Deck 14: Instrumental Variables for Simultaneous Equations, Endogenous Independent Variables, and Measurement Error

Question 1

Two-stage least squares

A)is an instrumental variable technique that can be used to control for endogeneity of an right hand side variable.
B)can be used to control for jointly determined simultaneous equations.
C)can be used to control for measurement error of an independent variable.
D)All of the above are correct.

Answer 1

D

Question 2

The first-stage in an instrumental variable approach to identify simultaneous equations is to regress

A)the endogenous right hand side variables on the instruments and all exogenous variables.
B)the dependent variable on the predicted endogenous right hand side variables and the exogenous variables in each equation.
C)instrumental variable on all exogenous variables.
D)the exogenous right hand side variables on only the instrumental variables.

Answer 2

A

Question 3

Simultaneous equations occur when two are more equations

A)that have the same error term.
B)contain variables that are related to each other.
C)contain the same independent variables.
D)contain autocorrelated variables.

Answer 3

B

Question 4

Simultaneous equations present a challenge because OLS estimates

A)do not properly weight the data for the undue influence of outliers.
B)do not account for the autoregressive structure of the error term.
C)treat the dependent variable as a continuous variable.
D)are biased because one or more right hand side variables from each equation are correlated with the error term due to the equations being jointly determined.

Question 5

Endogeneity of an independent variable presents a challenge because

A)two-stage least squares is biased and inconsistent.
B)OLS does not properly weight the data for the undue influence of outliers.
C)OLS does not account for the autoregressive structure of the error term.
D)OLS is unable to isolate the true marginal effect of endogenous independent variable.

Question 6

Two-stage least squares can be used to

A)control for heteroskedasticity.
B)control for measurement error in an independent variable.
C)deal with limited dependent variables.
D)account for the time-invariant component of the error term.

Question 7

Endogeneity of an independent variable presents a challenge because

A)OLS estimates are biased and inconsistent.
B)it causes the regression to be perfectly collinear.
C)it leads to heteroskedasticity.
D)OLS estimates remained unbiased but they are no longer BLUE.

Question 8

The first-stage in an instrumental variable approach to control for measurement error in an independent variable is

A)regressing the mis-measured variable on only the exogenous variables in the original regression equation and using those estimates to calculate predicted values of the mis-measured variable.
B)regressing the mis-measured variable on only the alternative value of the mis-measured variable.
C)estimating the original population regression model with the predicted values of the mis-measured variable substituted for the observed values of the endogenous variable.
D)regressing the mis-measured variable on both the alternative measure of the mis-measured variable and all of the remaining exogenous variables and using those estimates to calculate predicted values of the mis-measured variable.

Question 9

The second-stage in an instrumental variable approach to controlling for endogenous independent variables is to

A)regress the endogenous independent variable on the instrument and all of the remaining independent variables and using those estimates to calculate predicted values of the endogenous variable.
B)estimate the original population regression model with the residuals included as an independent variable.
C)estimate the original population regression model with the predicted values of the endogenous right hand side variable substituted for the observed values of the endogenous right hand side variables.
D)regress the endogenous variable on the instrument and all of the remaining independent variables and using those estimates to calculate the residuals.

Question 10

The first-stage in an instrumental variable approach to controlling for endogenous independent variables is to

A)regress the endogenous independent variable on the instrument and all of the remaining independent variables and using those estimates to calculate predicted values of the endogenous variable.
B)regress the endogenous variable on the instrument and all of the remaining independent variables and using those estimates to calculate the residuals.
C)estimate the original population regression model with the predicted values of the endogenous variable substituted for the observed values of the endogenous variable.
D)estimate the original population regression model with the predicted residuals included as an independent variable.

Question 11

Measurement error in an independent variable occurs when

A)the dependent variable is uncorrelated with the error term.
B)the true value of the independent variable is observed.
C)the true value of the left hand side variable is not known.
D)the variable is measured with error such that is the true value of the variable.

Question 12

Measurement error in an independent variable presents a challenge because

A)the independent variable is not correlated with the dependent variable.
B)the OLS estimates are biased.
C)the OLS estimates are unbiased but no longer BLUE.
D)the independent variable is not correlated with the error term.

Question 13

Exogeneity of an independent variable occurs when

A)an independent variable is correlated with the dependent variable.
B)the dependent variable is correlated with the error term.
C)an independent variable is uncorrelated with the error term.
D)the dependent variable is correlated with an independent variable.

Question 14

For an instrument to be valid it must be

A)correlated with both the dependent variable and the endogenous variable.
B)uncorrelated with both the dependent variable and the endogenous variable.
C)correlated with the endogenous variable but uncorrelated with the error term.
D)correlated with the error term but uncorrelated with the endogenous variable.

Question 15

The second-stage in an instrumental variable approach to control for measurement error in an independent variable is

A)estimating the original population regression model with the predicted values of the mis-measured variable substituted for the observed values of the endogenous variable.
B)regressing the mis-measured variable on only the exogenous variables in the original regression equation and using those estimates to calculate predicted values of the mis-measured variable.
C)regressing the mis-measured variable on only the alternative value of the mis-measured variable.
D)regressing the mis-measured variable on both the alternative measure of the mis-measured variable and all of the remaining exogenous variables and using those estimates to calculate predicted values of the mis-measured variable.

Question 16

The second-stage in an instrumental variable approach to identify simultaneous equations is to

A)include the residuals and the residuals squared from the first-stage in the second-stage estimation.
B)estimate the regression model and use the results to predict the simultaneously determined independent variables.
C)estimate the individual equations including the predicted values of the simultaneously determined independent variables on the right hand side of the equation.
D)include the predicted values of the dependent variables in the second-stage regressions and regress those predictions on the endogenous and exogenous variables.

Question 17

Endogeneity of an independent variable occurs when

A)an independent variable is correlated with the dependent variable.
B)an independent variable is correlated with the error term.
C)the dependent variable is correlated with the error term.
D)the dependent variable is correlated with an independent variable.

Question 18

Two-stage least squares can be used to

A)identify simultaneous equations.
B)control for heteroskedasticity.
C)account for the time-invariant component of the error term.
D)deal with limited dependent variables.

Question 19

Two-stage least squares can be used to

A)account for the time-invariant component of the error term.
B)control for heteroskedasticity.
C)control for measurement error in a dependent variable.
D)control for the endogeneity of independent variable.

Question 20

An instrumental variable is a variable that is correlated

A)with the endogenous right hand side variable but not correlated with the error term.
B)with the error term but not correlated with the endogenous right hand side variable.
C)with both the error term and the endogenous right hand side variable.
D)with both the endogenous right hand side variable and with another independent variable.

Question 21

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
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 22

Suppose you are interested in testing whether athletes receive better grades in high school but you are considered that the decision to compete in athletics is endogenous because athletes tend to have higher levels of motivation which results in the performing better at school work but cannot be measured and included as an independent variable in the regression.After collecting data for a sample of 32,416 high school seniors,you estimate the following instrumental variable model
a)Which of the two models is the regression model you are interested in estimating? Why is it not appropriate to estimate this model using OLS?
b)What two attributes does height need to have to make it a valid instrument? Do you think these hold in this circumstance?
c)Explain the intuition behind the first stage model.
d)Comment on the results above.
e)Why is it necessary to have such a large sample size when estimating an instrumental variable model? Explain.

Question 23

Suppose that in an effort to explain the demand for pineapples,you collect a weekly time series data set with 780 total observations and you propose the following demand and supply equations for pineapples
a)With a graph,explain estimating the demand equation alone would yield biased estimates.
b)Explain why this specification can be viewed as a simultaneous equation.Be as specific as possible.
c)Now with a similar graph explain how the supply shifter,rain,helps identify the demand equation.
d)Describe,using rain as an instrumental variable,how to estimate the demand equation for pineapples.
e)Describe,using income as an instrumental variable,how to estimate the supply equation for pineapples.
f)Why would this sample size be a concern for using instrumental variables in this circumstance?

Question 24

What is measurement error in an independent variable? How can instrumental variables be used to control for measurement error in independent variables? Why? Explain.

Question 25

What are endogenous independent variables? How can instrumental variables be used to control for endogenous independent variables? Why? Explain.

Question 26

What are simultaneous equations? How can instrumental variables be used to control for simultaneous equations? Why? Explain.