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 |
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