Recursive Partitioning for Heterogeneous Causal Effects

Susan Athey, Guido Imbens · PNAS / arXiv · 2016 · economics · 10.1073/pnas.1510489113 · record athey2016-causal-trees
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Where this record's text came from. faceted 2026-08 by reading the locally held text (pdftext); every evidence string verified as an exact substring of that text before merging. Extraction is clean apart from mathematical notation and occasional lost spaces (e.g. 'tradeoffbetween', 'meansquared'), which is why quotes were chosen from prose passages. method is recorded as 'simulation' because the only evidence the paper generates about its estimators' performance is a three-design Monte Carlo study; the analytic derivation of the honest criteria is theory rather than proof of a theorem, and no empirical dataset is analysed. Section 8 ('The Literature') distinguishes the approach from several numbered references, but those passages state differences rather than an explicit builds-on/extends/contradicts relation, so only the two unambiguous relations are recorded. The paper's citations are numeric, so relation targets can only be named as the paper itself names them. 2026-08-14, 2026-08-15 and 2026-08-25 schema-0.3 passes: every quote verified as an exact substring of the staged text and anchored at merge time; concept terms verified present; every edge endpoint an existing node. Update, 15 September 2026: EXCEPTION, measured with the merge gate's own predicate (Paper.locate): 1 quote(s) on this record are not found as one exact string in the current staged text - content_tags.findings[0].evidence. The sentence above does not hold for them as written. Where a row records why - the quote is grounded in another copy of the paper, joins two passages with an ellipsis, or differs from the staged text by extraction noise - that note stays on the row.

The quality of the text these quotes were cut from. symbol-font-not-extractable: 33 '(cid:NNN)' glyph-index markers remain in a staged text of 49,356 characters, where the PDF's embedded font had no ToUnicode map. THE QUOTES ON THIS RECORD ARE THE PAPER'S AND THE STAGED COPY IS THE DAMAGED ONE - which is the opposite of the usual case and is why it went unnoticed: one of its 55 live quotes is not an exact substring of this text, and it could NOT be located in it even by aligning the quote's WORD SEQUENCE under this damage, so the defect recorded here is present on the record but does not by itself account for the miss. Not repaired in place: editing the staged text moves every offset after the edit and re-hashes every anchor on the record. Measured at 113aae60fefc3eb1, re-measured unchanged at 54b63482778ddf56.

1 quote on this page breaks a word across a line. The PDF this text was extracted from hyphenated a word at the end of a printed line — adversar- ial, repre- sentations — and the extractor kept the hyphen and the space. The quotes keep them because a quote is reproduced exactly or it proves nothing: the break is the typesetter’s, not the author’s. A search of this page will not find the affected words.

1 quote on this page was cut from a different copy of this article. This project holds two extractions of this paper: the plain text every other quote here is anchored in, and the publisher’s own HTML edition, which we are not licensed to republish. It is verbatim in the second and cannot be found in the first — not because the tagging is wrong, but because the extraction damaged the passage: a page number dropped into the middle of a number, a formula moved out of its sentence, a ligature where two letters belong. The record names the copy for each one. The quote is the paper’s; the extraction is not.

How to read this page. The article itself is not reproduced here — this paper is not cleared for redistribution, so what follows is the tag layer alone. The evidence sentences are withheld with the article. The table at the foot lists every tag the record carries; each row names the facet it belongs to, and the whose words column says whether the tag records the paper's own wording or the tagger's sentence about the paper. Every tag links to each other paper in the corpus carrying it. The machine-readable edition of the same thing is the TEI file beside this one, where the tags live in standOff, and the article is at its publisher via the link below. When we have changed our mind. Some entries in the table begin with a word in capitals and the reason for it. EVIDENCE CORRECTED — the finding still stands, but we had quoted the wrong sentence from the paper, and the quotation has been replaced with the right one. RETRACTED — the entry itself was wrong; it stays on the page, marked, with the reason, rather than being deleted. WITHDRAWN AND REPLACED — the entry was wrong, and a corrected version of it appears in the entries below. Each mark carries its own reason, in brackets, because the reasons differ from one entry to the next. An entry we have WITHDRAWN is removed from this page and kept in the record, with its reason. A line reading Audit and a date is a later re-reading of the entry against its whole sentence: DOUBTFUL means it was kept, and the reason says what is loose about it. Quotation marks inside the tagger's sentence. Where a tag is the tagger's own sentence, a phrase in quotation marks inside it is borrowed from the paper — the tagger's wording around it is not. The paper's own sentence is the evidence quote for that row; on this page it is withheld with the article, and the article is at its publisher. Nothing inside quotation marks anywhere on this page is ours: if it is quoted, it is the paper's. Whose words a concept carries. A concept entry records a term the paper itself uses, so the term, the sense given for it, and its evidence are the paper's own words, quoted where the paper fixes them. This is the opposite of a sense entry in the tag table, which is the tagger's sentence about how the paper uses a term. Where a concept entry could not be grounded in the paper's words, the entry says so on its own row.

Other fields define these differently the same word, defined another way in another discipline
machine learning 14 fields · false-discovery-rate 6 fields · sample-size 5 fields · coverage 4 fields · null-hypothesis 3 fields · confidence-interval 2 fields · and 3 more →

Tags on this paper

Every tag the record carries, each linking to every other paper in the corpus that carries it. A tag appears here whether or not its words occur in the article — the spans below are only the ones a sentence in this paper licenses. Of the 9 concept tags on this paper, 5 are grounded in a quoted sentence.

causal inference treatment effect machine learning regression tree honest estimation adaptive unconfoundedness mean-squared error coverage honest estimation: use one sample to construct the tree partition and a separate sample to estimate treatment effects, removing overfitting bias treatment causal effects partition honest tree covariates estimation subgroup heterogeneous treatment effects treatment effects Bayesian confidence-interval confidence intervals false-discovery-rate multiple testing hypothesis-testing hypothesis tests mean mean of null-hypothesis null hypothesis p-value p-values regression sample-size sample size t-test T-statistic variance simulation

Legend

relation to other work	`claim_relations`	how this paper stands to another: agrees, contradicts, extends, qualifies
claim type	`claim_type`	the shape of the claim: existence, mechanism, method, critique, prediction, null
concept edge	`concept_edges`	an asserted relation between two concepts, with the sentence asserting it
concept	`concepts`	an idea the paper works with, quoted where the paper uses it
content tag	`content_tags`	a finding, definition, quantity, statistic or variable named in the paper
control	`controls`	an experiment run to eliminate a rival explanation
limitation	`limitations`	what the paper says its evidence cannot support
mechanism	`mechanisms`	how the reported effect is said to come about
method	`method`	how the paper produced its evidence
phenomenon	`phenomenon`	the effect or regularity under study
sense	`senses`	a distinct use of a term, quoted where the paper fixes it
transfer	`transfers`	a method or concept carried in from another field

The paper

The full text is not reproduced here. This article is not cleared for redistribution, so the page carries the tag layer only. Its evidence sentences are withheld; the grounding status remains with each tag, and the article itself is at https://doi.org/10.1073/pnas.1510489113. The reading view exists for the papers whose licence permits it.

Every tag on this page

claim_relations 3 · claim_type 1 · concept_edges 2 · concepts 5 · content_tags 16 · controls 1 · limitations 9 · mechanisms 1 · method 1 · phenomenon 1 · senses 3 · transfers 1

Relations on this page carry a quotation for the claim. Where a relation was separately evidenced — and so tested against the vocabulary for its type — the row says so; none of 2 relations here carry that mark. The rest are the tagger’s reading of the sentence quoted beside them.

facet	tag	field	conf.	whose words
claim_type	method Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_type`		the paper's words
phenomenon	heterogeneous treatment effects Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`phenomenon`		the paper's words
method	simulation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: simulation	`method`		the paper's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: honest estimation: use one sample to construct the tree partition and a separate sample to estimate treatment effects, removing overfitting bias	`mechanisms[0]`		the tagger's words
limitations	requires the unconfoundedness (conditional randomization) assumption Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`limitations[0]`		the tagger's words
limitations	Sample splitting for honest estimation costs precision, which is only partly offset by the removal of bias. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the precision of honest estimates: THERE IS A LOSS OF PRECISION DUE TO SAMPLE SPLITTING, offset in fit by the elimination of bias	`limitations[1]`		the tagger's words
limitations	In the simulations honest estimation is measurably worse than adaptive estimation on treatment-effect mean-squared error. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the recommendation itself, with the cost measured: THERE IS A COST TO HONEST ESTIMATION IN TERMS OF MSE-tau, VARYING BY DESIGN AND ESTIMATOR	`limitations[2]`		the tagger's words
limitations	The no-interference (SUTVA) assumption the methods rest on can fail when units are connected in a network. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: any application where units interact: the no-interference assumption MAY BE VIOLATED IN SETTINGS WHERE SOME UNITS ARE CONNECTED THROUGH NETWORKS	`limitations[3]`		the tagger's words
limitations	Hybrid variants (adaptive tree construction combined with honest leaf estimation) are left unexamined. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the hybrid variants: WE DO NOT CONSIDER THOSE VARIATIONS IN THIS PAPER	`limitations[4]`		the tagger's words
limitations	The quantity the method estimates is never observed for any unit in the data. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: any treatment-effect estimate produced by this method: unit-level causal effects are not observed for any unit, so the target is never available to check an estimate against	`limitations[5]`	1.0	the tagger's words
limitations	The paper's central adjective is a stipulated property of data use, not a claim about candour. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the word 'honest' as used throughout this paper: a model is honest if it does not use the same information for selecting the model structure and for estimation given that structure	`limitations[6]`	1.0	the tagger's words
limitations	The improvement claimed for honesty is measured in coverage, and the paper names what it costs. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the benefit reported for honest estimation: it is an improvement in confidence-interval coverage, attaining nominal rates, and the authors describe the cost as not much sacrifice in fitting treatment effects	`limitations[7]`	1.0	the tagger's words
limitations	The comparison class is conventional tree estimation under a name the paper assigns it. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the contrast drawn here between honest and adaptive estimation: adaptive is the label the authors give conventional CART, in which the same data builds the partition and estimates leaf effects	`limitations[8]`	1.0	the tagger's words
transfers	regression-tree (recursive partitioning) methods adapted to estimate heterogeneous treatment effects Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`transfers[0]`		the tagger's words
controls	three simulation designs differing in whether noise covariates are present and in how covariates enter the treatment effect Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: that the advantage of honest estimation depends on one particular data-generating design, in particular on the absence of noise covariates · outcome: held	`controls[0]`	0.8	the tagger's words
concepts	honest estimation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: honest estimation	`concepts[4]`		the paper's words
concepts	adaptive Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: adaptive	`concepts[5]`		the paper's words
concepts	unconfoundedness Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: unconfoundedness	`concepts[6]`		the paper's words
concepts	mean-squared error Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: mean-squared error	`concepts[7]`		the paper's words
concepts	coverage Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: coverage	`concepts[8]`		the paper's words
senses	'honest' - A STIPULATED PROPERTY OF DATA USE: a model is honest when the information selecting its structure is not the information estimating its parameters, which is sample splitting and nothing about truthfulness, candour or good faith - all of which the word carries anyway Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[0]`	1.0	the tagger's words
senses	'adaptive' - THE NAME GIVEN TO THE ALTERNATIVE: conventional CART, where one sample does both jobs, is labelled adaptive here so that the two can be compared; the word is the paper's, applied to a practice that did not call itself that Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[1]`	1.0	the tagger's words
senses	the estimand - UNOBSERVABLE FOR EVERY UNIT: unit-level causal effects are not observed for any unit at all, so unlike an ordinary prediction problem there is no held-out truth anywhere in the data against which a per-unit estimate could be scored Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[2]`	1.0	the tagger's words
claim_relations	builds-on → regression tree methods (machine learning) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_relations[0]`		the tagger's words
claim_relations	builds-on → standard CART regression trees ([4], [3]) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_relations[1]`		the tagger's words
claim_relations	builds-on → the Rubin Causal Model / potential outcome framework ([19], [11], [14]) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_relations[2]`		the tagger's words
concept_edges	EVIDENCE CORRECTED (RE-GROUNDED) · honest estimation —contrasted-with→ adaptive Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. EVIDENCE CORRECTED: RE-GROUNDED. The old span named only one endpoint. This sentence names both and states the contrast WITH ITS DIRECTION - honest estimation improves on adaptive, not merely differs. — strength of the relation: 1 also in: honest estimation · adaptive	`concept_edges[0]`		the tagger's words
concept_edges	honest estimation —contrasted-with→ adaptive Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 · note: RE-GROUNDS another row of this record: the old span named only ONE endpoint. also in: honest estimation · adaptive	`concept_edges[2]`	0.9	the tagger's words
content_tags	Honest estimation splits the sample: one half builds the partition, the other estimates each subpopulation's treatment effect. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.findings[1]`		the tagger's words
content_tags	covariates Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: covariates	`content_tags.variables[0]`		the tagger's words
content_tags	treatment effects Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: treatment effects	`content_tags.variables[1]`		the tagger's words
content_tags	honest estimation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: honest estimation	`content_tags.definitions[0]`		the tagger's words
content_tags	heterogeneous treatment effects Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. also in: heterogeneous treatment effects	`content_tags.definitions[1]`		the tagger's words
content_tags	Bayesian Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Bayesian	`content_tags.statistics[0]`		the tagger's words
content_tags	confidence-interval Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: confidence-interval	`content_tags.statistics[1]`		the tagger's words
content_tags	false-discovery-rate Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: false-discovery-rate	`content_tags.statistics[2]`		the tagger's words
content_tags	hypothesis-testing Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. also in: hypothesis-testing	`content_tags.statistics[3]`		the tagger's words
content_tags	mean Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: mean	`content_tags.statistics[4]`		the tagger's words
content_tags	null-hypothesis Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: THE QUOTE STOPS WHERE THE EXTRACTED TEXT GOES OUT OF ORDER: the extraction splices another line of the page ('If the two leaves are denoted L (Left) and') into this sentence, so the quote ends before that line, at 'the two potential', and the end of the sentence is not quoted. also in: null-hypothesis	`content_tags.statistics[5]`		the tagger's words
content_tags	p-value Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: p-value	`content_tags.statistics[6]`		the tagger's words
content_tags	regression Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. also in: regression	`content_tags.statistics[7]`		the tagger's words
content_tags	sample-size Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: sample-size	`content_tags.statistics[8]`		the tagger's words
content_tags	t-test Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: t-test	`content_tags.statistics[9]`		the tagger's words
content_tags	variance Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: variance	`content_tags.statistics[10]`		the tagger's words

Interpretive choices

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