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Chapter 7
- What accounts for the value of estimated intercept?
Factors affecting the estimated intercept
- True beta
- Mean of error term
- Affected by omitted variables (or other specification errors)
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
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)
- 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 Q (^) d = β 0 + β 1 ln P + є
- What does β 1 measure?
- β 1 =d (ln Q (^) d ) / d (ln P) which is approximately equal to E
- β 1 = E = (d Q (^) d / Q (^) d ) / (dP/ P)
- Do you expect β 1 to be positive or negative?
- Negative
- What if β 1 = -3; what does it mean?
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
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
Graphs
- Ln (weight) as a function ln (height)?
Slope = E = 2.
- Weight as a function of height?
Slope = ???
- ln w = β 0 + …..+ β 2 ln h + є
- β 2 = d (ln w) /d (ln h)
- β 2 = (dw/w) / (dh/h)
- β 2 = (dw/w) * (h/dh)
- β 2 = (dw/dh) * (h/w)
- Slope = dw/dh = β 2 (w/h)
- Slope = dw/dh = 2.7 (w/h)
Let’s look at the graph of double log
functions
0
10
20
30
40
50
0.1 0.25 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 B2 > 1 B2 < 0 0 < B2 < 1
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.
Thursday, March 17
• Exam 2 : Tuesday, March 22
Covers PP 93-
Closed book and notes
Data set: DRUGS (Chapter 5, PP 157-
available online at
http://pearsonhighered.com/studen
mund/
Return and discuss Asst 15
Recall our height-weight regression model.
Estimate the regression model that has gender and height as its independent variables.
- Is the coefficient of gender likely to be biased? Why or why not?
- 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.
E(βG^) = βG+ βomitted * r omitted, G
Bias = βomitted* r omitted, G <
Either
1) Βomitted <0 and r omitted, G >
Or
2) Βomitted >0 and r omitted, G <
Candidates omitted variable?
- Linda said?
- Others said?
- Jackie says: Can the omitted variable be age?
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.