Instrumental Variables & Endogeneity Test Bank Chapter 9

Chapter 9

True or False Questions

1. True or False: An instrumental variable explains both the endogenous independent variable of interest and the dependent variable.
2. True or False: The inclusion condition states that the instrument used must be a statistically significant determinant of Y.
3. True or False: We cannot test if an instrument satisfies the exclusion condition statistically.
4. True or False: To conduct an overidentification test we run 2SLS models separately for each instrumental variable.
5. True or False: A weak instrument (an instrument that does a poor job of explaining the endogenous variable) will always produce better results than OLS.
6. True or False: The variance of coefficient estimates in 2SLS is generally smaller than the variance of coefficient estimates in OLS.

Multiple Choice Questions

1. In order to statistically verify that an instrument satisfies the exclusion condition, we can:
   1. Run a regression of the instrument against the dependent variable of interest.
   2. Run a regression of the instrument against the independent variable of interest.
   3. There is no way to statistically satisfy the exclusion condition.
   4. Run an overidentification test.
2. Which of the following is a justification for overidentification tests?
   1. If each instrument satisfies both the inclusion and exclusion condition, than using each instrument alone should produce an unbiased estimate of B1.
   2. If each instrument satisfies both the inclusion and exclusion condition, than using each instrument alone will produce biased results.
   3. Once we identify the excessive identification condition, the efficiency of our estimates will improve.
   4. They allow us to identify weak instruments.
3. Which of the following is true about weak instruments?
   1. A weak instrument is correlated with the error term.
   2. The larger the sample size, the bigger the problem (bias) caused by the use of a weak instrument.
   3. A weak instrument is an instrument that does a poor job of explaining X.
   4. A weak instrument fails the exclusion condition.
4. Which one of the following are factors that influence the variance of 2SLS Bj estimates?
   1. Model fit
   2. Sample size
   3. Explanatory power of the instrument in explaining X
   4. Overall fit of the first stage regression
   5. All of the above
5. The variance of 2SLS Bj will be lower if:
   1. If we have a weak instrument
   2. If we have a worse fit at the first stage of the regression
   3. If the instrument has a high explanatory power for X
   4. If we have a smaller sample size
6. The estimation of an instrumental variable model requires:
   1. Allows only one endogenous regressor.
   2. Requires exact identification
   3. Requires exact identification or overidentificaion
   4. Requires more endogenous variables than instruments.
7. If we use a quasi instrument for to estimate a 2SLS, than the probability limit for the 2SLS estimate of B1^ is: (Note s=standard deviation)
   1. plimB1^=B1+(corr(X,e)/corr(Z, e))*(_e/_X1)
   2. plimB1^=B1+(corr(Z,e)/corr(Z, X))*(_e/_X1)
   3. plimB1^=B1+(corr(Z,e)/corr(X, e))*(_e/_X1)
   4. plimB1^=B1+(corr(Z,e)/corr(Z, Y))*( _e/_X1)
8. Which of the following best characterizes the conditions for a good instrument?
   1. Z is statistically significant in the first-stage and exerts a direct effect on Y.
   2. Z is statistically significant in the first-stage and exerts no direct effect on Y.
   3. Z is uncorrelated with both X and Y.
   4. Z needs to be included in both stages in order for 2SLS to be appropriate.
9. Given the model

Crime_it=B₀+B₁Police_i,t+e_it,

which one of the following potential instrumental variables do you think would not satisfy the inclusion condition?

• 1. The wealth of the city
  2. The population density of the city
  3. The number of guns in the city
  4. Number of candy stores in the city

1. Given the model

Crime_it=B₀+B₁Police_i,t+e_it

which one of the following variables do you think would satisfy the exclusion condition?

• 1. The number of guns in the city
  2. The wealth of the city
  3. The population density of the city
  4. The number of candy stores in the city

1. Suppose we wish to know if long prison sentences reduce the probability of recidivism. The basic model is

Repeat crime_i=B₀+B₁SentenceLength_i+e_i

Where repeat crime is 1 for released prisoners who end up being sent back to jail after release. Which of the following is viable as an instrumental variable?

• 1. A variable indicating the severity of the initial crime.
  2. A variable indicating that the person had been randomly assigned to a judge with a record of harsh sentencing.
  3. A variable indicating that the person had been randomly assigned to an educational program while in prison.
  4. A variable indicating whether the person was a high school dropout.

1. Please list two of the factors that influence the variance of 2SLS Bj estimates, and explain how they influence the variance of 2SLS Bj estimates.
2. If Z is a weak instrument, please explain how its use will influence the variance of Bj.
3. Please explain what an overidentification test is.

However, if we use each instrument alone and they produce varying estimates of the coefficient, then we must rethink the use of the instruments as one or both does not satisfy the conditions for a good instrumental variable.

1. Give the probability limit equations for OLS and 2SLS, and explain the scenario where 2SLS should be used instead of OLS when we have an imperfect instrument (either weak or quasi)

We would use a 2SLS estimate instead of an OLS estimate in the case where the correlation between the instrument (Z) and the error term is low and the correlation between the instrument (Z) and X1 is high. In such a case, 2SLS may give us better estimates than OLS.

1. Describe the process of blocking in a randomized experiment.
2. Describe the general steps that are undertaken when performing a randomized experiment.
3. Please explain how non-compliance could lead to a problem of endogeneity, and explain how ITT can be used to deal with the problem.
4. Please compare the benefits of using 2SLS and ITT approaches to deal with non-compliance.
5. Explain why attrition in randomized experiments can cause a problem, and explain one method of dealing with the problem of attrition.