Preface p. xxi
Introduction p. 1
Single-Equation Regression Models
The Nature of Regression Analysis p. 15
Historical Origin of the Term "Regression" p. 15
The Modern Interpretation of Regression p. 16
Examples p. 16
Statistical vs. Deterministic Relationships p. 19
Regression vs. Causation p. 20
Regression vs. Correlation p. 21
Terminology and Notation p. 22
The Nature and Sources of Data for Econometric Analysis p. 23
Types of Data p. 23
The Sources of Data p. 24
The Accuracy of Data p. 26
Summary and Conclusions p. 27
Exercises p. 28
Appendix 1A p. 29
Sources of Economic Data p. 29
Sources of Financial Data p. 31
Two-Variable Regression Analysis: Some Basic Ideas p. 32
A Hypothetical Example p. 32
The Concept of Population Regression Function (PRF) p. 36
The Meaning of the Term "Linear" p. 36
Linearity in the Variables p. 37
Linearity in the Parameters p. 37
Stochastic Specification of PRF p. 38
The Significance of the Stochastic Disturbance Term p. 39
The Sample Regression Function (SRF) p. 41
Summary and Conclusions p. 45
Exercises p. 45
Two-Variable Regression Model: The Problem of Estimation p. 52
The Method of Ordinary Least Squares p. 52
The Classical Linear Regression Model: The Assumptions Underlying the Method of Least Squares p. 59
How Realistic Are These Assumptions? p. 68
Precision or Standard Errors of Least-Squares Estimates p. 69
Properties of Least-Squares Estimators: The Gauss-Markov Theorem p. 72
The Coefficient of Determination r2: A Measure of "Goodness of Fit" p. 74
A Numerical Example p. 80
Illustrative Examples p. 83
Coffee Consumption in the United States, 1970-1980 p. 83
Keynesian Consumption Function for the United States, 1980-1991 p. 84
Computer Output for the Coffee Demand Function p. 85
A Note on Monte Carlo Experiments p. 85
Summary and Conclusions p. 86
Exercises p. 87
Questions p. 87
Problems p. 89
Appendix 3A p. 94
Derivation of Least-Squares Estimates p. 94
Linearity and Unbiasedness Properties of Least-Squares Estimators p. 94
Variances and Standard Errors of Least-Squares Estimators p. 95
Covariance between B1 and B2 p. 96
The Least-Squares Estimator of o2 p. 96
Minimum-Variance Property of Least-Squares Estimators p. 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 ui p. 101
The Normality Assumption p. 102
Properties of OLS Estimators under the Normality Assumption p. 104
The Method of Maximum Likelihood (ML) p. 107
Probability Distributions Related to the Normal Distribution: The t, Chi-square (X2), and F Distributions p. 107
Summary and Conclusions p. 109
Appendix 4A p. 110
Maximum Likelihood Estimation of Two-Variable Regression Model p. 110
Maximum Likelihood Estimation of the Consumption-Income Example p. 113
Appendix 4A Exercises p. 113
Two-Variable Regression: Interval Estimation and Hypothesis Testing p. 115
Statistical Prerequisites p. 115
Interval Estimation: Some Basic Ideas p. 116
Confidence Intervals for Regression Coefficients B1 and B2 p. 117
Confidence Interval for B2 p. 117
Confidence Interval for B1 p. 119
Confidence Interval for B1 and B2 Simultaneously p. 120
Confidence Interval for o2 p. 120
Hypothesis Testing: General Comments p. 121
Hypothesis Testing: The Confidence-Interval Approach p. 122
Two-Sided or Two-Tail Test p. 122
One-Sided or One-Tail Test p. 124
Hypothesis Testing: The Test-of-Significance Approach p. 124
Testing the Significance of Regression Coefficients: The t-Test p. 124
Testing the Significance of o2: the X2 Test p. 128
Hypothesis Testing: Some Practical Aspects p. 129
The Meaning of "Accepting" or "Rejecting" a Hypothesis p. 129
The "Zero" Null Hypothesis and the "2-t" Rule of Thumb p. 129
Forming the Null and Alternative Hypotheses p. 130
Choosing a, the Level of Significance p. 131
The Exact Level of Significance: The p Value p. 132
Statistical Significance versus Practical Significance p. 133
The Choice between Confidence-Interval and Test-of-Significance Approaches to Hypothesis Testing p. 134
Regression Analysis and Analysis of Variance p. 134
Application of Regression Analysis: The Problem of Prediction p. 137
Mean Prediction p. 137
Individual Prediction p. 138
Reporting the Results of Regression Analysis p. 140
Evaluating the Results of Regression Analysis p. 140
Normality Test p. 141
Other Tests of Model Adequacy p. 144
Summary and Conclusions p. 144
Exercises p. 145
Questions p. 145
Problems p. 147
Appendix 5A p. 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 Prediction p. 153
Variance of Individual Prediction p. 153
Extensions of the Two-Variable Linear Regression Model p. 155
Regression through the Origin p. 155
r2 for Regression-through-Origin Model An Illustrative Example: The Characteristic Line of Portfolio Theory p. 159
Scaling and Units of Measurement p. 161
A Numerical Example: The Relationship between GPDI and GNP, United States, 1974-1983 p. 163
A Word about Interpretation p. 164
Functional Forms of Regression Models p. 165
How to Measure Elasticity: The Log-Linear Model p. 165
An Illustrative Example: The Coffee Demand Function Revisited p. 167
Semilog Models: Log-Lin and Lin-Log Models p. 169
How to Measure the Growth Rate: The Log-Lin Model p. 169
The Lin-Log Model p. 172
Reciprocal Models p. 173
An Illustrative Example: The Phillips Curve for the United Kingdom, 1950-1966 p. 176
Summary of Functional Forms p. 176
A Note on the Nature of the Stochastic Error Term: Additive versus Multiplicative Stochastic Error Term p. 178
Summary and Conclusions p. 179
Exercises p. 180
Questions p. 180
Problems p. 183
Appendix 6A p. 186
Derivation of Least-Squares Estimators for Regression through the Origin p. 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 Estimation p. 191
The Three-Variable Model: Notation and Assumptions p. 192
Interpretation of Multiple Regression Equation p. 194
The Meaning of Partial Regression Coefficients p. 195
OLS and ML Estimation of the Partial Regression Coefficients p. 197
OLS Estimators p. 197
Variances and Standard Errors of OLS Estimators p. 198
Properties of OLS Estimators p. 199
Maximum Likelihood Estimators p. 201
The Multiple Coefficient of Determination R2 and the Multiple Coefficient of Correlation R p. 201
Example 7.1: The Expectations-Augmented Phillips Curve for the United States, 1970-1982 p. 203
Simple Regression in the Context of Multiple Regression: Introduction to Specification Bias p. 204
R2 and the Adjusted R2 p. 207
Comparing Two R2 Values p. 209
Example 7.2: Coffee Demand Function Revisited p. 210
The "Game" of Maximizing R2 p. 211
Partial Correlation Coefficients p. 211
Explanation of Simple and Partial Correlation Coefficients p. 211
Interpretation of Simple and Partial Correlation Coefficients p. 213
Example 7.3: The Cobb-Douglas Production Function: More on Functional Form p. 214
Polynomial Regression Models p. 217
Example 7.4: Estimating the Total Cost Function p. 218
Empirical Results p. 220
Summary and Conclusions p. 221
Exercises p. 221
Questions p. 221
Problems p. 224
Appendix 7A p. 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 Model p. 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 Inference p. 238
The Normality Assumption Once Again p. 238
Example 8.1: U.S. Personal Consumption and Personal Disposal Income Relation, 1956-1970 p. 239
Hypothesis Testing in Multiple Regression: General Comments p. 242
Hypothesis Testing about Individual Partial Regression Coefficients p. 242
Testing the Overall Significance of the Sample Regression p. 244
The Analysis of Variance Approach to Testing the Overall Significance of an Observed Multiple Regression: The F Test p. 245
An Important Relationship between R2 and F p. 248
The "Incremental," or "Marginal," Contribution of an Explanatory Variable p. 250
Testing the Equality of Two Regression Coefficients p. 254
Example 8.2: The Cubic Cost Function Revisited p. 255
Restricted Least Squares: Testing Linear Equality Restrictions p. 256
The t Test Approach p. 256
The F Test Approach: Restricted Least Squares p. 257
Example 8.3: The Cobb-Douglas Production Function for Taiwanese Agricultural Sector, 1958-1972 p. 259
General F Testing p. 260
Comparing Two Regressions: Testing for Structural Stability of Regression Models p. 262
Testing the Functional Form of Regression: Choosing between Linear and Log-Linear Regression Models p. 265
Example 8.5: The Demand for Roses p. 266
Prediction with Multiple Regression p. 267
The Troika of Hypothesis Tests: The Likelihood Ratio (LR), Wald (W), and Lagrange Multiplier (LM) Tests p. 268
Summary and Conclusions p. 269
The Road Ahead p. 269
Exercises p. 270
Questions p. 270
Problems p. 273
Appendix 8A p. 280
Likelihood Ratio (LR) Test p. 280
The Matrix Approach to Linear Regression Model p. 282
The k-Variable Linear Regression Model p. 282
Assumptions of the Classical Linear Regression Model in Matrix Notation p. 284
OLS Estimation p. 287
An Illustration p. 289
Variance-Covariance Matrix of B p. 290
Properties of OLS Vector B p. 291
The Coefficient of Determination R2 in Matrix Notation p. 292
The Correlation Matrix p. 292
Hypothesis Testing about Individual Regression Coefficients in Matrix Notation p. 293
Testing the Overall Significance of Regression: Analysis of Variance in Matrix Notation p. 294
Testing Linear Restrictions: General F Testing Using Matrix Notation p. 295
Prediction Using Multiple Regression: Matrix Formulation p. 296
Mean Prediction p. 296
Individual Prediction p. 296
Variance of Mean Prediction p. 297
Variance of Individual Prediction p. 298
Summary of the Matrix Approach: An Illustrative Example p. 298
Summary and Conclusions p. 303
Exercises p. 304
Appendix 9A p. 309
Derivation of k Normal or Simultaneous Equations p. 309
Matrix Derivation of Normal Equations p. 310
Variance-Covariance Matrix of B p. 310
Blue Property of OLS Estimators p. 311
Relaxing the Assumptions of the Classical Model
Multicollinearity and Micronumerosity p. 319
The Nature of Multicollinearity p. 320
Estimation in the Presence of Perfect Multicollinearity p. 323
Estimation in the Presence of "High" but "Imperfect" Multicollinearity p. 325
Multicollinearity: Much Ado about Nothing? Theoretical Consequences of Multicollinearity p. 325
Practical Consequences of Multicollinearity p. 327
Large Variances and Covariances of OLS Estimators p. 328
Wider Confidence Intervals p. 329
"Insignificant" t Ratios p. 330
A High R2 but Few Significant t Ratios p. 330
Sensitivity of OLS Estimators and Their Standard Errors to Small Changes in Data p. 331
Consequences of Micronumerosity p. 332
An Illustrative Example: Consumption Expenditure in Relation to Income and Wealth p. 332
Detection of Multicollinearity p. 335
Remedial Measures p. 339
Is Multicollinearity Necessarily Bad? Maybe Not If the Objective Is Prediction Only p. 344
Summary and Conclusions p. 345
Exercises p. 346
Questions p. 346
Problems p. 351
Heteroscedasticity p. 355
The Nature of Heteroscedasticity p. 355
OLS Estimation in the Presence of Heteroscedasticity p. 359
The Method of Generalized Least Squares (GLS) p. 362
Difference between OLS and GLS p. 364
Consequences of Using OLS in the Presence of Heteroscedasticity p. 365
OLS Estimation Allowing for Heteroscedasticity p. 365
OLS Estimation Disregarding Heteroscedasticity p. 366
Detection of Heteroscedasticity p. 367
Informal Methods p. 368
Formal Methods p. 369
Remedial Measures p. 381
When oi2 Is Known: The Method of Weighted Least Squares p. 381
When o12 Is Not Known p. 382
A Concluding Example p. 387
Summary and Conclusions p. 389
Exercises p. 390
Questions p. 390
Problems p. 392
Appendix 11A p. 398
Proof of Equation (11.2.2) p. 398
The Method of Weighted Least Squares p. 399
Autocorrelation p. 400
The Nature of the Problem p. 400
OLS Estimation in the Presence of Autocorrelation p. 406
The BLUE Estimator in the Presence of Autocorrelation p. 409
Consequences of Using OLS in the Presence of Autocorrelation p. 410
OLS Estimation Allowing for Autocorrelation p. 410
OLS Estimation Disregarding Autocorrelation p. 411
Detecting Autocorrelation p. 415
Graphical Method p. 415
The Runs Test p. 419
Durbin-Watson d Test p. 420
Additional Tests of Autocorrelation p. 425
Remedial Measures p. 426
When the Structure of Autocorrelation Is Known p. 427
When p Is Not Known p. 428
An Illustrative Example: The Relationship between Help-Wanted Index and the Unemployment Rate, United States: Comparison of the Methods p. 433
Autoregressive Conditional Heteroscedasticity (ARCH) Model p. 436
What to Do If ARCH Is Present? p. 438
A Word on the Durbin-Watson d Statistic and the ARCH Effect p. 438
Summary and Conclusions p. 439
Exercises p. 440
Questions p. 440
Problems p. 446
Appendix 12A p. 449
TSP Output of United States Wages (Y)-Productivity (X) Regression, 1960-1991 p. 449
Econometric Modeling I: Traditional Econometric Methodology p. 452
The Traditional View of Econometric Modeling: Average Economic Regression (AER) p. 452
Types of Specification Errors p. 455
Consequences of Specification Errors p. 456
Omitting a Relevant Variable (Underfitting a Model) p. 456
Inclusion of an Irrelevant Variable (Overfitting a Model) p. 458
Tests of Specification Errors p. 459
Detecting the Presence of Unnecessary Variables p. 460
Tests for Omitted Variables and Incorrect Functional Form p. 461
Errors of Measurement p. 467
Errors of Measurement in the Dependent Variable Y p. 468
Errors of Measurement in the Explanatory Variable X p. 469
An Example p. 470
Measurement Errors in the Dependent Variable Y Only p. 471
Errors of Measurement in X p. 472
Summary and Conclusions p. 472
Exercises p. 473
Questions p. 473
Problems p. 476
Appendix 13A p. 477
The Consequences of Including an Irrelevant Variable: The Unbiasedness Property p. 477
Proof of (13.5.10) p. 478
Econometric Modeling II: Alternative Econometric Methodologies p. 480
Learner's Approach to Model Selection p. 481
Hendry's Approach to Model Selection p. 485
Selected Diagnostic Tests: General Comments p. 486
Tests of Nonnested Hypothesis p. 487
The Discrimination Approach p. 487
The Discerning Approach p. 488
Summary and Conclusions p. 494
Exercises p. 494
Questions p. 494
Problems p. 495
Topics in Econometrics
Regression on Dummy Variables p. 499
The Nature of Dummy Variables p. 499
Example 15.1: Professor's Salary by Sex p. 500
Regression on One Quantitative Variable and One Qualitative Variable with Two Classes, or Categories p. 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 Classes p. 505
Regression on One Quantitative Variable and Two Qualitative Variables p. 507
Example 15.3: The Economics of "Moonlighting" p. 508
Testing for Structural Stability of Regression Models: Basic Ideas p. 509
Example 15.4: Savings and Income, United Kingdom, 1946-1963 p. 509
Comparing Two Regressions: The Dummy Variable Approach p. 512
Comparing Two Regressions: Further Illustration p. 514
Example 15.5: The Behavior of Unemployment and Unfilled Vacancies: Great Britain, 1958-1971 p. 514
Interaction Effects p. 516
The Use of Dummy Variables in Seasonal Analysis p. 517
Example 15.6: Profits-Sales Behavior in U.S. Manufacturing p. 517
Piecewise Linear Regression p. 519
Example 15.7: Total Cost in Relation to Output p. 521
The Use of Dummy Variables in Combining Time Series and Cross-Sectional Data p. 522
Pooled Regression: Pooling Time Series and Cross-Sectional Data p. 522
Example 15.8: Investment Functions for General Motors and Westinghouse Companies p. 524
Some Technical Aspects of Dummy Variable Technique p. 525
The Interpretation of Dummy Variables in Semilogarithmic Regressions p. 525
Example 15.9: Semilogarithmic Regression with Dummy Variable p. 525
Another Method of Avoiding the Dummy Variable Trap p. 526
Dummy Variables and Heteroscedasticity p. 527
Dummy Variables and Autocorrelation p. 527
Topics for Further Study p. 528
Summary and Conclusions p. 529
Exercises p. 530
Questions p. 530
Problems p. 535
Appendix 15A p. 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 Models p. 540
Dummy Dependent Variable p. 540
The Linear Probability Model (LPM) p. 541
Problems in Estimation of LPM p. 542
Nonnormality of the Disturbances ui p. 542
Heteroscedastic Variances of the Disturbances p. 543
Nonfulfillment of 0 [= E(Yi\X) [= 1 p. 544
Questionable Value of R2 as a Measure of Goodness of Fit p. 545
LPM: A Numerical Example p. 546
Applications of LPM p. 548
Example 16.1: Cohen-Rea-Lerman study p. 548
Example 16.2: Predicting a Bond Rating p. 551
Example 16.3: Predicting Bond Defaults p. 552
Alternatives to LPM p. 552
The Logit Model p. 554
Estimation of the Logit Model p. 556
The Logit Model: A Numerical Example p. 558
The Logit Model: Illustrative Examples p. 561
Example 16.4: "An Application of Logit Analysis to Prediction of Merger Targets" p. 561
Example 16.5: Predicting a Bond Rating p. 562
The Probit Model p. 563
The Probit Model: A Numerical Example p. 567
Logit versus Probit p. 567
Comparing Logit and Probit Estimates p. 568
The Marginal Effect of a Unit Change in the Value of a Regressor p. 569
The Probit Model: Example 16.5 p. 569
The Tobit Model p. 570
Summary and Conclusions p. 575
Exercises p. 576
Questions p. 576
Problems p. 578
Dynamic Econometric Model: Autoregressive and Distributed-Lag Models p. 584
The Role of "Time," or "Lag," in Economics p. 585
The Reasons for Lags p. 589
Estimation of Distributed-Lag Models p. 590
Ad Hoc Estimation of Distributed-Lag Models p. 590
The Koyck Approach to Distributed-Lag Models p. 592
The Median Lag p. 595
The Mean Lag p. 595
Rationalization of the Koyck Model: The Adaptive Expectations Model p. 596
Another Rationalization of the Koyck Model: The Stock Adjustment, or Partial Adjustment, Model p. 599
Combination of Adaptive Expectations and Partial Adjustment Models p. 601
Estimation of Autoregressive Models p. 602
The Method of Instrumental Variables (IV) p. 604
Detecting Autocorrelation in Autoregressive Models: Durbin h Test p. 605
A Numerical Example: The Demand for Money in India p. 607
Illustrative Examples p. 609
Example 17.7: The Fed and the Real Rate of Interest p. 609
Example 17.8: The Short- and Long-Run Aggregate Consumption Functions for the United States, 1946-1972 p. 611
The Almon Approach to Distributed-Lag Models: The Almon or Polynomial Distributed Lag (PDL) p. 612
Causality in Economics: The Granger Test p. 620
The Granger Test p. 620
Empirical Results p. 622
Summary and Conclusions p. 624
Exercises p. 624
Questions p. 624
Problems p. 630
Simultaneous-Equation Models
Simultaneous-Equation Models p. 635
The Nature of Simultaneous-Equation Models p. 635
Examples of Simultaneous-Equation Models p. 636
Example 18.1: Demand-and-Supply Model p. 636
Example 18.2: Keynesian Model of Income Determination p. 638
Example 18.3: Wage-Price Models p. 639
Example 18.4: The IS Model of Macroeconomics p. 639
Example 18.5: The LM Model p. 640
Example 18.6: Econometric Models p. 641
The Simultaneous-Equation Bias: Inconsistency of OLS Estimators p. 642
The Simultaneous-Equation Bias: A Numerical Example p. 645
Summary and Conclusions p. 647
Exercises p. 648
Questions p. 648
Problems p. 651
The Identification Problem p. 653
Notations and Definitions p. 653
The Identification Problem p. 657
Underidentification p. 657
Just, or Exact, Identification p. 660
Overidentification p. 663
Rules for Identification p. 664
The Order Condition of Identifiability p. 665
The Rank Condition of Identifiability p. 666
A Test of Simultaneity p. 669
Hausman Specification Test p. 670
Example 19.5: Pindyck-Rubinfeld Model of Public Spending p. 671
Tests for Exogeneity p. 672
A Note on Causality and Exogeneity p. 673
Summary and Conclusions p. 673
Exercises p. 674
Simultaneous-Equation Methods p. 678
Approaches to Estimation p. 678
Recursive Models and Ordinary Least Squares p. 680
Estimation of a Just Identified Equation: The Method of Indirect Least Squares (ILS) p. 682
An Illustrative Example p. 683
Properties of ILS Estimators p. 686
Estimation of an Overidentified Equation: The Method of Two-Stage Least Squares (2SLS) p. 686
2SLS: A Numerical Example p. 690
Illustrative Examples p. 693
Example 20.1: Advertising, Concentration, and Price Margins p. 693
Example 20.2: Klein's Model I p. 694
Example 20.3: The Capital Asset Pricing Model Expressed as a Recursive System p. 694
Example 20.4: Revised Form of St. Louis Model p. 697
Summary and Conclusions p. 699
Exercises p. 700
Questions p. 700
Problems p. 703
Appendix 20A p. 704
Bias in the Indirect Least-Squares Estimators p. 704
Estimation of Standard Errors of 2SLS Estimators p. 705
Time Series Econometrics
Time Series Econometrics I: Stationarity, Unit Roots, and Cointegration p. 709
A Look at Selected U.S. Economic Time Series p. 710
Stationary Stochastic Process p. 710
Test of Stationarity Based on Correlogram p. 714
The Unit Root Test of Stationarity p. 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 Process p. 722
Spurious Regression p. 724
Cointegration p. 725
Engle-Granger (EG) or Augmented Engle-Granger (AEG) Test p. 726
Cointegrating Regression Durbin-Watson (CRDW) Test p. 727
Cointegration and Error Correction Mechanism (ECM) p. 728
Summary and Conclusions p. 729
Exercises p. 730
Questions p. 730
Problems p. 731
Appendix 21A p. 732
A Random Walk Model p. 732
Time Series Econometrics II: Forecasting with ARIMA and VAR Models p. 734
Approaches to Economic Forecasting p. 734
AR, MA, and ARIMA Modeling of Time Series Data p. 736
An Autoregressive (AR) Process p. 736
A Moving Average (MA) Process p. 737
An Autoregressive and Moving Average (ARMA) Process p. 737
An Autoregressive Integrated Moving Average (ARIMA) Process p. 737
The Box-Jenkins (BJ) Methodology p. 738
Identification p. 739
Estimation of the ARIMA Model p. 742
Diagnostic Checking p. 743
Forecasting p. 744
Further Aspects of the BJ Methodology p. 745
Vector Autoregression (VAR) p. 746
Estimation of VAR p. 746
Forecasting with VAR p. 747
Some Problems with VAR Modeling p. 747
An Application of VAR: A VAR Model of the Texas Economy p. 750
Summary and Conclusions p. 752
Exercises p. 753
Questions p. 753
Problems p. 753
Appendixes
A Review of Some Statistical Concepts p. 755
Rudiments of Matrix Algebra p. 791
A List of Statistical Computer Packages p. 804
Statistical Tables p. 807
Areas under the Standardized Normal Distribution p. 808
Percentage Points of the t Distribution p. 809
Upper Percentage Points of the F Distribution p. 810
Upper Percentage Points of the X2 Distribution p. 816
Durbin-Watson d Statistic: Significant Points of dL and dU at 0.05 and 0.01 Levels of Significance p. 818
Critical Values of Runs in the Runs Test p. 822
Selected Bibliography p. 824
Indexes
Name Index p. 827
Subject Index p. 831