ECON 351 - Multiple Regression
Analysis: OLS Asymptotics
Maggie Jones
1 / 14
Large Sample Properties
I
In the last few sections we covered finite sample (a.k.a. small
sample, or exact) properties of the OLS estimators in the
population model
y = 0 + 1 x1
ECON 351 - Fundamentals of
Mathematical Statistics
Maggie Jones
1 / 43
Populations and Sampling
I
In econometrics our objective is to learn something about a
population given a specific sample of that population
I
Let Y be a random variable representing a
ECON 351 - Fundamentals of
Probability
Maggie Jones
1 / 32
Random Variables
I
A random variable is one that takes on numerical values, i.e.
numerical summary of a random outcome
I
I
A discrete random variable is one that takes on only a
finite (or countab
ECON 351 - Multiple Regression
Analysis: Inference
Maggie Jones
1 / 32
Sampling Distributions of OLS
Estimators
I
In order to perform statistical inference we need to know the
full sampling distribution of the j
I
And to determine the sampling distributio
ECON 351 - Interactions and
Dummies
Maggie Jones
1 / 25
Readings
I
Chapter 6: Section on Models with Interaction Terms
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Chapter 7: Full Chapter
2 / 25
Interaction Terms with Continuous
Variables
I
In some regressions we might expect the partial effect of
ECON 351 - Multiple Regression
Analysis: Estimation
Maggie Jones
1 / 27
Two Independent Variables
I
Assumption SLR. 4 (that all other factors affecting y are
uncorrelated with x) is often unrealistic
I
With multiple regression analysis we can control for
ECON 351 - The Simple Regression
Model
Maggie Jones
1 / 41
The Simple Regression Model
I
Our starting point will be the simple regression model
where we look at the relationship between two variables
I
In general, more complicated econometric models are u
ECON 351 - Program Evaluation,
Binary Dependent Variable, Misc.
Maggie Jones
()
1 / 17
Readings
I
Chapter 13: Section 13.2 on difference in differences
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Chapter 7: Section on binary dependent variables
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Chapter 6: Scaling, beta coefficients, log-level r
Simple regression model:
y = 0 + 1 x + u
Estimate of 0
Estimate of 1
()
0 = y 1 x
Pn
xi yi n
xy
1 = Pi=1
n
2
x2
i=1 xi n
1/7
Variance of the estimator 1
2
)2
i=1 (xi x
Var(1 ) = Pn
Estimate of the variance of the error (square root equals the
standard err
1. [20 pts] Assume that SLR. 1 - SLR. 5 hold for the single regression model.
a. See attached.
b. See attached.
2. [75 pts] Find the dataset that you downloaded from IPUMS for assignment 2.
a. See attached do-files.
The purpose of this do-file is to gener
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0 = y 1 x
Pn
Pn
Pn
x
y
n
x
y
(x
x
)y
(yi y)(xi x)
i
i
i
i
i=1
i=1
i=1
P
P
1 = Pn 2
=
=
n
n
x2
)2
)2
i=1 xi n
i=1 (xi x
i=1 (xi x
2
)2
i=1 (xi x
Var(1 ) = Pn
Pn 2
2
x
Pnn i=1 i 2
)
i=1 (xi x
Var(0 ) =
2
Pn
u2i
n2
i=1
=
2
)2
i=1 (xi x
\
Var(
1 ) = Pn
1
ECON 351: Notes on STATA
Descriptive Statistics
Variable This column indicates which variable is being described.
Obs This column tells you the number of observations (or cases) that
were valid (i.e., not missing) for that variable.
Percentiles - Percenti
ECON 351: Midterm 1 Review Notes
CHAPTER 1: ECONOMIC QUESTIONS AND DATA
Types of Questions
1. Quantitative: numerical questions with numerical answers
2. Casual: interested in the effect of one economic variable on another
Estimation of Casual Effects
A
ECON351 : Introductory Econometrics
Assignment #3 (due Mar. 11 at 3pm to the Assignment Box in Dunning Hall 2nd floor)
To receive full credit you need to answer AT LEAST 8 questions. You are encouraged to attempt and
answers will be provided for all quest
ECON351 : Introductory Econometrics
Assignment #4 (due Apr. 1 at 3pm to the Assignment Box in Dunning Hall 2nd floor)
To receive full credit you need to answer AT LEAST 4 questions. You are encouraged to attempt
and answers will be provided for all questi
ECON351 : Introductory Econometrics
Assignment #1 (due Jan. 19 at 3pm to the Assignment Box in Dunning Hall 2nd floor)
To receive full credit you need to answer AT LEAST 8 questions. You are encouraged to attempt
and answers will be provided for all quest
ECON351 : Introductory Econometrics
Assignment #2 (due Feb. 5 at 3pm to the Assignment Box in Dunning Hall 2nd floor)
To receive full credit you need to answer AT LEAST 8 questions. You are encouraged to attempt and answers will be provided for all questi
1.
The model estimated in 13.1 assumes that the effect of each explanatory variable,
except education, has remained constant. The coefficients on y84 (y72 is the base
year) indicates that holding everything else constant, a woman had on average -.545
less
The way to create a variable-generate
Week 3 lecture 2 January 21, 16 Simple regression model-Slide 5
Y=beta0+beta1x+u
Mean independent assumptions: E (u|x)=E(u) means that u and x are
uncorrelated
Zero conditional mean assumption: E(u|x)=0 , which also i
1. [40 pts] Reading and interpreting stata do files
a. See attached do-files.
b. In this do-file, we are generating the variables for assignment 4. We have the
standard preliminary commands, and the set seed command, which tells stata where
to start its r
1. [50 pts] Suppose you are an advisor for one of the local high schools in Kingston that is
considering implementing a school lunch program to boost student performance. Fortunately,
there is already a federal program in the U.S. that provides free lunch
ECON 351 Assignment 2
Instructor: Maggie Jones
Queens University, Department of Economics
Due: October 14th, 2016
Note: Students may work in groups of up to three. Please make sure you clearly list each
member of your group on the front page of the assign
ECON 351 Assignment 1
Instructor: Maggie Jones
Queens University, Department of Economics
Due: September 29th, 2016
Note: Students may work in groups of up to three. Please make sure you clearly list each
member of your group on the front page of the assi