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دانلود کتاب Econometrics
دانلود کتاب اقتصاد سنجی
مشخصات کتاب
Econometrics
ویرایش:
نویسندگان: Fumio Hayashi
سری:
ISBN (شابک) : 0691010188, 9780691010182
ناشر: Princeton University Press
سال نشر: 2000
تعداد صفحات: 686
زبان: English
فرمت فایل : PDF (درصورت درخواست کاربر به PDF، EPUB یا AZW3 تبدیل می شود)
حجم فایل: 9 مگابایت
قیمت کتاب (تومان) : 47,000
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توضیحاتی در مورد کتاب اقتصاد سنجی
اقتصاد سنجی هایاشی وعده می دهد که ترکیب بزرگ بعدی اقتصاد سنجی مدرن باشد. سال اول Ph.D را معرفی می کند. دانشجویان به مطالب استاندارد اقتصاد سنجی فارغ التحصیلان از دیدگاه مدرن. تمام مطالب استاندارد لازم برای درک تکنیک های اصلی اقتصاد سنجی از حداقل مربعات معمولی از طریق هم انباشتگی را پوشش می دهد. این کتاب همچنین در توسعه تجزیه و تحلیل سری زمانی و مقطعی به طور کامل متمایز است و به خواننده چارچوبی واحد برای درک و یکپارچه‌سازی نتایج می‌دهد. تمام تکنیک‌های تخمینی که احتمالاً می‌توانند در دوره تحصیلات تکمیلی سال اول تدریس شوند، به جز حداکثر احتمال، به عنوان موارد خاص GMM (روش‌های کلی لحظه‌ها) تلقی می‌شوند. برآوردگرهای حداکثر احتمال برای انواع مدل ها (مانند پروبیت و توبیت) در فصلی جداگانه جمع آوری شده اند. این ترتیب دانش‌آموزان را قادر می‌سازد تا تکنیک‌های مختلف برآورد را به شیوه‌ای کارآمد بیاموزند. هشت فصل از ده فصل شامل یک کاربرد تجربی جدی است که از اقتصاد کار، سازمان صنعتی، مالی داخلی و بین‌المللی و اقتصاد کلان استخراج شده است. این تمرین‌های تجربی در پایان هر فصل، تجربه عملی را برای دانش‌آموزان در استفاده از تکنیک‌های پوشش داده شده در فصل فراهم می‌کند. این نمایشگاه دقیق است و در عین حال برای دانش‌آموزانی که دانش عملی جبر خطی بسیار ابتدایی و تئوری احتمالات را دارند قابل دسترس است. تمام نتایج به صورت گزاره بیان می‌شوند تا دانش‌آموزان بتوانند نکات بحث و همچنین شرایطی را که آن نتایج تحت آن است، ببینند. بیشتر گزاره ها در متن اثبات شده اند. برای کسانی که قصد دارند پایان نامه ای در موضوعات کاربردی بنویسند، کاربردهای تجربی کتاب راه خوبی برای یادگیری نحوه انجام تحقیقات تجربی است. برای افرادی که تمایل به تئوری دارند، درمان بدون سازش با تکنیک های پایه آمادگی خوبی برای دوره های تئوری پیشرفته تر است.
توضیحاتی درمورد کتاب به خارجی
Hayashi's Econometrics promises to be the next great synthesis of modern econometrics. It introduces first year Ph.D. students to standard graduate econometrics material from a modern perspective. It covers all the standard material necessary for understanding the principal techniques of econometrics from ordinary least squares through cointegration. The book is also distinctive in developing both time-series and cross-section analysis fully, giving the reader a unified framework for understanding and integrating results.Econometrics has many useful features and covers all the important topics in econometrics in a succinct manner. All the estimation techniques that could possibly be taught in a first-year graduate course, except maximum likelihood, are treated as special cases of GMM (generalized methods of moments). Maximum likelihood estimators for a variety of models (such as probit and tobit) are collected in a separate chapter. This arrangement enables students to learn various estimation techniques in an efficient manner. Eight of the ten chapters include a serious empirical application drawn from labor economics, industrial organization, domestic and international finance, and macroeconomics. These empirical exercises at the end of each chapter provide students a hands-on experience applying the techniques covered in the chapter. The exposition is rigorous yet accessible to students who have a working knowledge of very basic linear algebra and probability theory. All the results are stated as propositions, so that students can see the points of the discussion and also the conditions under which those results hold. Most propositions are proved in the text.For those who intend to write a thesis on applied topics, the empirical applications of the book are a good way to learn how to conduct empirical research. For the theoretically inclined, the no-compromise treatment of the basic techniques is a good preparation for more advanced theory courses.
فهرست مطالب
Cover ... 1 Copyright Page ... 2 Preface ... 3 Prerequisites ... 3 Organization of the Book ... 3 Designing a Course Out of the Book ... 4 Review Questions and Analytical Exercises ... 5 Empirical Exercises ... 5 Mathematical Notation ... 6 Acknowledgments ... 6 Contents ... 8 CHAPTER 1 Finite-Sample Properties of ... 20 ABSTRACT ... 20 1.1 The Classical Linear Regression Model ... 20 The Linearity Assumption ... 21 Iqlatrix Notation ... 23 The Strict Exogeneity Assumption ... 24 Implications of Strict Exogeneity ... 25 Strict Exogeneity in Time-Series Models ... 26 Other Assumptions of the Model ... 27 The Classical Regression Model for Random Samples ... 29 \"Fixed\" Regressors ... 30 QUESTIONS FOR REVIEW ... 30 1.2 The Algebra of Least Squares ... 32 OLS Minimizes the Sum of Squared Residuals ... 32 Normal Equations ... 33 Two Expressions for the OLS Estimator ... 35 More Concepts and Algebra ... 35 Influential Analysis (optional) ... 38 A Note on the Computation of OLS Estimates ... 40 QUESTIONS FOR REVIEW ... 42 1.3 Finite-Sample Properties of OLS ... 44 Finite-Sample Distribution of b ... 44 Finite-Sample Properties of s^2 ... 47 Estimate of Var(b|X) ... 48 QUESTIONS FOR REVIEW ... 48 1.4 Hypothesis Testing under Normality ... 50 Normally Distributed Error Terms ... 50 Testing Hypotheses about Individual Regression Coefficients ... 52 Decision Rule for the t-Test ... 54 Confidence Interval ... 55 Linear Hypotheses ... 56 The F-Test ... 57 A More Convenient Expression for F ... 59 t versus F ... 60 An Example of a Test Statistic Whose Distribution Depends on X ... 62 QUESTIONS FOR REVIEW ... 63 1.5 Relation to Maximum Likelihood ... 64 The Maximum Likelihood Principle ... 64 Conditional versus Unconditional Likelihood ... 64 The Log Likelihood for the Regression Model ... 65 ML via Concentrated Likelihood ... 65 Cramer-Rao Bound for the Classical Regression Model ... 66 The F-Test as a Likelihood Ratio Test ... 69 Quasi-Maximum Likelihood ... 70 QUESTIONS FOR REVIEW ... 70 1.6 Generalized Least Squares (GLS) ... 71 Consequence of Relaxing Assumption 1.4 ... 72 Efficient Estimation with Known V ... 72 A Special Case: Weighted Least Squares (WLS) ... 75 Limiting Nature of GLS ... 75 QUESTIONS FOR REVIEW ... 76 1.7 Application: Returns to Scale in Electricity Supply ... 77 The Electricity Supply Industry ... 77 The Data ... 77 Why Do We Need Econometrics? 78 The Cobb-Douglas Technology ... 79 How Do We Know Things Are Cobb-Douglas? 80 Are the OLS Assumptions Satisfied? 81 Restricted Least Squares ... 82 Testing the Homogeneity of the Cost Function ... 82 Detour: A Cautionary Note on R^2 ... 84 Testing Constant Returns to Scale ... 84 Importance of Plotting Residuals ... 85 Subsequent Developments ... 85 QUESTIONS FOR REVIEW ... 87 PROBLEM SET FOR CHAPTER 1 ... 88 ANALYTICAL EXERCISES ... 88 MONTE CARLO EXERCISES ... 98 ANSWERS TO SELECTED QUESTIONS ... 101 CHAPTER 2 Large-Sample Theory ... 105 ABSTRACT ... 105 2.1 Review of Limit Theorems for Sequences of Random Variables ... 105 Various Modes of Convergence ... 106 Convergence in Probability ... 106 Almost Sure Convergence ... 106 Convergence in Mean Square ... 107 Convergence in Distribution ... 107 Three Useful Results ... 109 Viewing Estimators as Sequences of Random Variables ... 111 Laws of Large Numbers and Central Limit Theorems ... 112 QUESTIONS FOR REVIEW ... 113 2.2 Fundamental Concepts in Time-Series Analysis ... 114 Need for Ergodic Stationarity ... 114 Various Classes of Stochastic Processes ... 115 Different Formulation of Lack of Serial Dependence ... 123 QUESTIONS FOR REVIEW ... 125 2.3 Large-Sample Distribution of the OLS Estimator ... 126 The Model ... 126 Asymptotic Distribution of the OLS Estimator ... 130 s^2 Is Consistent ... 132 QUESTIONS FOR REVIEW ... 133 2.4 Hypothesis Testing ... 134 Testing Linear Hypotheses ... 134 The Test Is Consistent ... 136 Asymptotic Power ... 137 Testing Nonlinear Hypotheses ... 138 QUESTIONS FOR REVIEW ... 140 2.5 Estimating E(xix) Consistently ... 140 Using Residuals for the Errors ... 140 Data Matrix Representation of S ... 142 Finite-Sample Considerations ... 142 QUESTIONS FOR REVIEW ... 143 2.6 Implications of Conditional Homoskedasticity ... 143 Conditional versus Unconditional Homoskedasticity ... 143 Reduction to Finite-Sample Formulas ... 144 Large-Sample Distribution of t and F Statistics ... 145 Variations of Asymptotic Tests under C. onditional Homoskedasticity ... 145 QUESTIONS FOR REVIEW ... 147 2.7 Testing Conditional Homoskedasticity ... 148 QUESTION FOR REVIEW ... 150 2.8 Estimation with Parameterized Conditional Heteroskedasticity (optional) ... 150 The Functional Form ... 150 WLS with Known α 151 Regression of ei^2 on zi Provides a Consistent Estimate of α 152 WLS with Estimated α 153 OLS versus WLS ... 154 QUESTION FOR REVIEW ... 154 2.9 Least Squares Projection ... 154 Optimally Predicting the Value of the Dependent Variable ... 155 Best Linear Predictor ... 156 OLS Consistently Estimates the Projection Coefficients ... 157 QUESTION FOR REVIEW ... 157 2.10 Testing for Serial Correlation ... 158 Box-Pierce and Ljung-Box ... 159 Sample Autocorrelations Calculated from Residuals ... 161 Testing with Predetermined, but Not Strictly Exogenous, Regressors ... 163 An Auxiliary Regression-Based Test ... 164 QUESTION FOR REVIEW ... 166 2.11 Application: Rational Expectations Econometrics ... 167 The Efficient Market Hypotheses ... 167 Testable Implications ... 169 Testing for Serial Correlation ... 170 Is the Nominal Interest Rate the Optimal Predictor? 173 Rt Is Not Strictly Exogenous ... 175 Subsequent Developments ... 176 QUESTION FOR REVIEW ... 177 2.12 Time Regressions ... 177 The Asymptotic Distribution of the OLS Estimator ... 178 Hypothesis Testing for Time Regressions ... 180 QUESTION FOR REVIEW ... 181 Appendix 2.A: Asymptotics with Fixed Regressors ... 181 Appendix 2.B: Proof of Proposition 2.10 ... 182 PROBLEM SET FOR CHAPTER 2 ... 185 CHAPTER 3 Single-Equation GMM ... 203 ABSTRACT ... 203 3.1 Endogeneity Bias: Working\'s Example ... 204 A Simultaneous Equations Model of Market Equilibrium ... 204 Endogeneity Bias ... 205 Observable Supply Shifters ... 206 QUESTION FOR REVIEW ... 209 3.2 More Examples ... 210 A Simple Macroeconometric Model ... 210 Errors-in-Variables ... 211 Production Function ... 213 QUESTION FOR REVIEW ... 214 3.3 The General Formulation ... 215 Regressors and Instruments ... 215 Identification ... 217 Order Condition for Identification ... 219 The Assumption for Asymptotic Normality ... 219 QUESTION FOR REVIEW ... 220 3.4 Generalized Method of Moments Defined ... 221 Method of Moments ... 222 Generalized Method of Moments ... 223 Sampling Error ... 224 QUESTION FOR REVIEW ... 224 3.5 Large-Sample Properties of GMM ... 225 Asymptotic Distribution of the GMM Estimator ... 226 Estimation of Error Variance ... 227 Hypothesis Testing ... 228 Estimation of S ... 229 Efficient GMM Estimator ... 229 Asymptotic Power ... 231 Small-Sample Properties ... 232 QUESTION FOR REVIEW ... 232 3.6 Testing Overidentifying Restrictions ... 234 Testing Subsets of Orthogonality Conditions ... 235 QUESTION FOR REVIEW ... 238 3.7 Hypothesis Testing by the Likelihood-Ratio Principle ... 239 The LR Statistic for the Regression Model ... 240 Variable Addition Test (optional) ... 241 QUESTION FOR REVIEW ... 242 3.8 Implications of Conditional Homoskedasticity ... 242 Efficient GMM Becomes 2Sl.S ... 243 J Becomes Sargan\'s Statistic ... 244 Small-Sample Properties of 2SLS ... 246 Alternative Derivations of 2SLS ... 246 When Regressors Are Predetermined ... 248 Testing a Subset of Orthogonality Conditions ... 249 Testing Conditional Homoskedasticity ... 251 Testing for Serial Correlation ... 251 QUESTION FOR REVIEW ... 252 3.9 Application: Returns from Schooling ... 253 The NLS-Y Data ... 253 The Semi-Log Wage Equation ... 254 Omitted Variable Bias ... 255 IQ as the Measure of Ability ... 256 Errors-in-Variables ... 256 2SLS to Correct for the Bias ... 259 Subsequent Developments ... 260 QUESTION FOR REVIEW ... 260 PROBLEM SET FOR CHAPTER 3 ANALYTICAL EXERCISES ... 261 EMPIRICAL EXERCISES ... 267 CHAPTER 4 Multiple-quation GMM ... 275 ABSTRACT ... 275 4.1 The Multiple-Equation Model ... 276 Linearity ... 276 Stationarity and Ergodicity ... 277 Orthogonality Conditions ... 278 Identification ... 279 The Assumption for Asymptotic Normality ... 281 Connection to the \"Complete\" System of Simultaneous Equations ... 282 4.2 Multiple-Equation GMM Defined ... 282 4.3 Large-Sample Theory ... 285 4.4 Single-Equation versus Multiple-Equation Estimation ... 288 When Are They \"Equivalent\"? 289 Joint Estimation Can Be Hazardous ... 290 QUESTION FOR REVIEW ... 291 4.5 Special Cases of Multiple-Equation GMM: FIVE, 3SLS, and SUR ... 291 Conditional Homoskedasticity ... 291 Full-Information Instrumental Variables Efficient (FIVE) ... 292 Three-Stage Least Squares (3SLS) ... 293 Seemingly Unrelated Regressions (SUR) ... 296 SUR versus OLS ... 298 QUESTION FOR REVIEW ... 300 4.6 Common Coefficients ... 303 The Model with Common Coefficients ... 303 The GMM Estimator ... 304 Imposing Conditional Homoskedasticity ... 305 Pooled OLS ... 307 Beautifying the Formulas ... 309 The Restriction That Isn\'t ... 310 QUESTION FOR REVIEW ... 311 4.7 Application: Interrelated Factor Demands ... 313 The Translog Cost Function ... 313 Factor Shares ... 314 Substitution Elasticities ... 315 Properties of Cost Functions ... 316 Stochastic Specifications ... 317 The Nature of Restrictions ... 318 Multivariate Regression Subject to Cross-Equation Restrictions ... 319 Which Equation to Delete? 321 Results ... 322 QUESTION FOR REVIEW ... 324 PROBLEM SET FOR CHAPTER 4 ... 325 ANALYTICAL EXERCISES ... 325 EMPIRICAL EXERCISES ... 334 CHAPTER 5 Panel Data ... 340 ABSTRACT ... 340 5.1 The Error-Components Model ... 341 Error Components ... 341 Group Means ... 344 A Reparameterization ... 344 QUESTION FOR REVIEW ... 346 5.2 The Fixed-Effects Estimator ... 347 The Formula ... 347 Large-Sample Properties ... 348 Digression: When ηi Is Spherical ... 350 Random Effects versus Fixed Effects ... 351 Relaxing Conditional Homoskedasticity ... 352 QUESTION FOR REVIEW ... 353 5.3 Unbalanced Panels (optional) ... 354 \"Zeroing Out\" Missing Observations ... 355 Zeroing Out versus Compression ... 356 No Selectivity Bias ... 357 QUESTION FOR REVIEW ... 358 5.4 Application: International Differences in Growth Rates ... 359 Derivation of the Estimation Equation ... 359 Appending the Error Term ... 360 Treatment of αi ... 361 Consistent Estimation of Speed of Convergence ... 362 QUESTION FOR REVIEW ... 363 Appendix 5.A: Distribution of Hausman Statistic ... 363 PROBLEM SET FOR CHAPTER 5 ... 366 ANALYTICAL EXERCISES ... 366 EMPIRICAL EXERCISES ... 375 CHAPTER 6 Serial Correlation ... 382 ABSTRACT ... 382 6.1 Modeling Serial Correlation: Linear Processes ... 382 MA(q) ... 383 MA(∞) as a Mean Square Limit ... 383 Filters ... 386 Inverting Lag Polynomials ... 389 QUESTIONS FOR REVIEW ... 392 6.2 ARMA Processes ... 392 AR(1) and Its MA(∞) Representation ... 393 Autocovariances of AR(1) ... 395 AR(p) and Its MA(∞) Representation ... 395 ARMA(p, q) ... 397 ARMA(p, q) with Common Roots ... 399 Invertibility ... 400 Autocovariance-Generating Function and the Spectrum ... 400 QUESTIONS FOR REVIEW ... 402 6.3 Vector Processes ... 404 QUESTIONS FOR REVIEW ... 408 6.4 Estimating Autoregressions ... 409 Estimation of AR(1) ... 409 Estimation of AR(p) ... 410 Choice of Lag Length ... 411 Estimation of VAR$ 414 Estimation of ARMA(p, q) ... 415 QUESTIONS FOR REVIEW ... 416 6.5 Asymptotics for Sample Means of Serially Correlated Processes ... 417 LLN for Covariance-Stationary Processes ... 418 Two Central Limit Theorems ... 419 Multivariate Extension ... 421 QUESTIONS FOR REVIEW ... 422 6.6 Incorporating Serial Correlation in GMM ... 423 The Model and Asymptotic Results ... 423 Estimating S When Autocovariances Vanish after Finite Lags ... 424 Using Kernels to Estimate S ... 425 VARHAC ... 427 QUESTIONS FOR REVIEW ... 429 6.7 Estimation under Conditional Homoskedasticity (Optional) ... 430 Kernel-Based Estimation of S under Conditional Homoskedasticity ... 430 Data Matrix Representation of Estimated Long-Run Variance ... 431 Relation to GLS ... 432 QUESTIONS FOR REVIEW ... 434 6.8 Application: Forward Exchange Rates as Optimal Predictors ... 435 The Market Efficiency Hypothesis ... 436 Testing Whether the Unconditional Mean Is Zero ... 437 Regression Tests ... 440 QUESTIONS FOR REVIEW ... 444 PROBLEM SET FOR CHAPTER 6 ... 445 ANALYTICAL EXERCISES ... 445 EMPIRICAL EXERCISES ... 455 CHAPTER 7 Extremum Estimators ... 462 ABSTRACT ... 462 7.1 Extremum Estimators ... 463 \"Measurability\" of θ 463 Two Classes of Extremum Estimators ... 464 Maximum Likelihood (ML) ... 465 Conditional Maximum Likelihood ... 467 Invariance of ML ... 469 Nonlinear Least Squares (NLS) ... 470 Linear and Nonlinear GMM ... 471 QUESTIONS FOR REVIEW ... 472 7.2 Consistency ... 473 Two Consistency Theorems for Extremum Estimators ... 473 Consistency of M-Estimators ... 475 Concavity after Reparameterization ... 478 Identification in NLS and ML ... 479 Consistency of GMM ... 484 QUESTIONS FOR REVIEW ... 485 7.3 Asymptotic Normality ... 486 Asymptotic Normality of M-Estimators ... 487 Consistent Asymptotic Variance Estimation ... 490 Asymptotic Normality of Conditional ML ... 491 Two Examples ... 493 Asymptotic Normality of GMM ... 495 GMM versus ML ... 498 Expressing the Sampling Error in a Common Format ... 500 Consistency of GMM ... 503 7.4 Hypothesis Testing ... 504 The Null Hypothesis ... 504 The Working Assumptions ... 506 The Wald Statistic ... 506 The Lagrange Multiplier (LM) Statistic ... 508 The Likelihood Ratio (LR) Statistic ... 510 Summary of the Trinity ... 511 QUESTIONS FOR REVIEW ... 513 7.5 Numerical Optimization ... 514 Newton-Raphson ... 514 Gauss-Newton ... 515 Writing Newton-Raphson and Gauss-Newton in a Common Format ... 515 Equations Nonlinear in Parameters Only ... 516 QUESTIONS FOR REVIEW ... 517 PROBLEM SET FOR CHAPTER 7 ... 518 ANALYTICAL EXERCISES ... 518 CHAPTER 8 Examples of Maximum Likelihood ... 524 ABSTRACT ... 524 8.1 Qualitative Response (QR) Models ... 524 Score and Hessian for Observation t ... 525 Consistency ... 526 Asymptotic Normality ... 527 QUESTIONS FOR REVIEW ... 527 8.2 Truncated Regression Models ... 528 The Model ... 528 Truncated Distributions ... 529 The Likelihood Function ... 530 Reparameterizing the Likelihood Function ... 531 Verifying Consistency and Asymptotic Normality ... 532 Recovering Original Parameters ... 534 QUESTIONS FOR REVIEW ... 534 8.3 Censored Regression (Tobit) Models ... 535 Tobit Likelihood Function ... 535 Reparameterization ... 536 QUESTIONS FOR REVIEW ... 538 8.4 Multivariate Regressions ... 538 The Multivariate Regression Model Restated ... 539 The Likelihood Function ... 540 Maximum the Likelihood Function ... 541 Consistency and Asymptotic Normality ... 542 QUESTIONS FOR REVIEW ... 542 8.5 FIML ... 543 The Multiple-Equation Model with Common Instruments Restated ... 543 The Complete System of Simultaneous Equations ... 546 Relationship between (F0, !10) and &0 ... 547 The FIML Likelihood Function ... 548 The FIML Concentrated Likelihood Function ... 549 Testing Overidentifying Restrictions ... 550 Properties of the FIML Estimator ... 550 ML Estimation of the SUR Model ... 552 QUESTIONS FOR REVIEW ... 554 8.6 LIML ... 555 LIML Defined ... 555 Computation of LIML ... 557 LIML versus 2SLS ... 559 QUESTIONS FOR REVIEW ... 559 8.7 Serially Correlated Observations ... 560 Two Ouestions ... 560 Unconditional ML for Dependent Observations ... 562 ML Estimation of AR(1) Processes ... 563 Conditional ML Estimation of AR(1) Processes ... 564 Conditional ML Estimation of AR(p) and VAR(p) Processes ... 566 QUESTIONS FOR REVIEW ... 567 PROBLEM SET FOR CHAPTER 8 ... 568 ANALYTICAL EXERCISES ... 568 CHAPTER 9 Unit-Root Econometrics ... 574 ABSTRACT ... 574 9.1 Modeling Trends ... 574 Integrated Processes ... 575 Why Is It Important to Know if the Process Is I(1)? 577 Which Should le Taken as the Null, I(0) or I(1)? 579 Other Approaches to Modeling Trends ... 580 QUESTIONS FOR REVIEW ... 580 9.2 Tools for Unit-Root Econometrics ... 580 Linear I(0) Processes ... 580 Approximating I(1) by a Random Walk ... 581 Relation to ARMA Models ... 583 The Wiener Process ... 584 A Useful Lemma ... 587 QUESTIONS FOR REVIEW ... 589 9.3 Dickey-Fuller Tests ... 590 The AR(1) Model ... 590 Deriving the Limiting Distribution under the I(1) Null ... 591 Incorporating the Intercept ... 594 Incorporating Time Trend ... 598 QUESTIONS FOR REVIEW ... 600 9.4 Augmented Dickey-Fuller Tests ... 602 The Augmented Autoregression ... 602 Limiting Distribution of the OLS Estimator ... 603 Deriving Test Statistics ... 607 Testing Hypotheses about ξ 608 What to Do When p IS Unknown? 609 A Suggestion for the Choice of p_max(T) ... 611 Including the Intercept in the Regression ... 612 Incorporating Time Trend ... 614 Summary of the DF and ADF Tests and Other Unit-Root Tests ... 616 QUESTIONS FOR REVIEW ... 617 9.5 Which Unit-Root Test to Use? 618 Local-to-Unity Asymptotics ... 619 Small-Sample Properties ... 619 9.6 Application: Purchasing Power Parity ... 620 The Embarrassing Resiliency of the Random Walk Model? 621 PROBLEM SET FOR CHAPTER 9 ... 622 ANALYTICAL EXERCISES ... 622 MONTE CARLO EXERCISES ... 628 EMPIRICAL EXERCISES ... 630 CHAPTER 10 Cointegration ... 640 ABSTRACT ... 640 10.1 Cointegrated Systems ... 641 Linear Vector I(0) and I(1) Processes ... 641 The Beveridge-Nelson Decomposition ... 644 Cointegration Defined ... 646 QUESTIONS FOR REVIEW ... 649 10.2 Alternative Representations of Cointegrated Systems ... 650 Phillips\'s Triangular Representation ... 650 VAR and Cointegration ... 650 The Vector Error-Correction Model (VECM) ... 655 Johansen\'s ML Procedure ... 657 QUESTIONS FOR REVIEW ... 659 10.3 Testing the Null of No Cointegration ... 660 Spurious Regressions ... 660 The Residual-Based Test for Cointegration ... 661 Testing the Null of Cointegration ... 666 QUESTIONS FOR REVIEW ... 667 10.4 Inference on Cointegrating Vectors ... 667 The Bivariate Example ... 669 Continuing with the Bivariate Example ... 670 Allowing for Serial Correlation ... 671 General Case ... 674 Other Estimators and Finite-Sample Properties ... 675 QUESTIONS FOR REVIEW ... 676 10.5 Application: The Demand for Money in the United States ... 676 The Data ... 677 (m - p, y, R) as a Cointegrated System ... 677 DOLS ... 679 Unstable Money Demand? 680 PROBLEM SET FOR CHAPTER 10 ... 682 EMPIRICAL EXERCISES ... 682
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