Anderson–Rubin confidence set

The task

Task statement

Estimate the 95 percent Anderson-Rubin confidence set for the coefficient beta of endog in y = intercept + beta*endog + gamma*x + error, using excluded instruments z1 and z2. For each candidate beta, regress y-beta*endog on an intercept, x, z1, and z2. Use the conventional homoskedastic joint F test of both excluded-instrument coefficients, with numerator degrees of freedom 2 and denominator n-4. Accept beta when F is at most the 95th percentile of that F distribution. Invert this test over the entire real line, without a bounded search grid. The data yield two finite boundary points. Report their smaller and larger values as boundary_low and boundary_high. Report accepts_zero as 1 if zero belongs to the confidence set, otherwise 0. Report unbounded as 1 if the set includes arbitrarily large positive or negative beta values, otherwise 0. Report ar_f_at_one as the test statistic at beta=1. Use se=null and the full sample size as n_obs for every row. Determine set membership from the test inequality. A disjoint set is possible.

Data

One shared fixed dataset with 240 rows. Columns: y, endog, x, z1, z2.

Files

input.csv

Required output

Scored estimates: boundary_low, boundary_high, accepts_zero, unbounded, ar_f_at_one.

Reference output

A run succeeds when every scored estimate lies within 1 percent or 0.005 of its reference value, whichever is larger. Sample sizes are not scored.