|
|
- Leo Brooks
- 5 years ago
- Views:
Transcription
1 STOCKHOLM UNIVERSITY Department of Economics Course name: Empirical Methods Course code: EC40 Examiner: Lena Nekby Number of credits: 7,5 credits Date of exam: Saturday, May 9, 008 Examination time: 3 hours Write your name, Swedish personal number and the number of the question on every cover sheet. Do not write answers for more than one question in the same cover sheet. Explain notions/concepts and symbols. Only legible exams will be marked. No aids are allowed with the exception of calculators provided by exam administrators The exam consists of two parts. Part 1 consists of 0 multiple choice questions worth 40 points in total ( points each). All students must answer this part of the exam. Part consists of two discussion questions worth 60 points in total (30 points each). Discussion question 1 is worth 30 points for those that successfully acquired credit on the first credit assignment. Discussion question is worth 30 points for those that successfully acquired credit on the second credit assignment. If you have received credit you do not need to answer the respective discussion question on the exam. The exam is worth 100 points in total. For the grade E 40 points are required, for D 50 points, C 60 points, B 75 points and A 90 points If you think that a question is vaguely formulated: specify the conditions used for solving it Results will be posted on the notice board, House A, floor 3, June 14, 010 at the latest Good luck!
2 Part 1: Multiple Choice Questions (40 points). Circle the right answer. Only one answer per question. No credit will be given for multiple answers or additional explanations. Two points per question for correct answers. 1) The following are all least squares assumptions with the exception of: a. The conditional distribution of u i given X i has a mean of zero. b. The explanatory variable in regression model is normally distributed. c. ( X i, Yi ), i = 1,..., n are independently and identically distributed. d. Large outliers are unlikely. ) The reason why estimators have a sampling distribution is that a. economics is not a precise science. b. individuals respond differently to incentives. c. in real life you typically get to sample many times. d. the values of the explanatory variable and the error term differ across samples. 3) The sample average of the OLS residuals is a. some positive number since OLS uses squares. b. zero. c. unobservable since the population regression function is unknown. d. dependent on whether the explanatory variable is mostly positive or negative. 4) To obtain the slope estimator using the least squares principle, you divide the a. sample variance of X by the sample variance of Y. b. sample covariance of X and Y by the sample variance of Y. c. sample covariance of X and Y by the sample variance of X. d. sample variance of X by the sample covariance of X and Y. 5) With heteroskedastic errors, the weighted least squares estimator is BLUE. You should use OLS with heteroskedasticity-robust standard errors because a. this method is simpler. b. the exact form of the conditional variance is rarely known. c. the Gauss-Markov theorem holds. d. your spreadsheet program does not have a command for weighted least squares.
3 6) The t-statistic is calculated by dividing a. the OLS estimator by its standard error. b. the slope by the standard deviation of the explanatory variable. c. the estimator minus its hypothesized value by the standard error of the estimator. d. the slope by ) Finding a small value of the p-value (e.g. less than 5%) a. indicates evidence in favor of the null hypothesis. b. implies that the t-statistic is less than c. indicates evidence in against the null hypothesis. d. will only happen roughly one in twenty samples. 8) When there are omitted variables in the regression, which are determinants of the dependent variable, then a. you cannot measure the effect of the omitted variable, but the estimator of your included variable(s) is (are) unaffected. b. this has no effect on the estimator of your included variable because the other variable is not included. c. this will always bias the OLS estimator of the included variable. d. the OLS estimator is biased if the omitted variable is correlated with the included variable. 9) When you have an omitted variable problem, the assumption that E(u i X i ) = 0 is violated. This implies that a. the sum of the residuals is no longer zero. b. there is another estimator called weighted least squares, which is BLUE. c. the sum of the residuals times any of the explanatory variables is no longer zero. d. the OLS estimator is no longer consistent. 10) All of the following are true, with the exception of one condition: a. a high R or variable. b. a high c. a high R or R or d. a high R or regressors. R does not mean that the regressors are a true cause of the dependent R does not mean that there is no omitted variable bias. R always means that an added variable is statistically significant. R does not necessarily mean that you have the most appropriate set of
4 11) The interpretation of the slope coefficient in the model Y = β ln( ) 0 + β1 X + u is as follows: i i i a. a 1% change in X is associated with a β 1 % change in Y. b. a 1% change in X is associated with a change in Y of 0.01 β 1. c. a change in X by one unit is associated with a 100 β 1 % change in Y. d. a change in X by one unit is associated with a β 1 change in Y. 1) A nonlinear function a. makes little sense, because variables in the real world are related linearly. b. can be adequately described by a straight line between the dependent variable and one of the explanatory variables. c. is a concept that only applies to the case of a single or two explanatory variables since you cannot draw a line in four dimensions. d. is a function with a slope that is not constant. 13) A statistical analysis is internally valid if e. its inferences and conclusions can be generalized from the population and setting studied to other populations and settings. f. statistical inference is conducted inside the sample period. g. the hypothesized parameter value is inside the confidence interval. h. the statistical inferences about causal effects are valid for the population being studied. 14) Comparing the California test scores to test scores in Massachusetts is appropriate for external validity if a. Massachusetts also allowed beach walking to be an appropriate P.E. activity. b. the two income distributions were very similar. c. the student-to-teacher ratio did not differ by more than five on average. d. the institutional settings in California and Massachusetts, such as organization in classroom instruction and curriculum, were similar in the two states. 15) You try to explain the number of IBM shares traded in the stock market per day in 005. As an independent variable you choose the closing price of the share. This is an example of a. simultaneous causality. b. invalid inference due to a small sample size. c. sample selection bias since you should analyze more than one stock. d. a situation where homoskedasticity-only standard errors should be used since you only analyze one company.
5 16) Consider a panel regression of unemployment rates for the G7 countries (United States, Canada, France, Germany, Italy, United Kingdom, Japan) on a set of explanatory variables for the time period (annual data). If you included entity and time fixed effects, you would need to specify the following number of binary variables: a. 1. b. 6. c. 8. d ) A pattern in the coefficients of the time fixed effects binary variables may reveal the following in a study of the determinants of state unemployment rates using panel data: a. macroeconomic effects, which affect all states equally in a given year. b. attitude differences towards unemployment between states. c. there is no economic information that can be retrieved from these coefficients. d. regional effects, which affect all states equally, as long as they are a member of that region. 18) If the instruments are not exogenous, a. you cannot perform the first stage of TSLS. b. then, in order to conduct proper inference, it is essential that you use heteroskedasticityrobust standard errors. c. your model becomes overidentified. d. then TSLS is inconsistent. 19) Consider a model with one endogenous regressor and two instruments. Then the J-statistic will be large a. if the number of observations are very large. b. if the coefficients are very different when estimating the coefficients using one instrument at a time. c. if the TSLS estimates are very different from the OLS estimates. d. when you use homoskedasticity-only standard errors. 0) Causal effects that depend on the value of an observable variable, say W i, a. cannot be estimated. b. can be estimate by interacting the treatment variable with W i. c. result in the OLS estimator being inefficient. d. requires use of homoskedasticity-only standard errors.
6 Part : Discussion Questions (60 points) On separate sheets of paper, answer the following discussion questions. Write your name, personal number (personnummer) and the question number on each sheet. Answer each question clearly and concisely. Only legible answers will be considered, others will be disregarded. If you think that a question is vaguely formulated, specify the conditions used for solving it. Each question is worth 30 points. Discussion Question 1: NOTE: Those with credit on credit assignment 1 receive 30 points for this question and do not have to answer discussion question 1 Sir Francis Galton, a cousin of James Darwin, examined the relationship between the height of children and their parents towards the end of the 19 th century. It is from this study that the name regression originated. You decide to update his findings by collecting data from 110 college students, and estimate the following relationship: NO studenth = Midparh, R = 0.45, SER =.0 (7.) (0.10) where Studenth is the height of students in inches, and Midparh is the average of the parental heights. Values in parentheses are heteroskedasticity robust standard errors. (Following Galton s methodology, both variables were adjusted so that the average female height was equal to the average male height.) (a) Interpret the estimated coefficients. (b) What is the meaning of the regression R?. (c) What is the prediction for the height of a child whose parents have an average height of inches? (d) What is the interpretation of the SER here? (e) Given the positive intercept and the fact that the slope lies between zero and one, what can you say about the height of students who have quite tall parents? Who have quite short parents? (f) Test for the statistical significance of the slope coefficient.
7 (g) If children, on average, were expected to be of the same height as their parents, then this would imply two hypotheses, one for the slope and one for the intercept. (i) What should the null hypothesis be for the intercept? Calculate the relevant t-statistic and carry out the hypothesis test at the 1% level. (ii) What should the null hypothesis be for the slope? Calculate the relevant t-statistic and carry out the hypothesis test at the 5% level. (h) Can you reject the null hypothesis that the regression R is zero? (i) Construct a 95% confidence interval for a one inch increase in the average of parental height. (j) Galton was concerned about the height of the English aristocracy and referred to the above result as regression towards mediocrity. Can you figure out what his concern was? Why do you think that we refer to this result today as Galton s Fallacy?
8 Discussion Question : NOTE: Those with credit on credit assignment receive 30 points for this question and do not have to answer discussion question To analyze the year-to-year variation in temperature data for a given city, you regress the daily high temperature (Temp) for 100 randomly selected days in two consecutive years (1997 and 1998) for Phoenix. The results are (heteroskedastic-robust standard errors in parenthesis): NO PHX Temp 1998 PHX = Temp1997 ; (0.10) R = 0.65, SER = 9.63 (a) Calculate the predicted temperature for the current year if the temperature in the previous year was 40 0 F, 78 0 F, and F. How does this compare with you prior expectation? Sketch the regression line and compare it to the 45 degree line. What are the implications? (b) You recall having studied errors-in-variables before. Although the web site you received your data from seems quite reliable in measuring data accurately, what if the temperature contained measurement error in the following sense: for any given day, say January 8, there is a true underlying seasonal temperature (X), but each year there are different temporary weather patterns (v, w) which result in a temperature X ~ different from X. For the two years in your data set, the situation can be described as follows: ~ X 1997 = X +ν 1997 and X 1998 = X + ω1997 ~ ~ ~ ~ ~ Subtracting X1997 from X 1998, you get X 1998 X ω1998 ν Hence the population parameter for the intercept and slope are zero and one, as expected. It is not difficult to show that the OLS estimator for the slope is inconsistent, where v 1 σ x + σ v p ˆ β 1 σ As a result you consider estimating the slope and intercept by TSLS. You think about an instrument and consider the temperature one month ahead of the observation in the previous year. Discuss instrument validity for this case.
9 (c) The TSLS estimation result is as follows: NO PHX Temp 1998 PHX = Temp1997 ; (0.06) Perform a t-test on whether or not the slope is now significantly different from one. (d) Write a short essay about the Overidentifying Restrictions Test. What is meant exactly by overidentification? State the null hypothesis. Describe how to calculate the J-statistic and what its distribution is. Can the test be used in the above example, why or why not? Use an example of two instruments and one endogenous variable to explain under what situation the J - test will be likely to reject the null hypothesis. If your variables pass the test, is this sufficient for these variables to be good instruments? (e) What are the two conditions for instrument validity? The reason for the inconsistency of OLS is that corr( X i, ui ) 0. But if X and Z are correlated, and X and u are also correlated, then how can Z and u not be correlated? Explain..
STOCKHOLM UNIVERSITY Department of Economics Course name: Empirical Methods Course code: EC40 Examiner: Lena Nekby Number of credits: 7,5 credits Date of exam: Friday, June 5, 009 Examination time: 3 hours
More informationSTOCKHOLM UNIVERSITY Department of Economics Course name: Empirical Methods Course code: EC40 Examiner: Per Pettersson-Lidbom Number of creds: 7,5 creds Date of exam: Thursday, January 15, 009 Examination
More informationWrite your identification number on each paper and cover sheet (the number stated in the upper right hand corner on your exam cover).
STOCKHOLM UNIVERSITY Department of Economics Course name: Empirical Methods in Economics 2 Course code: EC2402 Examiner: Peter Skogman Thoursie Number of credits: 7,5 credits (hp) Date of exam: Saturday,
More informationWrite your identification number on each paper and cover sheet (the number stated in the upper right hand corner on your exam cover).
Formatmall skapad: 2011-12-01 Uppdaterad: 2015-03-06 / LP Department of Economics Course name: Empirical Methods in Economics 2 Course code: EC2404 Semester: Spring 2015 Type of exam: MAIN Examiner: Peter
More informationWISE International Masters
WISE International Masters ECONOMETRICS Instructor: Brett Graham INSTRUCTIONS TO STUDENTS 1 The time allowed for this examination paper is 2 hours. 2 This examination paper contains 32 questions. You are
More information8. Instrumental variables regression
8. Instrumental variables regression Recall: In Section 5 we analyzed five sources of estimation bias arising because the regressor is correlated with the error term Violation of the first OLS assumption
More informationContest Quiz 3. Question Sheet. In this quiz we will review concepts of linear regression covered in lecture 2.
Updated: November 17, 2011 Lecturer: Thilo Klein Contact: tk375@cam.ac.uk Contest Quiz 3 Question Sheet In this quiz we will review concepts of linear regression covered in lecture 2. NOTE: Please round
More informationEconometrics. Week 8. Fall Institute of Economic Studies Faculty of Social Sciences Charles University in Prague
Econometrics Week 8 Institute of Economic Studies Faculty of Social Sciences Charles University in Prague Fall 2012 1 / 25 Recommended Reading For the today Instrumental Variables Estimation and Two Stage
More informationWISE MA/PhD Programs Econometrics Instructor: Brett Graham Spring Semester, Academic Year Exam Version: A
WISE MA/PhD Programs Econometrics Instructor: Brett Graham Spring Semester, 2015-16 Academic Year Exam Version: A INSTRUCTIONS TO STUDENTS 1 The time allowed for this examination paper is 2 hours. 2 This
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 informationMGEC11H3Y L01 Introduction to Regression Analysis Term Test Friday July 5, PM Instructor: Victor Yu
Last Name (Print): Solution First Name (Print): Student Number: MGECHY L Introduction to Regression Analysis Term Test Friday July, PM Instructor: Victor Yu Aids allowed: Time allowed: Calculator and one
More informationIntroduction to Econometrics
Introduction to Econometrics T H I R D E D I T I O N Global Edition James H. Stock Harvard University Mark W. Watson Princeton University Boston Columbus Indianapolis New York San Francisco Upper Saddle
More informationThe Simple Linear Regression Model
The Simple Linear Regression Model Lesson 3 Ryan Safner 1 1 Department of Economics Hood College ECON 480 - Econometrics Fall 2017 Ryan Safner (Hood College) ECON 480 - Lesson 3 Fall 2017 1 / 77 Bivariate
More informationRegression with a Single Regressor: Hypothesis Tests and Confidence Intervals
Regression with a Single Regressor: Hypothesis Tests and Confidence Intervals (SW Chapter 5) Outline. The standard error of ˆ. Hypothesis tests concerning β 3. Confidence intervals for β 4. Regression
More informationReview of Econometrics
Review of Econometrics Zheng Tian June 5th, 2017 1 The Essence of the OLS Estimation Multiple regression model involves the models as follows Y i = β 0 + β 1 X 1i + β 2 X 2i + + β k X ki + u i, i = 1,...,
More informationEconomics Introduction to Econometrics - Fall 2007 Final Exam - Answers
Student Name: Economics 4818 - Introduction to Econometrics - Fall 2007 Final Exam - Answers SHOW ALL WORK! Evaluation: Problems: 3, 4C, 5C and 5F are worth 4 points. All other questions are worth 3 points.
More information1 Motivation for Instrumental Variable (IV) Regression
ECON 370: IV & 2SLS 1 Instrumental Variables Estimation and Two Stage Least Squares Econometric Methods, ECON 370 Let s get back to the thiking in terms of cross sectional (or pooled cross sectional) data
More informationEconometrics. Week 4. Fall Institute of Economic Studies Faculty of Social Sciences Charles University in Prague
Econometrics Week 4 Institute of Economic Studies Faculty of Social Sciences Charles University in Prague Fall 2012 1 / 23 Recommended Reading For the today Serial correlation and heteroskedasticity in
More informationEconometrics Problem Set 11
Econometrics Problem Set WISE, Xiamen University Spring 207 Conceptual Questions. (SW 2.) This question refers to the panel data regressions summarized in the following table: Dependent variable: ln(q
More informationECONOMETRICS FIELD EXAM Michigan State University May 9, 2008
ECONOMETRICS FIELD EXAM Michigan State University May 9, 2008 Instructions: Answer all four (4) questions. Point totals for each question are given in parenthesis; there are 00 points possible. Within
More informationAssessing Studies Based on Multiple Regression
Assessing Studies Based on Multiple Regression Outline 1. Internal and External Validity 2. Threats to Internal Validity a. Omitted variable bias b. Functional form misspecification c. Errors-in-variables
More informationLinear Regression with one Regressor
1 Linear Regression with one Regressor Covering Chapters 4.1 and 4.2. We ve seen the California test score data before. Now we will try to estimate the marginal effect of STR on SCORE. To motivate these
More informationEc1123 Section 7 Instrumental Variables
Ec1123 Section 7 Instrumental Variables Andrea Passalacqua Harvard University andreapassalacqua@g.harvard.edu November 16th, 2017 Andrea Passalacqua (Harvard) Ec1123 Section 7 Instrumental Variables November
More informationECON 4230 Intermediate Econometric Theory Exam
ECON 4230 Intermediate Econometric Theory Exam Multiple Choice (20 pts). Circle the best answer. 1. The Classical assumption of mean zero errors is satisfied if the regression model a) is linear in the
More informationEconometrics Summary Algebraic and Statistical Preliminaries
Econometrics Summary Algebraic and Statistical Preliminaries Elasticity: The point elasticity of Y with respect to L is given by α = ( Y/ L)/(Y/L). The arc elasticity is given by ( Y/ L)/(Y/L), when L
More informationEcon Spring 2016 Section 9
Econ 140 - Spring 2016 Section 9 GSI: Fenella Carpena March 31, 2016 1 Assessing Studies Based on Multiple Regression 1.1 Internal Validity Threat to Examples/Cases Internal Validity OVB Example: wages
More informationFinal Exam - Solutions
Ecn 102 - Analysis of Economic Data University of California - Davis March 19, 2010 Instructor: John Parman Final Exam - Solutions You have until 5:30pm to complete this exam. Please remember to put your
More informationIntroduction to Regression Analysis. Dr. Devlina Chatterjee 11 th August, 2017
Introduction to Regression Analysis Dr. Devlina Chatterjee 11 th August, 2017 What is regression analysis? Regression analysis is a statistical technique for studying linear relationships. One dependent
More informationECONOMETRICS HONOR S EXAM REVIEW SESSION
ECONOMETRICS HONOR S EXAM REVIEW SESSION Eunice Han ehan@fas.harvard.edu March 26 th, 2013 Harvard University Information 2 Exam: April 3 rd 3-6pm @ Emerson 105 Bring a calculator and extra pens. Notes
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 informationMidterm 2 - Solutions
Ecn 102 - Analysis of Economic Data University of California - Davis February 23, 2010 Instructor: John Parman Midterm 2 - Solutions You have until 10:20am to complete this exam. Please remember to put
More informationEcn Analysis of Economic Data University of California - Davis February 23, 2010 Instructor: John Parman. Midterm 2. Name: ID Number: Section:
Ecn 102 - Analysis of Economic Data University of California - Davis February 23, 2010 Instructor: John Parman Midterm 2 You have until 10:20am to complete this exam. Please remember to put your name,
More informationEMERGING MARKETS - Lecture 2: Methodology refresher
EMERGING MARKETS - Lecture 2: Methodology refresher Maria Perrotta April 4, 2013 SITE http://www.hhs.se/site/pages/default.aspx My contact: maria.perrotta@hhs.se Aim of this class There are many different
More informationLinear Regression with Multiple Regressors
Linear Regression with Multiple Regressors (SW Chapter 6) Outline 1. Omitted variable bias 2. Causality and regression analysis 3. Multiple regression and OLS 4. Measures of fit 5. Sampling distribution
More informationINTRODUCTION TO BASIC LINEAR REGRESSION MODEL
INTRODUCTION TO BASIC LINEAR REGRESSION MODEL 13 September 2011 Yogyakarta, Indonesia Cosimo Beverelli (World Trade Organization) 1 LINEAR REGRESSION MODEL In general, regression models estimate the effect
More informationApplied Statistics and Econometrics
Applied Statistics and Econometrics Lecture 6 Saul Lach September 2017 Saul Lach () Applied Statistics and Econometrics September 2017 1 / 53 Outline of Lecture 6 1 Omitted variable bias (SW 6.1) 2 Multiple
More informationWISE International Masters
WISE International Masters ECONOMETRICS Instructor: Brett Graham INSTRUCTIONS TO STUDENTS 1 The time allowed for this examination paper is 2 hours. 2 This examination paper contains 32 questions. You are
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 informationRecent Advances in the Field of Trade Theory and Policy Analysis Using Micro-Level Data
Recent Advances in the Field of Trade Theory and Policy Analysis Using Micro-Level Data July 2012 Bangkok, Thailand Cosimo Beverelli (World Trade Organization) 1 Content a) Classical regression model b)
More informationEconometrics Honor s Exam Review Session. Spring 2012 Eunice Han
Econometrics Honor s Exam Review Session Spring 2012 Eunice Han Topics 1. OLS The Assumptions Omitted Variable Bias Conditional Mean Independence Hypothesis Testing and Confidence Intervals Homoskedasticity
More informationDepartment of Economics, UCSB UC Santa Barbara
Department of Economics, UCSB UC Santa Barbara Title: Past trend versus future expectation: test of exchange rate volatility Author: Sengupta, Jati K., University of California, Santa Barbara Sfeir, Raymond,
More informationRockefeller College University at Albany
Rockefeller College University at Albany PAD 705 Handout: Suggested Review Problems from Pindyck & Rubinfeld Original prepared by Professor Suzanne Cooper John F. Kennedy School of Government, Harvard
More informationLinear Regression with Multiple Regressors
Linear Regression with Multiple Regressors (SW Chapter 6) Outline 1. Omitted variable bias 2. Causality and regression analysis 3. Multiple regression and OLS 4. Measures of fit 5. Sampling distribution
More informationP1.T2. Stock & Watson Chapters 4 & 5. Bionic Turtle FRM Video Tutorials. By: David Harper CFA, FRM, CIPM
P1.T2. Stock & Watson Chapters 4 & 5 Bionic Turtle FRM Video Tutorials By: David Harper CFA, FRM, CIPM Note: This tutorial is for paid members only. You know who you are. Anybody else is using an illegal
More informationWISE MA/PhD Programs Econometrics Instructor: Brett Graham Spring Semester, Academic Year Exam Version: A
WISE MA/PhD Programs Econometrics Instructor: Brett Graham Spring Semester, 2016-17 Academic Year Exam Version: A INSTRUCTIONS TO STUDENTS 1 The time allowed for this examination paper is 2 hours. 2 This
More informationUnit 6 - Introduction to linear regression
Unit 6 - Introduction to linear regression Suggested reading: OpenIntro Statistics, Chapter 7 Suggested exercises: Part 1 - Relationship between two numerical variables: 7.7, 7.9, 7.11, 7.13, 7.15, 7.25,
More informationLeast Squares Estimation-Finite-Sample Properties
Least Squares Estimation-Finite-Sample Properties Ping Yu School of Economics and Finance The University of Hong Kong Ping Yu (HKU) Finite-Sample 1 / 29 Terminology and Assumptions 1 Terminology and Assumptions
More informationUnless provided with information to the contrary, assume for each question below that the Classical Linear Model assumptions hold.
Economics 345: Applied Econometrics Section A01 University of Victoria Midterm Examination #2 Version 1 SOLUTIONS Spring 2015 Instructor: Martin Farnham Unless provided with information to the contrary,
More informationOSU Economics 444: Elementary Econometrics. Ch.10 Heteroskedasticity
OSU Economics 444: Elementary Econometrics Ch.0 Heteroskedasticity (Pure) heteroskedasticity is caused by the error term of a correctly speciþed equation: Var(² i )=σ 2 i, i =, 2,,n, i.e., the variance
More informationLecture 4: Heteroskedasticity
Lecture 4: Heteroskedasticity Econometric Methods Warsaw School of Economics (4) Heteroskedasticity 1 / 24 Outline 1 What is heteroskedasticity? 2 Testing for heteroskedasticity White Goldfeld-Quandt Breusch-Pagan
More informationThe F distribution. If: 1. u 1,,u n are normally distributed; and 2. X i is distributed independently of u i (so in particular u i is homoskedastic)
The F distribution If: 1. u 1,,u n are normally distributed; and. X i is distributed independently of u i (so in particular u i is homoskedastic) then the homoskedasticity-only F-statistic has the F q,n-k
More informationEconometrics. Final Exam. 27thofJune,2008. Timeforcompletion: 2h30min
Econometrics Final Exam 27thofJune,2008 João Valle e Azevedo António José Morgado Tiago Silva Vieira Timeforcompletion: 2h30min Give your answers in the space provided. Usedraftpapertoplanyouranswersbeforewritingthemontheexampaper.
More informationMidterm 2 - Solutions
Ecn 102 - Analysis of Economic Data University of California - Davis February 24, 2010 Instructor: John Parman Midterm 2 - Solutions You have until 10:20am to complete this exam. Please remember to put
More informationWISE MA/PhD Programs Econometrics Instructor: Brett Graham Spring Semester, Academic Year Exam Version: A
WISE MA/PhD Programs Econometrics Instructor: Brett Graham Spring Semester, 2016-17 Academic Year Exam Version: A INSTRUCTIONS TO STUDENTS 1 The time allowed for this examination paper is 2 hours. 2 This
More informationAnswer Key: Problem Set 6
: Problem Set 6 1. Consider a linear model to explain monthly beer consumption: beer = + inc + price + educ + female + u 0 1 3 4 E ( u inc, price, educ, female ) = 0 ( u inc price educ female) σ inc var,,,
More informationEconometrics -- Final Exam (Sample)
Econometrics -- Final Exam (Sample) 1) The sample regression line estimated by OLS A) has an intercept that is equal to zero. B) is the same as the population regression line. C) cannot have negative and
More informationExam D0M61A Advanced econometrics
Exam D0M61A Advanced econometrics 19 January 2009, 9 12am Question 1 (5 pts.) Consider the wage function w i = β 0 + β 1 S i + β 2 E i + β 0 3h i + ε i, where w i is the log-wage of individual i, S i is
More informationLinear Regression with 1 Regressor. Introduction to Econometrics Spring 2012 Ken Simons
Linear Regression with 1 Regressor Introduction to Econometrics Spring 2012 Ken Simons Linear Regression with 1 Regressor 1. The regression equation 2. Estimating the equation 3. Assumptions required for
More informationFinQuiz Notes
Reading 10 Multiple Regression and Issues in Regression Analysis 2. MULTIPLE LINEAR REGRESSION Multiple linear regression is a method used to model the linear relationship between a dependent variable
More informationECONOMETFUCS FIELD EXAM Michigan State University May 11, 2007
ECONOMETFUCS FIELD EXAM Michigan State University May 11, 2007 Instructions: Answer all four (4) questions. Point totals for each question are given in parenthesis; there are 100 points possible. Within
More informationLECTURE 11. Introduction to Econometrics. Autocorrelation
LECTURE 11 Introduction to Econometrics Autocorrelation November 29, 2016 1 / 24 ON PREVIOUS LECTURES We discussed the specification of a regression equation Specification consists of choosing: 1. correct
More informationLectures 5 & 6: Hypothesis Testing
Lectures 5 & 6: Hypothesis Testing in which you learn to apply the concept of statistical significance to OLS estimates, learn the concept of t values, how to use them in regression work and come across
More informationECON 497 Midterm Spring
ECON 497 Midterm Spring 2009 1 ECON 497: Economic Research and Forecasting Name: Spring 2009 Bellas Midterm You have three hours and twenty minutes to complete this exam. Answer all questions and explain
More informationECON Introductory Econometrics. Lecture 7: OLS with Multiple Regressors Hypotheses tests
ECON4150 - Introductory Econometrics Lecture 7: OLS with Multiple Regressors Hypotheses tests Monique de Haan (moniqued@econ.uio.no) Stock and Watson Chapter 7 Lecture outline 2 Hypothesis test for single
More informationMultiple Regression Analysis: Heteroskedasticity
Multiple Regression Analysis: Heteroskedasticity y = β 0 + β 1 x 1 + β x +... β k x k + u Read chapter 8. EE45 -Chaiyuth Punyasavatsut 1 topics 8.1 Heteroskedasticity and OLS 8. Robust estimation 8.3 Testing
More informationUnit 6 - Simple linear regression
Sta 101: Data Analysis and Statistical Inference Dr. Çetinkaya-Rundel Unit 6 - Simple linear regression LO 1. Define the explanatory variable as the independent variable (predictor), and the response variable
More informationMetrics Honors Review
Metrics Honors Review petertu@fas.harvard.edu Harvard University Department of Economics 26 March 2015 : Logistics Exam Date: Wednesday, April 8 from 3-6pm in Sever Hall 113 The exam covers material from
More informationEconometrics Review questions for exam
Econometrics Review questions for exam Nathaniel Higgins nhiggins@jhu.edu, 1. Suppose you have a model: y = β 0 x 1 + u You propose the model above and then estimate the model using OLS to obtain: ŷ =
More informationECON Introductory Econometrics. Lecture 13: Internal and external validity
ECON4150 - Introductory Econometrics Lecture 13: Internal and external validity Monique de Haan (moniqued@econ.uio.no) Stock and Watson Chapter 9 Lecture outline 2 Definitions of internal and external
More informationLECTURE 10. Introduction to Econometrics. Multicollinearity & Heteroskedasticity
LECTURE 10 Introduction to Econometrics Multicollinearity & Heteroskedasticity November 22, 2016 1 / 23 ON PREVIOUS LECTURES We discussed the specification of a regression equation Specification consists
More informationConfidence Intervals for Comparing Means
Comparison 2 Solutions COR1-GB.1305 Statistics and Data Analysis Confidence Intervals for Comparing Means 1. Recall the class survey. Seventeen female and thirty male students filled out the survey, reporting
More informationECON Introductory Econometrics. Lecture 5: OLS with One Regressor: Hypothesis Tests
ECON4150 - Introductory Econometrics Lecture 5: OLS with One Regressor: Hypothesis Tests Monique de Haan (moniqued@econ.uio.no) Stock and Watson Chapter 5 Lecture outline 2 Testing Hypotheses about one
More informationApplied Econometrics (MSc.) Lecture 3 Instrumental Variables
Applied Econometrics (MSc.) Lecture 3 Instrumental Variables Estimation - Theory Department of Economics University of Gothenburg December 4, 2014 1/28 Why IV estimation? So far, in OLS, we assumed independence.
More informationPBAF 528 Week 8. B. Regression Residuals These properties have implications for the residuals of the regression.
PBAF 528 Week 8 What are some problems with our model? Regression models are used to represent relationships between a dependent variable and one or more predictors. In order to make inference from the
More informationECON3150/4150 Spring 2016
ECON3150/4150 Spring 2016 Lecture 6 Multiple regression model Siv-Elisabeth Skjelbred University of Oslo February 5th Last updated: February 3, 2016 1 / 49 Outline Multiple linear regression model and
More informationEconomics 241B Estimation with Instruments
Economics 241B Estimation with Instruments Measurement Error Measurement error is de ned as the error resulting from the measurement of a variable. At some level, every variable is measured with error.
More informationCorrelation and Linear Regression
Correlation and Linear Regression Correlation: Relationships between Variables So far, nearly all of our discussion of inferential statistics has focused on testing for differences between group means
More informationECON3150/4150 Spring 2015
ECON3150/4150 Spring 2015 Lecture 3&4 - The linear regression model Siv-Elisabeth Skjelbred University of Oslo January 29, 2015 1 / 67 Chapter 4 in S&W Section 17.1 in S&W (extended OLS assumptions) 2
More informationMathematics for Economics MA course
Mathematics for Economics MA course Simple Linear Regression Dr. Seetha Bandara Simple Regression Simple linear regression is a statistical method that allows us to summarize and study relationships between
More informationIntroduction to Econometrics. Heteroskedasticity
Introduction to Econometrics Introduction Heteroskedasticity When the variance of the errors changes across segments of the population, where the segments are determined by different values for the explanatory
More informationA Course in Applied Econometrics Lecture 7: Cluster Sampling. Jeff Wooldridge IRP Lectures, UW Madison, August 2008
A Course in Applied Econometrics Lecture 7: Cluster Sampling Jeff Wooldridge IRP Lectures, UW Madison, August 2008 1. The Linear Model with Cluster Effects 2. Estimation with a Small Number of roups and
More informationCHAPTER 4 & 5 Linear Regression with One Regressor. Kazu Matsuda IBEC PHBU 430 Econometrics
CHAPTER 4 & 5 Linear Regression with One Regressor Kazu Matsuda IBEC PHBU 430 Econometrics Introduction Simple linear regression model = Linear model with one independent variable. y = dependent variable
More informationEconometrics Problem Set 6
Econometrics Problem Set 6 WISE, Xiamen University Spring 2016-17 Conceptual Questions 1. This question refers to the estimated regressions shown in Table 1 computed using data for 1988 from the CPS. The
More informationLab 11 - Heteroskedasticity
Lab 11 - Heteroskedasticity Spring 2017 Contents 1 Introduction 2 2 Heteroskedasticity 2 3 Addressing heteroskedasticity in Stata 3 4 Testing for heteroskedasticity 4 5 A simple example 5 1 1 Introduction
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 informationA Non-Parametric Approach of Heteroskedasticity Robust Estimation of Vector-Autoregressive (VAR) Models
Journal of Finance and Investment Analysis, vol.1, no.1, 2012, 55-67 ISSN: 2241-0988 (print version), 2241-0996 (online) International Scientific Press, 2012 A Non-Parametric Approach of Heteroskedasticity
More information9. Linear Regression and Correlation
9. Linear Regression and Correlation Data: y a quantitative response variable x a quantitative explanatory variable (Chap. 8: Recall that both variables were categorical) For example, y = annual income,
More informationHypothesis testing Goodness of fit Multicollinearity Prediction. Applied Statistics. Lecturer: Serena Arima
Applied Statistics Lecturer: Serena Arima Hypothesis testing for the linear model Under the Gauss-Markov assumptions and the normality of the error terms, we saw that β N(β, σ 2 (X X ) 1 ) and hence s
More informationEco 391, J. Sandford, spring 2013 April 5, Midterm 3 4/5/2013
Midterm 3 4/5/2013 Instructions: You may use a calculator, and one sheet of notes. You will never be penalized for showing work, but if what is asked for can be computed directly, points awarded will depend
More informationRecent Advances in the Field of Trade Theory and Policy Analysis Using Micro-Level Data
Recent Advances in the Field of Trade Theory and Policy Analysis Using Micro-Level Data July 2012 Bangkok, Thailand Cosimo Beverelli (World Trade Organization) 1 Content a) Endogeneity b) Instrumental
More informationHypothesis Tests and Confidence Intervals in Multiple Regression
Hypothesis Tests and Confidence Intervals in Multiple Regression (SW Chapter 7) Outline 1. Hypothesis tests and confidence intervals for one coefficient. Joint hypothesis tests on multiple coefficients
More informationFinal Exam - Solutions
Ecn 102 - Analysis of Economic Data University of California - Davis March 17, 2010 Instructor: John Parman Final Exam - Solutions You have until 12:30pm to complete this exam. Please remember to put your
More informationEcon 1123: Section 5. Review. Internal Validity. Panel Data. Clustered SE. STATA help for Problem Set 5. Econ 1123: Section 5.
Outline 1 Elena Llaudet 2 3 4 October 6, 2010 5 based on Common Mistakes on P. Set 4 lnftmpop = -.72-2.84 higdppc -.25 lackpf +.65 higdppc * lackpf 2 lnftmpop = β 0 + β 1 higdppc + β 2 lackpf + β 3 lackpf
More informationG. S. Maddala Kajal Lahiri. WILEY A John Wiley and Sons, Ltd., Publication
G. S. Maddala Kajal Lahiri WILEY A John Wiley and Sons, Ltd., Publication TEMT Foreword Preface to the Fourth Edition xvii xix Part I Introduction and the Linear Regression Model 1 CHAPTER 1 What is Econometrics?
More informationEconometrics - 30C00200
Econometrics - 30C00200 Lecture 11: Heteroskedasticity Antti Saastamoinen VATT Institute for Economic Research Fall 2015 30C00200 Lecture 11: Heteroskedasticity 12.10.2015 Aalto University School of Business
More informationREVIEW 8/2/2017 陈芳华东师大英语系
REVIEW Hypothesis testing starts with a null hypothesis and a null distribution. We compare what we have to the null distribution, if the result is too extreme to belong to the null distribution (p
More informationEcon 1123: Section 2. Review. Binary Regressors. Bivariate. Regression. Omitted Variable Bias
Contact Information Elena Llaudet Sections are voluntary. My office hours are Thursdays 5pm-7pm in Littauer Mezzanine 34-36 (Note room change) You can email me administrative questions to ellaudet@gmail.com.
More informationEconometrics Problem Set 6
Econometrics Problem Set 6 WISE, Xiamen University Spring 2016-17 Conceptual Questions 1. This question refers to the estimated regressions shown in Table 1 computed using data for 1988 from the CPS. The
More informationAn Introduction to Econometrics. A Self-contained Approach. Frank Westhoff. The MIT Press Cambridge, Massachusetts London, England
An Introduction to Econometrics A Self-contained Approach Frank Westhoff The MIT Press Cambridge, Massachusetts London, England How to Use This Book xvii 1 Descriptive Statistics 1 Chapter 1 Prep Questions
More informationBasic econometrics. Tutorial 3. Dipl.Kfm. Johannes Metzler
Basic econometrics Tutorial 3 Dipl.Kfm. Introduction Some of you were asking about material to revise/prepare econometrics fundamentals. First of all, be aware that I will not be too technical, only as
More information