Oaxaca decomposition

The task

Task statement

Use Python. Read ./input.csv. Available columns: id, y, x, z, group.

Decompose the difference in mean y between group 1 and group 0. Fit separate OLS regressions of y on an intercept, x, and z in each group. Use group 0 coefficients as the reference. Let Xbar_g include the intercept 1. Report gap=mean(y|group=1)-mean(y|group=0), explained=(Xbar_1-Xbar_0) times beta_0, and unexplained=Xbar_1 times (beta_1-beta_0). Also report explained_x=(mean(x|group=1)-mean(x|group=0))*beta_0_x. Include every row. Set se=null and n_obs to the full sample size for all rows. The components describe this regression decomposition and do not establish causal discrimination.

Report the requested point estimates. Standard errors are not requested. Use json.dump to write result.json with the following structure. Replace each <number> with the computed value. Report at least eight significant digits.
{
  "task_id": "broad_oaxaca",
  "platform": "python",
  "estimates": [
    {
      "term": "gap",
      "estimate": "<number>",
      "se": null,
      "n_obs": 360
    },
    {
      "term": "explained",
      "estimate": "<number>",
      "se": null,
      "n_obs": 360
    },
    {
      "term": "unexplained",
      "estimate": "<number>",
      "se": null,
      "n_obs": 360
    },
    {
      "term": "explained_x",
      "estimate": "<number>",
      "se": null,
      "n_obs": 360
    }
  ],
  "method_metadata": {},
  "diagnostics": {}
}

Data

One shared fixed dataset with 360 rows. Columns: id, y, x, z, group.

Files

input.csv

Required output

Scored estimates: gap, explained, unexplained, explained_x.

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.