. 620
The Granger Testp. 620
Empirical Resultsp. 622
Summary and Conclusionsp. 624
Exercisesp. 624
Questionsp. 624
Problemsp. 630
Simultaneous-Equation Models
Simultaneous-Equation Modelsp. 635
The Nature of Simultaneous-Equation Modelsp. 635
Examples of Simultaneous-Equation Modelsp. 636
Example 18.1: Demand-and-Supply Modelp. 636
Example 18.2: Keynesian Model of Income Determinationp. 638
Example 18.3: Wage-Price Modelsp. 639
Example 18.4: The IS Model of Macroeconomicsp. 639
Example 18.5: The LM Modelp. 640
Example 18.6: Econometric Modelsp. 641
The Simultaneous-Equation Bias: Inconsistency of OLS Estimatorsp. 642
The Simultaneous-Equation Bias: A Numerical Examplep. 645
Summary and Conclusionsp. 647
Exercisesp. 648
Questionsp. 648
Problemsp. 651
The Identification Problemp. 653
Notations and Definitionsp. 653
The Identification Problemp. 657
Underidentificationp. 657
Just, or Exact, Identificationp. 660
Overidentificationp. 663
Rules for Identificationp. 664
The Order Condition of Identifiabilityp. 665
The Rank Condition of Identifiabilityp. 666
A Test of Simultaneityp. 669
Hausman Specification Testp. 670
Example 19.5: Pindyck-Rubinfeld Model of Public Spendingp. 671
Tests for Exogeneityp. 672
A Note on Causality and Exogeneityp. 673
Summary and Conclusionsp. 673
Exercisesp. 674
Simultaneous-Equation Methodsp. 678
Approaches to Estimationp. 678
Recursive Models and Ordinary Least Squaresp. 680
Estimation of a Just Identified Equation: The Method of Indirect Least Squares (ILS)p. 682
An Illustrative Examplep. 683
Properties of ILS Estimatorsp. 686
Estimation of an Overidentified Equation: The Method of Two-Stage Least Squares (2SLS)p. 686
2SLS: A Numerical Examplep. 690
Illustrative Examplesp. 693
Example 20.1: Advertising, Concentration, and Price Marginsp. 693
Example 20.2: Klein's Model Ip. 694
Example 20.3: The Capital Asset Pricing Model Expressed as a Recursive Systemp. 694
Example 20.4: Revised Form of St. Louis Modelp. 697
Summary and Conclusionsp. 699
Exercisesp. 700
Questionsp. 700
Problemsp. 703
Appendix 20Ap. 704
Bias in the Indirect Least-Squares Estimatorsp. 704
Estimation of Standard Errors of 2SLS Estimatorsp. 705
Time Series Econometrics
Time Series Econometrics I: Stationarity, Unit Roots, and Cointegrationp. 709
A Look at Selected U.S. Economic Time Seriesp. 710
Stationary Stochastic Processp. 710
Test of Stationarity Based on Correlogramp. 714
The Unit Root Test of Stationarityp. 718
Is the U.S. GDP Time Series Stationary?p. 720
Is the First-Differenced GDP Series Stationary?p. 721
Trend-Stationary (TS) and Difference-Stationary (DS) Stochastic Processp. 722
Spurious Regressionp. 724
Cointegrationp. 725
Engle-Granger (EG) or Augmented Engle-Granger (AEG) Testp. 726
Cointegrating Regression Durbin-Watson (CRDW) Testp. 727
Cointegration and Error Correction Mechanism (ECM)p. 728
Summary and Conclusionsp. 729
Exercisesp. 730
Questionsp. 730
Problemsp. 731
Appendix 21Ap. 732
A Random Walk Modelp. 732
Time Series Econometrics II: Forecasting with ARIMA and VAR Modelsp. 734
Approaches to Economic Forecastingp. 734
AR, MA, and ARIMA Modeling of Time Series Datap. 736
An Autoregressive (AR) Processp. 736
A Moving Average (MA) Processp. 737
An Autoregressive and Moving Average (ARMA) Processp. 737
An Autoregressive Integrated Moving Average (ARIMA) Processp. 737
The Box-Jenkins (BJ) Methodologyp. 738
Identificationp. 739
Estimation of the ARIMA Modelp. 742
Diagnostic Checkingp. 743
Forecastingp. 744
Further Aspects of the BJ Methodologyp. 745
Vector Autoregression (VAR)p. 746
Estimation of VARp. 746
Forecasting with VARp. 747
Some Problems with VAR Modelingp. 747
An Application of VAR: A VAR Model of the Texas Economyp. 750
Summary and Conclusionsp. 752
Exercisesp. 753
Questionsp. 753
Problemsp. 753
A Review of Some Statistical Conceptsp. 755
Rudiments of Matrix Algebrap. 791
A List of Statistical Computer Packagesp. 804
Statistical Tablesp. 807
Areas under the Standardized Normal Distributionp. 808
Percentage Points of the t Distributionp. 809
Upper Percentage Points of the F Distributionp. 810
Upper Percentage Points of the X2 Distributionp. 816
Durbin-Watson d Statistic: Significant Points of dL and dU at 0.05 and 0.01 Levels of Significancep. 818
Critical Values of Runs in the Runs Testp. 822
Selected Bibliographyp. 824
Name Indexp. 827
Subject Indexp. 831
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