2SLS Second Stage

Problem

Perform the second stage of two-stage least squares: fit x_hat from the first-stage OLS of x on z, then regress y on x_hat with an intercept.

Return [intercept, slope]; if the first stage is degenerate return [mean(y), 0.0], and empty input returns [0.0, 0.0].

Hint

The second stage regresses the outcome on the instrument-fitted regressor.

case 1

in: [[1,2,3,4],[2,4,6,8],[1,3,5,7]]

expected: [-1,1]

case 2

in: [[1,2,3],[3,5,4],[1,2,4]]

expected: [-9.666666666666666,3]

case 3

in: [[2,2,2],[1,2,3],[5,6,7]]

expected: [6,0]

case 4

in: [[],[],[]]

expected: [0,0]

Starter codePython

def tsls_second_stage(z, x, y):
    # Returns [intercept, slope]
    # Your code here
    pass

4 test cases · run your code against them in the editor