Deck 11: Regression Discontinuity: Looking for Jumps in Data

Question 1

A key assumption for RD is that the error term does not jump at the point of discontinuity.

Answer 1

True

Question 2

If the assignment variable is correlated with the error term, then a RD model will provide a biased estimate of the treatment effect.

Answer 2

False

Question 3

Using polynomial models in RD can produce bumps at the cutoff that are larger than they should be.

Answer 3

True

Question 4

The smaller the window we use around the RD cutoff, the less we have to worry about the functional form of the model.

Question 5

One of the main problems faced by RD is the fact that the error can be discontinuous at the treatment threshold.

Question 6

Which of the following is a diagnostic test to assess the appropriateness of using a RD model?

A) Use a histogram in order to make sure there is clustering on one side of the cutoff.
B) Run a RD model and see if the effect is statistically significant
C) Run a RD using other covariates as the dependent variable.
D) See if the results are the same using each cutoff separately.

Question 7

Consider a plot of a model of the form Y_i = B₀ +B1T_i + B2(X_1i-C) + e_i. Which of the following is true?

A) B0 is the bump at the cutoff
B) B1 is the slope of the line
C) B2 is the slope of the line
D) B2 is the bump at the cutoff

Question 8

Which one of the following is a key assumption in regression discontinuity models?

A) The cutoff is random
B) The error term jumps at the cutoff
C) The error term is continuous and does not jump at the cutoff
D) The assignment variable is uncorrelated with the error term

Question 9

Which of the following shows the varying slopes RD model?

A) Y_i = B₀ + B1T_i + B2(X_1i-C) + B3(X_1i-C) T_i + e_i
B) Y_i = B₀ + B1T_i + B2(X_1i-C) + B3(X_1i-C) T_i ² + e_i
C) Y_i = B₀ + B1T_i + B2(X_1i-C) + B3(X_1i-C) ² + e_i
D) Y_i = B₀ + B1T_i + B2(X_1i-C) + e_i

Question 10

Which of the following is the reason polynomial RD models can be dangerous to use?

A) There is no danger in using a polynomial model instead of a varying slopes model.
B) Polynomial models are sensitive and can produce bumps at the cutoff that are larger than they should be.
C) Polynomial models lead to further endogeneity when the error term is not continuous.
D) Polynomial models can produce multicollinearity.

Question 11

One of the drawbacks of narrowing the window/range of the assignment variable is:

A) Decrease in statistical power
B) Leads to bias if used on linear model
C) Leads to bias if used on a non-linear model.
D) Underestimates the effect of the treatment at the cutoff

Question 12

We employ binned graphs in order to.

A) Help us ignore the functional form of model and allow use to use a liner model regardless of the true relationship.
B) Help us determine the functional form of the model.
C) Increase the statistical power of the model.
D) Deal with endogeneity.

Question 13

What is the consequence of having an error term that jumps at cutoff in a RD model?

A) B1, the coefficient for the treatment effect is biased.
B) B2, the coefficient for the slope is biased.
C) We need to use a polynomial model.
D) We need to use a varying slopes model.

Question 14

In order to diagnose if variables other than Y (dependent variable) jump at the cutoff, one must use which of the following equations:

A) Y_i=B₀+B1T_i+B2(X_1i-C) +B3(X_1i-C) T_i +e_i
B) Y_i=B₀+B1T_i+B2(X_1i-C) +B3(X_2i) T_i +e_i
C) X_2i=g₀+g1T_i+g2(X_1i-C) +v_i
D) X_i=B₀+B1Y_i+B2(Y_i-C) +B3(X_2i) T_i +e_i

Question 15

What is one of the limitations of using RD models in order to help make/shape policy decisions?

A) The treatment effect may not be generalizable.
B) The cost of running and setting up an experiment to run an RD model can be prohibitively expensive.
C) Different assignment variables (and corresponding cutoff) can show treatment effects, difficult to tell which assignment variable is accurate.
D) Policymakers are much more comfortable randomly assigning treatment status than assigning treatment based on some assignment variable such as a test score or needs index.

Question 16

Show and explain why the correlation between the error term and T disappears when we control for the assignment variable.

Question 17

Please explain how to asses if other variables act differently at the point of discontinuity, and explain the consequence of other variables jumping at the point of discontinuity.

Question 18

Explain why we may choose to employ a varying slopes RD model instead of a linear RD model.

Question 19

Provide the equation for a polynomial RD model and explain a potential drawback of using a polynomial model and how we can deal with such a drawback.

Question 20

Describe the benefits and drawbacks of adjusting the window of an RD model.