Fundamentals of applied econometrics

CHMATH 11/11/2011 11:50:22 Page 698 FFIRS 11/21/2011 18:42:57 Page FUNDAMENTALS OF APPLIED ECONOMETRICS by RICHARD A ASHLEY Economics Department Virginia Tech John Wiley and Sons, Inc FFIRS 11/21/2011 18:42:57 Page Vice President & Executive Publisher Project Editor Assistant Editor Editorial Assistant Associate Director of Marketing Marketing Manager Marketing Assistant Executive Media Editor Media Editor Senior Production Manager Associate Production Manager Assistant Production Editor Cover Designer Cover Photo Credit George Hoffman Jennifer Manias Emily McGee Erica Horowitz Amy Scholz Jesse Cruz Courtney Luzzi Allison Morris Greg Chaput Janis Soo Joyce Poh Yee Lyn Song Jerel Seah #AveryPhotography/iStockphoto This book was set in 10/12 Times Roman by Thomson Digital and printed and bound by RR Donnelley The cover was printed by RR Donnelly This book is printed on acid-free paper Founded in 1807, John Wiley & Sons, Inc has been a valued source of knowledge and understanding for more than 200 years, helping people around the world meet their needs and fulfill their aspirations Our company is built on a foundation of principles that include responsibility to the communities we serve and where we live and work In 2008, we launched a Corporate Citizenship Initiative, a global effort to address the environmental, social, economic, and ethical challenges we face in our business Among the issues we are addressing are carbon impact, paper specifications and procurement, ethical conduct within our business and among our vendors, and community and charitable support For more information, please visit our Web site: www.wiley.com/go/citizenship Copyright # 2012 John Wiley & Sons, Inc All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright 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desk copy Outside of the United States, please contact your local sales representative Library of Congress Cataloging-in-Publication Data Ashley, Richard A (Richard Arthur), 1950Fundamentals of applied econometrics / by Richard Ashley – 1st ed p cm Includes index ISBN 978-0-470-59182-6 (hardback) Econometrics Econometrics–Statistical methods Econometrics–Data processing I Title HB139.A84 2012 2011041421 330.0105195–dc23 Printed in the United States of America 10 FFIRS 11/21/2011 18:42:57 Page For Rosalind and Elisheba FTOC 11/21/2011 18:58:36 Page BRIEF CONTENTS What’s Different about This Book Working with Data in the “Active Learning Exercises” Acknowledgments Notation Part I Chapter Chapter Chapter Chapter INTRODUCTION AND STATISTICS REVIEW xiii xxii xxiii xxiv INTRODUCTION A REVIEW OF PROBABILITY THEORY ESTIMATING THE MEAN OF A NORMALLY DISTRIBUTED RANDOM VARIABLE STATISTICAL INFERENCE ON THE MEAN OF A NORMALLY DISTRIBUTED RANDOM VARIABLE 11 46 Part II REGRESSION ANALYSIS 97 Chapter THE BIVARIATE REGRESSION MODEL: INTRODUCTION, ASSUMPTIONS, AND PARAMETER ESTIMATES THE BIVARIATE LINEAR REGRESSION MODEL: SAMPLING DISTRIBUTIONS AND ESTIMATOR PROPERTIES THE BIVARIATE LINEAR REGRESSION MODEL: INFERENCE ON b THE BIVARIATE REGRESSION MODEL: R2 AND PREDICTION THE MULTIPLE REGRESSION MODEL DIAGNOSTICALLY CHECKING AND RESPECIFYING THE MULTIPLE REGRESSION MODEL: DEALING WITH POTENTIAL OUTLIERS AND HETEROSCEDASTICITY IN THE CROSS-SECTIONAL DATA CASE STOCHASTIC REGRESSORS AND ENDOGENEITY INSTRUMENTAL VARIABLES ESTIMATION DIAGNOSTICALLY CHECKING AND RESPECIFYING THE MULTIPLE REGRESSION MODEL: THE TIME-SERIES DATA CASE (PART A) DIAGNOSTICALLY CHECKING AND RESPECIFYING THE MULTIPLE REGRESSION MODEL: THE TIME-SERIES DATA CASE (PART B) Chapter Chapter Chapter Chapter Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 68 99 131 150 178 191 224 259 303 342 389 Part III ADDITIONAL TOPICS IN REGRESSION ANALYSIS 455 Chapter 15 Chapter 16 Chapter 17 REGRESSION MODELING WITH PANEL DATA (PART A) REGRESSION MODELING WITH PANEL DATA (PART B) A CONCISE INTRODUCTION TO TIME-SERIES ANALYSIS AND FORECASTING (PART A) A CONCISE INTRODUCTION TO TIME-SERIES ANALYSIS AND FORECASTING (PART B) PARAMETER ESTIMATION BEYOND CURVE-FITTING: MLE (WITH AN APPLICATION TO BINARY-CHOICE MODELS) AND GMM (WITH AN APPLICATION TO IV REGRESSION) CONCLUDING COMMENTS 459 507 Chapter 18 Chapter 19 Chapter 20 Mathematics Review 536 595 647 681 693 iv FTOC02 11/24/2011 13:31:44 Page TABLE OF CONTENTS What’s Different about This Book Working with Data in the “Active Learning Exercises” Acknowledgments Notation xiii xxii xxiii xxiv Part I INTRODUCTION AND STATISTICS REVIEW Chapter INTRODUCTION 1.1 Preliminaries 1.2 Example: Is Growth Good for the Poor? 1.3 What’s to Come ALE 1a: An Econometrics “Time Capsule” ALE 1b: Investigating the Slope Graphically Using a Scatterplot ALE 1c: Examining Some Disturbing Variations on Dollar & Kraay’s Model ALE 1d: The Pitfalls of Making Scatterplots with Trended Time-Series Data Chapter (Online) (Online) (Online) A REVIEW OF PROBABILITY THEORY 11 2.1 Introduction 2.2 Random Variables 2.3 Discrete Random Variables 2.4 Continuous Random Variables 2.5 Some Initial Results on Expectations 2.6 Some Results on Variances 2.7 A Pair of Random Variables 2.8 The Linearity Property of Expectations 2.9 Statistical Independence 2.10 Normally Distributed Random Variables 2.11 Three Special Properties of Normally Distributed Variables 2.12 Distribution of a Linear Combination of Normally Distributed Random Variables 11 12 13 17 19 20 22 24 26 29 31 32 v FTOC02 11/24/2011 13:31:44 vi Page TABLE OF CONTENTS 2.13 Conclusion 36 Exercises 37 ALE 2a: The Normal Distribution 42 ALE 2b: Central Limit Theorem Simulators on the Web (Online) Appendix 2.1: The Conditional Mean of a Random Variable 44 Appendix 2.2: Proof of the Linearity Property for the Expectation of a Weighted Sum of Two Discretely Distributed Random Variables 45 Chapter Chapter ESTIMATING THE MEAN OF A NORMALLY DISTRIBUTED RANDOM VARIABLE 46 3.1 Introduction 3.2 Estimating m by Curve Fitting 3.3 The Sampling Distribution of Y 3.4 Consistency – A First Pass 3.5 Unbiasedness and the Optimal Estimator 3.6 The Squared Error Loss Function and the Optimal Estimator 3.7 The Feasible Optimality Properties: Efficiency and BLUness 3.8 Summary 3.9 Conclusions and Lead-in to Next Chapter Exercises ALE 3a: Investigating the Consistency of the Sample Mean and Sample Variance Using Computer-Generated Data ALE 3b: Estimating Means and Variances Regarding the Standard & Poor’s SP500 Stock Index 46 48 51 54 55 56 58 61 62 62 STATISTICAL INFERENCE ON THE MEAN OF A NORMALLY DISTRIBUTED RANDOM VARIABLE 64 (Online) 68 4.1 Introduction 68 4.2 Standardizing the distribution of Y 69 69 4.3 Confidence Intervals for m When s2 Is Known 71 4.4 Hypothesis Testing when s2 Is Known 75 4.5 Using S2 to Estimate s2 (and Introducing the Chi-Squared Distribution) 4.6 Inference Results on m When s2 Is Unknown (and Introducing the Student’s t Distribution) 78 4.7 Application: State-Level U.S Unemployment Rates 82 4.8 Introduction to Diagnostic Checking: Testing the Constancy of m across the Sample 84 4.9 Introduction to Diagnostic Checking: Testing the Constancy of s2 across the Sample 87 4.10 Some General Comments on Diagnostic Checking 89 4.11 Closing Comments 90 Exercises 91 ALE 4a: Investigating the Sensitivity of Hypothesis Test p -Values to Departures from the NIID(m, s2) Assumption Using Computer-Generated Data 93 ALE 4b: Individual Income Data from the Panel Study on Income Dynamics (PSID) – Does Birth-Month Matter? (Online) FTOC02 11/24/2011 13:31:44 Page vii TABLE OF CONTENTS Part II REGRESSION ANALYSIS 97 Chapter THE BIVARIATE REGRESSION MODEL: INTRODUCTION, ASSUMPTIONS, AND PARAMETER ESTIMATES 99 5.1 Introduction 99 5.2 The Transition from Mean Estimation to Regression: Analyzing the Variation of Per Capita Real Output across Countries 100 5.3 The Bivariate Regression Model – Its Form and the “Fixed in Repeated Samples” Causality Assumption 105 5.4 The Assumptions on the Model Error Term, Ui 106 5.5 Least Squares Estimation of a and b 109 5.6 Interpreting the Least Squares Estimates of a and b 118 5.7 Bivariate Regression with a Dummy Variable: Quantifying the Impact of College Graduation on Weekly Earnings 120 Exercises 127 ALE 5a: Exploring the Penn World Table Data 128 ^ à over a Very Small Data Set (Online) ALE 5b: Verifying a ^ Ãols and b ols ALE 5c: Extracting and Downloading CPS Data from the Census Bureau Web Site (Online) ^ à on a Dummy Variable Equals the ALE 5d: Verifying That b ols Difference in the Sample Means (Online) ^ à When xi Is a Dummy Variable Appendix 5.1: b 130 ols Chapter THE BIVARIATE LINEAR REGRESSION MODEL: SAMPLING DISTRIBUTIONS AND ESTIMATOR PROPERTIES 6.1 Introduction 6.2 Estimates and Estimators ^ as a Linear Estimator and the Least Squares Weights 6.3 b ^ 6.4 The Sampling Distribution of b ^ Consistency 6.5 Properties of b: ^ Best Linear Unbiasedness 6.6 Properties of b: 131 131 132 132 134 140 140 143 144 6.7 Summary Exercises ALE 6a: Outliers and Other Perhaps Overly Influential Observations: Investigating ^ to an Outlier Using Computer-Generated Data the Sensitivity of b 147 ^ Using Computer-Generated Data (Online) ALE 6b: Investigating the Consistency of b Chapter THE BIVARIATE LINEAR REGRESSION MODEL: INFERENCE ON b 150 7.1 Introduction 7.2 A Statistic for b with a Known Distribution 7.3 A 95% Confidence Interval for b with s2 Given 7.4 Estimates versus Estimators and the Role of the Model Assumptions 7.5 Testing a Hypothesis about b with s2 Given 7.6 Estimating s2 7.7 Properties of S2 7.8 A Statistic for b Not Involving s2 150 152 152 154 156 158 159 160 FTOC02 11/24/2011 13:31:44 Page viii TABLE OF CONTENTS 7.9 A 95% Confidence Interval for b with s2 Unknown 160 162 7.10 Testing a Hypothesis about b with s2 Unknown 7.11 Application: The Impact of College Graduation on Weekly Earnings (Inference Results) 164 7.12 Application: Is Growth Good for the Poor? 168 7.13 Summary 169 Exercises 169 ALE 7a: Investigating the Sensitivity of Slope Coefficient Inference to Departures 172 from the Ui $ NIID(0, s2) Assumption Using Computer-Generated Data ALE 7b: Distorted Inference in Time-Series Regressions with Serially Correlated Model Errors: An Investigation Using Computer-Generated Data (Online) ^ 177 Appendix 7.1: Proof That S2 Is Independent of b Chapter Chapter THE BIVARIATE REGRESSION MODEL: R2 AND PREDICTION 178 8.1 Introduction 8.2 Quantifying How Well the Model Fits the Data 8.3 Prediction as a Tool for Model Validation 8.4 Predicting YNỵ1 given xNỵ1 Exercises ALE 8a: On the Folly of Trying Too Hard: A Simple Example of “Data Mining” 178 179 182 184 188 189 THE MULTIPLE REGRESSION MODEL 191 9.1 Introduction 9.2 The Multiple Regression Model 9.3 Why the Multiple Regression Model Is Necessary and Important 9.4 Multiple Regression Parameter Estimates via Least Squares Fitting ^ ols; k ^ ols; ::: b 9.5 Properties and Sampling Distribution of b 191 191 192 193 195 202 205 206 208 9.6 Overelaborate Multiple Regression Models 9.7 Underelaborate Multiple Regression Models 9.8 Application: The Curious Relationship between Marriage and Death 9.9 Multicollinearity 9.10 Application: The Impact of College Graduation and Gender on Weekly Earnings 9.11 Application: Vote Fraud in Philadelphia Senatorial Elections Exercises ALE 9a: A Statistical Examination of the Florida Voting in the November 2000 Presidential Election – Did Mistaken Votes for Pat Buchanan Swing the Election from Gore to Bush? ALE 9b: Observing and Interpreting the Symptoms of Multicollinearity ALE 9c: The Market Value of a Bathroom in Georgia Appendix 9.1: Prediction Using the Multiple Regression Model Chapter 10 210 214 218 220 (Online) (Online) 222 DIAGNOSTICALLY CHECKING AND RESPECIFYING THE MULTIPLE REGRESSION MODEL: DEALING WITH POTENTIAL OUTLIERS AND HETEROSCEDASTICITY IN THE CROSS-SECTIONAL DATA CASE 224 10.1 Introduction 10.2 The Fitting Errors as Large-Sample Estimates of the Model Errors, U1 UN 224 227 CHMATH 11/11/2011 11:50:22 Page 698 BINDEX01 11/21/2011 18:55:42 Page 699 INDEX A Abramowitz, 65n15, 81n10 Acemoglu, D., 292nn41, 42, 305, 308n9, 309, 332, 332n35 adjusted R2, 205 Aitken, A C., 374n45, 375, 375n50 Akaike Information Criterion (AIC), 205 Alfred, Crosby, 333 alternative hypothesis, 71 Altug, S., 636n61 analogous stability test, 445 Anderson, A A., 627–629, 627n37 Anderson, H., 632, 632n49 Andrews, D W K., 422n44 Angrist, J D., 282–289, 307n6, 308–309, 308n10, 309, 322n25, 665, 681, 681n2, 688 Angrist-Krueger model, 309–310, 318, 321, 324, 329, 665–666, 667n30 bootstrapping, 282–289 AR(1) model, 509 application to U.S consumption function errors, 370–374 for serial dependence in time-series, 363–367 AR(1) models, 577 Arellano, M., 433n52, 470n17, 522–523, 523n18 Arellano/Bover GLS transformation, 433n53 Arellano-Bond Estimator, 522–529 ARMA(p,d,q) models, 595–604, See also time-series analysis and forecasting (Part B) ARMA(p,q) models, 581–585 Arora, S S., 480n29 Ashley, R., 58n9, 204, 204n11, 227n7, 252n39, 282n31, 305n2, 306n4, 309, 309n12, 324n30, 330, 343nn2, 3, 346n10, 394n6, 406, 406n26, 414n34, 433n53, 522n14, 542n13, 570n59, 595n1, 601n4, 623, 623n31, 624, 624nn32, 33, 630n42, 633, 633nn50, 52, 635, 635nn55, 57, 536–637, 636nn60, 61, 637, 639n64, 640n65, 641, 670n35, 685n10, 686nn13, 15, 691–692 asymmetric loss function on estimation errors, 55 asymmetric preferences, 542 asymptotic correlation, 320 asymptotic efficiency, 267 asymptotic sampling distribution derivation of instrumental variables slope estimator, 336–339 of OLS slope estimator, 299–302 distribution of w ^1ols in AR(1) model, 384–388 asymptotic theory, 264–269, 343 for OLS slope estimator with stochastic regressor, 269–271 ‘asymptotic uncorrelatedness’, 270, 313 asymptotic variance, 267, 271, 288 Augmented Dickey-Fuller (ADF) test, 401, 424, 426, 432, 448, 601, 604 autocorrelation of mean-zero time-series, 349 autocovariance of mean-zero time-series, 349 autometrics procedure, 621n27 autoregressive conditional heteroscedasticity (ARCH), 635 autoregressive model of order one, See AR(1) model auxiliary regression, 239–241 B Bai-Perron test, 226, 422n44 Baker, R., 310n15, 692 balanced vs unbalanced panel data, 459n1 Baltagi, B H., 480n29, 488n44, 496, 496n57 Baltagi/Chang adjustment, 480n29 Baltagi/Li estimator, 496 699 BINDEX01 11/21/2011 18:55:42 Page 700 700 Bao, Y., 364n29 Barnett, W A., 545–546, 635n55 Bartlett interval, 549 Bartlett, M S., 545–546, 545n23 Becker, G S., 508n1, 519n10, 522 ‘begin large’ approach, 414 ‘begin small’ approach, 413 ‘beneath contempt’ forecast, 640–643 Best Fit estimator, 47 Best Linear Unbiasedness (BLUness), 47, 58–61, 99, 140–143, 239 between effects model, 468–478, 479n27 advantage, 477 Bhargava, A., 508n2 bias property, 52 biased forecast, 538–543 BIC goodness-of-fit measure, 445 ‘bilinear’ family of nonlinear models, 627 binary-choice regression models, MLE of, 653–658 bivariate linear regression model (inference on b), 150–177 application college graduation impact on weekly earnings, 164–168 growth good for the poor, question of, 168–169 95% confidence interval for b with s2 given, 152–154 with s2 unknown, 160–162 estimates versus estimators, 154–155 s2, estimating, 158–159 hypothesis about b, testing with s2 given, 156–158 model assumptions role, 154–155 poorgrowi versus meangrowi data, 151 S2, properties of, 159 statistic for b not involving s2, 160 statistic for b with a known distribution, 152 student’s t density function, 163 unit normal density function, 153, 157 bivariate linear regression model, 131–149 b^ as a linear estimator, 132–134 b^ , properties, 140 best linear unbiasedness, 140–143 consistency, 140 sensitivity of, 147–149 b^ , sampling distribution of, 134–140 explantory data chosen to minimize variance of b^, 139 estimates, 132 estimators, 132 properties, 131–149 least squares weights, 132–134 properties, 134 MLE estimation of, 648–653 bivariate regression model, 23, 99–130 assumptions, 99–130 with a dummy variable, 120–126 collegegrad variable, 121–126 INDEX pternwa variable, 121–126 quantifying the impact of college graduation on weekly earnings, 120–126 ‘fixed in repeated samples’ causality assumption, 105–106 dependent variable, 106–107 explanatory variable, 105–107 model error term, 105–107 form, 105–106 introduction, 99–130 least squares estimation of a and b, 109–118 fitting error, 112 guessed-at fitted line drawn in, 111 interpreting, 118–120 population regression line drawn in, 110 squared fitting errors, 113–114, 113n12 mean estimation to regression transition, 100–104 model error term, assumptions on, 106–109 parameter estimates, 99–130 per capita real output variation across countries, analyzing, 100–104 log(real per capita GDP) versus log(real per capital stock), 104 log(rgdpl) values, histogram of, 102 real per capita GDP versus real per capita capital stock, 103 rgdpl variable, histogram of, 100 bivariate regression model (R2 and prediction), 178– 190, See also goodness-of-fit measure (R2) model fitting the data, quantifying, 179–182 model validation, prediction as a tool for, 182184 predicting YNỵ1 given xNỵ1, 184187 prediction error, 185 SST vs SSR vs SSE, 181 bivariate time-series regression model, 348–352 autocorrelation of mean-zero time-series, 349 autocovariance of mean-zero time-series, 349 with fixed regressors but serially correlated model errors, 348–352 Bond, S., 523, 523n18 bootstrap approximation, 281–282 Angrist-Krueger model, bootstrapping, 282–289 Bound, J., 310n15, 692 Bover, 433n52 Box, G E P., 405n23, 448n82, 452n87, 538n4, 550n31, 577, 581, 583n77, 601n4, 618n20, 619 Box-Jenkins approach/algorithm, 345, 581–585, 596, 599, 601–602 Breusch, T S., 241n26 Brock, Dechert and Scheinkman (BDS) test, 635 Brock, W A., 536n61, 635n56, 636n60 C Cameron, A C., 434n7, 464n7, 483n35, 495n54, 523n18, 658n18 Castle, J L., 636n60 BINDEX01 11/21/2011 18:55:43 Page 701 701 INDEX ‘causality’, definition, 306 Cawley, J., 214n21 censored regression, 657 Center for Research in Security Prices (CRSP), 345 Central Limit Theorem (CLT), 31, 32n21, 107, 197, 229, 268, 384, 385n56, 386–387, 386n59 Lindeberg – Levy version, 31 central moments, 15 Chang, Y., 480n29 chi-squared distribution, 75–78 Chow test, 203n10 Chumlea, W., 220n25 Clark, T E, 623, 623n30 cluster-robust standard error estimates, 466n10, 472–474, 480, 483n34, 485n38, 489, 495–497 Cobb-Douglas production technology, 103 Cochrane-Orcutt estimator, 375 cointegration concept, 424–431 ‘cointegrating’ regression model, 425 Colditz, G., 220n25 collegegrad variable, 121–126 collegegradi – pesexi, 213 combination forecast, 643–644 conditional distribution of Yi given xi, 106, 106n4 conditional mean of a random variable, 23, 44 conditional-mean forecast, primacy of, 538–543 conditional variance of time-series, 630 confidence interval, 33, 150, 152–154, 160–162 for m when s2 is known, 69–71 consistency property, 54, 64, 261, 266–270 of b^ , 140 consistent estimator, 47 ‘contemptibility’ criterion value, 642 continuous random variables, 12, 17–19 convergence in distribution, 267 ‘convergence in probability’, 265 ‘convergence to a stochastic probability limit’, 267 correlated instrument, 308 correlation versus causation, 305–311 ‘country-effect’ on Yi;t, 481 covariance of a pair of random variables, 23–24 covariance stationarity, 346n10, 349n16, 397n12, 543–544 Cox, D R., 405n23 Crame´r-Rao lower bound, 673n39 cross-sectional data, 345–347, See also under time-series data case (Part A) heteroscedasticity in, 224–258 vs time-series vs panel data, 260 Current Population Survey (CPS), 121 curve fitting m estimation by, 48–51 parameter estimation beyond, 647–680, See also generalized Method of Moments (GMM); maximum Likelihood Estimation (MLE) D David, Dollar, 4, 4n1 Davidson, R., 302n57, 338, 338n44, 372n40, 402, 402n18, 663n25, 667n27, 678n45, 692 De Jong, R., 661n24 Dechert W., 635n56 degrees of freedom, 205, 212 density function, 18 unit normal density function, 29–30 deseasonalizing time-series data, 611–617 deterministic vs stochastic trend, 596 diagnostic checking, 84–87, 224–258, 342–388, 389– 453, 683–685, See also time-series data case (Part A); time-series data case (Part B) computer software in, 89 constancy of s2 across the sample, 87–89 constancy of m across the sample, 84–87 data requirement in, 90 Dollar-Kraay model, 252–255 of estimated panel data model, 490–500 failed test, 89–90 general comments on, 89–90 need for, 89 situationally specific optimal amount, 90 skillset required for, 90 differential calculus, 696 DiNardo, J., 159n3, 307, 307n6 discrete random variables, 12, 13–17 central moments, 15 kth moment, 15 population mean, 14 population variance, 16 ‘distributed lag’, 559 division property, 270, 313, 369 Dollar, David, 4nn1, 2, 6, 150, 168, 343n3, 252, 252nn38, 39 Dollar-Kraay model, diagnostically checking, 252–255 Doornick and Hendry procedure, 621 Doornik, J A., 621, 621nn26, 623n31, 637n62 dummy variable, 120–126, See also under bivariate Regression Model b*ols when xi is a dummy variable, 130 Durbin-Watson test, 372n40 Dwyer, G P., 632n47 dynamic model respecification, 374–382 dynamic multiple regression model, 390–395, 430, 621 autoregressive model of order one, 390 bivariate regression model, 390 dynamics variable, 507–515 E economic vs statistical significance, 168 efficiency, 58–61, 141, 143n9 efficient estimator, 47 Einstein, Albert, 681n1 BINDEX01 11/21/2011 18:55:43 Page 702 702 elasticity concept, 120n15 Elliott, G T., 403n20 empirical distribution, 280 empirical model, 462–468 Enders, W., 538n4, 630, 630n41 endogeneity, 259–302, See also endogenous regressors sources, 260 joint determination (simultaneity), 260 measurement error, 260 omitted variables, 260 endogenous regressors, 303–305 vs exogenous variable, 274, 274n19, 303–305, 461–464, 490, 496n56 macroeconomic and microeconomic models, joint determination, 274–278 measurement error, 273–274 omitted variables, 272 ‘endogenous()’ option, 526n21 ‘endogenous’ random variable, 106 ‘endogenous regressors’ problem, Engle-Granger ADF test, 426–428 ‘equispaced’ time-series, 343 Ericsson, N R., 621, 621n26, 623n31 error-correction terms, 429 Eryuăruăk, G., 670n36 estat sargan command, 527n24 estimated generalized least squares (EGLS), 244n29 estimation errors, asymmetric loss function on, 55 s2, estimating, 158–159 EViews Scatterplot, 5–6 exactly identified variable, 307n6 exogenous regressors, 274n19 expectations conditional mean, 23 initial results on, 19–20 linearity property of, 19, 24–26 proof of, 45 exponential smoothing, 612n17 F F distribution, 87 density function for, 88 Fair, R C., 590, 590n87 FAIRMODEL equations, 589n86, 591n91 Feasible Generalized Least Squares (FGLS), 374, 496 Cochrane-Orcutt implementation of, 375 Hildreth-Lu implementation of, 375 feasible optimality properties, 58–61 BLUness, 58–61 efficiency, 58–61 figure of merit, 204 Final Prediction Error (FPE) criterion, 205 finite sample vs limiting (asymptotic) distribution, 286, 288n39 first-differences model, 468, 490, 496n56, 515–528 INDEX fitting errors as large-sample estimates of model errors, U1 UN, 227–228 vs prediction error, 184–185 ‘fixed constant’ term, 26n13 fixed effects model, 462, 468–478 fixed in repeated samples, 105–106, 227, 259, 274, 274n19, 277, 306, 479n28 fixedregressors, 259 bivariate time-series regression model with, 348–352 Flores-Lagunes, A., 531, 532n28 Florida Comprehensive Assessment Test (FCAT), 531, 531n29 forecasting, 595–646, See also time-series analysis and forecasting (Part B) ‘forward orthogonal deviations’ transformation, 522n14 fractional integration, tests for, 601n4 Freund, John, 13n5 ftest.exe program, 88n18 G Galiardini, P., 661n24 Gallant, A R., 635n55, 637n62 ‘Gaussian’ distribution, 29–30 ‘gaustail.exe’ program, 30 Generalized Empirical Likelihood (GEL) class, 523n17 generalized Hausman test, 470n18, 487–488 stata code for, 503–506 generalized least squares (GLS) estimator, 374 generalized method of moments (GMM), 251n37, 308n7, 318n21, 375n46, 465n9, 496n58, 518n9, 647–680 application to IV regression, 647–680 b in bivariate regression model, GMM estimation of, 678–680 Hansen’s J test, 669 two-step GMM estimator, 665 generated time-series with deterministic time trend #1, 596–597 with deterministic time trend #2, 596, 598 Giraitis, L., 403n21 Goncalves, S., 281n29 ‘goodness’ concept, 33, 46 goodness-of-fit measure (R2), 179 adjusted R2, 205 as consistent estimator, 181 definition, 181 R2 within, 475–476 Granger, C W J., 306, 306n4, 414n34, 424, 538n4, 540–541, 541 nn10, 11, 612n17, 624, 624n33, 627–629, 627n37, 633n51 Granger-causation, 624 formalism, 306–307 testing for, 622–623 BINDEX01 11/21/2011 18:55:43 Page 703 INDEX Graybill, F A., 268n14 ‘The Great Moderation’, 553n35 Greene, W H., 682n6, 692 grid search, 375 Grossman, M., 508n1, 519n10 H Haggan, V., 631n43 Hamilton, J D., 266n9, 298n52, 368n33, 385nn56, 57, 538n4, 544n18, 631, 631n44, 636n61 Han, C., 523n17, 661n24 Hausman test, 487–488 generalized Hausman Test, 470n18, 487–488, 503– 506 Hansen’s J test, 669 Hausman, J A., 323n27, 468n15, 486n39 Hausman-Taylor approach, 468, 489, 519n11 Heckman, J., 214n21 Hendry, D F., 414n35, 621, 621n26, 636n60, 636n60, 637n62 Heracleous, M., 630n41 heterogeneity across units, periods, or explanatory variable values, 464n7, 467n14, 469 heteroscedasticity, 107, 407n31 and its consequences, 237–239 in cross-sectional data case, 224–258 of known form, correcting for, 243–248 testing for, 239–242 of unknown form, correcting for, 248–251 Hildreth-Lu estimator, 375 Hinich, M J., 627n36, 635n55, 636, 636nn59, 61 Hinich bicovariance test, 636 ‘hold-out’ sample, 439n64 homogeneity, 547 homoscedasticity, 107, 664 vs heteroscedasticity, 237 Hsieh, D A., 536n61, 636n60 h-step-ahead forecast, 538–540, 564, 574, 583 hybrid approach, 596, 603–604 hypothesis test, 156–158, 467n12 when s2 is known, 71–74 I I(0) Time-Series, 398, 400–406, 424–431 identically and independently (IID) random variables, 311–312 ‘idiosyncratic shock’, 466 imperfect multicollinearity, 209 ‘impulse response function’ form, 522n14 independent random variables, 26 indirect least squares (ILS), 277–278 inference results on m when s2 is unknown, 78–82 Inference Using Lag-Augmented Models (both ways), 389–394 influential observation, 230 influential outliers, 229–233 703 ‘inst()’ option, 526n21 instrumental variables (IV) technique, 647–680, See also generalized method of moments (GMM); maximum likelihood estimation (MLE) instrumental variables estimation, 227, 303–341 correlation versus causation, 305–311 education and wages, relationship between, 321–330 slope estimator in Bivariate Regression Model, 311–313 inference using, 313–317 two-stage least squares estimator for overidentified case, 317–321 integrated – ARMA(p,d,q) models, 595–604, See also time-series analysis and forecasting (Part B) integrated time-series issue, 389n1 invertible MA(q) model, 563–565 identification/estimation/checking/forecasting of, 563–565 linearly-deterministic component, 565 ‘invertibility’ in nonlinear modeling context, 628 J jackknife method, 280 Jaeger, D., 310n15, 692 Jenkins, G M., 448n82, 452n87, 538n4, 577, 581, 583n77, 601n4 Jensen, M J., 635n55 Jessica, M., 217n24 Johnson, S., 292n41, 308, 308n9, 332, 332n35 Johnston, J., 77n8, 159n3, 307, 307n6 Jungeilges, J A., 635n55 Jushan, Bai, 226n4, 422n44 K Kaplan, D T., 635n55 Keane, M P., 685n10, 691n17 Kennedy, P., 323n28 Kilian, L., 281n29 Kmenta, J., 278n23, 372n40, 657n17 Kraay, Aart, 4n1, 2, 6, 150, 168, 252, 252nn38, 39, 343n3 Krueger, A., 282–289, 308, 308n10, 309, 322n25, 665, 688 kth moment, 15 L ‘lag-augmented’ model, 434, 436–437, 446n77 lag length, 349n14 ‘lag operator’, 448 and its inverse, polynomial in, 559–563 linear time-series models, 559–563 lagged dependent variables, 507–515 Lam, P., 631, 631n44 ‘latent’ variable, 654 BINDEX01 11/21/2011 18:55:43 Page 704 704 Law of Large Numbers (LLN), 265–266, 313, 315, 364n32 least absolute deviations (LAD), 50, 111, 147, 648n1 least squares estimation of a and b, 109–118, See also under bivariate Regression Model least squares weights, 196, 132–134, 193–195 properties, 134 wjiols vs wiols, 196 least-squares curve-fitting, 648 LeBaron, B D., 536n61, 636n60 leptokurtic distribution, 325, 491n48, 652n8 Li, Q., 488n44, 496, 496n57 Li, W K., 635n58 likelihood ratio test, 652 ‘limited dependent variable’ models, 657 censored regression, 657 multinomial probit, 657 ordered probit, 657 truncated regression, 657 Lindeberg – Levy version of central limit theorem, 31 linear combination of normally distributed random variables distribution, 32–36 linear filter, 565n51 linear function, 225–226, 232 ‘linear probability model’, 658 linear regression model, 133n2 linear time-series models, understanding and manipulating, 559–563 linearity property, 35, 53, 85, 270, 369 of expectations, 19, 24–26 linearly-deterministic component, 565 Ljung, G M., 550n31 Locke, P., 632n47 log-likelihood function vs likelihood function, 650– 655 loss function on forecast error – Loss(eN,h), 539–542 M MA(1) Model, 560n41 MacKinnon, J G., 302n57, 338, 338n44, 372n40, 377n50, 402, 402n18, 663n25, 667n27, 678n45, 692 Madalla, G S., 372n40 Maddison, 463n6 Magdalinos, T., 403n21 marginal effect, 656–657 Markov switching models, 631 Marriott, F H C., 545–546, 545n23 Martian logarithm disposable income, 370 maximum likelihood estimation (MLE), 647–680 application to binary-choice models, 647–680 of binary-choice regression models, 653–658 latent-variable model, 654 observed-variable model, 654 ‘probit’ model, 653 of simple bivariate regression model, 648–653 ‘maxldep()’ option, 524 INDEX McCracken, M W, 623, 623n30 McLeod, A I., 635n58 McLeod-Li test, 635–636 mean estimation to regression transition, 100–104 mean square error (MSE), 56, 204, 570 meaningful MA(q) process, 567n52 measurement error, 12 method of moments estimation, 658–664 Michels, K B., 220n25 minimum MSE estimator, 47 model errors assumptions on, 106–109 vs fitting errors, 228–257 ‘model identification’ in time-series analysis, 567 model parameter instability, 193 model respecification, 683–685 modeling ‘in changes’ vs modeling ‘in levels’, 447–448 modeling in levels, 403 ‘monte carlo’ method, 280 monthly U.S treasury bill rate, modeling, 604–611 January 1934 to September 2010, 605 January 1984 to September 2010, 606–608 partial correlogram of change in, 609 Mood, A M., 268n14 moving average process (MA(q)) model, 563–564 multicollinearity, 208–210 imperfect multicollinearity, 209 multinomial probit, 657 multiple regression model, 191–223, 318 applications college graduation and gender impact on weekly earnings, 210–214 marriage and death, relationship between, 206–208 vote fraud in Philadelphia senatorial elections, 214–217 b^ ols;1 :: b^ ols;, properties and sampling distribution of, 195–202 vs bivariate regression model, 192 with fixed-regressors, 393 assumptions, 393–394 importance, 192–193 multicollinearity, 208–210 imperfect multicollinearity, 209 need for, 192–193 overelaborate, 202–205 parameter estimates via least squares fitting, 193–195 OLS estimate of b3, 194 prediction using, 222–223 respecifying, 342–453, See also time-series data case (Part A); time-series data case (Part B) under-elaborate, 205–206 multiple regression model (diagnostically checking and respecifying) Bai-Perron test, 226 BINDEX01 11/21/2011 18:55:43 Page 705 INDEX dealing with potential outliers, 224–258 fitting errors as large-sample estimates of model errors, U1 UN, 227–228 fundamental categories, 225 heteroscedasticity in cross-sectional data case, 224–258 normality of model errors, U1 UN, reasons for checking, 228–257 Dollar-Kraay model, diagnostically checking, 252–255 heteroscedasticity and its consequences, 237–239, See also heteroscedasticity influential observation, 230 sktest varname, 229n12 swilks varname, 229n12 ‘structural change’, tests for, 226 multiple time-series, generalizing results to, 389–390 multiplicative property for independent random variables, 27 for uncorrelated random variables, 26 multivariate empirical example, 462–468 multivariate time-series models, 617–622 ‘intervention analysis’ framework, 618 transfer function model, 618 Murphy, K M., 508n1, 519n10 ‘myopic’ model, 508n1, 516n7, 519n10 N National Longitudinal Surveys (NLS) of Labor Market Experience, 459 ‘natural’ null hypothesis, 426 Newbold, P., 414n34, 540–542, 538n4, 612n17 Newey, W., 670n36 Newey-West standard errors, 377–378, 395n8 ‘noconstant’ option, 525 nonautocorrelation, 108–109 assumption, 371, 371n37 vs serial independence, 624, 624n32 non-exogenous (endogenous) explanatory variables, 224 nonlinear serial dependence in time-series, modeling, 623–637 ‘bilinear’ family of nonlinear models, 627–628 Brock, Dechert and Scheinkman (BDS) test, 635 conditional variance of, 630 exponential AR(1) model, 631 general features of, 626 Hinich Bicovariance test, 636 ‘invertibility’ in, 628 Markov switching models, 631 McLeod-Li test, 635–636 pre-whitening, 635 Threshold Autoregression (TAR) model, 631 unconditional variance of, 630 nonlinearity in model, 192–193 nonparametric bootstrap method, 279n25 ‘normdist’ function, 30n17 705 normal equations, 116 normally distributed random variables, 29–30, 42–43 linear combination of, distribution, 32–36 properties of, 31–32 linear combination, 31 uncorrelatedness, 31 weighted sum, 31 normally distributed random variable, mean of, estimating, 46–67 consistency, a first pass, 54 m by curve fitting, 48–51, See also population mean (m) estimation errors, asymmetric loss function on, 55 feasible optimality properties, 58–61 BLUness, 58–61 efficiency, 58–61 ‘mean square error’, 56  51–54 sampling distribution of Y, squared error loss function, 56–58 unbiasedness and the optimal estimator, 55–56 normally distributed random variable, mean of, statistical inference on, 68–96 confidence intervals for m when s2 is known, 69–71 diagnostic checking, 84–87 hypothesis testing when s2 is known, 71–74 inference results on m when s2 is unknown, 78–82  69 standardizing the distribution of Y, using S2 to estimate s2, 75–78 notational convention, 13n4 null hypothesis, 71, 549 Nychka, D W., 637n62 Nychkam, D W., 637n62 O omitted variable issue, 404, 471 one-tailed ADF test, critical points for, 402 one-tailed hypothesis test, 74 vs two-tailed hypothesis test, 157 optimal estimator, 55–58 optimal forecasts, 538–543 biased forecast, 538–543 conditional-mean forecast, primacy of, 538–543 optimal GMM Weights, 663 ordered probit, 657 ordinary least squares (OLS) value, 111, 114, 304 Ouliaris, S., 426n48 outliers, 229 outlying observation, 229 over-differenced time-series, 447–448 overelaborate multiple regression models, 202–205 over-elaborate vs under-elaborate model, 191–223 overidentification, two-stage least squares estimator for, 317 overidentified vs exactly identified model, 307n6 overidentifying restrictions, 669 Ozaki, T., 631n43 BINDEX01 11/21/2011 18:55:43 Page 706 706 P P one-step-ahead forecast, 622 Pagan, A R., 241n26 pair of random variables, 22–24 panel data methods, 466 Panel Study of Income Dynamics (PSID), 459 parameter estimation beyond curve-fitting, 647–680, See also generalized method of moments (GMM); maximum likelihood estimation (MLE) least-squares curve-fitting, 648 OLS curve-fitting approach, 648 parameter instability, 226 parametric bootstrap method, 279n25 Park, B., 661n24 Parmeter, C., 305n2, 309, 309n12, 324n30, 330, 343n2, 394n6, 595n1, 685n10, 670n35, 691–692 Patterson, D M., 346n10, 595n1, 601n4, 624n32, 633n50, 635–637, 635nn55, 57, 636nn59, 61, 686n13 Patton, A J., 540n7 Pemberton, M., 563n46, 679n46 Penn World Table (PWT), 100–104, 128–129, 259, 459 data from, 460–462 per capita real output variation across countries, analyzing, 100–104 percentile method, 279n27 Perron, Pierre, 226n4, 403n19, 422n44, 602n6 pesexi, 211 Phillips, P C B., 403n21, 426n48, 523n17, 595n1 Pierce, D.A., 550n31 Pigou effect, 406, 417, 438 Pischke, J., 307n6, 681, 681n2 Politis, D N., 281n29 Polizzi, 309, 330 polynomial in lag operator and its inverse, 559–563 ‘pooled estimation results’, 466 pooled regression model, 461–466, 479n27, 481, 488 Pope, J A., 545–546, 545n23 population mean (m) estimation, 14, 46 confidence intervals for, when s2 is known, 69–71 m constancy across the sample, testing, 84–87 by curve fitting, 48–51 sum of squared fitting errors (SSE), 49 sum of the absolute fitting errors (SAD), 50 population variance (s2), 16, 46, 75 constancy of s2 across the sample, testing, 87–89 portmanteau (or Q) test, 549, 580n74, 635 positive estimation errors, 56n7 ‘postsample’ forecasting, 182, 622–623 ‘recursive’ forecast, 622 rolling window forecast, 622 ‘post-sample period’, 439n64, 569 Potter, S M., 632, 636n60, 636n61 practical shrinkage forecasting, 637–640 INDEX ‘pre()’ option, 526n21 ‘predetermined’ variable, 471 ‘predict’ command, 525n20, 534n39 ‘pre-whitening’ time-series, 635 Priestley, M B., 637n62 ‘Prob>chi2’ entry, 487 probability limit, 265–272 algebra of, 298 probability theory, 11–45, See also expectations, linearity property random variables, 12–13, See also individual entry statistical independence, 26–29 variances, 20–21 ‘Probit Regression’, 655 ‘probit’ model, 653 pseudo-random numbers, 65–66, 547n29 pternwa variable, 121–126 p-value, 72, 72n4, 156, 163 for one-tailed hypothesis test, 74 for two-tailed hypothesis test, 74 Q ‘Q’ test, 549 quasi-difference transformation, 483–484, 485n37 ‘quasi-differenced’ variables, 519 R random effects model, 462, 467n14, 468, 470, 474n23, 478–490 random variables, 12–13 continuous, 12–13, 17–19 discrete, 12, 13–17 IID random variables, 31–32 independent, 26 multiplicative property for, 27 normally distributed, 29–30 properties of, 31–32 pair of, 22–24 standard deviation of, 16 uncorrelated, multiplicative property for, 26 random walk time-series, 395–404, 599 AR(1) model, 396 Augmented Dickey-Fuller (ADF) test, 401 covariance stationary time-series, 397n12 detrended logarithm of S&P 500 stock market index, 399 with drift, 367 logarithm of S&P 500 stock market index, 399 modeling in levels, 403 one-tailed ADF test, critical points for, 402 sample correlogram, 400 Rapach, D E., 644n66 ‘rational’ model, 508n1, 516n7 Rau, N., 563n46 ‘recursive’ forecast, 622 reduction to ordinary limit property, 270, 369 Reed, W R., 496n56 BINDEX01 11/21/2011 18:55:43 Page 707 INDEX regression analysis four ‘big mistakes’, 685–690 danger of neglecting trends and/or strong serial dependence, 685 danger of overextrapolation, 686–687 tyranny of the vocal (but temporary) minority, 686 wrongly-omitted-variable trap, 687–688 omitted-variables tactic, 688 attempt to fix the problem using IV regression, 690–692 drop the problematic included variables, 689 include the omitted variable, 688 reinterpret the estimated coefficients, 689–690 regression modeling with panel data (Part A), 459–506 data from Penn World Table, 460–462 estimated panel data model, diagnostic checking of, 490–500 eit estimates, 492 ni estimates, 492 Ti values, 493 fixed effects and the between effects models, 469–478 ‘omitted variables’ problem, 471 strict exogeneity assumption, 471 large data sets, source of, 459–460 multivariate empirical example, 462–468 panel data methods, 466 ‘pooled estimation results’, 466 regression modeling with panel data (Part B), 507–535, See also relaxing strict exogeneity relaxing strict exogeneity, 507–515 dynamics variable, 507–515 first-differences model, 515–528 lagged dependent variables, 507–515 ‘quasi-differenced’ value, 510 strict exogeneity assumption, 514 ‘resampling’, 281 restricted sum of squares (RSS), 201 reverse causation, 274, 305–307 rgdpl variable, 100–104 Robinson, J A., 292n41, 308, 308n9, 332, 332n35 robust regression method (LAD), 235 robust standard error estimates, 249–252 rolling window forecast, 622 Romano, J P., 281n29 Rosner, B A., 220n25 Rothenberg, T J., 403n20 Rothman, P., 536n61, 628n38, 636n60 ‘Rule of Law’, 332–335 S S2, properties of, 159 sample correlogram, 400, 543–559 sample moment conditions vs population moment conditions, 658, 665 707 sampling distribution of an estimator, 131–149 of Y, 51–54 Sargan test, 527n24 Sargan, J D., 508n2 Sargent, T J., 564n48 Satterthwaite, F E., 88–89, 88n19 Scheinkman J., 635n56 Schraalensee, R., 306n4, 624, 624n33 Schwarz Criterion (SC)/BIC, 205, 374, 381, 381n52, 436–438, 436n60 Scott, Long, J., 658n18 seasonal difference, 345n7, 613 seasonally adjusted at annual rates (SAAR), 343–345, 407n29 vs not seasonally adjusted data, 612, 612n15 ‘selection bias’, 657 sensitivity analysis, 685, 691–692 ‘serial correlation’ concept, 624 ‘serial dependence’, 623 in a time-series, AR(1) model for, 363–367 serially correlated regression errors, straightforward test for, 370–374 ‘shrinkage forecast’, 638 ‘sigmamore’ option, 487n42 Sims, C A., 434, 434n54, 621n23, 682n4 single-equation modeling, single sums, 693 algebra with, 694 double sums, 694 skewness-kurtosis normality test, 412n32 sktest varname, 229n12 Slutsky theorem, 266, 315 ‘smaller deviations’ concept, 667 smaller mean square error (MSE), 622 Smith, R J., 670n36 smooth transition autoregression (STAR) models, 632 software packages, Eviews, 3–6 Stata, 3–6 Spanos, A., 630n41 spurious regression due to data mining, 183 squared error consistency, 140 squared error loss function, 56–58, 569 squared fitting errors (SSE), 374n44 squared-error loss function, 540 standard deviation, of a random variable, 16 standardizing the distribution of Y, 69 ‘structural change’, tests for, 226 stata ‘xtreg’ command, 495 stata probit command, 656n13 Stata syntax, 655 stationarity, 544 covariance stationarity, 544 non-stationary, 544 strict stationarity, 544 BINDEX01 11/21/2011 18:55:43 Page 708 708 stationary AR(p) model, 575–581 identification/estimation/checking/forecasting of, 575–581 statistical independence, 26–29 stochastic regressors, 259–302, 342, 348, 364, 367 Bivariate Regression Model with, 371n37, 379 how large a sample is large enough?, 278–282 OLS parameter estimator asymptotic results for, 269–271 with stochastic regressor independent of model errors, 261–264 Stock, J H., 310n15, 403n20, 426n47, 434, 434n54, 474n23, 644n66 Strauss, J K., 644n66 strict exogeneity assumption, 471, 514 strict stationarity, 544 strictly exogenous explanatory variable vs predetermined, 462, 471–472 vs weakly exogenous, 472 structural equation vs reduced form equation, 277 structural parameters, 275 student’s t distribution, 78–82, 163, 316 unit normal distribution and, 79 Sul, D., 523n17 sum of squared fitting errors (SSE), 49, 113–116, 201, 381n52, 650 sum of squares total (SST), 212 sum of the absolute fitting errors (SAD), 50 summation notation, 13n3 Summers, R., 463, 463n6, 499 sup-Wald test of Andrews, 422n44 Swamy, P A V B., 480n29 swilks varname, 229n12 T Taylor Rule, 377 Taylor, W E., 468n15 tdist function, 164n5 Teraăsvirta, T., 632, 632n49, 633n51 ‘textbook’ method, 413 Theil, H., 59n10, 651, 673n39 threshold autoregression (TAR) model, 631 Tiao, G C., 618n20, 619 time-plot, 543–559 ‘time-series analysis’, time-series analysis and forecasting (Part A), 536–594, See also optimal forecasts annualized quarterly growth rate in U.S GNP from 1947II to 2010II, 551 from 1953I to 2010II, 551 from 1981II to 2005II, 552 from 1981II to 2010II, 552 AR(1) generated data, 553 plus a mild time trend, 558 plus a shift in the mean, 557 plus an outlier, 556 sample correlogram of, 554 INDEX AR(p) or AR() model for, 576 ARMA(p,q) models, 581–585 Box-Jenkins modeling algorithm, 581–585 crucial assumption and fundamental tools, 543–559 invertible MA(q) model, 563–565 time-series econometrics, 536–538 time-series analysis and forecasting (Part B), 595–646 combining forecasts, gains from, 643–644 deterministic trend #1, 596–597 deterministic trend #2, 596, 598 forecast ‘beneath contempt’, 640–643 Granger-causation, testing for, 622–623 integrated – ARIMA(p,d,q) models, 595–604 monthly U.S treasury bill rate, modeling, 604–611, See also individual entry multivariate time-series models, 617–622 nonlinear serial dependence in time-series, modeling, 623–637 post-sample model forecast evaluation, 622–623 practical shrinkage forecasting, 637–640 ‘shrinkage forecast’, 638 stochastic time trend (random walk), 600 ‘trendlike’ behavior, 595–604 U.S total nonfarm payroll time-series, 611–617, See also individual entry time-series data case (Part A), 342–388, See also bivariate time-series regression model AR(1) model for serial dependence in time-series, 363–367 consistency of w1ols as an estimator of w1 in AR(1) model, 367–370 cross-sectional data versus, 347 display, 345–346 homogeneity issue, 346 model error term, 347 disastrous parameter inference with correlated model errors, 353–363, See also U.S consumption expenditures data example issues and methods associated with, 347 time-series data case (Part B), 389–453 capstone example part 1, 404–424 consumption spending versus lagged growth rate in disposable income, 411 fitting errors, 419 growth rate in disposable income, 412 model in changes versus model in levels decision, 406 monthly U.S consumption expenditures in growth rates, modeling, 404–424 real disposable income, 409 real personal consumption expenditures, 408 capstone example part 2, 424–431 monthly U.S consumption expenditures in growth rates, modeling, 424–431 capstone example part 3, 431–446 BINDEX01 11/21/2011 18:55:43 Page 709 709 INDEX level of monthly U.S consumption expenditures, modeling, 431–446 dynamic multiple regression model, 390–395 generalizing the results to multiple time-series, 389–390 I(1), 395–404, See also random walk time-series to model in levels or to model in changes?, 447–448 time-series econometrics, versus time-series analysis, 536–538 Timko, T., 531–532, 532n28 Toda, H Y., 389n1, 434, 434n55 Toda-Yamamoto rearrangement, 434 Tong, H., 632n45 transfer function model, 618 ‘trendlike’ behavior, 595–604 Trivedi, P K., 434n7, 464n7, 483n35, 495n54, 523n18, 658n18 Trojani, F., 661n24 truncated regression, 657 Tsang, 686n15 Tsay, R S., 636n61 ttail.exe program, 81n10, 175n20 two-sided filter, 612 two-stage least squares (2SLS) estimation, 307n6, 313, 318–321, 318n21, 523n16, 659, 665–668 as asymptotically uncorrelated with model error term, 340–341 for overidentified case, 317–321 ‘twostep’ option, 524, 526n22 two-tailed test, 73–74, 157 of null hypothesis, 446n77 two-way random effects model, 483n35 type i error, 72n5 U ‘unpacking’ process, 678 U.S consumption expenditures data example, 353–363 AR(1) model application to, 370–374 dynamic model respecification, 374–382 expenditures vs disposable income, 353 fitting errors from regression of, 355–357, 362, 380 personal consumption expenditures and disposable income for both U.S and Mars, 360 real personal consumption expenditures versus detrended logarithm of martian disposable income, 361 versus detrended logarithm of real disposable income, 361 versus martian logarithm of disposable income, 358–359 U.S real disposable income, 354 U.S real personal consumption, 354 U.S total nonfarm payroll time-series, 611–617 ARMA deseasonalization of, 611–617 fitting errors, 615–616 seasonal time-series data, 611–617 Udny Yule, G., 364n29 unbiasedness, 55–56, 140–143 vs consistency vs BLUness vs efficiency, 202 unbiased estimator, 47 unbiasedness property, 52 unconditional variance of time-series, 630 uncorrelated instrument, 308 uncorrelated random variables, multiplicative property for, 26 under-elaborate multiple regression models, 205–206 unimodality, 541n9 unit normal density function, 29–30 unit root, 367, 562n43, 563 unit-roots test approach, 596, 601–602 Urga, G., 661n24 V valid vs invalid instrument, 324 variances, 20–21 vce(cluster countrynum) option, 495 ‘vce(robust)’ option, 526, 526n22, 527n24 vector autoregression (VAR) model, 433n53, 590n87, 621 structural VAR models, 621n24 vector error-correction model (VECM), 424–425, 429, 432–433, 447 Verbrugge, R., 406, 406n26, 433n53, 522n14, 633, 633n52, 636n60, 686n15 volkert, Volcker subperiod dummy variable, 420 Vytlacil, E., 214n21 W Wallis, K F., 612n16 Watson, M W., 426n47, 434, 434n54, 474n23, 644n66 ‘weak instruments’ problem, 310 Welch, B L., 88n19 West, K., 623nn30 White, H., 385n57 White-Eicker ‘robust’ standard error, 249, 271n16, 339, 377, 421, 423, 436, 441–442, 446n77, 460, 465n9, 472–473, 474n23, 667n33 Willett, W C., 220n25 ‘within’ transformation, 469 vs random effects transformation, 470 Windmeijer, F., 523, 670n36 Wold, H., 564n48 Wright, J., 310n15 Wu, P X., 463n6, 496n57 X ‘xtabond’ command, 526 ‘xthtaylor’ command, 489 ‘xtreg’ command, 533n33 ‘xttest0’ command, 488 BINDEX01 11/21/2011 18:55:43 Page 710 710 Y Yamada, H., 434n55 Yamamoto, T., 389n1, 434, 434n55 Ye, H., 204, 204n11, 496n56, 623, 623n31 ‘ydat’ variable, 582n76 Yogo M., 310n15 INDEX Yu, W., 632n47 Yule, G Udny, 364n29 ‘Yule-Walker’ equations, 578–579 Z Zellner, A., 541n12 BENDP 11/21/2011 16:10:2 Page Active Learning Exercise 1a: An Econometrics “Time Capsule” Active Learning Exercise 1b: Investigating the Slope Graphically Using a Scatterplot Active Learning Exercise 1c: Examining Some Disturbing Variations on Dollar & Kraay’s Model Active Learning Exercise 1d: The Pitfalls of Making Scatterplots with Trended Time-Series Data Active Learning Exercise 2a: The Normal Distribution Active Learning Exercise 2b: Central Limit Theorem Simulators on the Web Active Learning Exercise 3a: Investigating the Consistency of the Sample Mean and Sample Variance Using Computer-Generated Data Active Learning Exercise 3b: Estimating Means and Variances Regarding the Standard & Poor’s SP500 Stock Index Active Learning Exercise 4a: Investigating the Sensitivity of Hypothesis Test p-Values to Departures from the NIID(m, s2) Assumption Using Computer-Generated Data Active Learning Exercise 4b: Individual Income Data from the Panel Study on Income Dynamics (PSID) – Does Birth-Month Matter? Active Learning Exercise 5a: Exploring the Penn World Table Data ^ à Over a Very Small Data Set Active Learning Exercise 5b: Verifying a ^ Ãols and b ols Active Learning Exercise 5c: Extracting and Downloading Current Population Survey (CPS) Data from the Census Bureau Web Site à ^ on a Dummy Variable Equals the Difference in Active Learning Exercise 5d: Verifying That b ols the Sample Means Active Learning Exercise 6a: Outliers and Other Perhaps Overly Influential Observations: ^ to an Outlier Using Computer-Generated Data Investigating the Sensitivity of b ^ Using Computer-Generated Data Active Learning Exercise 6b: Investigating the Consistency of b Active Learning Exercise 7a: Investigating the Sensitivity of Slope Coefficient Inference to Departures from the Ui $ NIID(0, s2) Assumption Using Computer-Generated Data Active Learning Exercise 7b: Distorted Inference in Time-Series Regressions with Serially Correlated Model Errors: An Investigation Using Computer-Generated Data Active Learning Exercise 8a: On the Folly of Trying Too Hard: A Simple Example of “Data Mining” Active Learning Exercise 9a: A Statistical Examination of the Florida Voting in the November 2000 Presidential Election – Did Mistaken Votes for Pat Buchanan Swing the Election from Gore to Bush? Active Learning Exercise 9b: Observing and Interpreting the Symptoms of Multicollinearity Active Learning Exercise 9c: The Market Value of a Bathroom in Georgia Active Learning Exercise 10a: The Fitting Errors as Approximations for the Model Errors BENDP 11/21/2011 16:10:2 Page Active Learning Exercise 10b: Does Output Per Person Depend on Human Capital? (A Test of the Augmented Solow Model of Growth) Active Learning Exercise 10c: Is Trade Good or Bad for the Environment? (First Pass) ^ OLS in the Bivariate Active Learning Exercise 11a: Central Limit Theorem Convergence for b Regression Model Active Learning Exercise 11b: Bootstrap Analysis of the Convergence of the Asymptotic Sampling Distributions for Multiple Regression Model Parameter Estimators Active Learning Exercise 12a: The Role of Institutions (“Rule of Law”) in Economic Growth Active Learning Exercise 12b: Is Trade Good or Bad for the Environment? (Completion) Active Learning Exercise 12c: The Impact of Military Service on the Smoking Behavior of Veterans Active Learning Exercise 12d: The Effect of Measurement-Error Contamination on OLS Regression Estimates and the Durbin/Bartlett IV Estimator Active Learning Exercise 14a: Analyzing the Food Price Sub-Index of the Monthly U.S Consumer Price Index Active Learning Exercise 14b: Estimating Taylor Rules for How the U.S Fed Sets Interest Rates Active Learning Exercise 16a: Assessing the Impact of 4-H Participation on the Standardized Test Scores of Florida Schoolchildren Active Learning Exercise 16b: Using Panel Data Methods to Reanalyze Data from a Public Goods Experiment Active Learning Exercise 17a: Conditional Forecasting Using a Large-Scale Macroeconometric Model Active Learning Exercise 17b: Modeling U.S GNP Active Learning Exercise 18a: Modeling the South Korean Won–U.S Dollar Exchange Rate Active Learning Exercise 18b: Modeling the Daily Returns to Ford Motor Company Stock Active Learning Exercise 19a: Probit Modeling of the Determinants of Labor Force Participation ... Outside of the United States, please contact your local sales representative Library of Congress Cataloging-in-Publication Data Ashley, Richard A (Richard Arthur), 195 0Fundamentals of applied econometrics. .. (Online) Appendix 2.1: The Conditional Mean of a Random Variable 44 Appendix 2.2: Proof of the Linearity Property for the Expectation of a Weighted Sum of Two Discretely Distributed Random Variables... understanding of the part they often have great difficulty learning on their own: the underlying theory and practice of econometrics In fact, generally speaking, learning how to instruct the software