University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Chapter 5
Multiple Regression
Chapter Objectives: In this chapter we shall consider regression models with two regressors.
We shall obtain the OLS estimators of the population regression model, understand the
properties of the OLS estimators and learn how
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Tutorial 2
1. Let
Solutions
Y i= 1 + 2 X i +ui
be the population regression model and let
Y i= ^1 + ^
2 X i + u^ i be the OLS estimated model.
Adding and dividing by n, we get
Y i=n ^1 + ^ 2 X i + u^ i
Y i = ^ + ^2 X i ( u^ =0)
1
n
i
n
Y = ^1 + ^
2
X
S
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Chapter 7
Transformation of Variables
Chapter Objectives
We have considered regression models linear in parameters and variables for estimation by
Ordinary Least Square Method. Quite often we encounter models which are non linear in
parameter and variable
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Singapore Institute of Management
University of London
PRACTICE QUESTION 2
SIMPLE REGRESSION
2
1. Suppose the true relationship between two variables is Yi 1 2 X i 3 X i + i
where Xi is a deterministic sequence, E ( i ) 0 for all i. A researcher, instead
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Singapore Institute of Management
University of London
Practice Questions 1
1. Consider the model
Yt X t u t , t 1, 2,.,6, E (u t ) 0, E (u t2 ) 2 and E (u s u t ) 0 if s t.
The observations on Xt are
X1
X2
X3
X4
X5
X6
1
2
3
4
5
6
~
1
8
Consider an estima
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Tutorial 1
Solutions
1. To prove that
2
2
V ( aX +bY )=a V ( X )+ b V ( Y ) +2 abcov ( X , Y )
2
2
By definition V ( ax+ bY )=E ( aX +bY ) cfw_ E(aX+ bY )
2
E [ a2 X 2 +b2 Y 2+ 2abXY ] [ aE ( X ) +bE (Y ) ]
2
2
a2 E ( X 2 ) +b 2 E ( Y 2 ) +2 abE ( XY )
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Chapter 3
Simple Regression
Introduction
We have observed earlier that for a specified value of an explanatory variable, X the
response variable, Y is stochastic. We wish to estimate the average value of the response
variable at a given value of X. The av
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
University of London
Tutorial 2 Simple Regression Model
2
1. R2, the coefficient of determination is defined as R
Explained Sum of Squares
Total Sum of Squares
.
Show that R2 lies between 0 and 1 when there is an intercept term in the model.
2. Let the r
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Chapter 4
Normal Linear Regression
Introduction
Observe that the application of the method of OLS to classical linear regression model
does not require any assumptions about the probability distribution of the disturbances
ui. It requires only the assumpt
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
University of London
Tutorial 1 Review of Basics
1. Let X and Y be two random variables. Show that
V (aX bY ) a 2V ( X ) b 2V (Y ) 2ab COV ( X , Y ) , where a and b are known constants.
Explain how this results changes if X and Y are independent.
2. A sim
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Ec220IntroductiontoEconometrics/Ec221PrinciplesofEconometrics
A Brief Introduction to Stata
Note:
Commandsthatyouhavetotypeinastheyare,arewritteninCourierNewfont,i.e.command.Youwill
havetospecifywordswritteninitalicdependingonyourneeds,i.e.variablename.
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Ec220  Introduction to Econometrics
Problem Set 6
1. Consider the following regression results for average hourly earnings for American workers aged 25 to 34 in 1998. The variables in the regression are the following:
College
Female
Age
Northeast
Midwest
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Introduction to Causal Questions
Ec220 Introduction to Econometrics
JrnSteen Pischke
LSE
September 26, 2016
Pischke (LSE)
Causal Questions
September 26, 2016
1 / 30
Welcome to Ec220 Introduction to Econometrics/Ec221
Principles of Econometrics
This cours
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Ec220  Introduction to Econometrics
Problem Set 1
1. Consider the following three causal questions:
Many firms, particularly in southern European countries, are small, and owned
and run by families. Are family owned firms growing more slowly than firms
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Ec220  Introduction to Econometrics
Problem Set 3
1. Download the data TeachingRatings.dta from Moodle. This data set contains data
on the teaching evaluations of 463 professors at the University of Texas, and various
attributes of the professor and cour
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Ec220  Introduction to Econometrics
Problem Set 7
1. Download the data ajr.dta from the Moodle website. The data set contains per capita
income in 1995 as well as a number of other variables for 62 nonEuropean countries.
The data have been collected by
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Ec220  Introduction to Econometrics
Problem Set 5
1. Use the dataset attend.dta to analyse whether attending lectures has a causal eect
on nal exam performance. The data set contains 674 observations on college students
who took a particular course. Most
University of London The London School of Economics and Political Science
Principles of Econometrics
EC 221

Fall 2016
Ec220  Introduction to Econometrics
Problem Set 4
1. Return to the auto.dta data on automobiles, which you used in problem set 2 already.
(a) Run a regression of price on foreign. By how much does the average price
of imported cars dier from that of dome