Homework 2 Excel Assignment
Solutions Form: Using Excel to Learn about Supply and Demand
Part A: Filling in the Spreadsheet
Use correct cell references and turn in your excel spreadsheet along with this completed form.
Part B: Some Study Questions
1. When
Summary and Conclusions
Carrying Out an Empirical Project
Economics 20 - Prof. Anderson
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Choosing a Topic
Start with a general area or set of questions
Make sure you are interested in the topic
Use on-line services such as EconLit to
investigate past wor
Testing for Unit Roots
Consider an AR(1): yt = + yt-1 + et
Let H0: = 1, (assume there is a unit root)
Define = 1 and subtract yt-1 from both
sides to obtain yt = + yt-1 + et
Unfortunately, a simple t-test is
inappropriate, since this is an I(1) process
A
Limited Dependent Variables
P(y = 1|x) = G(0 + x )
y* = 0 + x + u, y = max(0,y*)
Economics 20 - Prof. Anderson
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Binary Dependent Variables
Recall the linear probability model, which
can be written as P(y = 1|x) = 0 + x
A drawback to the linear probabilit
Simultaneous Equations
y1 = 1y2 + 1z1 + u1
y2 = 2y1 + 2z2 + u2
Economics 20 - Prof. Anderson
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Simultaneity
Simultaneity is a specific type of
endogeneity problem in which the
explanatory variable is jointly determined
with the dependent variable
As with
Instrumental Variables & 2SLS
y = 0 + 1x1 + 2x2 + . . . kxk + u
x1 = 0 + 1z + 2x2 + . . . kxk + v
Economics 20 - Prof. Anderson
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Why Use Instrumental
Variables?
Instrumental Variables (IV) estimation is
used when your model has endogenous xs
That is, whe
Fixed Effects Estimation
When there is an observed fixed effect, an
alternative to first differences is fixed
effects estimation
Consider the average over time of yit =
1xit1 + kxitk + ai + uit
The average of ai will be ai, so if you
subtract the mean, ai
Panel Data Methods
yit = 0 + 1xit1 + . . . kxitk + uit
Economics 20 - Prof. Anderson
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A True Panel vs.
A Pooled Cross Section
Often loosely use the term panel data to
refer to any data set that has both a crosssectional dimension and a time-series
dimens
Time Series Data
yt = 0 + 1xt1 + . . .+ kxtk + ut
2. Further Issues
Economics 20 - Prof. Anderson
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Testing for AR(1) Serial
Correlation
Want to be able to test for whether the
errors are serially correlated or not
Want to test the null that = 0 in ut = u
Stationary Stochastic Process
A stochastic process is stationary if for
every collection of time indices 1 t1 < <
tm the joint distribution of (xt1, , xtm) is the
same as that of (xt1+h, xtm+h) for h 1
Thus, stationarity implies that the xts are
identical
Time Series Data
yt = 0 + 1xt1 + . . .+ kxtk + ut
1. Basic Analysis
Economics 20 - Prof. Anderson
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Time Series vs. Cross Sectional
Time series data has a temporal ordering,
unlike cross-section data
Will need to alter some of our assumptions
to take into
Multiple Regression Analysis
y = 0 + 1x1 + 2x2 + . . . kxk + u
7. Specification and Data Problems
Economics 20 - Prof. Anderson
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Functional Form
Weve seen that a linear regression can
really fit nonlinear relationships
Can use logs on RHS, LHS or both
Ca
Multiple Regression Analysis
y = 0 + 1x1 + 2x2 + . . . kxk + u
6. Heteroskedasticity
Economics 20 - Prof. Anderson
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What is Heteroskedasticity
Recall the assumption of homoskedasticity
implied that conditional on the explanatory
variables, the variance o
Multiple Regression Analysis
y = 0 + 1x1 + 2x2 + . . . kxk + u
5. Dummy Variables
Economics 20 - Prof. Anderson
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Dummy Variables
A dummy variable is a variable that takes
on the value 1 or 0
Examples: male (= 1 if are male, 0
otherwise), south (= 1 if in
Multiple Regression Analysis
y = 0 + 1x1 + 2x2 + . . . kxk + u
4. Further Issues
Economics 20 - Prof. Anderson
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Redefining Variables
Changing the scale of the y variable will
lead to a corresponding change in the scale
of the coefficients and standard er
Multiple Regression Analysis
y = 0 + 1x1 + 2x2 + . . . kxk + u
3. Asymptotic Properties
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Consistency
Under the Gauss-Markov assumptions OLS
is BLUE, but in other cases it wont always
be possible to find unbiased estimators
Multiple Regression Analysis
y = 0 + 1x1 + 2x2 + . . . kxk + u
2. Inference
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Assumptions of the Classical
Linear Model (CLM)
So far, we know that given the GaussMarkov assumptions, OLS is BLUE,
In order to do classical hypot
Multiple Regression Analysis
y = 0 + 1x1 + 2x2 + . . . kxk + u
1. Estimation
Economics 20 - Prof. Anderson
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Parallels with Simple Regression
0 is still the intercept
1 to k all called slope parameters
u is still the error term (or disturbance)
Still need
The Simple Regression Model
y = 0 + 1x + u
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Some Terminology
In the simple linear regression model,
where y = 0 + 1x + u, we typically refer to
y as the
Dependent Variable, or
Left-Hand Side Variable, or
Explained Variable, or
Regressand
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Some Terminolo
What is Econometrics?
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Why study Econometrics?
Rare in economics (and many other areas
without labs!) to have experimental data
Need to use nonexperimental, or
observational, data to make inferences
Important to be able to apply economic
theory to real w