1. By hand exercises

Testing whether there is a causal effect

Suppose you have the following data-set from an experiment on the effect of gender (as implied by the name on an applicant's CV) on her likelihood to be invited for a job interview:

Gender Invitation
F 0
F 0
F 0
F 1
F 1
M 0
M 1
M 1
M 1

Calculate a test for the null hypothesis that gender does not affect the likelihood to be invited for an interview.

2. Matlab exercises

Write code which performs the following:

  1. Generate \(n\) pairs of potential outcomes \(Y_i^1, Y_i^0\) which are just independent draws from the standard normal distribution. What is the ATE for this data generating process?

  2. Generate \(D=\mathbf{1}(Y_i^1>Y_i^0)\), and the corresponding \(Y\) based on the potential outcome equation $$Y= D\cdot Y^1 + (1-D) \cdot Y^0.$$

    Calculate \(\overline{Y}_1 - \overline{Y}_0\).

  3. Repeat 2, but with \(D=\mathbf{1}(Y_i^1 \leq Y_i^0)\).

  4. Repeat 2, but with \(D\) independent Bernoulli 0.5 draws.

  5. Using the data from 4, calculate a 0.95 confidence interval for the \(ATE\).

Matlab commands which you might find useful: