Outline. 2. Logarithmic Functional Form and Units of Measurement. Functional Form. I. Functional Form: log II. Units of Measurement
|
|
- Blake Hopkins
- 6 years ago
- Views:
Transcription
1 Outline 2. Logarithmic Functional Form and Units of Measurement I. Functional Form: log II. Units of Measurement Read Wooldridge (2013), Chapter 2.4, 6.1 and Functional Form I. Functional Form: log OLS can be used for relationships that are not strictly linear in x and y by using nonlinear functions of x and y. Note that SLR.1 (linear in the parameters) is not violated Can take the natural log of x, y or both Can use quadratic forms of x Can use interactions of x variables 1) level level form: Linear variables in simple regression models Eg. salary in thousands of dollars sales in millions of dollars = sales (112.8) (0.0089) n=209; R 2 = See Table in Page 5 Interpret = Find the elasticity of CEO salary with respect to sales. 3 4
2 Descriptive Statistics from Eviews Elasticity: (log log model) Date: 05/10/03 Time: 11:30 SALARY SALES Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability 0 0 Observations ) log log form: both Y and X are in logarithmic form. This is called a constant elasticity model. log( ) = log(sales) (0.288) (0.035) n=209 R 2 = = This is the elasticity of salary with respect to sales Find the partial effect of sales on salary in thousands of dollars. See Table in Page Level log Model Digression: Percentage point vs. Percent 3) level log form: independent variable in logarithmic form salary in thousands of dollars log(sales) sales in millions of dollars = log(sales) (771.5) (92.36) n=209 R 2 = Interpretation: percentage point change vs. percentage change Unemployment rate: 8% to 9% rate = 1. This is a one percentage point change. log(rate): log(9) log(8)= This is an approximate increase of 11.8% The exact increase is 12.5 %. Interpret: =
3 Semi elasticity (log level) 4) log level form: dependent variable in logarithmic form log(wage) wages in dollars per hour educ years of education log( ) = educ n=526, R 2 =.0186 Interpret: = Find the semi elasticity of wages with respect to education. Find the elasticity of wages with respect to education. See Table in Page 5 Descriptive Statistics from Eviews Date: 06/02/09 Time: 09:10 Sample: WAGE EDUC Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability 0 0 Sum Sum Sq. Dev Observations Logarithmic Functional Forms Approximate change vs. exact change Logarithmic Functional Forms log(x) : natural log of x Eg. log( ) = edu When education increases by one year, wages increase approximately by 8.3% (or 100(0.083)) This estimate is approximated or inexact. Approximate percentage change log( ) = + educ log( ) = educ When education increases by one year, the hourly wage increases by approximately 8.3% (100(0.083)) Let y=wage; x=educ. This is because as the change in log(y) becomes larger and larger, the approximation % y 100 log (y) becomes more and more inexact. Exact percentage change in the predicted y is % y = 100[exp( ) 1] = 8.654% One more year of education increases the predicted wages exactly by 8.65% 11 12
4 Interpretation of Log Models Summary If the model is y = x + u 1 is the change in y for a unit change in x. If the model is log(y) = log(x) + u 1 is the percentage change in y for a percentage change in x. If the model is log(y) = x + u 100* 1 is approximately the percentage change in y for a unit change in x If the model is y = log(x) + u 1 /100 is approximately the change in y for a percentage change in x II. Units of Measurement In summary, for data scaling on y, Let salardol be salary in dollars. salardol = 1000salary = roe = 963, ,501roe s.e. (213,240) (11,123) n = 209 R 2 = roe (in percentage points) The old values (residuals, coefficients, s.e.) are multiplied by c 1 =1000 to get the corresponding new values. Note that statistics involving ratios (R 2, t statistic) are unaffected. Interpret: = 18,501 The predicted CEO salary increases by $18,500 when roe increases by 1 percentage point
5 Data Scaling on Independent Variable In summary, for data scaling on x, Independent variable roe roedec roedec = (1/100)roe in percent in fraction The OLS coefficient and its standard error (as well as residuals) are divided by c 2 =1/100 to get the corresponding new values. = roe = roedec (213.2) (1112) n = 209 R 2 = Note that the intercept and other statistics involving ratios (R 2, t statistics) are unaffected. Interpretation: If roedec increases by 0.01, the salary is predicted to increase by 18.5 thousand dollars Redefining Variables Rescaling and Log Form Changing the scale of the y variable will lead to a corresponding change in the scale of the coefficients and standard errors, so no change in the significance or interpretation Changing the scale of one x variable will lead to a change in the scale of that coefficient and standard error, so no change in the significance or interpretation Let y i * = c 1 y i let x i * = c 2 x i In summary, if the dependent variable or independent variables are in logarithmic form, eg., log(y i *), log(x i *), changing the units of measurement does not affect the slope coefficient. Only OLS intercept is affected
6 Example: CEO Salary and Sales log( ) = log(sales) Dependent Variable: LOG(SALARY) sales = millions of dollars salary: thousands of dollars (1) log( ) = log(sales) (s.e.) (0.288) (0.035) n=209, R 2 = salarydol = 1000salary (2) log( ) = log(sales) (s.e.) (0.288) (0.035) salesdol = 1,000,000sales Method: Least Squares Date: 06/05/08 Time: 05:38 Included observations: 209 Variable Coefficient Std. Error t-statistic Prob. C LOG(SALES) R-squared Mean dependent var Adjusted R-squared S.D. dependent var (3) log( ) = log(salesdol) (s.e.) (0.764) (0.035) S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Are R 2 different in three models? Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) log ) = log(sales) log( ) = log(salesdol) Dependent Variable: LOG(SALARY*1000) Method: Least Squares Included observations: 209 Variable Coefficient Std. Error t-statistic Prob. C LOG(SALES) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Dependent Variable: LOG(SALARY) Method: Least Squares Included observations: 209 Variable Coefficient Std. Error t-statistic Prob. C LOG(SALES* ) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic)
7 Log is cool... Rules of Thumb for taking logs Reasons why taking logs are preferable: 1. Gauss Markov assumptions (SLR.1 SLR.5) For example, heteroskedasticty. 2. Estimates less sensitive to outlying (extreme) values 3. Meaningful economic interpretation 1. a variable with positive dollar amount Eg. wages, salaries, firm sales, and market capitalization value 2. a variable with large integer values Eg. population, total number of employees 3. Maybe, a proportion or percent Eg. unemployment rate, participation rate Variables in their original form Variables measured in years Eg. education, experience, tenure, age Recap Functional Form: log Units of Measurement 2. Unites of Measurement and Logarithmic Functional Form. Quantitative Methods of Economic Analysis Chairat Aemkulwat 27
7. Prediction. Outline: Read Section 6.4. Mean Prediction
Outline: Read Section 6.4 II. Individual Prediction IV. Choose between y Model and log(y) Model 7. Prediction Read Wooldridge (2013), Chapter 6.4 2 Mean Prediction Predictions are useful But they are subject
More informationThe Simple Regression Model. Part II. The Simple Regression Model
Part II The Simple Regression Model As of Sep 22, 2015 Definition 1 The Simple Regression Model Definition Estimation of the model, OLS OLS Statistics Algebraic properties Goodness-of-Fit, the R-square
More informationLecture 8. Using the CLR Model
Lecture 8. Using the CLR Model Example of regression analysis. Relation between patent applications and R&D spending Variables PATENTS = No. of patents (in 1000) filed RDEXP = Expenditure on research&development
More informationModel Specification and Data Problems. Part VIII
Part VIII Model Specification and Data Problems As of Oct 24, 2017 1 Model Specification and Data Problems RESET test Non-nested alternatives Outliers A functional form misspecification generally means
More informationCHAPTER 6: SPECIFICATION VARIABLES
Recall, we had the following six assumptions required for the Gauss-Markov Theorem: 1. The regression model is linear, correctly specified, and has an additive error term. 2. The error term has a zero
More informationLecture 8. Using the CLR Model. Relation between patent applications and R&D spending. Variables
Lecture 8. Using the CLR Model Relation between patent applications and R&D spending Variables PATENTS = No. of patents (in 000) filed RDEP = Expenditure on research&development (in billions of 99 $) The
More informationRegression with Qualitative Information. Part VI. Regression with Qualitative Information
Part VI Regression with Qualitative Information As of Oct 17, 2017 1 Regression with Qualitative Information Single Dummy Independent Variable Multiple Categories Ordinal Information Interaction Involving
More informationHeteroscedasticity 1
Heteroscedasticity 1 Pierre Nguimkeu BUEC 333 Summer 2011 1 Based on P. Lavergne, Lectures notes Outline Pure Versus Impure Heteroscedasticity Consequences and Detection Remedies Pure Heteroscedasticity
More informationIntroduction to Econometrics Chapter 4
Introduction to Econometrics Chapter 4 Ezequiel Uriel Jiménez University of Valencia Valencia, September 2013 4 ypothesis testing in the multiple regression 4.1 ypothesis testing: an overview 4.2 Testing
More informationEconomics 471: Econometrics Department of Economics, Finance and Legal Studies University of Alabama
Economics 471: Econometrics Department of Economics, Finance and Legal Studies University of Alabama Course Packet The purpose of this packet is to show you one particular dataset and how it is used in
More informationStatistical Inference. Part IV. Statistical Inference
Part IV Statistical Inference As of Oct 5, 2017 Sampling Distributions of the OLS Estimator 1 Statistical Inference Sampling Distributions of the OLS Estimator Testing Against One-Sided Alternatives Two-Sided
More informationMultiple Regression Analysis: Further Issues
Multiple Regression Analysis: Further Issues Ping Yu School of Economics and Finance The University of Hong Kong Ping Yu (HKU) MLR: Further Issues 1 / 36 Effects of Data Scaling on OLS Statistics Effects
More informationThe general linear regression with k explanatory variables is just an extension of the simple regression as follows
3. Multiple Regression Analysis The general linear regression with k explanatory variables is just an extension of the simple regression as follows (1) y i = β 0 + β 1 x i1 + + β k x ik + u i. Because
More informationMultiple Regression Analysis. Part III. Multiple Regression Analysis
Part III Multiple Regression Analysis As of Sep 26, 2017 1 Multiple Regression Analysis Estimation Matrix form Goodness-of-Fit R-square Adjusted R-square Expected values of the OLS estimators Irrelevant
More information5. Erroneous Selection of Exogenous Variables (Violation of Assumption #A1)
5. Erroneous Selection of Exogenous Variables (Violation of Assumption #A1) Assumption #A1: Our regression model does not lack of any further relevant exogenous variables beyond x 1i, x 2i,..., x Ki and
More information2) For a normal distribution, the skewness and kurtosis measures are as follows: A) 1.96 and 4 B) 1 and 2 C) 0 and 3 D) 0 and 0
Introduction to Econometrics Midterm April 26, 2011 Name Student ID MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. (5,000 credit for each correct
More informationECNS 561 Topics in Multiple Regression Analysis
ECNS 561 Topics in Multiple Regression Analysis Scaling Data For the simple regression case, we already discussed the effects of changing the units of measurement Nothing different here Coefficients, SEs,
More information4. Nonlinear regression functions
4. Nonlinear regression functions Up to now: Population regression function was assumed to be linear The slope(s) of the population regression function is (are) constant The effect on Y of a unit-change
More informationExercise Sheet 6: Solutions
Exercise Sheet 6: Solutions R.G. Pierse 1. (a) Regression yields: Dependent Variable: LC Date: 10/29/02 Time: 18:37 Sample(adjusted): 1950 1985 Included observations: 36 after adjusting endpoints C 0.244716
More informationOutline. 11. Time Series Analysis. Basic Regression. Differences between Time Series and Cross Section
Outline I. The Nature of Time Series Data 11. Time Series Analysis II. Examples of Time Series Models IV. Functional Form, Dummy Variables, and Index Basic Regression Numbers Read Wooldridge (2013), Chapter
More informationHeteroskedasticity. Part VII. Heteroskedasticity
Part VII Heteroskedasticity As of Oct 15, 2015 1 Heteroskedasticity Consequences Heteroskedasticity-robust inference Testing for Heteroskedasticity Weighted Least Squares (WLS) Feasible generalized Least
More information13. Time Series Analysis: Asymptotics Weakly Dependent and Random Walk Process. Strict Exogeneity
Outline: Further Issues in Using OLS with Time Series Data 13. Time Series Analysis: Asymptotics Weakly Dependent and Random Walk Process I. Stationary and Weakly Dependent Time Series III. Highly Persistent
More informationAbout the seasonal effects on the potential liquid consumption
About the seasonal effects on the potential liquid consumption Lucie Ravelojaona Guillaume Perrez Clément Cousin ENAC 14/01/2013 Consumption raw data Figure : Evolution during one year of different family
More informationEastern Mediterranean University Department of Economics ECON 503: ECONOMETRICS I. M. Balcilar. Midterm Exam Fall 2007, 11 December 2007.
Eastern Mediterranean University Department of Economics ECON 503: ECONOMETRICS I M. Balcilar Midterm Exam Fall 2007, 11 December 2007 Duration: 120 minutes Questions Q1. In order to estimate the demand
More informationPractice Questions for the Final Exam. Theoretical Part
Brooklyn College Econometrics 7020X Spring 2016 Instructor: G. Koimisis Name: Date: Practice Questions for the Final Exam Theoretical Part 1. Define dummy variable and give two examples. 2. Analyze the
More informationNovember 9th-12th 2010, Port of Spain, Trinidad
By: Damie Sinanan and Dr. Roger Hosein 42nd Annual Monetary Studies Conference Financial Stability, Crisis Preparedness and Risk Management in the Caribbean November 9th-12th 2010, Port of Spain, Trinidad
More informationRomanian Economic and Business Review Vol. 3, No. 3 THE EVOLUTION OF SNP PETROM STOCK LIST - STUDY THROUGH AUTOREGRESSIVE MODELS
THE EVOLUTION OF SNP PETROM STOCK LIST - STUDY THROUGH AUTOREGRESSIVE MODELS Marian Zaharia, Ioana Zaheu, and Elena Roxana Stan Abstract Stock exchange market is one of the most dynamic and unpredictable
More informationLampiran. Lampiran 1 Data Penelitian TAHUN Y X1 X2 X3 X4_AS X4_JPG X4_INDH 1995
Lampiran Lampiran 1 Data Penelitian TAHUN Y X1 X2 X3 X4_AS X4_JPG X4_INDH 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 3,107,163 3,102,431 3,443,555
More informationMultiple Regression Analysis. Basic Estimation Techniques. Multiple Regression Analysis. Multiple Regression Analysis
Multiple Regression Analysis Basic Estimation Techniques Herbert Stocker herbert.stocker@uibk.ac.at University of Innsbruck & IIS, University of Ramkhamhaeng Regression Analysis: Statistical procedure
More informationMultiple Linear Regression CIVL 7012/8012
Multiple Linear Regression CIVL 7012/8012 2 Multiple Regression Analysis (MLR) Allows us to explicitly control for many factors those simultaneously affect the dependent variable This is important for
More information2. Linear regression with multiple regressors
2. Linear regression with multiple regressors Aim of this section: Introduction of the multiple regression model OLS estimation in multiple regression Measures-of-fit in multiple regression Assumptions
More informationUnivariate linear models
Univariate linear models The specification process of an univariate ARIMA model is based on the theoretical properties of the different processes and it is also important the observation and interpretation
More informationApplied Econometrics. Applied Econometrics Second edition. Dimitrios Asteriou and Stephen G. Hall
Applied Econometrics Second edition Dimitrios Asteriou and Stephen G. Hall MULTICOLLINEARITY 1. Perfect Multicollinearity 2. Consequences of Perfect Multicollinearity 3. Imperfect Multicollinearity 4.
More informationECON2228 Notes 2. Christopher F Baum. Boston College Economics. cfb (BC Econ) ECON2228 Notes / 47
ECON2228 Notes 2 Christopher F Baum Boston College Economics 2014 2015 cfb (BC Econ) ECON2228 Notes 2 2014 2015 1 / 47 Chapter 2: The simple regression model Most of this course will be concerned with
More informationWooldridge, Introductory Econometrics, 4th ed. Chapter 2: The simple regression model
Wooldridge, Introductory Econometrics, 4th ed. Chapter 2: The simple regression model Most of this course will be concerned with use of a regression model: a structure in which one or more explanatory
More informationExercise Sheet 5: Solutions
Exercise Sheet 5: Solutions R.G. Pierse 2. Estimation of Model M1 yields the following results: Date: 10/24/02 Time: 18:06 C -1.448432 0.696587-2.079327 0.0395 LPC -0.306051 0.272836-1.121740 0.2640 LPF
More informationResearch Center for Science Technology and Society of Fuzhou University, International Studies and Trade, Changle Fuzhou , China
2017 3rd Annual International Conference on Modern Education and Social Science (MESS 2017) ISBN: 978-1-60595-450-9 An Analysis of the Correlation Between the Scale of Higher Education and Economic Growth
More informationECON 366: ECONOMETRICS II. SPRING TERM 2005: LAB EXERCISE #10 Nonspherical Errors Continued. Brief Suggested Solutions
DEPARTMENT OF ECONOMICS UNIVERSITY OF VICTORIA ECON 366: ECONOMETRICS II SPRING TERM 2005: LAB EXERCISE #10 Nonspherical Errors Continued Brief Suggested Solutions 1. In Lab 8 we considered the following
More information4. Examples. Results: Example 4.1 Implementation of the Example 3.1 in SAS. In SAS we can use the Proc Model procedure.
4. Examples Example 4.1 Implementation of the Example 3.1 in SAS. In SAS we can use the Proc Model procedure. Simulate data from t-distribution with ν = 6. SAS: data tdist; do i = 1 to 500; y = tinv(ranuni(158),6);
More informationx i = 1 yi 2 = 55 with N = 30. Use the above sample information to answer all the following questions. Show explicitly all formulas and calculations.
Exercises for the course of Econometrics Introduction 1. () A researcher is using data for a sample of 30 observations to investigate the relationship between some dependent variable y i and independent
More informationBrief Sketch of Solutions: Tutorial 3. 3) unit root tests
Brief Sketch of Solutions: Tutorial 3 3) unit root tests.5.4.4.3.3.2.2.1.1.. -.1 -.1 -.2 -.2 -.3 -.3 -.4 -.4 21 22 23 24 25 26 -.5 21 22 23 24 25 26.8.2.4. -.4 - -.8 - - -.12 21 22 23 24 25 26 -.2 21 22
More informationPractical Econometrics. for. Finance and Economics. (Econometrics 2)
Practical Econometrics for Finance and Economics (Econometrics 2) Seppo Pynnönen and Bernd Pape Department of Mathematics and Statistics, University of Vaasa 1. Introduction 1.1 Econometrics Econometrics
More information1 Linear Regression Analysis The Mincer Wage Equation Data Econometric Model Estimation... 11
Econ 495 - Econometric Review 1 Contents 1 Linear Regression Analysis 4 1.1 The Mincer Wage Equation................. 4 1.2 Data............................. 6 1.3 Econometric Model.....................
More informationInference in Regression Analysis
ECNS 561 Inference Inference in Regression Analysis Up to this point 1.) OLS is unbiased 2.) OLS is BLUE (best linear unbiased estimator i.e., the variance is smallest among linear unbiased estimators)
More informationEconometrics Homework 1
Econometrics Homework Due Date: March, 24. by This problem set includes questions for Lecture -4 covered before midterm exam. Question Let z be a random column vector of size 3 : z = @ (a) Write out z
More informationCHAPTER 4. > 0, where β
CHAPTER 4 SOLUTIONS TO PROBLEMS 4. (i) and (iii) generally cause the t statistics not to have a t distribution under H. Homoskedasticity is one of the CLM assumptions. An important omitted variable violates
More informationStatistics II. Management Degree Management Statistics IIDegree. Statistics II. 2 nd Sem. 2013/2014. Management Degree. Simple Linear Regression
Model 1 2 Ordinary Least Squares 3 4 Non-linearities 5 of the coefficients and their to the model We saw that econometrics studies E (Y x). More generally, we shall study regression analysis. : The regression
More informationLab 6 - Simple Regression
Lab 6 - Simple Regression Spring 2017 Contents 1 Thinking About Regression 2 2 Regression Output 3 3 Fitted Values 5 4 Residuals 6 5 Functional Forms 8 Updated from Stata tutorials provided by Prof. Cichello
More informationSpatial Aspects of Trade Liberalization in Colombia: A General Equilibrium Approach. Eduardo Haddad Jaime Bonet Geoffrey Hewings Fernando Perobelli
Spatial Aspects of Trade Liberalization in Colombia: A General Equilibrium Approach Eduardo Haddad Jaime Bonet Geoffrey Hewings Fernando Perobelli Outline Motivation The CEER model Simulation results Final
More information5. Let W follow a normal distribution with mean of μ and the variance of 1. Then, the pdf of W is
Practice Final Exam Last Name:, First Name:. Please write LEGIBLY. Answer all questions on this exam in the space provided (you may use the back of any page if you need more space). Show all work but do
More informationFunctional Form. So far considered models written in linear form. Y = b 0 + b 1 X + u (1) Implies a straight line relationship between y and X
Functional Form So far considered models written in linear form Y = b 0 + b 1 X + u (1) Implies a straight line relationship between y and X Functional Form So far considered models written in linear form
More information4.1 Least Squares Prediction 4.2 Measuring Goodness-of-Fit. 4.3 Modeling Issues. 4.4 Log-Linear Models
4.1 Least Squares Prediction 4. Measuring Goodness-of-Fit 4.3 Modeling Issues 4.4 Log-Linear Models y = β + β x + e 0 1 0 0 ( ) E y where e 0 is a random error. We assume that and E( e 0 ) = 0 var ( e
More informationEcon 427, Spring Problem Set 3 suggested answers (with minor corrections) Ch 6. Problems and Complements:
Econ 427, Spring 2010 Problem Set 3 suggested answers (with minor corrections) Ch 6. Problems and Complements: 1. (page 132) In each case, the idea is to write these out in general form (without the lag
More informationOLS Assumptions Violation and Its Treatment: An Empirical Test of Gross Domestic Product Relationship with Exchange Rate, Inflation and Interest Rate
J. Appl. Environ. Biol. Sci., 6(5S)43-54, 2016 2016, TextRoad Publication ISSN: 2090-4274 Journal of Applied Environmental and Biological Sciences www.textroad.com OLS Assumptions Violation and Its Treatment:
More informationx = 1 n (x = 1 (x n 1 ι(ι ι) 1 ι x) (x ι(ι ι) 1 ι x) = 1
Estimation and Inference in Econometrics Exercises, January 24, 2003 Solutions 1. a) cov(wy ) = E [(WY E[WY ])(WY E[WY ]) ] = E [W(Y E[Y ])(Y E[Y ]) W ] = W [(Y E[Y ])(Y E[Y ]) ] W = WΣW b) Let Σ be a
More information11. Simultaneous-Equation Models
11. Simultaneous-Equation Models Up to now: Estimation and inference in single-equation models Now: Modeling and estimation of a system of equations 328 Example: [I] Analysis of the impact of advertisement
More information10. Time series regression and forecasting
10. Time series regression and forecasting Key feature of this section: Analysis of data on a single entity observed at multiple points in time (time series data) Typical research questions: What is the
More informationTjalling C. Koopmans Research Institute
Tjalling C. Koopmans Research Institute Tjalling C. Koopmans Research Institute Utrecht School of Economics Utrecht University Janskerkhof 12 3512 BL Utrecht The Netherlands telephone +31 30 253 9800 fax
More informationAccompanying Notes on Data and Methods: The Economics of Hurricanes in the United States. William D. Nordhaus December 21, 2006
Accompanying Notes on Data and Methods: The Economics of Hurricanes in the United States William D. Nordhaus December 21, 2006 This document describes the procedures used and background data for William
More informationAnalysis of Gross Domestic Product Evolution under the Influence of the Final Consumption
Theoretical and Applied Economics Volume XXII (2015), No. 4(605), Winter, pp. 45-52 Analysis of Gross Domestic Product Evolution under the Influence of the Final Consumption Constantin ANGHELACHE Bucharest
More information3. Linear Regression With a Single Regressor
3. Linear Regression With a Single Regressor Econometrics: (I) Application of statistical methods in empirical research Testing economic theory with real-world data (data analysis) 56 Econometrics: (II)
More informationAPPLIED MACROECONOMETRICS Licenciatura Universidade Nova de Lisboa Faculdade de Economia. FINAL EXAM JUNE 3, 2004 Starts at 14:00 Ends at 16:30
APPLIED MACROECONOMETRICS Licenciatura Universidade Nova de Lisboa Faculdade de Economia FINAL EXAM JUNE 3, 2004 Starts at 14:00 Ends at 16:30 I In Figure I.1 you can find a quarterly inflation rate series
More informationThe GARCH Analysis of YU EBAO Annual Yields Weiwei Guo1,a
2nd Workshop on Advanced Research and Technology in Industry Applications (WARTIA 2016) The GARCH Analysis of YU EBAO Annual Yields Weiwei Guo1,a 1 Longdong University,Qingyang,Gansu province,745000 a
More informationCHAPTER 5 FUNCTIONAL FORMS OF REGRESSION MODELS
CHAPTER 5 FUNCTIONAL FORMS OF REGRESSION MODELS QUESTIONS 5.1. (a) In a log-log model the dependent and all explanatory variables are in the logarithmic form. (b) In the log-lin model the dependent variable
More informationBrief Suggested Solutions
DEPARTMENT OF ECONOMICS UNIVERSITY OF VICTORIA ECONOMICS 366: ECONOMETRICS II SPRING TERM 5: ASSIGNMENT TWO Brief Suggested Solutions Question One: Consider the classical T-observation, K-regressor linear
More information6. Assessing studies based on multiple regression
6. Assessing studies based on multiple regression Questions of this section: What makes a study using multiple regression (un)reliable? When does multiple regression provide a useful estimate of the causal
More informationLecture 12. Functional form
Lecture 12. Functional form Multiple linear regression model β1 + β2 2 + L+ β K K + u Interpretation of regression coefficient k Change in if k is changed by 1 unit and the other variables are held constant.
More informationApplied Econometrics (QEM)
Applied Econometrics (QEM) based on Prinicples of Econometrics Jakub Mućk Department of Quantitative Economics Jakub Mućk Applied Econometrics (QEM) Meeting #3 1 / 42 Outline 1 2 3 t-test P-value Linear
More information1 Quantitative Techniques in Practice
1 Quantitative Techniques in Practice 1.1 Lecture 2: Stationarity, spurious regression, etc. 1.1.1 Overview In the rst part we shall look at some issues in time series economics. In the second part we
More informationIn Chapter 2, we learned how to use simple regression analysis to explain a dependent
3 Multiple Regression Analysis: Estimation In Chapter 2, we learned how to use simple regression analysis to explain a dependent variable, y, as a function of a single independent variable, x. The primary
More information[ ESS ESS ] / 2 [ ] / ,019.6 / Lab 10 Key. Regression Analysis: wage versus yrsed, ex
Lab 1 Key Regression Analysis: wage versus yrsed, ex wage = - 4.78 + 1.46 yrsed +.126 ex Constant -4.78 2.146-2.23.26 yrsed 1.4623.153 9.73. ex.12635.2739 4.61. S = 8.9851 R-Sq = 11.9% R-Sq(adj) = 11.7%
More informationin the time series. The relation between y and x is contemporaneous.
9 Regression with Time Series 9.1 Some Basic Concepts Static Models (1) y t = β 0 + β 1 x t + u t t = 1, 2,..., T, where T is the number of observation in the time series. The relation between y and x
More informationProblem Set 2: Box-Jenkins methodology
Problem Set : Box-Jenkins methodology 1) For an AR1) process we have: γ0) = σ ε 1 φ σ ε γ0) = 1 φ Hence, For a MA1) process, p lim R = φ γ0) = 1 + θ )σ ε σ ε 1 = γ0) 1 + θ Therefore, p lim R = 1 1 1 +
More informationIntermediate Econometrics
Intermediate Econometrics Markus Haas LMU München Summer term 2011 15. Mai 2011 The Simple Linear Regression Model Considering variables x and y in a specific population (e.g., years of education and wage
More informationForecasting Seasonal Time Series 1. Introduction. Philip Hans Franses Econometric Institute Erasmus University Rotterdam
Forecasting Seasonal Time Series 1. Introduction Philip Hans Franses Econometric Institute Erasmus University Rotterdam SMU and NUS, Singapore, April-May 2004 1 Outline of tutorial lectures 1 Introduction
More informationFrequency Forecasting using Time Series ARIMA model
Frequency Forecasting using Time Series ARIMA model Manish Kumar Tikariha DGM(O) NSPCL Bhilai Abstract In view of stringent regulatory stance and recent tariff guidelines, Deviation Settlement mechanism
More informationPREDICTIONS AGGREGATION BY COUNTRY TO IMPROVE THE ACCURACY OF EUROPEAN UNION GDP RATE FORECASTS? Mihaela Simionescu *
PREDICTIONS AGGREGATION BY COUNTRY TO IMPROVE THE ACCURACY OF EUROPEAN UNION GDP RATE FORECASTS? Mihaela Simionescu * Address for corespondence: Institute for Economic Forecasting of the Romanian Academy
More informationFinancial Time Series Analysis: Part II
Department of Mathematics and Statistics, University of Vaasa, Finland Spring 2017 1 Unit root Deterministic trend Stochastic trend Testing for unit root ADF-test (Augmented Dickey-Fuller test) Testing
More informationThe Evolution of Snp Petrom Stock List - Study Through Autoregressive Models
The Evolution of Snp Petrom Stock List Study Through Autoregressive Models Marian Zaharia Ioana Zaheu Elena Roxana Stan Faculty of Internal and International Economy of Tourism RomanianAmerican University,
More informationFinal Exam Financial Data Analysis at the University of Freiburg (Winter Semester 2008/2009) Friday, November 14, 2008,
Professor Dr. Roman Liesenfeld Final Exam Financial Data Analysis at the University of Freiburg (Winter Semester 2008/2009) Friday, November 14, 2008, 10.00 11.30am 1 Part 1 (38 Points) Consider the following
More informationWednesday, October 10 Handout: One-Tailed Tests, Two-Tailed Tests, and Logarithms
Amherst College Department of Economics Economics 360 Fall 2012 Wednesday, October 10 Handout: One-Tailed Tests, Two-Tailed Tests, and Logarithms Preview A One-Tailed Hypothesis Test: The Downward Sloping
More informationARDL Cointegration Tests for Beginner
ARDL Cointegration Tests for Beginner Tuck Cheong TANG Department of Economics, Faculty of Economics & Administration University of Malaya Email: tangtuckcheong@um.edu.my DURATION: 3 HOURS On completing
More informationForecasting Foreign Direct Investment Inflows into India Using ARIMA Model
Forecasting Foreign Direct Investment Inflows into India Using ARIMA Model Dr.K.Nithya Kala & Aruna.P.Remesh, 1 Assistant Professor, PSGR Krishnammal College for Women, Coimbatore, Tamilnadu, India 2 PhD
More informationEconomics 113. Simple Regression Assumptions. Simple Regression Derivation. Changing Units of Measurement. Nonlinear effects
Economics 113 Simple Regression Models Simple Regression Assumptions Simple Regression Derivation Changing Units of Measurement Nonlinear effects OLS and unbiased estimates Variance of the OLS estimates
More informationAnswers to Problem Set #4
Answers to Problem Set #4 Problems. Suppose that, from a sample of 63 observations, the least squares estimates and the corresponding estimated variance covariance matrix are given by: bβ bβ 2 bβ 3 = 2
More informationBUSINESS FORECASTING
BUSINESS FORECASTING FORECASTING WITH REGRESSION MODELS TREND ANALYSIS Prof. Dr. Burç Ülengin ITU MANAGEMENT ENGINEERING FACULTY FALL 2015 OVERVIEW The bivarite regression model Data inspection Regression
More informationWednesday, October 17 Handout: Hypothesis Testing and the Wald Test
Amherst College Department of Economics Economics 360 Fall 2012 Wednesday, October 17 Handout: Hypothesis Testing and the Wald Test Preview No Money Illusion Theory: Calculating True] o Clever Algebraic
More informationChapter 9: The Regression Model with Qualitative Information: Binary Variables (Dummies)
Chapter 9: The Regression Model with Qualitative Information: Binary Variables (Dummies) Statistics and Introduction to Econometrics M. Angeles Carnero Departamento de Fundamentos del Análisis Económico
More informationEconometrics I Lecture 3: The Simple Linear Regression Model
Econometrics I Lecture 3: The Simple Linear Regression Model Mohammad Vesal Graduate School of Management and Economics Sharif University of Technology 44716 Fall 1397 1 / 32 Outline Introduction Estimating
More informationRegression Analysis with Cross-Sectional Data
89782_02_c02_p023-072.qxd 5/25/05 11:46 AM Page 23 PART 1 Regression Analysis with Cross-Sectional Data P art 1 of the text covers regression analysis with cross-sectional data. It builds upon a solid
More informationChapter 3. Regression-Based Models for Developing Commercial Demand Characteristics Investigation
Chapter Regression-Based Models for Developing Commercial Demand Characteristics Investigation. Introduction Commercial area is another important area in terms of consume high electric energy in Japan.
More informationWooldridge, Introductory Econometrics, 4th ed. Chapter 6: Multiple regression analysis: Further issues
Wooldridge, Introductory Econometrics, 4th ed. Chapter 6: Multiple regression analysis: Further issues What effects will the scale of the X and y variables have upon multiple regression? The coefficients
More informationExercise sheet 3 The Multiple Regression Model
Exercise sheet 3 The Multiple Regression Model Note: In those problems that include estimations and have a reference to a data set the students should check the outputs obtained with Gretl. 1. Let the
More informationLecture 8: Functional Form
Lecture 8: Functional Form What we know now OLS - fitting a straight line y = b 0 + b 1 X through the data using the principle of choosing the straight line that minimises the sum of squared residuals
More information7. Integrated Processes
7. Integrated Processes Up to now: Analysis of stationary processes (stationary ARMA(p, q) processes) Problem: Many economic time series exhibit non-stationary patterns over time 226 Example: We consider
More informationECONOMETRIA II. CURSO 2009/2010 LAB # 3
ECONOMETRIA II. CURSO 2009/2010 LAB # 3 BOX-JENKINS METHODOLOGY The Box Jenkins approach combines the moving average and the autorregresive models. Although both models were already known, the contribution
More informationProblem set 1: answers. April 6, 2018
Problem set 1: answers April 6, 2018 1 1 Introduction to answers This document provides the answers to problem set 1. If any further clarification is required I may produce some videos where I go through
More informationProblem 4.1. Problem 4.3
BOSTON COLLEGE Department of Economics EC 228 01 Econometric Methods Fall 2008, Prof. Baum, Ms. Phillips (tutor), Mr. Dmitriev (grader) Problem Set 3 Due at classtime, Thursday 14 Oct 2008 Problem 4.1
More informationMore on Specification and Data Issues
More on Specification and Data Issues Ping Yu School of Economics and Finance The University of Hong Kong Ping Yu (HKU) Specification and Data Issues 1 / 35 Functional Form Misspecification Functional
More information7. Integrated Processes
7. Integrated Processes Up to now: Analysis of stationary processes (stationary ARMA(p, q) processes) Problem: Many economic time series exhibit non-stationary patterns over time 226 Example: We consider
More information