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)
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Factors Affecting the Estimated Intercept in Linear Regression and Elasticity Measurement, Slides of Research Methodology
The factors that account for the value of the estimated intercept in linear regression, including true beta and mean of the error term. It also explains the importance of including an intercept in the regression model and how elasticity is measured using linear and double log models. Examples are provided to illustrate the concepts.
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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.