DOCSLIB.ORG

Econometrics Streamlined, Applied and E-Aware

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Econometrics Streamlined, Applied and E-Aware Econometrics Streamlined, Applied and e-Aware Francis X. Diebold University of Pennsylvania Edition 2014 Version Thursday 31st July, 2014 Econometrics Econometrics Streamlined, Applied and e-Aware Francis X. Diebold Copyright c 2013 onward, by Francis X. Diebold. This work is licensed under the Creative Commons Attribution-NonCommercial- NoDerivatives 4.0 International License. (Briefly: I retain copyright, but you can use, copy and distribute non-commercially, so long as you give me attribution and do not modify.) To view a copy of the license, visit http://creativecommons.org/licenses/by-nc-nd/4.0. To my undergraduates, who continually surprise and inspire me Brief Table of Contents About the Author xxi About the Cover xxiii Guide to e-Features xxv Acknowledgments xxvii Preface xxxv 1 Introduction to Econometrics1 2 Graphical Analysis of Economic Data 11 3 Sample Moments and Their Sampling Distributions 27 4 Regression 41 5 Indicator Variables in Cross Sections and Time Series 73 6 Non-Normality, Non-Linearity, and More 105 7 Heteroskedasticity in Cross-Section Regression 143 8 Serial Correlation in Time-Series Regression 151 9 Heteroskedasticity in Time-Series Regression 207 10 Endogeneity 241 11 Vector Autoregression 243 ix x BRIEF TABLE OF CONTENTS 12 Nonstationarity 279 13 Big Data: Selection, Shrinkage and More 317 I Appendices 325 A Construction of the Wage Datasets 327 B Some Popular Books Worth Reading 331 Detailed Table of Contents About the Author xxi About the Cover xxiii Guide to e-Features xxv Acknowledgments xxvii Preface xxxv 1 Introduction to Econometrics1 1.1 Welcome..............................1 1.1.1 Who Uses Econometrics?.................1 1.1.2 What Distinguishes Econometrics?...........3 1.2 Types of Recorded Economic Data...............3 1.3 Online Information and Data..................4 1.4 Software..............................5 1.5 Tips on How to use this book..................7 1.6 Exercises, Problems and Complements.............8 1.7 Historical and Computational Notes............... 10 1.8 Concepts for Review....................... 10 2 Graphical Analysis of Economic Data 11 2.1 Simple Techniques of Graphical Analysis............ 11 2.1.1 Univariate Graphics................... 12 2.1.2 Multivariate Graphics.................. 12 2.1.3 Summary and Extension................. 15 2.2 Elements of Graphical Style................... 17 2.3 U.S. Hourly Wages........................ 18 xi xii DETAILED TABLE OF CONTENTS 2.4 Concluding Remarks....................... 19 2.5 Exercises, Problems and Complements............. 20 2.6 Historical and Computational Notes............... 23 2.7 Concepts for Review....................... 23 2.8 Graphics Legend: Edward Tufte................. 25 3 Sample Moments and Their Sampling Distributions 27 3.1 Populations: Random Variables, Distributions and Moments. 27 3.1.1 Univariate......................... 27 3.1.2 Multivariate........................ 30 3.2 Samples: Sample Moments.................... 31 3.2.1 Univariate......................... 31 3.2.2 Multivariate........................ 34 3.3 Finite-Sample and Asymptotic Sampling Distributions of the Sample Mean........................... 34 3.3.1 Exact Finite-Sample Results............... 34 3.3.2 Approximate Asymptotic Results (Under Weaker As- sumptions)........................ 35 3.4 Exercises, Problems and Complements............. 36 3.5 Historical and Computational Notes............... 38 3.6 Concepts for Review....................... 38 4 Regression 41 4.1 Preliminary Graphics....................... 41 4.2 Regression as Curve Fitting................... 41 4.2.1 Bivariate, or Simple, Linear Regression......... 41 4.2.2 Multiple Linear Regression................ 46 4.2.3 Onward.......................... 47 4.3 Regression as a Probability Model................ 47 4.3.1 A Population Model and a Sample Estimator..... 47 4.3.2 Notation, Assumptions and Results........... 48 A Bit of Matrix Notation................. 49 Assumptions: The Full Ideal Conditions (FIC)..... 50 Results........................... 51 4.4 A Wage Equation......................... 52 4.4.1 Mean dependent var 2.342................ 54 4.4.2 S.D. dependent var .561................. 55 DETAILED TABLE OF CONTENTS xiii 4.4.3 Sum squared resid 319.938................ 55 4.4.4 Log likelihood -938.236.................. 55 4.4.5 F statistic 199.626.................... 56 4.4.6 Prob(F statistic) 0.000000............... 56 4.4.7 S.E. of regression .492.................. 56 4.4.8 R-squared .232...................... 57 4.4.9 Adjusted R-squared .231............... 58 4.4.10 Akaike info criterion 1.423................ 58 4.4.11 Schwarz criterion 1.435.................. 58 4.4.12 Hannan-Quinn criter. 1.427............... 59 4.4.13 Durbin-Watson stat. 1.926................ 59 4.4.14 The Residual Scatter................... 60 4.4.15 The Residual Plot..................... 60 4.5 Exercises, Problems and Complements............. 61 4.6 Historical and Computational Notes............... 66 4.7 Regression's Inventor: Carl Friedrich Gauss........... 67 4.8 Concepts for Review....................... 67 5 Indicator Variables in Cross Sections and Time Series 73 5.1 Cross Sections: Group Effects.................. 73 5.1.1 0-1 Dummy Variables................... 73 5.1.2 Group Dummies in the Wage Regression........ 75 5.2 Time Series: Trend and Seasonality............... 76 5.2.1 Linear Trend....................... 76 5.2.2 Seasonality........................ 79 Seasonal Dummies.................... 79 More General Calendar Effects............. 81 5.2.3 Trend and Seasonality in Liquor Sales.......... 81 5.3 Structural Change........................ 83 5.3.1 Gradual Parameter Evolution.............. 83 5.3.2 Sharp Parameter Breaks................. 84 Exogenously-Specified Breaks.............. 84 Endogenously-Selected Breaks.............. 86 5.3.3 Liquor Sales........................ 87 5.4 Panel Regression......................... 87 5.4.1 Panel Data........................ 88 xiv DETAILED TABLE OF CONTENTS 5.4.2 Individual and Time Effects............... 89 Individual Effects..................... 89 Time Effects........................ 89 Individual and Time Effects............... 90 5.5 Binary Regression......................... 90 5.5.1 Binary Response..................... 90 5.5.2 The Logit Model..................... 91 Logit............................ 91 Ordered Logit....................... 92 Dynamic Logit...................... 93 Complications....................... 93 5.5.3 Classification and \0-1 Forecasting"........... 94 5.6 Exercises, Problems and Complements............. 94 5.7 Historical and Computational Notes............... 101 5.8 Concepts for Review....................... 101 5.9 Dummy Variables, ANOVA, and Sir Ronald Fischer...... 103 6 Non-Normality, Non-Linearity, and More 105 6.1 Non-Normality.......................... 106 6.1.1 \y Problems" (via "): Non-Normality.......... 106 OLS Without Normality................. 106 Assessing Residual Non-Normality............ 107 Nonparametric Density Estimation........... 107 Outliers.......................... 108 6.1.2 \X Problems": Measurement Error and Multicollinearity109 Measurement Error.................... 109 Collinearity and Multicollinearity............ 110 Leverage.......................... 111 6.1.3 Estimation......................... 111 Robustness Iteration................... 112 Least Absolute Deviations................ 112 6.1.4 Wages and Liquor Sales................. 113 Wages........................... 113 Liquor Sales........................ 113 6.2 Non-Linearity........................... 114 6.2.1 Parametric Non-Linearity................ 114 DETAILED TABLE OF CONTENTS xv Models Linear in Transformed Variables........ 114 Intrinsically Non-Linear Models............. 116 Interactions........................ 117 A Final Word on Nonlinearity and the FIC....... 117 Testing for Non-Linearity................ 118 Non-Linearity in Wage Determination.......... 119 Non-linear Trends..................... 122 More on Non-Linear Trend................ 125 Non-Linearity in Liquor Sales Trend.......... 126 6.2.2 Non-Parametric Non-Linearity.............. 127 Series Expansions..................... 127 Step Functions (Dummies)................ 128 Regression Splines.................... 129 Smoothing Splines.................... 130 Local Polynomial Regression............... 131 Neural Networks..................... 132 Kernel Regression..................... 133 6.2.3 Dimensions and Interactions............... 133 Higher Dimensions: Generalized Additive Models... 133 Dummies......................... 133 Trees............................ 133 Forrests.......................... 133 Bagging.......................... 133 Boosting.......................... 133 6.3 Exercises, Problems and Complements............. 133 6.4 Historical and Computational Notes............... 140 6.5 Concepts for Review....................... 140 7 Heteroskedasticity in Cross-Section Regression 143 7.1 Exercises, Problems and Complements............. 149 7.2 Historical and Computational Notes............... 150 7.3 Concepts for Review....................... 150 8 Serial Correlation in Time-Series Regression 151 8.1 Observed Time Series....................... 151 8.1.1 Characterizing Time-Series Dynamics.......... 151 Covariance Stationary Time Series........... 152 xvi DETAILED TABLE OF CONTENTS 8.1.2 White Noise........................ 155 8.1.3 Estimation and Inference for the Mean, Autocorrela- tion and Partial Autocorrelation Functions....... 159
Load more

Recommended publications
  • Power Comparisons of Five Most Commonly Used Autocorrelation Tests
    Pak.j.stat.oper.res. Vol.16 No. 1 2020 pp119-130 DOI: http://dx.doi.org/10.18187/pjsor.v16i1.2691 Pakistan Journal of Statistics and Operation Research Power Comparisons of Five Most Commonly Used Autocorrelation Tests Stanislaus S. Uyanto School of Economics and Business, Atma Jaya Catholic University of Indonesia, [email protected] Abstract In regression analysis, autocorrelation of the error terms violates the ordinary least squares assumption that the error terms are uncorrelated. The consequence is that the estimates of coefficients and their standard errors will be wrong if the autocorrelation is ignored. There are many tests for autocorrelation, we want to know which test is more powerful. We use Monte Carlo methods to compare the power of five most commonly used tests for autocorrelation, namely Durbin-Watson, Breusch-Godfrey, Box–Pierce, Ljung Box, and Runs tests in two different linear regression models. The results indicate the Durbin-Watson test performs better in the regression model without lagged dependent variable, although the advantage over the other tests reduce with increasing autocorrelation and sample sizes. For the model with lagged dependent variable, the Breusch-Godfrey test is generally superior to the other tests. Key Words: Correlated error terms; Ordinary least squares assumption; Residuals; Regression diagnostic; Lagged dependent variable. Mathematical Subject Classification: 62J05; 62J20. 1. Introduction An important assumption of the classical linear regression model states that there is no autocorrelation in the error terms. Autocorrelation of the error terms violates the ordinary least squares assumption that the error terms are uncorrelated, meaning that the Gauss Markov theorem (Plackett, 1949, 1950; Greene, 2018) does not apply, and that ordinary least squares estimators are no longer the best linear unbiased estimators.
    [Show full text]
  • Multiple Regression
    ICPSR Blalock Lectures, 2003 Bootstrap Resampling Robert Stine Lecture 4 Multiple Regression Review from Lecture 3 Review questions from syllabus - Questions about underlying theory - Math and notation handout from first class Review resampling in simple regression - Regression diagnostics - Smoothing methods (modern regr) Methods of resampling – which to use? Today Multiple regression - Leverage, influence, and diagnostic plots - Collinearity Resampling in multiple regression - Ratios of coefficients - Differences of two coefficients - Robust regression Yes! More t-shirts! Bootstrap Resampling Multiple Regression Lecture 4 ICPSR 2003 2 Locating a Maximum Polynomial regression Why bootstrap in least squares regression? Question What amount of preparation (in hours) maximizes the average test score? Quadmax.dat Constructed data for this example Results of fitting a quadratic Scatterplot with added quadratic fit (or smooth) 0 5 10 15 20 HOURS Least squares regression of the model Y = a + b X + c X2 + e gives the estimates a = 136 b= 89.2 c = –4.60 So, where’s the maximum and what’s its CI? Bootstrap Resampling Multiple Regression Lecture 4 ICPSR 2003 3 Inference for maximum Position of the peak The maximum occurs where the derivative of the fit is zero. Write the fit as f(x) = a + b x + c x2 and then take the derivative, f’(x) = b + 2cx Solving f’(x*) = 0 for x* gives b x* = – 2c ≈ –89.2/(2)(–4.6)= 9.7 Questions - What is the standard error of x*? - What is the 95% confidence interval? - Is the estimate biased? Bootstrap Resampling Multiple Regression Lecture 4 ICPSR 2003 4 Bootstrap Results for Max Location Standard error and confidence intervals (B=2000) Standard error is slightly smaller with fixed resampling (no surprise)… Observation resampling SE* = 0.185 Fixed resampling SE* = 0.174 Both 95% intervals are [9.4, 10] Bootstrap distribution The kernel looks pretty normal.
    [Show full text]
  • Regression Diagnostics and Model Selection
    Regression diagnostics and model selection MS-C2128 Prediction and Time Series Analysis Fall term 2020 MS-C2128 Prediction and Time Series Analysis Regression diagnostics and model selection Week 2: Regression diagnostics and model selection 1 Regression diagnostics 2 Model selection MS-C2128 Prediction and Time Series Analysis Regression diagnostics and model selection Content 1 Regression diagnostics 2 Model selection MS-C2128 Prediction and Time Series Analysis Regression diagnostics and model selection Regression diagnostics Questions: Does the model describe the dependence between the response variable and the explanatory variables well 1 contextually? 2 statistically? A good model describes the dependencies as well as possible. Assessment of the goodness of a regression model is called regression diagnostics. Regression diagnostics tools: graphics diagnostic statistics diagnostic tests MS-C2128 Prediction and Time Series Analysis Regression diagnostics and model selection Regression model selection In regression modeling, one has to select 1 the response variable(s) and the explanatory variables, 2 the functional form and the parameters of the model, 3 and the assumptions on the residuals. Remark The first two points are related to defining the model part and the last point is related to the residuals. These points are not independent of each other! MS-C2128 Prediction and Time Series Analysis Regression diagnostics and model selection Problems in defining the model part (i) Linear model is applied even though the dependence between the response variable and the explanatory variables is non-linear. (ii) Too many or too few explanatory variables are chosen. (iii) It is assumed that the model parameters are constants even though the assumption does not hold.
    [Show full text]
  • Outlier Detection Based on Robust Parameter Estimates
    International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 23 (2017) pp.13429-13434 © Research India Publications. http://www.ripublication.com Outlier Detection based on Robust Parameter Estimates Nor Azlida Aleng1, Nyi Nyi Naing2, Norizan Mohamed3 and Kasypi Mokhtar4 1,3 School of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Terengganu, Malaysia. 2 Institute for Community (Health) Development (i-CODE), Universiti Sultan Zainal Abidin, Gong Badak Campus, 21300 Kuala Terengganu, Malaysia. 4 School of Maritime Business and Management, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Terengganu, Malaysia. Orcid; 0000-0003-1111-3388 Abstract evidence that the outliers can lead to model misspecification, incorrect analysis result and can make all estimation procedures Outliers can influence the analysis of data in various different meaningless, (Rousseeuw and Leroy, 1987; Alma, 2011; ways. The outliers can lead to model misspecification, incorrect Zimmerman, 1994, 1995, 1998). Outliers in the response analysis results and can make all estimation procedures variable represent model failure. Outliers in the regressor meaningless. In regression analysis, ordinary least square variable values are extreme in X-space are called leverage estimation is most frequently used for estimation of the points. parameters in the model. Unfortunately, this estimator is sensitive to outliers. Thus, in this paper we proposed some Rousseeuw and Lorey (1987) defined that outliers in three statistics for detection of outliers based on robust estimation, types; 1) vertical outliers, 2) bad leverage point, 3) good namely least trimmed squares (LTS). A simulation study was leverage point. Vertical outlier is an observation that has performed to prove that the alternative approach gives a better influence on the error term of y-dimension (response) but is results than OLS estimation to identify outliers.
    [Show full text]
  • Ravinder Et Al. Validating Regression Assumptions
    Ravinder et al. Validating Regression Assumptions DECISION SCIENCES INSTITUTE Validating Regression Assumptions Through Residual Plots – Can Students Do It? Handanhal Ravinder Montclair State University Email: [email protected] Mark Berenson Montclair State University Email: [email protected] Haiyan Su Montclair State University Email: [email protected] ABSTRACT In linear regression an important part of the procedure is to check for the validity of the four key assumptions. Introductory courses in business statistics take a graphical approach by displaying residual plots of situations where these assumptions are violated. Yet it is not clear that students at this level can assess residual plots well enough to make judgments about the violation of the assumptions. This paper discusses the details of an experiment in progress that addresses this issue using a two-period crossover design. Preliminary results are presented. KEYWORDS: Regression, Linearity, Homoscedasticity, Scatterplot, Cross-over design INTRODUCTION When assessing the assumptions of linearity, independence of error, normality, and equal spread in simple linear regression modeling, students of introductory business statistics are typically presented with an exploratory, graphical approach to the topic of residual analysis (for example, Donnelly, 2015: Anderson, Sweeney & Williams, 2016; Levine, Szabat, & Stephan, 2016). Except for the assumption of independence of error where the Durbin-Watson technique (1951) is presented, no basic text covers any confirmatory approach to any of the other assumptions. Berenson (2013) however, raises a basic question – are inexperienced undergraduate business students really capable of critically assessing residual plots? If this is not the case, it would be imperative to introduce confirmatory, inferential approaches to supplement the graphical, exploratory approaches currently found in texts and taught in classrooms.
    [Show full text]
  • Detection of Outliers and Influential Observations in Regression Models
    Old Dominion University ODU Digital Commons Mathematics & Statistics Theses & Dissertations Mathematics & Statistics Summer 1989 Detection of Outliers and Influential Observations in Regression Models Anwar M. Hossain Old Dominion University Follow this and additional works at: https://digitalcommons.odu.edu/mathstat_etds Part of the Statistics and Probability Commons Recommended Citation Hossain, Anwar M.. "Detection of Outliers and Influential Observations in Regression Models" (1989). Doctor of Philosophy (PhD), Dissertation, Mathematics & Statistics, Old Dominion University, DOI: 10.25777/gte7-c039 https://digitalcommons.odu.edu/mathstat_etds/80 This Dissertation is brought to you for free and open access by the Mathematics & Statistics at ODU Digital Commons. It has been accepted for inclusion in Mathematics & Statistics Theses & Dissertations by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. DETECTION OF OUTLIERS AND INFLUENTIAL OBSERVATIONS IN REGRESSION MODELS By Anwar M. Hossain M. Sc. 1976, Jahangirnagar University, Bangladesh B. Sc. (Honors), 1975, Jahangirnagar University, Bangladesh A Dissertation Submitted to the Faculty of Old Dominion University in Partial Fulfilment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Comnutional and Applied Mathematics OLD DOMINION UNIVERSITY August, 1989 Approved by: Dayanand N. Naik (Director) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT DETECTION OF OUTLIERS AND INFLUENTIAL OBSERVATIONS IN REGRESSION MODELS ANWAR M. HOSSAIN Old Dominion University, 1989 Director: Dr. Dayanand N. Naik Observations arising from a linear regression model, lead one to believe that a particular observation or a set of observations are aberrant from the rest of the data. These may arise in several ways: for example, from incorrect or faulty measurements or by gross errors in either response or explanatory variables.
    [Show full text]
  • A New Diagnostic Test for Regression
    Western University Scholarship@Western Electronic Thesis and Dissertation Repository 4-19-2013 12:00 AM A New Diagnostic Test for Regression Yun Shi The University of Western Ontario Supervisor Dr. Ian McLeod The University of Western Ontario Graduate Program in Statistics and Actuarial Sciences A thesis submitted in partial fulfillment of the equirr ements for the degree in Master of Science © Yun Shi 2013 Follow this and additional works at: https://ir.lib.uwo.ca/etd Part of the Applied Statistics Commons, Biostatistics Commons, Statistical Methodology Commons, Statistical Models Commons, and the Statistical Theory Commons Recommended Citation Shi, Yun, "A New Diagnostic Test for Regression" (2013). Electronic Thesis and Dissertation Repository. 1238. https://ir.lib.uwo.ca/etd/1238 This Dissertation/Thesis is brought to you for free and open access by Scholarship@Western. It has been accepted for inclusion in Electronic Thesis and Dissertation Repository by an authorized administrator of Scholarship@Western. For more information, please contact [email protected]. A New Diagnostic Test for Regression (Thesis format: Monograph) by Yun Shi Graduate Program in Statistics and Actuarial Science A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science The School of Graduate and Postdoctoral Studies The University of Western Ontario London, Ontario, Canada © Yun Shi 2013 ABSTRACT A new diagnostic test for regression and generalized linear models is discussed. The test is based on testing if the residuals are close together in the linear space of one of the covariates are correlated. This is a generalization of the famous problem of spurious correlation in time series regression.
    [Show full text]
  • Chapter 1: the Purpose of This Dissertation
    ABSTRACT Title of Dissertation: REGRESSION DIAGNOSTICS FOR COMPLEX SURVEY DATA: IDENTIFICATION OF INFLUENTIAL OBSERVATIONS. Jianzhu Li, Doctor of Philosophy, 2007 Dissertation Directed By: Professor Richard Valliant Joint Program in Survey Methodology Discussion of diagnostics for linear regression models have become indispensable chapters or sections in most of the statistical textbooks. However, survey literature has not given much attention to this problem. Examples from real surveys show that sometimes the inclusion and exclusion of a small number of the sampled units can greatly change the regression parameter estimates, which indicates that techniques of identifying the influential units are necessary. The goal of this research is to extend and adapt the conventional ordinary least squares influence diagnostics to complex survey data, and determine how they should be justified. We assume that an analyst is looking for a linear regression model that fits reasonably well for the bulk of the finite population and chooses to use the survey weighted regression estimator. Diagnostic statistics such as DFBETAS, DFFITS, and modified Cook’s Distance are constructed to evaluate the effect on the regression coefficients of deleting a single observation. As components of the diagnostic statistics, the estimated variances of the coefficients are obtained from design-consistent estimators which account for complex design features, e.g. clustering and stratification. For survey data, sample weights, which are computed with the primary goal of estimating finite population statistics, are sources of influence besides the response variable and the predictor variables, and therefore need to be incorporated into influence measurement. The forward search method is also adapted to identify influential observations as a group when there is possible masked effect among the outlying observations.
    [Show full text]
  • A Graphical Method for Assessing the Fit of a Logistic Regression Model
    A Graphical Method for Assessing the Fit of a Logistic Regression Model Iain Pardoe ¤ R. Dennis Cook ¤ Charles H. Lundquist College of Business School of Statistics University of Oregon University of Minnesota April 11, 2002 Abstract Before a logistic regression model is used to describe the relationship between a binary response variable and predictors, the fit of the model should be assessed. The nature of any model deficiency may indicate that some aspect of the model should be reformulated or that poorly fitting observations need to be considered separately. We propose graphical methodol- ogy based on a Bayesian framework to address issues such as this. Publicly available software allows diagnostic plots to be constructed quickly and easily for any model of interest. These plots are more intuitive and meaningful than traditional graphical diagnostics such as residual plots. Key Words: Bayesian methodology; Diagnostic plot; Marginal model plot; Model criticism; Posterior predictive distribution. ¤Iain Pardoe is Assistant Professor, Department of Decision Sciences, Charles H. Lundquist College of Business, University of Oregon, Eugene, OR 97403–1208 (email: [email protected]); R. Dennis Cook is Professor, School of Statistics, University of Minnesota, Minneapolis, MN 55455 (email: [email protected]). The authors thank the editor and two anonymous reviewers for helpful comments on an earlier version of this article. This research was partially supported by National Science Foundation grants DMS-9703777 and DMS-0103983. 1 INTRODUCTION Cook and Pardoe (2000) suggested a graphical technique for assessing the fit of a regression model, which they called a “Gibbs marginal model plot.” This methodology was developed for normal linear models and additive models in Pardoe (2001b), in which the plots were renamed “Bayes marginal model plots” (BMMPs).
    [Show full text]
  • Classical Linear Regression Model Assumptions and Diagnostic Tests
    4 Classical linear regression model assumptions and diagnostic tests Learning Outcomes In this chapter, you will learn how to ● Describe the steps involved in testing regression residuals for heteroscedasticity and autocorrelation ● Explain the impact of heteroscedasticity or autocorrelation on the optimality of OLS parameter and standard error estimation ● Distinguish between the Durbin--Watson and Breusch--Godfrey tests for autocorrelation ● Highlight the advantages and disadvantages of dynamic models ● Test for whether the functional form of the model employed is appropriate ● Determine whether the residual distribution from a regression differs significantly from normality ● Investigate whether the model parameters are stable ● Appraise different philosophies of how to build an econometric model ● Conduct diagnostic tests in EViews 4.1 Introduction Recall that five assumptions were made relating to the classical linear re- gression model (CLRM). These were required to show that the estimation technique, ordinary least squares (OLS), had a number of desirable proper- ties, and also so that hypothesis tests regarding the coefficient estimates could validly be conducted. Specifically, it was assumed that: (1) E(ut ) = 0 2 (2) var(ut ) = σ < ∞ (3) cov(ui ,u j ) = 0 129 130 Introductory Econometrics for Finance (4) cov(ut ,xt ) = 0 2 (5) ut ∼ N(0, σ ) These assumptions will now be studied further, in particular looking at the following: ● How can violations of the assumptions be detected? ● What are the most likely causes of the violations in practice? ● What are the consequences for the model if an assumption is violated but this fact is ignored and the researcher proceeds regardless? The answer to the last of these questions is that, in general, the model could encounter any combination of three problems: ● the coefficient estimates (βˆs) are wrong ● the associated standard errors are wrong ● the distributions that were assumed for the test statistics are inappro- priate.
    [Show full text]
  • SAS/STAT® 13.2 User’S Guide the REG Procedure This Document Is an Individual Chapter from SAS/STAT® 13.2 User’S Guide
    SAS/STAT® 13.2 User’s Guide The REG Procedure This document is an individual chapter from SAS/STAT® 13.2 User’s Guide. The correct bibliographic citation for the complete manual is as follows: SAS Institute Inc. 2014. SAS/STAT® 13.2 User’s Guide. Cary, NC: SAS Institute Inc. Copyright © 2014, SAS Institute Inc., Cary, NC, USA All rights reserved. Produced in the United States of America. For a hard-copy book: 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, or otherwise, without the prior written permission of the publisher, SAS Institute Inc. For a Web download or e-book: Your use of this publication shall be governed by the terms established by the vendor at the time you acquire this publication. The scanning, uploading, and distribution of this book via the Internet or any other means without the permission of the publisher is illegal and punishable by law. Please purchase only authorized electronic editions and do not participate in or encourage electronic piracy of copyrighted materials. Your support of others’ rights is appreciated. U.S. Government License Rights; Restricted Rights: The Software and its documentation is commercial computer software developed at private expense and is provided with RESTRICTED RIGHTS to the United States Government. Use, duplication or disclosure of the Software by the United States Government is subject to the license terms of this Agreement pursuant to, as applicable, FAR 12.212, DFAR 227.7202-1(a), DFAR 227.7202-3(a) and DFAR 227.7202-4 and, to the extent required under U.S.
    [Show full text]
  • 18 Assessing Student Ability to Interpret Regression Diagnostic Plots Handanhal Ravinder Montclair State University Haiyan Su
    Assessing Student Ability to Interpret Regression Diagnostic Plots Handanhal Ravinder Montclair State University Haiyan Su Montclair State University Mark Berenson Montclair State University Author Note Handanhal Ravinder and Mark Berenson (Emeritus), Department of Information & Business Analytics; Haiyan Su, College of Science & Mathematics Correspondence regarding this article should be addressed to Handanhal Ravinder, Information Management & Business Analytics Department, Feliciano School of Business, Montclair State University, 1 Normal Avenue, Montclair, NJ 07043; E-mail: [email protected]. Abstract Simple linear regression analysis is an important component of introductory statistics courses, and testing the validity of its assumptions is an important part of regression modeling and analysis. The traditional approach in introductory statistics courses is to use residual plots to assess possible departures from the key assumptions. Confirmatory statistics are typically not used. But do undergraduate students in these introductory courses have the ability to assess residual plots correctly? This paper presents the results of an Institutional Review Board (IRB) approved study to address this question. The results are interesting and have implications for the teaching of regression in introductory courses as well as for textbook authors who cater to these courses. Keywords: regression assumptions, normality, homoscedasticity, residual analysis 18 STUDENT ABILITY TO INTERPRET REGRESSION DIAGNOSTIC PLOTS Undergraduate students in introductory statistics classes are typically presented with residual plots when assessing the assumptions of regression modeling. Aside from the Durbin- Watson (1951) procedure for assessing the independence assumption, no introductory statistics text covers confirmatory approaches to residual analysis for the assumptions of linearity, normality and homoscedasticity. The basic question addressed in this paper is whether undergraduate students have enough experience and ability to accurately assess residual plots.
    [Show full text]