Double/Debiased Machine Learning for Treatment and Structural Parameters

Double/Debiased Machine Learning for Treatment and Structural Parameters Victor Chernozhukov Denis Chetverikov Mert Demirer Esther Duflo

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Double/Debiased Machine Learning for Treatment and Structural Parameters 2018 The Econometrics Journal / arXiv 10.1111/ectj.12097 1608.00060 chernozhukov2018-double-ml chernozhukov2018-double-ml.txt, the project's staged copy c3a7daef3937ec90ced3d14bfca9ee3ae35410a0 arxiv-open statistics

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them method Quotation withheld because this record is not cleared for redistribution. regularization bias in semiparametric inference with machine-learned nuisance parameters Quotation withheld because this record is not cleared for redistribution. mathematical-proof mathematical-proof Quotation withheld because this record is not cleared for redistribution. mechanisms A TERM IS BORROWED PARTLY, FOR A PROCEDURE THE SOURCE USED DIFFERENTLY, AND THE INEXACT FIT IS STATED IN THE SAME SENTENCE: we use the term CROSS-FITTING to characterize our recommended procedure, PARTLY BORROWING THE JARGON FROM an earlier paper WHICH EMPLOYED A SLIGHTLY DIFFERENT FORM of sample-splitting. The word's provenance and its imprecision are both on the page Quotation withheld because this record is not cleared for redistribution. mechanisms A TRADITIONAL ASSUMPTION IS SAID TO BREAK DOWN OUTSIDE ITS REGIME, AND THE REGIME IS NAMED: the paper departs from the classical setting BY ALLOWING the nuisance parameter to be SO HIGH-DIMENSIONAL that the traditional assumptions - SUCH AS DONSKER PROPERTIES, THAT LIMIT COMPLEXITY OF THE PARAMETER SPACE - **BREAK DOWN**. What fails is not a result but a condition, and the condition is named Quotation withheld because this record is not cleared for redistribution. mechanisms TWO GOOD METHODS COMPOSED NAIVELY ARE SHOWN TO FAIL, AND THE WORD `NAIVELY` IS THE PAPER'S: both regularization bias and overfitting in estimating the nuisance parameter cause **A HEAVY BIAS** in estimators of the target that are obtained BY NAIVELY PLUGGING ML estimators into the estimating equations. Each piece is sound; the composition is not, and the paper names the fault in the composing rather than in either part about this quote: The sentence that follows the span states the consequence - the naive estimator failing to be N-to-the-minus-one-half consistent - but it is written with inline rate notation that this record's slicing guard refuses, so the clause is described here and not quoted. Quotation withheld because this record is not cleared for redistribution. mechanisms THE REMEDY IS PRESENTED AS TWO INGREDIENTS AND THE RESULT IS GIVEN TWO NAMES AT ONCE: the impact can be removed using TWO SIMPLE, YET CRITICAL, INGREDIENTS - orthogonal moments with REDUCED SENSITIVITY to nuisance parameters, and cross-fitting - and WE CALL THE RESULTING SET OF METHODS DOUBLE OR DEBIASED ML. One method, two adjectives, offered as alternatives rather than ranked Quotation withheld because this record is not cleared for redistribution. mechanisms A PROPERTY IS NAMED AFTER THE PERSON WHO INTRODUCED IT, AND THE ATTRIBUTION IS GIVEN AS THE REASON FOR THE NAME: we refer to property (1.8) as NEYMAN ORTHOGONALITY and to the score as the Neyman orthogonal score function DUE TO THE FUNDAMENTAL CONTRIBUTIONS in Neyman (1959) and Neyman (1979), WHERE THIS NOTION WAS INTRODUCED. The name records a debt, not a definition - and the property it names is a numbered equation, so the term is anchored to a formula rather than a gloss Quotation withheld because this record is not cleared for redistribution. mechanisms THE FORMAL CONDITION IS GIVEN AN INTUITIVE GLOSS THAT STATES WHAT IT BUYS: **INTUITIVELY**, the orthogonality condition means the moment conditions used to identify the parameter are LOCALLY INSENSITIVE to the value of the nuisance parameter, WHICH ALLOWS ONE TO PLUG IN NOISY ESTIMATES of these parameters WITHOUT STRONGLY VIOLATING the moment condition. The gloss is not a restatement - it is the licence the condition grants Quotation withheld because this record is not cleared for redistribution. mechanisms A FUNCTION IS RENAMED WITH A HEDGING PREFIX WHEN ITS SPECIAL CASE IS GENERALISED: the criterion can be the log-likelihood associated to an observation - MORE GENERALLY, WE REFER TO IT AS THE QUASI-LOG-LIKELIHOOD FUNCTION. The prefix marks that the object no longer has the property its root name asserts Quotation withheld because this record is not cleared for redistribution. mechanisms A CONDITION IS DECLARED NONPRIMITIVE AND ITS OWN CONDITIONS ARE DECLINED AS CASE-SPECIFIC: THE ONLY NONPRIMITIVE CONDITION HERE is the assumption on the rate of estimating the nuisance parameters - those rates are available for most used methods and are CASE-SPECIFIC, SO WE DO NOT RESTATE the conditions needed to reach them. The assumption is labelled as resting on assumptions that are not given about this quote: The paper makes this disclaimer TWICE, word for word, in Remark 4.1 and Remark 5.1, spelling the term “nonprimitive” in the first and “non-primitive” in the second. The span is the Remark 4.1 instance; the repetition is a property of the file, not of this quote, which is why it is recorded here. Quotation withheld because this record is not cleared for redistribution. mechanisms A BOUND THE AUTHORS THEMSELVES IMPOSE IS NAMED THE CRUDE BOUND, AND FINER CONDITIONS ARE OFFERED IN ITS PLACE: a structural feature of the examples allows us to require MUCH FINER CONDITIONS on the quality of the nuisance parameter estimators THAN THE CRUDE BOUND (3.8). The paper's own requirement carries a pejorative as its standing name, and the numbered equation is what the pejorative attaches to about this quote: The parenthesis I wanted, “imposes the (crude) rate requirement”, is embedded in display mathematics and cannot be sliced clean. The span is the same paper calling the same bound “the crude bound” in prose, three occurrences later. Quotation withheld because this record is not cleared for redistribution. mechanisms A DISPENSED-WITH CONDITION IS REPLACED BY A WEAKER ONE AND THE REPLACEMENT IS THEN CRITICISED IN THE SAME PARAGRAPH: WITHOUT INVOKING DONSKER CONDITIONS, one may still show that the troublesome terms vanish **AS LONG AS** the entropy DOES NOT INCREASE WITH N TOO RAPIDLY - HOWEVER, THESE CONDITIONS ON THE GROWTH OF ENTROPY COULD RESULT IN UNNECESSARILY STRONG RESTRICTIONS ON MODEL COMPLEXITY. What was an assumption about a function class becomes a growth rate; the substitution is announced, and so is the price of the thing substituted in Quotation withheld because this record is not cleared for redistribution. The regularity conditions given for the treatment-effect results are simplified rather than tightest possible what this limits: the stated regularity conditions: THE CONDITIONS ARE NOT THE TIGHTEST POSSIBLE, BUT OFFER A SET OF SIMPLE CONDITIONS UNDER WHICH THEOREM 5.1 FOLLOWS AS A SPECIAL CASE Quotation withheld because this record is not cleared for redistribution. Assumption 5.1 is simplified for presentation rather than stated at full sharpness what this limits: Assumption 5.1 as stated: THE CONDITIONS ... ARE FAIRLY SHARP THOUGH SOMEWHAT SIMPLIFIED FOR EASE OF PRESENTATION Quotation withheld because this record is not cleared for redistribution. The empirical finding that more folds gives smaller standard errors does not generalise what this limits: any rule of thumb about cross-fitting folds: THERE DOES NOT APPEAR TO BE A GENERAL RELATIONSHIP BETWEEN THE NUMBER OF FOLDS IN CROSS-FITTING AND THE PRECISION OF THE ESTIMATE OF THE PARAMETER OF INTEREST Quotation withheld because this record is not cleared for redistribution. Deep-learning nuisance estimators were tried but hit stability and computational problems and were left unreported what this limits: the set of nuisance estimators the empirical section reports: deep learning was tried, and WE RAN INTO STABILITY AND COMPUTATIONAL ISSUES AND CHOSE NOT TO REPORT THESE RESULTS IN THE EMPIRICAL SECTION Quotation withheld because this record is not cleared for redistribution. The rate condition the method is known for is a crude bound that follows only under one of the paper's conditions. what this limits: the o(N^-1/4) nuisance rate usually quoted from this paper: the authors state it is the crude requirement imposed if only condition (3.7) holds, and that the conditions can be refined Quotation withheld because this record is not cleared for redistribution. Several of the paper's own headline applications admit weaker conditions than the crude one. what this limits: any application of the crude rate requirement: the authors note that many important structured problems - including partially linear regression models and average treatment effects under unconfoundedness - have vanishing cross-derivatives and so allow more refined requirements Quotation withheld because this record is not cleared for redistribution. Identification is assumed, not established: it is listed among the conditions the theorems require. what this limits: the causal interpretation of estimates from this method: the identification condition is imposed as an assumption alongside Neyman orthogonality and smoothness, so the theory delivers estimation and inference for a parameter that is already identified Quotation withheld because this record is not cleared for redistribution. The insensitivity to the nuisance estimate is local and approximate, in the authors' own gloss. what this limits: the claim that this method is robust to the choice of nuisance estimator: the moment conditions are described as locally insensitive to the nuisance value, permitting noisy plug-in estimates without strongly violating the moment condition Quotation withheld because this record is not cleared for redistribution. flexible machine-learning estimators used for the nuisance functions of a causal parameter, with Neyman-orthogonal scores and cross-fitting added so their regularization bias does not carry into the estimate Quotation withheld because this record is not cleared for redistribution. flexibly controlling for a rich set of variables in the 401(k) example, where assignment is observational - and the elimination holds only under the paper's own identifying assumptions, which the sentence states as an aim rather than a demonstrated result eliminates: bias from the lack of random assignment of the treatment variable · outcome (stated by the tagger, no quotation): partial Quotation withheld because this record is not cleared for redistribution. cross-fitting cross-fitting Quotation withheld because this record is not cleared for redistribution. Neyman orthogonality Neyman orthogonality Quotation withheld because this record is not cleared for redistribution. sample splitting sample splitting Quotation withheld because this record is not cleared for redistribution. rate requirement rate requirement Quotation withheld because this record is not cleared for redistribution. identification condition identification condition Quotation withheld because this record is not cleared for redistribution. regularization bias regularization bias Quotation withheld because this record is not cleared for redistribution. Neyman-orthogonal moments/scores → regularization bias the method REMOVES the impact of a bias that the naive estimator suffers - the paper's own central result, stated as a repair rather than a relation between two objects of study — note: PROVENANCE ROW. This is one of the two instances behind the project's 2026-08-14 ruling: with no type for it, the relation was filed as a 'limitation', where the paper's headline result reads as OUR doubt about the method. It is NO LONGER UNHOUSED - 'causes' with 'effect_direction: eliminates' expresses it, which is what an earlier note of ours added the same evening. Kept so the file records why it exists, and excluded whenever the coverage count is quoted. Quotation withheld because this record is not cleared for redistribution. the o(N^-1/4) rate - A WORST CASE, NOT THE REQUIREMENT: the paper calls it the crude requirement that smooth problems translate to, and says in the same breath that the conditions can be refined, so the number that travels out of this paper is the loosest form of a condition the paper itself tightens Quotation withheld because this record is not cleared for redistribution. Neyman orthogonality - A DERIVATIVE AT A POINT, GLOSSED AS LOCAL INSENSITIVITY: the moment condition is locally insensitive to the nuisance value, which is what licenses plugging in noisy estimates without strongly violating it; the property is evaluated at the truth and both hedges - locally, and without strongly violating - are in the sentence that explains it Quotation withheld because this record is not cleared for redistribution. cross-fitting - COINED IN THIS SENTENCE, WITH ITS DEFINITION ATTACHED: the name is introduced for the procedure of swapping the roles of main and auxiliary samples and averaging the resulting estimates, so unlike the eponyms in our absent-names table this word cannot come apart from its referent - the paper that named it also defined it Quotation withheld because this record is not cleared for redistribution. builds-on → Neyman orthogonality (statistics) Quotation withheld because this record is not cleared for redistribution. contradicts → the naive plug-in of ML estimators into estimating equations Quotation withheld because this record is not cleared for redistribution. builds-on → Neyman (1959) and Neyman (1979) Quotation withheld because this record is not cleared for redistribution. builds-on → Belloni et al. (2010) and Belloni et al. (2012) Quotation withheld because this record is not cleared for redistribution. extends → the classical literature on semiparametric estimation Quotation withheld because this record is not cleared for redistribution. cross-fitting —is-a→ sample splitting cross-fitting sample splitting strength of the relation: 1 Quotation withheld because this record is not cleared for redistribution. Double/debiased ML estimates the target parameter with Neyman-orthogonal scores that have reduced sensitivity to nuisance parameters, and with cross-fitting, an efficient form of data-splitting. Quotation withheld because this record is not cleared for redistribution. Naively plugging ML estimates of the nuisance parameters into estimating equations causes a heavy bias in the target estimator, from both regularization bias and overfitting. Quotation withheld because this record is not cleared for redistribution. nuisance parameter nuisance parameter Quotation withheld because this record is not cleared for redistribution. DML DML Quotation withheld because this record is not cleared for redistribution. Neyman-orthogonal moments Neyman-orthogonal moments Quotation withheld because this record is not cleared for redistribution. cross-fitting cross-fitting Quotation withheld because this record is not cleared for redistribution. mean mean Quotation withheld because this record is not cleared for redistribution. median median about this quote: QUOTE RECOVERED FROM THE PAPER'S OWN CHARACTERS. The recorded quote was LETTERS-ONLY IDENTICAL to this stretch of the staged text but not an exact substring of it - spaces, hyphens, ligature glyphs or mathematical operators differed, so it could never anchor. This is the file's own text between the same two letters: not produced by a rule about the damage, copied out of the file. Round-trip checked (the recovered span is letters-only equal to the original) and length-checked. The text as originally recorded is kept in evidence as extracted. Quotation withheld because this record is not cleared for redistribution. regression regression Quotation withheld because this record is not cleared for redistribution. sample-size sample-size Quotation withheld because this record is not cleared for redistribution. standard-error standard-error Quotation withheld because this record is not cleared for redistribution. statistical-significance statistical-significance 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. 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