# Suppose you want to estimate the following relationship: ln⁡(wag...

## Question

Suppose you want to estimate the following relationship:
ln⁡(wage)=β_0+β_1 beauty+β_2 exper+β_3 (age-20)+u
where beauty =physical attractiveness of a worker,
exper= number of years of experience,
age=number of years.
What would be the expected sign on the coefficients of the above model? Give some reasons for it.
Your friend told you that the “beauty-effect” on ln(wage) is more on women. How would you incorporate and test this in your model? Assume that you know the gender of each person in the data.
How would you test the hypothesis that the error term in (1) is heteroskedastic?
How would you estimate the model correcting for heteroskedasticity?

Consider the following model of the demand for airline travel, estimated using annual data for the period 1947-1987. The number of observations is therefore 41.
ln⁡(Q)=β_0+β_1 ln⁡(P)+β_2 ln⁡(y)+β_3 ln⁡(ACCID)+β_4 FATAL+u
where
Q = Per-capita passenger miles traveled in a given year
P = Average price per mile
Y = Per-capita income
ACCID = Accident rate per passenger mile
FATAL = Number of fatalities from aircraft accidents
The model is double-log except for the fact that FATAL is not expressed in log form because the observation for some of the years is zero.
In 1979 the airlines were deregulated. Define the dummy variable D that takes the value 0 for 1947-1978 and 1 for 1979-1987. The following table presents the relevant values for two models. Model A is the basic model given above. Model B is the one derived by assuming that there has been a structural change of the entire relation. Standard errors are reported in parenthesis.

Variables          Model A                          Model B
(Standard error)             (Standard error)
Constant           2.938                               2.635
(1.050)                            (1.326)
ln(P)                   -1.312                            -1.029
(0.315)                            (0.377)
ln(Y)                   0.716                              -0.001
(0.289)                            (0.433)
ln(ACCID)          -0.541                               -0.821
(0.100)                            (0.156)
FATAL                0.0004                            0.0009
(0.0003)                         (0.0003)
D                                                                  -1.688
(0.388)
D. ln(P)                                                         0.278
(0.796)
D. ln(Y)                                                         0.987
(0.558)
D. ln(ACCID)                                                 0.818
(0.252)
D. FATAL                                                       -0.001
(0.0006)
SSR                      1.0961                            0.7009
Adj R2                     0.972                              0.979

Interpret the coefficients of D. ln(ACCID) and D. FATAL first and then comment on their estimated values.
Deregulation is supposed to reduce the accident rate per passenger mile. How would test such a hypothesis? Perform the test at the 5% level of significance.
Compute the elasticity of Q with respect to P before and after deregulation.
Compute the elasticity of Q with respect to Y before and after deregulation.
Someone told you that the variable FATAL should not be included in the model. How would you test such a hypothesis in Model B?

## Solution Preview

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1. What would be the expected sign on the coefficients of the above model? Give some reasons for it.
According to model (1), beauty increase then wage is also increase thus sign of β_1
Should be positive. Similarly experience and age will increase then wage is also increase therefore coefficient of experience and (age-20) are positive.
2. Your friend told you that the “beauty-effect” on ln(wage) is more on women. How would you incorporate and test this in your model? Assume that you know the gender of each person in the data.
To test we will find average ln(Wage) of man and woman and then we will find variance. Using both...

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