University of Waterloo
Department of Economics
ECON 321 001 W14
Assignment # 2
Due: June 10, 11:59pm
Explain/show work for full marks. Hand in assignment at drop-box outside of HH210.
1. Suppose we have the following simple regression model:
Y i =0 + 1 X
Weighted Least Squares
Suppose that we wish to estimate the following
regression
Y i=01 X iui
but,
2
var ui | Xi = hXi
If we know the function h(X), then we can use
Weighted Least Squares (WLS) to account for
heteroskedasticity.
Introduction to Econometr
Sample Exercises on Material for Midterm 2
Note: Answers are not going to be posted. You are welcome to check your answers with mine through
my office hours, after class or by scanning your work and email it to me. I will be happy to check your
answers or
1. Introduction & Review
(Appendices & chapter 1)
Introduction to Econometrics, Notes 1, p.1
Math, Probability, Stats Review
Constant something that does not change
Variable something that takes on different
values for different observations
Parameters co
Chapter 9
Assessing Studies
Based on Multiple
Regression
Assessing Studies Based on
Multiple Regression (SW Chapter 9)
Is there a systematic way to assess
regression studies?
A Framework for Assessing
Statistical Studies: Internal and
External Validity (S
Chapter 11
Regression with a
Binary Dependent
Variable
Regression with a Binary
Dependent Variable (SW Chapter 11)
Example: Mortgage denial and race
The Boston Fed HMDA data set
The Linear Probability Model
(SW Section 11.1)
The linear probability model,
Chapter 8
Nonlinear Regression
Functions
Nonlinear Regression Functions
(SW Chapter 8)
The TestScore STR relation looks
linear (maybe)
But the TestScore Income relation
looks nonlinear.
Nonlinear Regression Population Regression
Functions General Ideas (S
Introduction to
Econometrics
The Statistical Analysis
of Economic
(and related) Data
Brief Overview of the Course
2
This course is about using data to
measure causal effects.
3
In this course you will:
4
Review of Probability and Statistics
(SW Chapters 2
Summary: Multiple Regression
Multiple regression allows you to estimate the effect on Y
of a change in X1, holding other included variables
constant.
If you can measure a variable, you can avoid omitted
variable bias from that variable by including it.
If
Chapter 6
Introduction to
Multiple Regression
Outline
1.
2.
3.
4.
5.
Omitted variable bias
Causality and regression analysis
Multiple regression and OLS
Measures of fit
Sampling distribution of the OLS estimator
Omitted Variable Bias
(SW Section 6.1)
Omit
Econ 321 Mid-Term 2
Part A: Definitions (12 pts)
Question 1 (3 pts)
Suppose the following regression equation: Y=0 + 1X1 + 2X2 + 3X3 + u in which you include X1 , X2 and X3 as
explanatory variables. Explain the concepts (and give example) of perfect multi
Practice Exercises
Note: Answers are not going to be posted. You are welcome to check your answers
with mine through my office hours, after class or by email. During my office hours, I
will check your answers.
Part I: Probability
Question 0
Let G=
with Ui
Outliers
Outliers or influential observations can arise
due to errors in the data, or because some of
the data may be generated by a different
model than the other data
Outliers observations that are substantially
different from the majority of the data.
Measurement Error
Measurement error in a data set can occur
either because we cannot collect the precise
data we require
Measurement error can also occur because of
inaccurate reporting or data entry.
Although the consequences of measurement
error are sim
Simultaneous Causality
Usually we assume that causality is one way.
Ex/ more education increases productivity
which increases wages.
But what if causality runs both ways?
Simultaneous Causality when X causes Y
AND Y causes X simultaneously.
Ex/ # of polic
Review of Statistics
Part I
Econ 321
Introduction to
Econometrics
Wooldridge Appendices:
Econ 321-Stphanie Lluis
1
Main Steps in Statistical
Analysis
Two Major Steps: Estimation and Testing
The analysis requires the following
concepts:
Population, random
Introduction
Econ 321
Introduction to Econometrics
Winter 2014
Prof. Stphanie Lluis
Office: HH 239
Office hours: M-W:
4:00-5:00pm
Econ 321 - Stphanie
1
Why Econometrics?
A knowledge of statistics is like a
knowledge of foreign languages; it may
prove of u
Summary Chapter 2
Estimation of a 2 variable relationship
Beta OLS definition and derivation
E(
Properties of beta:
) and Var( )
BLUE
Best linear unbiased estimator
Among the list of all linear unbiased estimators, OLS
estimator has the smallest variance
Multiple Regression
Chapter 3 Part II
Econ 321
Introduction to
Econometrics
Econ 321-Stphanie Lluis
1
Outline
Multiple Regression
Interpretation of the Results
Omitting variables
Adding Irrelevant variables
Multicollinearity
Properties of OLS in the k-var
Assignment # 1
Due Friday Jan 24th in the Econ department drop box #9
Before 2pm.
Instructions: While cooperating on the assignment is encouraged, plagiarism is not. Please add
the name of the student you worked with to your assignment. Do NOT submit your
University of Waterloo
Department of Economics
Econ 321
Introduction to Econometrics
Winter 2014
M-W 2:30-3:50 in HH1101
Instructor Information
Instructor: Professor Stphanie Lluis
Office: Hagey Hall, Room 239
Office Phone (519) 888-4567, ext. 32960
E-mai
Review of Statistics
Part II
Econ 321
Introduction to Econometrics
Econ 321-Stphanie Lluis
1
Main Steps in Statistical Analysis
Central Limit Theorem
The sampling distribution of Y
The standard normal distribution
Other basic distributions
t-distribu
Review of Statistics
Last Part
Econ 321
Introduction to Econometrics
Wooldridge: appendices B & C and
Chapter 1
Econ 321-Stphanie Lluis
1
Additional Tools and Issues in Statistical
Analysis
Properties of Estimators
Joint and conditional distribution
Mu
Inference
Chapter 4
Econ 321
Introduction to Econometrics
Econ 321-Stphanie Lluis
1
Outline
Test of single parameter (t-test)
The F-test for testing multiple joint restrictions
Test of single linear combination of
parameters
Econ 321-Stphanie Lluis
2
H
Chapter 5
Regression with a Single
Regressor: Hypothesis Tests
and Confidence Intervals
Regression with a Single Regressor:
Hypothesis Tests and Confidence Intervals
(SW Chapter 5)
But first a big picture view
(and review)
Object of interest: 1 in,
Hypoth