{"args":{"dataset":"grid","income":"income","tax":"tax","weights":"weight"},"checks":[{"abs_tol":1e-06,"bind":"any","column":null,"failure_class":null,"field":"value","interval":false,"key":"kakwani","kind":"figure_close","min_lre":null,"note":"","open_interval":false,"rel_tol":null,"required":true,"source_id":null,"table":null,"tool":null,"value":-0.20568976583619003,"weight":1.0,"where":null}],"datasets":{"grid":{"columns":null,"description":"lognormal income, log-SD 0.8, 20,000 points (weighted grid, cells finer in the tails); columns income and weight, tax = 0.001\u00b7income^0.5","file_sha256":null,"format":null,"frame_sha256":null,"generator":"magi_bench.suites.closed_form:lognormal_grid","kind":"generator","licence":null,"member":null,"object":null,"params":{"columns":{"tax":[0.001,0.5]},"mu":7.0,"n":20000,"sigma":0.8,"weighted":true},"path":null,"read_kw":{},"records":null,"role":"agent","sha256":null,"transforms":[],"url":null}},"difficulty":"E","id":"closed_form.kakwani.regressive_tax","level":"T1","meta":{},"question":"","requires":[],"runner":null,"sources":[],"split":"public","suite":"closed_form","tags":["progressivity","lognormal","weights"],"target":"tool","tool":"core.kakwani","truth":"a tax of 0.001\u00b7income^0.5 on a lognormal, \u03c3 = 0.8: its concentration index is the Gini of a lognormal with log-SD 0.5\u03c3, so K = 2\u03a6(0.5\u03c3/\u221a2) \u2212 2\u03a6(\u03c3/\u221a2) = -0.20569 (Kakwani 1977)"}