000 | 00000cam u2200205 a 4500 | |

001 | 000000715471 | |

005 | 20200409094525 | |

008 | 000509s2000 njua b 001 0 eng | |

010 | ▼a 00034665 | |

020 | ▼a 0691010188 (alk. paper) | |

040 | ▼a DLC ▼c DLC ▼d C#P ▼d 211009 | |

049 | 1 | ▼l 111192135 |

050 | 0 0 | ▼a HB139 ▼b .H39 2000 |

082 | 0 0 | ▼a 330/.01/5195 ▼2 23 |

084 | ▼a 330.015195 ▼2 DDCK | |

090 | ▼a 330.015195 ▼b H413e | |

100 | 1 | ▼a Hayashi, Fumio. |

245 | 1 0 | ▼a Econometrics / ▼c Fumio Hayashi. |

260 | ▼a Princeton, N.J. : ▼b Princeton University Press, ▼c c2000. | |

300 | ▼a xxiii, 683 p. : ▼b ill. ; ▼c 27 cm. | |

504 | ▼a Includes bibliographical references and index. | |

650 | 0 | ▼a Econometrics. |

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### Contents information

#### Table of Contents

CONTENTS List of Figures = xvii Preface = xix 1 Finite-Sample Properties of OLS = 3 1.1 The Classical Linear Regression Model = 3 The Linearity Assumption = 4 Matrix Notation = 6 The Strict Exogeneity Assumption = 7 Implications of Strict Exogeneity = 8 Strict Exogeneity in Time-Series Models = 9 Other Assumptions of the Model = 10 The Classical Regression Model for Random Samples = 12 "Fixed" Regressors = 13 1.2 The Algebra of Least Squares = 15 OLS Minimizes the Sum of Squared Residuals = 15 Normal Equations = 16 Two Expressions for the OLS Estimator = 18 More Concepts and Algebra = 18 Influential Analysis (optional) = 21 A Note on the Computation of OLS Estimates = 23 1.3 Finite-Sample Properties of OLS = 27 Finite-Sample Distribution of b = 27 Finite-Sample Properties of s2 = 30 Estimate of Var(b｜X) = 31 1.4 Hypothesis Testing under Normality = 33 Normally Distributed Error Terms = 33 Testing Hypotheses about Individual Regression Coefficients = 35 Decision Rule for the t-Test = 37 Confidence Interval = 38 p-Value = 38 Linear Hypotheses = 39 The F-Test = 40 A More Convenient Expression for F = 42 t versus F = 43 An Example of a Test Statistic Whose Distribution Depends on Ⅹ = 45 1.5 Relation to Maximum Likelihood = 47 The Maximum Likelihood Principle = 47 Conditional versus Unconditional Likelihood = 47 The Log Likelihood for the Regression Model = 48 ML via Concentrated Likelihood = 48 Cramer-Rao Bound for the Classical Regression Model = 49 The F-Test as a Likelihood Ratio Test = 52 Quasi-Maximum Likelihood = 53 1.6 Generalized Least Squares (GLS) = 54 Consequence of Relaxing Assumption 1.4 = 55 Efficient Estimation with Known Ⅴ = 55 A Special Case : Weighted Least Squares (WLS) = 58 Limiting Nature of GLS = 58 1.7 Application : Returns to Scale in Electricity Supply = 60 The Electricity Supply Industry = 60 The Data = 60 Why Do We Need Econometrics? = 61 The Cobb-Douglas Technology = 62 How Do We Know Things Are Cobb-Douglas? 63 Are the OLS Assumptions Satisfied? = 64 Restricted Least Squares = 65 Testing the Homogeneity of the Cost Function = 65 Detour : A Cautionary Note on R2 = 67 Testing Constant Returns to Scale = 67 Importance of Plotting Residuals = 68 Subsequent Developments = 68 Problem Set = 71 Answers to Selected Questions = 84 2 Large-Sample Theory = 88 2.1 Review of Limit Theorems for Sequences of Random Variables = 88 Various Modes of Convergence = 89 Three Useful Results = 92 Viewing Estimators as Sequences of Random Variables = 94 Laws of Large Numbers and Central Limit Theorems = 95 2.2 Fundamental Concepts in Time-Series Analysis = 97 Need for Ergodic Stationarity = 97 Various Classes of Stochastic Processes = 98 Different Formulation of Lack of Serial Dependence = 106 The CLT for Ergodic Stationary Martingale Differences Sequences = 106 2.3 Large-Sample Distribution of the OLS Estimator = 109 The Model = 109 Asymptotic Distribution of the OLS Estimator = 113 s2 Is Consistent = 115 2.4 Hypothesis Testing = 117 Testing Linear Hypotheses = 117 The Test Is Consistent = 119 Asymptotic Power = 120 Testing Nonlinear Hypotheses = 121 2.5 Estimating E( ?i 2 xi xi ) Consistently = 123 Using Residuals for the Errors = 123 Data Matrix Representation of S = 125 Finite-Sample Considerations = 125 2.6 Implications of Conditional Homoskedasticity = 126 Conditional versus Unconditional Homoskedasticity = 126 Reduction to Finite-Sample Formulas = 127 Large-Sample Distribution of t and F Statistics = 128 Variations of Asymptotic Tests under Conditional Homoskedasticity = 129 2.7 Testing Conditional Homoskedasticity = 131 2.8 Estimation with Parameterized Conditional Heteroskedasticity(optional) = 133 The Functional Form = 133 WLS with Known α = 134 Regression of ei 2 on zi Provides a Consistent Estimate of α = 135 WLS with Estimated α = 136 OLS versus WLS = 137 2.9 Least Squares Projection = 137 Optimally Predicting the Value of the Dependent Variable = 138 Best Linear Predictor = 139 OLS Consistently Estimates the Projection Coefficients = 140 2.10 Testing for Serial Correlation = 141 Box-Pierce and Ljung-Box = 142 Sample Autocorrelations Calculated from Residuals = 144 Testing with Predetermined, but Not Strictly Exogenous, Regressors = 146 An Auxiliary Regression-Based Test = 147 2.11 Application : Rational Expectations Econometrics = 150 The Efficient Market Hypotheses = 150 Testable Implications = 152 Testing for Serial Correlation = 153 Is the Nominal Interest Rate the Optimal Predictor? = 156 Rt Is Not Strictly Exogenous = 158 Subsequent Developments = 159 2.12 Time Regressions = 160 The Asymptotic Distribution of the OLS Estimator = 161 Hypothesis Testing for Time Regressions = 163 Appendix 2.A : Asymptotics with Fixed Regressors = 164 Appendix 2.B : Proof of Proposition 2.10 = 165 Problem Set = 168 Answers to Selected Questions = 183 3 Single-Equation GMM = 186 3.1 Endogeneity Bias : Working's Example = 187 A Simultaneous Equations Model of Market Equilibrium = 187 Endogeneity Bias = 188 Observable Supply Shifters = 189 3.2 More Examples = 193 A Simple Macroeconometric Model = 193 Errors-in-Variables = 194 Production Function = 196 3.3 The General Formulation = 198 Regressors and Instruments = 198 Identification = 200 Order Condition for Identification = 202 The Assumption for Asymptotic Normality = 202 3.4 Generalized Method of Moments Defined = 204 Method of Moments = 205 Generalized Method of Moments = 206 Sampling Error = 207 3.5 Large-Sample Properties of GMM = 208 Asymptotic Distribution of the GMM Estimator = 209 Estimation of Error Variance = 210 Hypothesis Testing = 211 Estimation of S = 212 Efficient GMM Estimator = 212 Asymptotic Power = 214 Small-Sample Properties = 215 3.6 Testing Overidentifying Restrictions = 217 Testing Subsets of Orthogonality Conditions = 218 3.7 Hypothesis Testing by the Likelihood-Ratio Principle = 222 The LR Statistic for the Regression Model = 223 Variable Addition Test(optional) = 224 3.8 Implications of Conditional Homoskedasticity = 225 Efficient GMM Becomes 2SLS = 226 J Becomes Sargan's Statistic = 227 Small-Sample Properties of 2SLS = 229 Alternative Derivations of 2SLS = 229 When Regressors Are Predetermined = 231 Testing a Subset of Orthogonality Conditions = 232 Testing Conditional Homoskedasticity = 234 Testing for Serial Correlation = 234 3.9 Application : Returns from Schooling = 236 The NLS-Y Data = 236 The Semi-Log Wage Equation = 237 Omitted Variable Bias = 238 IQ as the Measure of Ability = 239 Errors-in-Variables = 239 2SLS to Correct for the Bias = 242 Subsequent Developments = 243 Problem Set = 244 Answers to Selected Questions = 254 4 Multiple-Equation GMM = 258 4.1 The Multiple-Equation Model = 259 Linearity = 259 Stationarity and Ergodicity = 260 Orthogonality Conditions = 261 Identification = 262 The Assumption for Asymptotic Normality = 264 Connection to the "Complete" System of Simultaneous Equations = 265 4.2 Multiple-Equation GMM Defined = 265 4.3 Large-Sample Theory = 268 4.4 Single-Equation versus Multiple-Equation Estimation = 271 When Are They "Equivalent"? = 272 Joint Estimation Can Be Hazardous = 273 4.5 Special Cases of Multiple-Equation GMM : FIVE, 3SLS, and SUR = 274 Conditional Homoskedasticity = 274 Full-Information Instrumental Variables Efficient(FIVE) = 275 Three-Stage Least Squares(3SLS) = 276 Seemingly Unrelated Regressions(SUR) = 279 SUR versus OLS = 281 4.6 Common Coefficients = 286 The Model with Common Coefficients = 286 The GMM Estimator = 287 Imposing Conditional Homoskedasticity = 288 Pooled OLS = 290 Beautifying the Formulas = 292 The Restriction That Isn't = 293 4.7 Application : Interrelated Factor Demands = 296 The Translog Cost Function = 296 Factor Shares = 297 Substitution Elasticities = 298 Properties of Cost Functions = 299 Stochastic Specifications = 300 The Nature of Restrictions = 301 Multivariate Regression Subject to Cross-Equation Restrictions = 302 Which Equation to Delete? = 304 Results = 305 Problem Set = 308 Answers to Selected Questions = 320 5 Panel Data = 323 5.1 The Error-Components Model = 324 Error Components = 324 Group Means = 327 A Reparameterization = 327 5.2 The Fixed-Effects Estimator = 330 The Formula = 330 Large-Sample Properties = 331 Digression : When ηi Is Spherical = 333 Random Effects versus Fixed Effects = 334 Relaxing Conditional Homoskedasticity = 335 5.3 Unbalanced Panels(optional) = 337 "Zeroing Out" Missing Observations = 338 Zeroing Out versus Compression = 339 No Selectivity Bias = 340 5.4 Application : International Differences in Growth Rates = 342 Derivation of the Estimation Equation = 342 Appending the Error Term = 343 Treatment of αi = 344 Consistent Estimation of Speed of Convergence = 345 Appendix 5.A : Distribution of Hausman Statistic = 346 Problem Set = 349 Answers to Selected Questions = 363 6 Serial Correlation = 365 6.1 Modeling Serial Correlation : Linear Processes = 365 MA(q) = 366 MA(∞) as a Mean Square Limit = 366 Filters = 369 Inverting Lag Polynomials = 372 6.2 ARMA Processes = 375 AR(1) and Its MA(∞) Representation = 376 Autocovariances of AR(1) = 378 AR(p) and Its MA(∞) Representation = 378 ARMA(p, q) = 380 ARMA(p, q) with Common Roots = 382 Invertibility = 383 Autocovariance-Generating Function and the Spectrum = 383 6.3 Vector Processes = 387 6.4 Estimating Autoregressions = 392 Estimation of AR(1) = 392 Estimation of AR(p) = 393 Choice of Lag Length = 394 Estimation of VARs = 397 Estimation of ARMA(p, q) = 398 6.5 Asymptotics for Sample Means of Serially Correlated Processes = 400 LLN for Covariance-Stationary Processes = 401 Two Central Limit Theorems = 402 Multivariate Extension = 404 6.6 Incorporating Serial Correlation in GMM = 406 The Model and Asymptotic Results = 406 Estimating S When Autocovariances Vanish after Finite Lags = 407 Using Kernels to Estimate S = 408 VARHAC = 410 6.7 Estimation under Conditional Homoskedasticity(Optional) = 413 Kernel-Based Estimation of S under Conditional Homoskedasticity = 413 Data Matrix Representation of Estimated Long-Run Variance = 414 Relation to GLS = 415 6.8 Application : Forward Exchange Rates as Optimal Predictors = 418 The Market Efficiency Hypothesis = 419 Testing Whether the Unconditional Mean Is Zero = 420 Regression Tests = 423 Problem Set = 428 Answers to Selected Questions = 441 7 Extremum Estimators = 445 7.1 Extremum Estimators = 446 "Measurability" of = 446 Two Classes of Extremum Estimators = 447 Maximum Likelihood(ML) = 448 Conditional Maximum Likelihood = 450 Invariance of ML = 452 Nonlinear Least Squares(NLS) = 453 Linear and Nonlinear GMM = 454 7.2 Consistency = 456 Two Consistency Theorems for Extremum Estimators = 456 Consistency of M-Estimators = 458 Concavity after Reparameterization = 461 Identification in NLS and ML = 462 Consistency of GMM = 467 7.3 Asymptotic Normality = 469 Asymptotic Normality of M-Estimators = 470 Consistent Asymptotic Variance Estimation = 473 Asymptotic Normality of Conditional ML = 474 Two Examples = 476 Asymptotic Normality of GMM = 478 GMM versus ML = 481 Expressing the Sampling Error in a Common Format = 483 7.4 Hypothesis Testing = 487 The Null Hypothesis = 487 The Working Assumptions = 489 The Wald Statistic = 489 The Lagrange Multiplier(LM) Statistic = 491 The Likelihood Ratio(LR) Statistic = 493 Summary of the Trinity = 494 7.5 Numerical Optimization = 497 Newton-Raphson = 497 Gauss-Newton = 498 Writing Newton-Raphson and Gauss-Newton in a Common Format = 498 Equations Nonlinear in Parameters Only = 499 Problem Set = 501 Answers to Selected Questions = 505 8 Examples of Maximum Likelihood = 507 8.1 Qualitative Response (QR) Models = 507 Score and Hessian for Observation t = 508 Consistency = 509 Asymptotic Normality = 510 8.2 Truncated Regression Models = 511 The Model = 511 Truncated Distributions = 512 The Likelihood Function = 513 Reparameterizing the Likelihood Function = 514 Verifying Consistency and Asymptotic Normality = 515 Recovering Original Parameters = 517 8.3 Censored Regression(Tobit) Models = 518 Tobit Likelihood Function = 518 Reparameterization = 519 8.4 Multivariate Regressions = 521 The Multivariate Regression Model Restated = 522 The Likelihood Function = 523 Maximizing the Likelihood Function = 524 Consistency and Asymptotic Normality = 525 8.5 FIML = 526 The Multiple-Equation Model with Common Instruments Restated = 526 The Complete System of Simultaneous Equations = 529 Relationship between ( Γ0 , B0 ) and δ0 = 530 The FIML Likelihood Function = 531 The FIML Concentrated Likelihood Function = 532 Testing Overidentifying Restrictions = 533 Properties of the FIML Estimator = 533 ML Estimation of the SUR Model = 535 8.6 LIML = 538 LIML Defined = 538 Computation of LIML = 540 LIML versus 2SLS = 542 8.7 Serially Correlated Observations = 543 Two Questions = 543 Unconditional ML for Dependent Observations = 545 ML Estimation of AR(1) Processes = 546 Conditional ML Estimation of AR(1) Processes = 547 Conditional ML Estimation of AR(p) and VAR(p) Processes = 549 Problem Set = 551 9 Unit-Root Econometrics = 557 9.1 Modeling Trends = 557 Integrated Processes = 558 Why Is It Important to Know if the Process Is Ⅰ(1)? = 560 Which Should Be Taken as the Null, Ⅰ(0) or Ⅰ(1)? = 562 Other Approaches to Modeling Trends = 563 9.2 Tools for Unit-Root Econometrics = 563 Linear Ⅰ(0) Processes = 563 Approximating Ⅰ(1) by a Random Walk = 564 Relation to ARMA Models = 566 The Wiener Process = 567 A Useful Lemma = 570 9.3 Dickey-Fuller Tests = 573 The AR(1) Model = 573 Deriving the Limiting Distribution under the Ⅰ(1) Null = 574 Incorporating the Intercept = 577 Incorporating Time Trend = 581 9.4 Augmented Dickey-Fuller Tests = 585 The Augmented Autoregression = 585 Limiting Distribution of the OLS Estimator = 586 Deriving Test Statistics = 590 Testing Hypotheses aboutζ = 591 What to Do When p Is Unknown? = 592 A Suggestion for the Choice of Pm ax (T) = 594 Including the Intercept in the Regression = 595 Incorporating Time Trend = 597 Summary of the DF and ADF Tests and Other Unit-Root Tests = 599 9.5 Which Unit-Root Test to Use? = 601 Local-to-Unity Asymptotics = 602 Small-Sample Properties = 602 9.6 Application : Purchasing Power Parity = 603 The Embarrassing Resiliency of the Random Walk Model? = 604 Problem Set = 605 Answers to Selected Questions = 619 10 Cointegration = 623 10.1 Cointegrated Systems = 624 Linear Vector Ⅰ(0) and Ⅰ(1) Processes = 624 The Beveridge-Nelson Decomposition = 627 Cointegration Defined = 629 10.2 Alternative Representations of Cointegrated Systems = 633 Phillips's Triangular Representation = 633 VAR and Cointegration = 636 The Vector Error-Correction Model(VECM) = 638 Johansen's ML Procedure = 640 10.3 Testing the Null of No Cointegration = 643 Spurious Regressions = 643 The Residual-Based Test for Cointegration = 644 Testing the Null of Cointegration = 649 10.4 Inference on Cointegrating Vectors = 650 The SOLS Estimator = 650 The Bivariate Example = 652 Continuing with the Bivariate Example = 653 Allowing for Serial Correlation = 654 General Case = 657 Other Estimators and Finite-Sample Properties = 658 10.5 Application : The Demand for Money in the United States = 659 The Data = 660 (m-p, y, R) as a Cointegrated System = 660 DOLS = 662 Unstable Money Demand? = 663 Problem Set = 665 Appendix A : Partitioned Matrices and Kronecker Products = 670 Addition and Multiplication of Partitioned Matrices = 671 Inverting Partitioned Matrices = 672 Index = 675