Transcript Week Ten Class Presentation

Marietta College
Spring 2011
Econ 420: Applied
Regression Analysis
Dr. Jacqueline Khorassani
Week 10
1
Thursday, March 15
Exam 2: Tuesday, March 22
Exam 3: Monday, April 25, 12- 2:30PM
Return Asst 14
2
Collect Asst 15
 Recall our height-weight regression
 Estimate the regression that has gender and
height as its independent variables
1. Is the coefficient of gender likely to be
biased? Why or why not?
2. Suppose that we suspect the coefficient of
gender to be biased downward. Suggest an
omitted variable that is likely to be the
cause of this bias. Discuss your reasoning.
3
Midterm grade configuration
• Total possible points = 380
100 points on Exam 1
280 points on Assts
• If you received more than 90% of 380  A
• If you received more than 80% of 380  B
• …..
4
Upper level Econ classes Next Year
Fall 2011
Econ 301 (Money & Banking)
Econ 350 (Environmental
Econ)
Econ 360 (Law & Econ)
Econ 421 (Empirical Research)
Spring 2012
Econ 340 (Sports Econ)
Econ 349 (Micro II)
Econ 414 (Int’l Trade)
Econ 420 (Applied
Regression Analysis)
Major in econ = 33 to 34 hours
Minor in econ = 18 hours
5
Chapter 7
• What accounts for the value of estimated
intercept?
Factors affecting the estimated intercept
1. True beta
2. Mean of error term
– Affected by omitted variables (or other
specification errors)
6
Should we exclude intercept ?
• No
• Why not?
• Which assumption may be violated? (Page 94)
– Assumption II mean of error = zero
– If not, intercept captures it
– If don’t include intercept  violated assumption II
• OLS will not yield a BLUE
• Graph
– When you suppress constant, you are forcing the
intercept to be zero
– May not get the best fit
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Hand out of useful rules
• Do they ring a bell??
• Linear regression equation
Slope = ?
dY/dX = β1 = constant
Elasticity of Y with respect to X = ?
% dY / %dX
Is it constant?
(dY/Y)/(dX/X)= ?
(dY/dX) * (X/Y)
Elasticity varies based on values of X and Y
8
Double log Models
• Let’s do some econ
• What is the price elasticity of demand, E?
Percentage change in quantity demanded divided by
percentage change in price
E = (d Qd/ Qd ) / (d P/ P)
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• Suppose
–
–
–
–
•
•
•
•
Theory suggests that E is constant at all levels of price
Your goal is to estimate the price elasticity of demand (E)
Will a linear function work?
No, because it allows for elasticity to vary
You can use a double log function
ln Qd = β0 + β1 ln P + є
What does β1 measure?
β1 =d (ln Qd) / d (ln P)
which is approximately equal to E
•
•
•
•
β1 = E = (d Qd/ Qd ) / (dP/ P)
Do you expect β1 to be positive or negative?
Negative
What if β1 = -3; what does it mean?
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Note
• The double-log model is appropriate
if you believe that the elasticity of Qd
w.r.t. P is a constant:
– A given % change in P is associated
with a constant % change in Qd .
11
Let’s go back to our height weight
example
• Suppose the theory suggests that the
elasticity of weight with respect to height is
constant
• Let’s use Eviews to estimate the elasticity of
weight with respect to height
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How can we estimate the model using
EViews?
• Transform the model to a linear model
Open your workfile
Then click on quick
Generate series
Type
lnh = log (h)
Do it again for w
Then run the regression
lnw c lnh g
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Dependent Variable: LNW
Method: Least Squares
Date: 03/15/11 Time: 09:47
Sample: 1 17
Included observations: 17
Variable
C
LNH
G
Coefficient
-6.338596
2.659653
0.109758
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Std. Error
5.723760
1.374604
0.172338
0.663009
0.614867
0.162567
0.369991
8.411704
13.77206
0.000494
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
t-Statistic
-1.107418
1.934851
0.636879
Prob.
0.2868
0.0735
0.5345
4.995731
0.261955
-0.636671
-0.489633
-0.622055
2.056212
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Graphs
1. Ln (weight) as a function ln (height)?
Slope = E = 2.7
2. Weight as a function of height?
Slope = ???
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•
•
•
•
•
•
•
ln w = β0 + …..+ β2 ln h + є
β2 = d (ln w) /d (ln h)
β2 = (dw/w) / (dh/h)
β2 = (dw/w) * (h/dh)
β2 = (dw/dh) * (h/w)
Slope = dw/dh = β2 (w/h)
Slope = dw/dh = 2.7 (w/h)
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dw/dh= 2.7 (w/h)
• When w is zero, slope is ?
• As w goes up, what is the slope?
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Let’s look at the graph of double log
functions
50
40
30
20
10
0
0.1
0.25
0.5
1
1.5
B2 > 1
2
2.5
B2 < 0
3
3.5
0 < B2 < 1
4
4.5
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Asst 16: Due Thursday in class
• Use Chick (Chapter 6) data set
– Variables are defined on Page 172
• Assuming that the elasticity of per capita
chicken consumption with respect to the price
of chicken is constant, estimates Y as a
function of PC, PB and YD.
– Is the demand for chicken elastic or inelastic?
Why?
• Attach your work.
19
Semi Log Models
Suppose a theory suggests that, holding
everything else constant, for each additional
inch in height, a person’s weight changes by a
constant and positive percentage.
ln weight= β0 + β1 height +….
d (ln weight)/ d (height) = β1
Do you expect β1 to be positive or negative?
Positive
Estimate β1 using our data set
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Thursday, March 17
• Exam 2: Tuesday, March 22
Covers PP 93-220
Closed book and notes
Data set: DRUGS (Chapter 5, PP 157158)
available online at
http://pearsonhighered.com/studen
mund/
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Return and discuss Asst 15
 Recall our height-weight regression model.
 Estimate the regression model that has
gender and height as its independent
variables.
1. Is the coefficient of gender likely to be
biased? Why or why not?
2. Suppose that we suspect the coefficient of
gender to be biased downward. Suggest an
omitted variable that is likely to be the
cause of this bias. Discuss your reasoning.
22
Key
Wi^ = - 417.72 + 8.28 Hi – 3.06 Gi
Holding height constant, on average a male
weighs 3.06 pounds less than a female!
We Suspect a downward (negative) bias
Why suspect?
Why aren’t we sure?
Nate?
If you said there is a bias, you lost 0.5 points
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E(βG^) = βG+ βomitted* r omitted, G
Bias = βomitted* r omitted, G <0
Either
1) Βomitted <0 and r omitted, G >0
Or
2) Βomitted >0 and r omitted, G <0
Candidates omitted variable?
• Linda said?
• Others said?
• Jackie says: Can the omitted variable be age?
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Collect and discuss Asst 16
• Use Chick (Chapter 6) data set
– Variables are defined on Page 172
• Assuming that the elasticity of per capita
chicken consumption with respect to the price
of chicken is constant, estimates Y as a
function of PC, PB and YD.
– Is the demand for chicken elastic or inelastic?
Why?
• Attach your work.
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Elasticity
Dependent Variable: LNY
Method: Least Squares
Date: 03/16/11 Time: 15:49
Sample: 1974 2002
Included observations: 29
Variable
C
LNPB
LNPC
LNYD
Coefficient
2.055126
-0.033464
-0.102825
0.540969
R-squared
Adjusted R-squared
S.E. of regression
Sum squared resid
Log likelihood
F-statistic
Prob(F-statistic)
Do the appropriate test
to see if the coefficient
significant at 5%?
Std. Error
0.292408
0.090345
0.027901
0.044874
0.984550
0.982696
0.036620
0.033526
56.91021
531.0463
0.000000
t-Statistic
7.028284
-0.370403
-3.685405
12.05533
Prob.
0.0000
0.7142
0.0011
0.0000
Mean dependent var
S.D. dependent var
Akaike info criterion
Schwarz criterion
Hannan-Quinn criter.
Durbin-Watson stat
4.139678
0.278389
-3.648980
-3.460387
-3.589915
0.674244
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Do you recall producer’s total revenue
(or consumer’s total expenditures) curve
from econ 211?
• How does it look?
• The theory suggests that
as Q (quantity of output) increases, TR (producer’s
total revenue) increases at a declining rate and
And, eventually it decreases
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Total Revenue Curve
20
16
TR
TR
12
8
4
0
0
1
2
3
4
5
Quantityfig of output
6
7
Would this equation capture the
theoretical shape of TR curve?
•
•
•
•
TR = B0 + B1Q + error
d TR/d Q = ?
d TR/d Q = B1
No, B1 can be either positive or negative but
not both.
• Graph
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How about this model?
•
•
•
•
TR = B0 + B1Q2 + error
d TR /d Q = ?
d TR /d Q = 2B1Q
No, Q is either 0 or positive. So, depending on
the sign of B1, the slope is either positive,
zero, or negative but not all
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How about this one?
•
•
•
•
•
•
•
TR = B0 + B1Q + B2 Q2 + є
d TR/d Q = ?
d TR/d Q = B1 + 2 B2 Q
When Q is zero slope is ?
We expect B1 to be ?
And we expect B2 to be ?
At high levels of Q, the negative component of the
slope(2B2Q) will be greater than the positive
component of the slope (B1)
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Another Example
• Recall the Woody’s Restaurant problem (PP7778)
• Suppose the theory suggests that there exists a
positive but declining relationship between the
income and the number of customers.
• Y= B0 + B1 I + B2I2 + B3P + B4N+ error
• d Y/d I = B1+ 2 B2I
• We expect B1>0 and B2 <0
• How do we set the null and alternative
hypotheses to test the theory?
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Open the data set Woody in Chapter 3
1.
2.
3.
4.
Quick
Generate series
isquare= i*i
Now run the regression
Y c i isquare p n
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Dependent Variable: Y
Method: Least Squares
Date: 03/17/11 Time: 10:38
Sample: 1 33
Included observations: 33
Variable
Coefficient
Std. Error
t-Statistic
Prob.
C
42745.84
44034.73
0.970730
0.3400
I
6.959679
4.061301
1.713657
0.0976
ISQUARE
-0.000125
8.90E-05
-1.408781
0.1699
N
-9885.677
2099.168
-4.709330
0.0001
P
0.380099
0.073722
5.155867
0.0000
Did you find evidence for your hypothesized relationship
between income and number of customers at 10
percent level of significance (α = 10%)?
34