A guide to basic econometric techniques

A Guide to Basic Econometric Techniques A Guide to Basic Econometric Techniques Second Edition Elia Kacapyr First published 2014 by M.E Sharpe Published 2015 by Routledge Park Square, Milton Park, Abingdon, Oxon OX14 4RN 711 Third Avenue, New York, NY 10017, USA Routledge is an imprint of the Taylor & Francis Group, an informa business Copyright © 2014 Taylor & Francis All rights reserved No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers Notices No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use of operation of any methods, products, instructions or ideas contained in the material herein Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infrine Library of Congress Cataloging-in-Publication Data Kacapyr, Elia, 1956[Introductory econometrics for undergraduates] A guide to basic econometric techniques / by Elia Kacapyr – Second edition pages cm Revised edition of the author’s Introductory econometrics for undergraduates Includes bibliographical references and index ISBN 978-0-7656-4477-0 (alk paper) Econometrics I Title HB139.K26 2014 330.01′5195—dc23 2013043917 ISBN 13: 9780765644770 (pbk) Contents Note on Supplementary Materials for Students and Instructors Preface Chapter 1: The Nature of Econometrics Chapter 2: Simple Regression Analysis Chapter 3: Residual Statistics Chapter 4: Hypothesis Testing Chapter 5: Multiple Regression Chapter 6: Alternate Functional Forms Chapter 7: Dichotomous Variables Chapter 8: Properties of Ordinary Least-Squares Estimators Chapter 9: Multicollinearity Chapter 10: Heteroskedasticity Chapter 11: Serial Correlation Chapter 12: Time-Series Models Chapter 13: Forecasting with Regression Models Chapter 14: Forecasting with ARIMA Models References Solutions to Odd End-of-Chapter Problems Solutions to Test Yourself Problems Critical Values Tables Subject and Name Index Note on Supplementary Materials for Students and Instructors All of the input data required for solving the end-of-chapter problems in this text beginning in Chapter are available at www.mesharpe-student.com The data files are in Excel format, which allows them to be imported into a variety of statistical software packages including Eviews and gretl Eviews by IHS was used to solve the problems in the book, but any package will Free shareware is available (such as gretl) that can all the problems in this text Excel by Microsoft can be used to run regressions, but it does not calculate all the residual statistics needed in later chapters Adopting instructors may obtain a full complement of ancillary materials from the Publisher at www.mesharpe-instructor.com Preface Econometrics can be a real eye-opener for students as they come to understand that many of the theories they have learned can be questioned and tested using real-world data This Second Edition of A Guide to Basic Econometric Techniques serves as a universal supplement for all introductory econometrics courses Whether used by undergraduates or students in advanced programs or by practitioners, this student-friendly book provides an introduction to econometrics and economic forecasting, with an emphasis on the proper application and interpretation of regression results “Student-friendly” does not mean superficial or easy It means that the explanations of essential concepts are concise, yet clearly illustrated step by step For instance, the derivation of the ordinary least-squares estimators is shown with simple algebra once the chain rule is applied Skip this derivation if you are interested only in applications Most of the concepts are demonstrated with interesting examples, and students apply what they have learned by solving problems at the back of each chapter Seven full-length exams, enabling students to gauge their mastery of these concepts, are provided throughout the book The solutions to the odd-numbered problems and to the questions in the exams are presented in the back of the book The data sets required to solve the end-of-chapter problems can be found at M.E Sharpe’s student Web site (www.mesharpe-student.com) These data sets can be used with a wide variety of statistical software packages In addition, instructors have access to PowerPoint slides and problemsolving and testing materials This supplemental material can be found at the password-protected M.E Sharpe Web site for instructors (www.mesharpeinstructor.com) A course with terms like “heteroskedasticity,” “first-order Markov 2013 2014 2015 2016 2017 2018 2019 2020 24.216 24.216 24.216 24.216 24.216 24.216 24.216 24.216 Linear trend forecasts: 2013 2014 2015 2016 2017 2018 2019 2020 23.30193 23.66017 24.01841 24.37665 24.73489 25.09313 25.45136 25.80960 C) Does ZEE follow a random walk, a random walk with drift, or neither? Explain how you reached your conclusion Depending on which tests are done, different conclusions will be reached Random walk since β1 is not statistically different from and β0 is not significantly different than in an autoregression: ZEEt1+et Random walk since β1 is not significantly different from in a linear trend regression: Random walk since β1 is not statistically different from and β0 and are not significantly different from in D) Based on your response above, make forecasts of ZEE for 2013 through 2020 Random walk forecasts 2013 2014 2015 2016 2017 2018 2019 2020 2013 2014 2015 2016 2017 2018 2019 2020 1.282 1.282 1.282 1.282 1.282 1.282 1.282 1.282 0.027058 0.027050 0.027046 0.027046 0.027047 0.027050 0.027052 0.027054 Critical Values Tables Critical Values of the t-Distribution As indicated by the chart below, the areas given at the top of this table are the right tail areas for the t-value inside the table For a one-tailed test at the 5% critical level with degrees of freedom, look in the 5% column at the sixth row to get tc = 1.943 For a two-tailed test at the 5% critical level with degrees of freedom, look in the 2.5% column at the sixth row to get tc = 2.447 df 10 11 12 13 14 15 16 17 18 19 20 10% 3.078 1.886 1.638 1.533 1.476 1.440 1.415 1.397 1.383 1.372 1.363 1.356 1.350 1.345 1.341 1.337 1.333 1.330 1.328 1.325 5% 6.314 2.920 2.353 2.132 2.015 1.943 1.895 1.860 1.833 1.812 1.796 1.782 1.771 1.761 1.753 1.746 1.740 1.734 1.729 1.725 2.5% 12.71 4.303 3.182 2.776 2.571 2.447 2.365 2.306 2.262 2.228 2.201 2.179 2.160 2.145 2.131 2.120 2.110 2.101 2.093 2.086 1% 31.82 6.965 4.541 3.747 3.365 3.143 2.998 2.896 2.821 2.764 2.718 2.681 2.650 2.624 2.602 2.583 2.567 2.552 2.539 2.528 21 22 23 24 25 26 27 28 29 30 40 50 60 80 100 1000 ∞ 1.323 1.321 1.319 1.318 1.316 1.315 1.314 1.313 1.311 1.310 1.303 1.295 1.296 1.292 1.290 1.282 1.282 1.721 1.717 1.714 1.711 1.708 1.706 1.703 1.701 1.699 1.697 1.684 1.676 1.671 1.664 1.660 1.646 1.640 2.080 2.074 2.069 2.064 2.060 2.056 2.052 2.048 2.045 2.042 2.021 2.009 2.000 1.990 1.984 1.962 1.960 2.518 2.508 2.500 2.492 2.485 2.479 2.473 2.467 2.462 2.457 2.423 2.403 2.390 2.374 2.364 2.330 2.326 Critical Values of the F-Distribution (5%) The table below shows critical values of the F distribution at the 5% level of significance For example, the critical F (Fc) for degrees of freedom in the numerator and 25 degrees of freedom in the denominator is 2.99 Critical Values of the χ2-Distribution d.f 10% 2.71 4.61 5% 3.84 5.99 1% 6.63 9.21 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 50 60 80 100 6.25 7.78 9.24 10.64 12.02 13.36 14.68 15.99 17.29 18.55 19.81 21.06 22.31 23.54 24.77 25.99 27.20 28.41 29.62 30.81 32.01 33.20 34.38 35.56 36.74 37.92 39.09 40.26 51.81 63.17 74.40 96.58 118.50 7.81 9.49 11.07 12.53 14.07 15.51 16.92 18.31 19.68 21.03 22.36 23.68 25.00 26.30 27.59 28.87 30.14 31.41 39.67 33.92 35.17 36.42 37.65 38.89 40.11 41.34 42.56 43.77 55.76 67.50 79.08 101.90 124.30 11.34 13.23 15.09 16.81 18.48 20.09 21.67 23.21 24.72 26.22 27.69 29.14 30.58 32.00 33.41 34.81 36.19 37.57 38.93 40.29 41.64 42.98 44.31 45.64 46.96 48.28 49.59 50.89 63.69 76.15 88.38 112.30 135.80 Subject and Name Index Akaike information criterion, 53 alternate functional forms, 63 Andersen, L and Jordan, J., 50 Andersen, Leonall C., 193 ARIMA model, 174 augmented Dickey-Fuller test, 147, 183 autocorrelation, 124 autoregressive model, 129, 132, 149, 175, 188 best estimator, proof, 98 bias proporation, 162 biometrics, BLUE, 95 Box, G.E.P., 194 Box, George, 193 Breusch, T.,S., 193 Caudill, Steven, 102, 193, 216 classical linear regression model, 100 coefficient of determination (r2), 27 cointegration, 148 confidence interval, 38 correlation coefficient, 42 correlogram, 144, 179 covariance proportion, 162 critical level, 35, 42 culprit variable, 120 Dasgupta, S., 193 dichotomous variables, 78, 87 Dickey, D.A., 193 Dickey-Fuller test, 147, 182 distributed lag model, 139 double-log model, 65 Dubner, Stephen J., 194 Durbin, J., 193 Durbin-Watson test, 128 error term, calculated, 18 error term, explained, 20 Eviews, 49, 60, 61, 136, 147, 149, 154, 171, 172, 182, 183, 189, 190, 191, 192, 231, 234, 237, 243, 244, 245, 254, 257, 259 ex ante forecast, 170 ex poste forecast, 170 Excel, 37, 41, 49 first difference, 144, 180 first-order Markov scheme, 0, 125, 127, 130, 135 F-statistic, 42 Fuller, W.A., 193 functional form, 71 Gauss-Markov proof, 100, 101, 115 generalized least-squares, 130 Godfrey, L.G., 193 Granger test, 141 Granger, C.W.J., 193 heteroskedasticity, 114 in-sample forecast, 159 integration, 177 interactive term, 81 interval forecast, 158, 170 Jenkins, Gwilym, 193 Jordan, Jerry L., 193 Keynes, John Maynard, 1, 2, 5, 193 Koyck model, 140 Koyck, L.M., 193 Lagrange multiplier test, 129, 140, 151, 225, 226 Leamer, Edward, 194 level of significance, 35 Levitt, Steven D., 5, 194 linear estimator, proof, 95 linear probability model, 82 linear trend, 163 lin-log model, 68 lin-log trend, 164 Ljung, G.M., 194 logistic model, 85 log-lin model, 67 margin of error, 170 marginal propensity to consume, 5, 64, 65 Marshall, Alfred, 194 maximum likelihood procedure, 87, 132 Mazzeo, Michael, 194 measures of goodness-of-fit, 26, 49 model specification, 52 Monte Carlo study, 96, 101 multicollinearity, 105 multiple regression, 47 negative sign test, 38 Newey, W K., 194 Newey-West technique, 118, 120, 121, 122, 132, 134, 135, 136, 220, 224 nonstationarity, 142 normal equation, 16, 17, 33, 47, 48, 62, 209, 242, 246 Okun, Arthur M., 194 ordinary least-squares, 12 Ordinary least-squares estimators, derived, 15 out-of-sample forecast, 170 overspecification, 55 panel data, Park test, 116 Park, R.E., 194 perfect multicollinearity, 105 point forecast, 157 polynomial model, 69 polynomial trend, 166 positive sign test, 39 probability values, 41 pseudoautocorrelation, 0, 130, 131, 141 psychometrics, Q statistic, 179 Ramsey, J.B., 53, 194 random walk, 170 random walk with drift, 170 reciprocal model, 69 regression through the origin, 63 repeated sampling, 29 r-squared, 27 sabermetrics, Schwarz criterion, 53 seasonal adjustment, 80 second difference, 181 Second differences, 149 second-order serial correlation, 125, 130, 132 serial correlation, 124 sociometrics, Specific value test, 39 Spector, Lee C., 194 spurious correlation, 142, 149 standard error of the forecast, 158, 160 standard error of the regression (SER), 26 standard error, of estimator, 28, 29, 49 stationary time-series, 142, 177, 189 stochastic parameter, 30 test for r = 0, 40 test for r2 = 0, 41 test of significance, 35 Theil, Henri., 1, 194 time-series model, 139 t-ratio, 37, 40, 42 trend variable, 71 TYPE I error, 35, 42 TYPE II error, 36, 43, 62, 107, 108, 204, 246 unbiased estimator, proof, 96 unit root test, 147, 182 variance inflation factor, 107 variance proportion, 162 Wang, H., 193 Watson, G.S., 193 weighted least-squares, 118 West, K.D., 194 white noise, 125, 130, 135, 185, 189, 190, 238 White test, 117 White, H., 194 ... identification and explanation without intent to infrine Library of Congress Cataloging-in-Publication Data Kacapyr, Elia, 1956[Introductory econometrics for undergraduates] A guide to basic econometric. .. can take on different values depending on the sample data and are stochastic variables, as are the ei’s Structural parameter – In an econometric model, parameters and are the structural Chapter... Chapter are available at www.mesharpe-student.com The data files are in Excel format, which allows them to be imported into a variety of statistical software packages including Eviews and gretl