<p><strong><font size="3"><span id="btAsinTitle">Econometrics (Hardcover)</span><!--Element not supported - Type: 8 Name: #comment--><br/></font></strong>by <a href="http://www.amazon.com/exec/obidos/search-handle-url?%5Fencoding=UTF8&amp;search-type=ss&amp;index=books&amp;field-author=Fumio%20Hayashi"><font color="#003399">Fumio Hayashi</font></a> (Author) </p><p><a href="http://www.amazon.com/gp/reader/0691010188/ref=sib_dp_pt#reader-link"><img id="prodImage" height="240" alt="Econometrics" src="http://ecx.images-amazon.com/images/I/31pZkOy36BL._SL500_BO2,204,203,200_PIlitb-dp-500-arrow,TopRight,45,-64_OU01_AA240_SH20_.jpg" width="240" border="0"/></a></p><li><b>Hardcover:</b> 690 pages </li><li><b>Publisher:</b> Princeton University Press (December 15, 2000) </li><li><b>Language:</b> English </li><li><strong>Review<br/>Dale Jorgensen, Harvard University</strong> : Students of econometrics and their teachers will find this book to be the best introduction to the subject at the graduate and advanced undergraduate level. Starting with least squares regression, Hayashi provides an elegant exposition of all the standard topics of econometrics, including a detailed discussion of stationary and non-stationary time series. The particular strength of the book is the excellent balance between econometric theory and its applications, using GMM as an organizing principle throughout. Each chapter includes a detailed empirical example taken from classic and current applications of econometrics.<br/><br/><br/><b>Jerry A. Hausman, Massachusetts Institute of Technology</b> : <i>Econometrics</i> will be a very useful book for intermediate and advanced graduate courses. It covers the topics with an easy to understand approach while at the same time offering a rigorous analysis. The computer programming tips and problems should also be useful to students. I highly recommend this book for an up-to-date coverage and thoughtful discussion of topics in the methodology and application of econometrics.<br/><br/><br/><b>Mark W. Watson, Princeton University</b> : <i>Econometrics</i> covers both modern and classic topics without shifting gears. The coverage is quite advanced yet the presentation is simple. Hayashi brings students to the frontier of applied econometric practice through a careful and efficient discussion of modern economic theory. The empirical exercises are very useful. . . . The projects are carefully crafted and have been thoroughly debugged.<br/><br/><br/><b>James H. Stock, John F. Kennedy School of Government, Harvard University</b> : <i>Econometrics</i> strikes a good balance between technical rigor and clear exposition. . . . The use of empirical examples is well done throughout. I very much like the use of old 'classic' examples. It gives students a sense of history--and shows that great empirical econometrics is a matter of having important ideas and good data, not just fancy new methods. . . . The style is just great, informal and engaging.<br/><br/><br/><b>Product Description</b><br/><p>Hayashi's <i>Econometrics</i> 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.</p><p><i>Econometrics</i> 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.</p><p>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.</p></li><li><p>
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</p></li><li><p><b>TABLE OF CONTENTS:</b></p><p>List of Figures xvii<br/>Preface xix<br/><strong>1 Finite-Sample Properties of OLS 3</strong><br/>1.1 The Classical Linear Regression Model 3<br/>The Linearity Assumption 4<br/>Matrix Notation 6<br/>The Strict Exogeneity Assumption 7<br/>Implications of Strict Exogeneity 8<br/>Strict Exogeneity in Time-Series Models 9<br/>Other Assumptions of the Model 10<br/>The Classical Regression Model for Random Samples 12<br/>"Fixed" Regressors 13<br/>1.2 The Algebra of Least Squares 15<br/>OLS Minimizes the Sum of Squared Residuals 15<br/>Normal Equations 16<br/>Two Expressions for the OLS Estimator 18<br/>More Concepts and Algebra 18<br/>Influential Analysis (optional) 21<br/>A Note on the Computation of OLS Estimates 23<br/>1.3 Finite-Sample Properties of OLS 27<br/>Finite-Sample Distribution of <b>b</b> 27<br/>Finite-Sample Properties of <i>s</i><sup>2</sup> 30<br/>Estimate of Var(<b>b | X</b>) 31<br/>1.4 Hypothesis Testing under Normality 33<br/>Normally Distributed Error Terms 33<br/>Testing Hypotheses about Individual Regression Coefficients 35<br/>Decision Rule for the <i>t</i>-Test 37<br/>Confidence Interval 38<br/><i>p</i>-Value 38<br/>Linear Hypotheses 39<br/>The <i>F</i>-Test 40<br/>A More Convenient Expression for <i>F</i> 42<br/><i>t</i> versus <i>F</i> 43<br/>An Example of a Test Statistic Whose Distribution Depends on <b>X</b> 45<br/>1.5 Relation to Maximum Likelihood 47<br/>The Maximum Likelihood Principle 47<br/>Conditional versus Unconditional Likelihood 47<br/>The Log Likelihood for the Regression Model 48<br/>ML via Concentrated Likelihood 48<br/>Cramer-Rao Bound for the Classical Regression Model 49<br/>The <i>F</i>-Test as a Likelihood Ratio Test 52<br/>Quasi-Maximum Likelihood 53<br/>1.6 Generalized Least Squares (GLS) 54<br/>Consequence of Relaxing Assumption 1.4 55<br/>Efficient Estimation with Known <b>V</b> 55<br/>A Special Case: Weighted Least Squares (WLS) 58<br/>Limiting Nature of GLS 58<br/>1.7 Application: Returns to Scale in Electricity Supply 60<br/>The Electricity Supply Industry 60<br/>The Data 60<br/>Why Do We Need Econometrics? 61<br/>The Cobb-Douglas Technology 62<br/>How Do We Know Things Are Cobb-Douglas? 63<br/>Are the OLS Assumptions Satisfied? 64<br/>Restricted Least Squares 65<br/>Testing the Homogeneity of the Cost Function 65<br/>Detour: A Cautionary Note on R<sup>2</sup> 67<br/>Testing Constant Returns to Scale 67<br/>Importance of Plotting Residuals 68<br/>Subsequent Developments 68<br/>Problem Set 71<br/>Answers to Selected Questions 84<br/><strong>2 Large-Sample Theory 88</strong><br/>2.1 Review of Limit Theorems for Sequences of Random Variables 88<br/>Various Modes of Convergence 89<br/>Three Useful Results 92<br/>Viewing Estimators as Sequences of Random Variables 94<br/>Laws of Large Numbers and Central Limit Theorems 95<br/>2.2 Fundamental Concepts in Time-Series Analysis 97<br/>Need for Ergodic Stationarity 97<br/>Various Classes of Stochastic Processes 98<br/>Different Formulation of Lack of Serial Dependence 106<br/>The CLT for Ergodic Stationary Martingale Differences Sequences 106<br/>2.3 Large-Sample Distribution of the OLS Estimator 109<br/>The Model 109<br/>Asymptotic Distribution of the OLS Estimator 113<br/><i>s</i><sup>2</sup> Is Consistent 115<br/>2.4 Hypothesis Testing 117<br/>Testing Linear Hypotheses 117<br/>The Test Is Consistent 119<br/>Asymptotic Power 120<br/>Testing Nonlinear Hypotheses 121<br/>2.5 Estimating E([<i>not displayable</i>]) Consistently 123<br/>Using Residuals for the Errors 123<br/>Data Matrix Representation of <b>S</b> 125<br/>Finite-Sample Considerations 125<br/>2.6 Implications of Conditional Homoskedasticity 126<br/>Conditional versus Unconditional Homoskedasticity 126<br/>Reduction to Finite-Sample Formulas 127<br/>Large-Sample Distribution of <i>t</i> and <i>F</i> Statistics 128<br/>Variations of Asymptotic Tests under Conditional Homoskedasticity 129<br/>2.7 Testing Conditional Homoskedasticity 131<br/>2.8 Estimation with Parameterized Conditional Heteroskedasticity (optional) 133<br/>The Functional Form 133<br/>WLS with Known [alpha] 134<br/>Regression of <i>e<sup>2</sup><sub>i</sub></i> on <b>z</b><sub><i>i</i></sub> Provides a Consistent Estimate of [alpha] 135<br/>WLS with Estimated [alpha] 136<br/>OLS versus WLS 137<br/>2.9 Least Squares Projection 137<br/>Optimally Predicting the Value of the Dependent Variable 138<br/>Best Linear Predictor 139<br/>OLS Consistently Estimates the Projection Coefficients 140<br/>2.10 Testing for Serial Correlation 141<br/>Box-Pierce and Ljung-Box 142<br/>Sample Autocorrelations Calculated from Residuals 144<br/>Testing with Predetermined, but Not Strictly Exogenous, Regressors 146<br/>An Auxiliary Regression-Based Test 147<br/>2.11 Application: Rational Expectations Econometrics 150<br/>The Efficient Market Hypotheses 150<br/>Testable Implications 152<br/>Testing for Serial Correlation 153<br/>Is the Nominal Interest Rate the Optimal Predictor? 156<br/><i>R<sub>t</sub></i> Is Not Strictly Exogenous 158<br/>Subsequent Developments 159<br/>2.12 Time Regressions 160<br/>The Asymptotic Distribution of the OLS Estimates 161<br/>Hypothesis Testing for Time Regressions 163<br/>2.A Asymptotics with Fixed Regressors 164<br/>2.B Proof of Proposition 2.10 165<br/>Problem Set 168<br/>Answers to Selected Questions 183<br/><strong>3 Single-Equation GMM 186</strong><br/>3.1 Endogeneity Bias: Working's Example 187<br/>A Simultaneous Equations Model of Market Equilibrium 187<br/>Endogeneity Bias 188<br/>Observable Supply Shifters 189<br/>3.2 More Examples 193<br/>A Simple Macroeconometric Model 193<br/>Errors-in-Variables 194<br/>Production Function 196<br/>3.3 The General Formulation 198<br/>Regressors and Instruments 198<br/>Identification 200<br/>Order Condition for Identification 202<br/>The Assumption for Asymptotic Normality 202<br/>3.4 Generalized Method of Moments Defined 204<br/>Method of Moments 205<br/>Generalized Method of Moments 206<br/>Sampling Error 207<br/>3.5 Large-Sample Properties of GMM 208<br/>Asymptotic Distribution of the GMM Estimator 209<br/>Estimation of Error Variance 210<br/>Hypothesis Testing 211<br/>Estimation of <b>S</b> 212<br/>Efficient GMM Estimator 212<br/>Asymptotic Power 214<br/>Small-Sample Properties 215<br/>3.6 Testing Overidentifying Restrictions 217<br/>Testing Subsets of Orthogonality Conditions 218<br/>3.7 Hypothesis Testing by the Likelihood-Ratio Principle 222<br/>The <i>LR</i> Statistic for the Regression Model 223<br/>Variable Addition Test (optional) 224<br/>3.8 Implications of Conditional Homoskedasticity 225<br/>Efficient GMM Becomes 2SLS 226<br/><i>J</i> Becomes Sargan's Statistic 227<br/>Small-Sample Properties of 2SLS 229<br/>Alternative Derivations of 2SLS 229<br/>When Regressors Are Predetermined 231<br/>Testing a Subset of Orthogonality Conditions 232<br/>Testing Conditional Homoskedasticity 234<br/>Testing for Serial Correlation 234<br/>3.9 Application: Returns from Schooling 236<br/>The NLS-Y Data 236<br/>The Semi-Log Wage Equation 237<br/>Omitted Variable Bias 238<br/>IQ as the Measure of Ability 239<br/>Errors-in-Variables 239<br/>2SLS to Correct for the Bias 242<br/>Subsequent Developments 243<br/>Problem Set 244<br/>Answers to Selected Questions 254<br/><strong>4 Multiple-Equation GMM 258</strong><br/>4.1 The Multiple-Equation Model 259<br/>Linearity 259<br/>Stationarity and Ergodicity 260<br/>Orthogonality Conditions 261<br/>Identification 262<br/>The Assumption for Asymptotic Normality 264<br/>Connection to the "Complete" System of Simultaneous Equations 265<br/>4.2 Multiple-Equation GMM Defined 265<br/>4.3 Large-Sample Theory 268<br/>4.4 Single-Equation versus Multiple-Equation Estimation 271<br/>When Are They "Equivalent"? 272<br/>Joint Estimation Can Be Hazardous 273<br/>4.5 Special Cases of Multiple-Equation GMM: FIVE, 3SLS, and SUR 274<br/>Conditional Homoskedasticity 274<br/>Full-Information Instrumental Variables Efficient (FIVE) 275<br/>Three-Stage Least Squares (3SLS) 276<br/>Seemingly Unrelated Regressions (SUR) 279<br/>SUR versus OLS 281<br/>4.6 Common Coefficients 286<br/>The Model with Common Coefficients 286<br/>The GMM Estimator 287<br/>Imposing Conditional Homoskedasticity 288<br/>Pooled OLS 290<br/>Beautifying the Formulas 292<br/>The Restriction That Isn't 293<br/>4.7 Application: Interrelated Factor Demands 296<br/>The Translog Cost Function 296<br/>Factor Shares 297<br/>Substitution Elasticities 298<br/>Properties of Cost Functions 299<br/>Stochastic Specifications 300<br/>The Nature of Restrictions 301<br/>Multivariate Regression Subject to Cross-Equation Restrictions 302<br/>Which Equation to Delete? 304<br/>Results 305<br/>Problem Set 308<br/>Answers to Selected Questions 320<br/><strong>5 Panel Data 323</strong><br/>5.1 The Error-Components Model 324<br/>Error Components 324<br/>Group Means 327<br/>A Reparameterization 327<br/>5.2 The Fixed-Effects Estimator 330<br/>The Formula 330<br/>Large-Sample Properties 331<br/>Digression: When [<b>eta</b>]<sub><i>i</i></sub> Is Spherical 333<br/>Random Effects versus Fixed Effects 334<br/>Relaxing Conditional Homoskedasticity 335<br/>5.3 Unbalanced Panels (optional) 337<br/>"Zeroing Out" Missing Observations 338<br/>Zeroing Out versus Compression 339<br/>No Selectivity Bias 340<br/>5.4 Application: International Differences in Growth Rates 342<br/>Derivation of the Estimation Equation 342<br/>Appending the Error Term 343<br/>Treatment of [alpha]<sub><i>i</i></sub> 344<br/>Consistent Estimation of Speed of Convergence 345<br/>Appendix 5.A: Distribution of Hausman Statistic 346<br/>Problem Set 349<br/>Answers to Selected Questions 363<br/><strong>6 Serial Correlation 365</strong><br/>6.1 Modeling Serial Correlation: Linear Processes 365<br/>MA(<i>q</i>) 366<br/>MA([infinity]) as a Mean Square Limit 366<br/>Filters 369<br/>Inverting Lag Polynomials 372<br/>6.2 ARMA Processes 375<br/>AR(1) and Its MA([infinity]) Representation 376<br/>Autocovariances of AR(1) 378<br/>AR(<i>p</i>) and Its MA([infinity]) Representation 378<br/>ARMA(<i>p,q</i>) 380<br/>ARMA(<i>p</i>) with Common Roots 382<br/>Invertibility 383<br/>Autocovariance-Generating Function and the Spectrum 383<br/>6.3 Vector Processes 387<br/>6.4 Estimating Autoregressions 392<br/>Estimation of AR(1) 392<br/>Estimation of AR(<i>p</i>) 393<br/>Choice of Lag Length 394<br/>Estimation of VARs 397<br/>Estimation of ARMA(<i>p,q</i>) 398<br/>6.5 Asymptotics for Sample Means of Serially Correlated Processes 400<br/>LLN for Covariance-Stationary Processes 401<br/>Two Central Limit Theorems 402<br/>Multivariate Extension 404<br/>6.6 Incorporating Serial Correlation in GMM 406<br/>The Model and Asymptotic Results 406<br/>Estimating <b>S</b> When Autocovariances Vanish after Finite Lags 407<br/>Using Kernels to Estimate <b>S</b> 408<br/>VARHAC 410<br/>6.7 Estimation under Conditional Homoskedasticity (Optional) 413<br/>Kernel-Based Estimation of <b>S</b> under Conditional Homoskedasticity 413<br/>Data Matrix Representation of Estimated Long-Run Variance 414<br/>Relation to GLS 415<br/>6.8 Application: Forward Exchange Rates as Optimal Predictors 418<br/>The Market Efficiency Hypothesis 419<br/>Testing Whether the Unconditional Mean Is Zero 420<br/>Regression Tests 423<br/>Problem Set 428<br/>Answers to Selected Questions 441<br/><strong>7 Extremum Estimators 445</strong><br/>7.1 Extremum Estimators 446<br/>"Measurability" of [theta] 446<br/>Two Classes of Extremum Estimators 447<br/>Maximum Likelihood (ML) 448<br/>Conditional Maximum Likelihood 450<br/>Invariance of ML 452<br/>Nonlinear Least Squares (NLS) 453<br/>Linear and Nonlinear GMM 454<br/>7.2 Consistency 456<br/>Two Consistency Theorems for Extremum Estimators 456<br/>Consistency of M-Estimators 458<br/>Concavity after Reparameterization 461<br/>Identification in NLS and ML 462<br/>Consistency of GMM 467<br/>7.3 Asymptotic Normality 469<br/>Asymptotic Normality of M-Estimators 470<br/>Consistent Asymptotic Variance Estimation 473<br/>Asymptotic Normality of Conditional ML 474<br/>Two Examples 476<br/>Asymptotic Normality of GMM 478<br/>GMM versus ML 481<br/>Expressing the Sampling Error in a Common Format 483<br/>7.4 Hypothesis Testing 487<br/>The Null Hypothesis 487<br/>The Working Assumptions 489<br/>The Wald Statistic 489<br/>The Lagrange Multiplier (LM) Statistic 491<br/>The Likelihood Ratio (LR) Statistic 493<br/>Summary of the Trinity 494<br/>7.5 Numerical Optimization 497<br/>Newton-Raphson 497<br/>Gauss-Newton 498<br/>Writing Newton-Raphson and Gauss-Newton in a Common Format 498<br/>Equations Nonlinear in Parameters Only 499<br/>Problem Set 501<br/>Answers to Selected Questions 505<br/><strong>8 Examples of Maximum Likelihood 507<br/></strong>8.1 Qualitative Response (QR) Models 507<br/>Score and Hessian for Observation <i>t</i> 508<br/>Consistency 509<br/>Asymptotic Normality 510<br/>8.2 Truncated Regression Models 511<br/>The Model 511<br/>Truncated Distributions 512<br/>The Likelihood Function 513<br/>Reparameterizing the Likelihood Function 514<br/>Verifying Consistency and Asymptotic Normality 515<br/>Recovering Original Parameters 517<br/>8.3 Censored Regression (Tobit) Models 518<br/>Tobit Likelihood Function 518<br/>Reparameterization 519<br/>8.4 Multivariate Regressions 521<br/>The Multivariate Regression Model Restated 522<br/>The Likelihood Function 523<br/>Maximizing the Likelihood Function 524<br/>Consistency and Asymptotic Normality 525<br/>8.5 FIML 526<br/>The Multiple-Equation Model with Common Instruments Restated 526<br/>The Complete System of Simultaneous Equations 529<br/>Relationship between ([<b>Gamma</b>]<sub>0</sub>, [<b>Beta</b>]<sub>0</sub>) and [<b>delta</b>]<sub>0</sub> 530<br/>The FIML Likelihood Function 531<br/>The FIML Concentrated Likelihood Function 532<br/>Testing Overidentifying Restrictions 533<br/>Properties of the FIML Estimator 533<br/>ML Estimation of the SUR Model 535<br/>8.6 LIML 538<br/>LIML Defined 538<br/>Computation of LIML 540<br/>LIML versus 2SLS 542<br/>8.7 Serially Correlated Observations 543<br/>Two Questions 543<br/>Unconditional ML for Dependent Observations 545<br/>ML Estimation of AR.1/ Processes 546<br/>Conditional ML Estimation of AR(1) Processes 547<br/>Conditional ML Estimation of AR(<i>p</i>) and VAR(<i>p</i>) Processes 549<br/>Problem Set 551<br/><strong>9 Unit-Root Econometrics 557</strong><br/>9.1 Modeling Trends 557<br/>Integrated Processes 558<br/>Why Is It Important to Know if the Process Is I(1)? 560<br/>Which Should Be Taken as the Null, I(0) or I(1)? 562<br/>Other Approaches to Modeling Trends 563<br/>9.2 Tools for Unit-Root Econometrics 563<br/>Linear I(0) Processes 563<br/>Approximating I(1) by a Random Walk 564<br/>Relation to ARMA Models 566<br/>The Wiener Process 567<br/>A Useful Lemma 570<br/>9.3 Dickey-Fuller Tests 573<br/>The AR(1) Model 573<br/>Deriving the Limiting Distribution under the I(1) Null 574<br/>Incorporating the Intercept 577<br/>Incorporating Time Trend 581<br/>9.4 Augmented Dickey-Fuller Tests 585<br/>The Augmented Autoregression 585<br/>Limiting Distribution of the OLS Estimator 586<br/>Deriving Test Statistics 590<br/>Testing Hypotheses about [zeta] 591<br/>What to Do When <i>p</i> Is Unknown? 592<br/>A Suggestion for the Choice of <i>p<sub>max</sub></i>(<i>T</i>) 594<br/>Including the Intercept in the Regression 595<br/>Incorporating Time Trend 597<br/>Summary of the DF and ADF Tests and Other Unit-Root Tests 599<br/>9.5 Which Unit-Root Test to Use? 601<br/>Local-to-Unity Asymptotics 602<br/>Small-Sample Properties 602<br/>9.6 Application: Purchasing Power Parity 603<br/>The Embarrassing Resiliency of the Random Walk Model? 604<br/>Problem Set 605<br/>Answers to Selected Questions 619<br/><strong>10 Cointegration 623</strong><br/>10.1 Cointegrated Systems 624<br/>Linear Vector I(0) and I(1) Processes 624<br/>The Beveridge-Nelson Decomposition 627<br/>Cointegration Defined 629<br/>10.2 Alternative Representations of Cointegrated Systems 633<br/>Phillips's Triangular Representation 633<br/>VAR and Cointegration 636<br/>The Vector Error-Correction Model (VECM) 638<br/>Johansen's ML Procedure 640<br/>10.3 Testing the Null of No Cointegration 643<br/>Spurious Regressions 643<br/>The Residual-Based Test for Cointegration 644<br/>Testing the Null of Cointegration 649<br/>10.4 Inference on Cointegrating Vectors 650<br/>The SOLS Estimator 650<br/>The Bivariate Example 652<br/>Continuing with the Bivariate Example 653<br/>Allowing for Serial Correlation 654<br/>General Case 657<br/>Other Estimators and Finite-Sample Properties 658<br/>10.5 Application: the Demand for Money in the United States 659<br/>The Data 660<br/>(<i>m - p, y, R</i>) as a Cointegrated System 660<br/>DOLS 662<br/>Unstable Money Demand? 663<br/>Problem Set 665<br/>Appendix. Partitioned Matrices and Kronecker Products 670<br/>Addition and Multiplication of Partitioned Matrices 671<br/><strong>Inverting Partitioned Matrices 672</strong></p></li>
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