Suppose you are interested in determining the degree to which the speed one normally drives correlates with the number of accidents in which one has been involved but you are afraid that self-reported driving speed is measured with error because respondents tend to under-report their true driving speeds.After collecting data for a sample of 123,897 married drivers between 25 and 40,you estimate the following model Second-Stage:
$$\begin{array} { lllll }
Ac\widehat {clde}nts _ { i } = & 1.4 .6 +& 0.045 SelfRe\widehat {port}Speed _ { i } +& 0.004 \text { Miles Driven } _ { i } +& 1.23 \text { Male } _ { i } \
&( 0.354 )& ( 0.0034 ) & ( 0.002 ) & ( 0.01 )
\end{array}$$
First-Stage:
SelfRe$\widehat {port}$Speed $_ { i }$
$$\begin{array}{ lllll }
= 3.23 + &6.029 \text { SpouseRepSpeed } _ { i } +& 2.396 \text { MilesDriven } _ { i } + &4.076 \text { Male } _ { i } \
(2.54) &(2.137) & (1.002)&(1.382)\
\end{array}$$
a)Explain what type of issues using self report speed creates for estimating the second stage model using OLS.
b)Spouse Rep speed is another variable where the spouse of the driver is also asked how fast the individual is driving.Spouse reported speed is measured with error but the error is not related to the error in self report speed.Explain how to use the new measure as an instrument for self report speed.
c)Comment on the instrumental variable results above.
d)Do you believe the self reported speed or spouse reported speed is a more accurate measure? Are there any other independent variables that you believe are measured with error? Why or why not?

Question

Suppose you are interested in determining the degree to which the speed one normally drives correlates with the number of accidents in which one has been involved but you are afraid that self-reported driving speed is measured with error because respondents tend to under-report their true driving speeds.After collecting data for a sample of 123,897 married drivers between 25 and 40,you estimate the following model Second-Stage:
$$\begin{array} { lllll } 
Ac\widehat {clde}nts  _ { i } = & 1.4 .6 +& 0.045 SelfRe\widehat {port}Speed _ { i } +& 0.004 \text { Miles Driven } _ { i } +& 1.23 \text { Male } _ { i } \
&( 0.354 )& ( 0.0034 ) & ( 0.002 ) & ( 0.01 )
\end{array}$$
First-Stage:
SelfRe$\widehat {port}$Speed $_ { i }$
$$\begin{array}{ lllll } 
= 3.23 + &6.029 \text { SpouseRepSpeed } _ { i } +& 2.396 \text { MilesDriven } _ { i } + &4.076 \text { Male } _ { i } \
(2.54) &(2.137) & (1.002)&(1.382)\
\end{array}$$ 
a)Explain what type of issues using self report speed creates for estimating the second stage model using OLS.
b)Spouse Rep speed is another variable where the spouse of the driver is also asked how fast the individual is driving.Spouse reported speed is measured with error but the error is not related to the error in self report speed.Explain how to use the new measure as an instrument for self report speed.
c)Comment on the instrumental variable results above.
d)Do you believe the self reported speed or spouse reported speed is a more accurate measure? Are there any other independent variables that you believe are measured with error? Why or why not?

Quizplus · Accepted Answer

The Answer of Suppose you are interested in determining the degree to which the speed one normally drives correlates with the number of accidents in which one has been involved but you are afraid that self-reported driving speed is measured with error because respondents tend to under-report their true driving speeds.After collecting data for a sample of 123,897 married drivers between 25 and 40,you estimate the following model Second-Stage:
$$\begin{array} { lllll } 
Ac\widehat {clde}nts  _ { i } = & 1.4 .6 +& 0.045 SelfRe\widehat {port}Speed _ { i } +& 0.004 \text { Miles Driven } _ { i } +& 1.23 \text { Male } _ { i } \
&( 0.354 )& ( 0.0034 ) & ( 0.002 ) & ( 0.01 )
\end{array}$$
First-Stage:
SelfRe$\widehat {port}$Speed $_ { i }$
$$\begin{array}{ lllll } 
= 3.23 + &6.029 \text { SpouseRepSpeed } _ { i } +& 2.396 \text { MilesDriven } _ { i } + &4.076 \text { Male } _ { i } \
(2.54) &(2.137) & (1.002)&(1.382)\
\end{array}$$ 
a)Explain what type of issues using self report speed creates for estimating the second stage model using OLS.
b)Spouse Rep speed is another variable where the spouse of the driver is also asked how fast the individual is driving.Spouse reported speed is measured with error but the error is not related to the error in self report speed.Explain how to use the new measure as an instrument for self report speed.
c)Comment on the instrumental variable results above.
d)Do you believe the self reported speed or spouse reported speed is a more accurate measure? Are there any other independent variables that you believe are measured with error? Why or why not?

Suppose You Are Interested in Determining the Degree to Which