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arxiv: 2011.06695 · v8 · submitted 2020-11-13 · 💰 econ.EM · stat.ME

When Should We (Not) Interpret Linear IV Estimands as LATE?

Tymon S{\l}oczy\'nski This is my paper

Pith reviewed 2026-05-24 14:14 UTC · model grok-4.3

classification 💰 econ.EM stat.ME
keywords instrumental variablesLATEmonotonicitynegative weightscovariatesinteracted instrumentspretrial detention
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The pith

Linear IV estimands can assign negative weights to conditional LATEs under weaker monotonicity when covariates enter without interactions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines when the linear instrumental variables estimand remains interpretable as a weighted average of conditional local average treatment effects. It focuses on cases where covariates are needed for identification but the reduced-form and first-stage equations are misspecified because they impose an implicit restriction that instrument effects do not vary with covariates. Under a weaker monotonicity condition—compliers but no defiers at some covariate values and defiers but no compliers at others—the weights on some conditional LATEs become negative, so the overall estimand is no longer a causal effect. The problem is avoided by the interacted specification that allows the instrument effects to differ across covariate values.

Core claim

When additional covariates are required for identification, the standard linear IV specification imposes homogeneity on the effects of the instrument in the reduced form and first stage. This leads to an IV estimand that equals a weighted sum of conditional LATEs in which some weights are negative whenever monotonicity holds only conditionally, with the direction of compliance varying across covariate values. The interacted IV specification avoids misspecification and restores an interpretation with nonnegative weights.

What carries the argument

Decomposition of the linear IV estimand into weights on conditional LATEs, where the weights derive from the misspecified reduced-form and first-stage regressions and can turn negative under conditional monotonicity.

If this is right

  • The standard linear IV estimand with covariates need not represent any causal effect even when there are no defiers in the overall population.
  • The interacted specification of Angrist and Imbens (1995) yields an estimand that remains a convex combination of conditional LATEs.
  • In the pretrial detention application, the interacted instruments produce estimates that differ economically and statistically from the non-interacted ones.
  • Applied researchers should verify whether the homogeneity restriction is plausible before interpreting linear IV estimates with covariates as causal effects.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Many existing IV applications that include covariates without interactions may produce estimates that are not causal if compliance direction varies with those covariates.
  • The same logic suggests checking for sign changes in the first stage across covariate strata before relying on non-interacted 2SLS.
  • This issue is likely to appear in other linear estimators that impose homogeneity restrictions when identification requires covariates.

Load-bearing premise

The reduced-form and first-stage regressions are correctly specified without interactions between the instrument and the covariates.

What would settle it

An empirical setting in which the first-stage effect of the instrument changes sign across covariate-defined groups, combined with rejection of uniform monotonicity, such that the linear IV estimate differs from the interacted-instrument estimate in the direction predicted by negative weights.

Figures

Figures reproduced from arXiv: 2011.06695 by Tymon S{\l}oczy\'nski.

Figure 1
Figure 1. Figure 1: Estimated Bias of βˆ RIV 0 0.2 0.4 0.6 0.8 1 Absolute normalized bias 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 θ Notes: The data are Card (1995)’s subsample of the National Longitudinal Survey of Young Men (NLSYM). The sample and the covariate specification are as in [PITH_FULL_IMAGE:figures/full_fig_p029_1.png] view at source ↗
read the original abstract

In this paper I revisit the interpretation of the linear instrumental variables (IV) estimand as a weighted average of conditional local average treatment effects (LATEs). I focus on a situation in which additional covariates are required for identification while the reduced-form and first-stage regressions may be misspecified due to an implicit homogeneity restriction on the effects of the instrument. I show that the weights on some conditional LATEs are negative and the IV estimand is no longer interpretable as a causal effect under a weaker version of monotonicity, i.e. when there are compliers but no defiers at some covariate values and defiers but no compliers elsewhere. The problem of negative weights disappears in the interacted specification of Angrist and Imbens (1995), which avoids misspecification and seems to be underused in applied work. I illustrate my findings in an application to the causal effects of pretrial detention on case outcomes. In this setting, I reject the stronger version of monotonicity, demonstrate that the interacted instruments are sufficiently strong for consistent estimation using the jackknife methodology, and present several estimates that are economically and statistically different, depending on whether the interacted instruments are used.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper claims that the linear IV estimand is not generally interpretable as a weighted average of conditional LATEs when covariates are needed for identification. Under a weaker monotonicity condition (compliers but no defiers in some covariate cells, and defiers but no compliers in others), the homogeneity restriction implicit in non-interacted first-stage and reduced-form regressions produces negative weights on some conditional LATEs, rendering the estimand uninterpretable as a causal effect. The interacted specification of Angrist and Imbens (1995) removes the restriction, restores non-negative weights, and yields different estimates in an application to pretrial detention.

Significance. If the result holds, the paper clarifies an important practical limitation of the most common IV specification and shows why the interacted instruments are preferable when monotonicity is only conditional. It supplies both the weighting formula under the weaker monotonicity and an empirical demonstration that the interacted instruments are strong enough for jackknife estimation while producing economically distinct results. This strengthens the case for routine use of interacted IV when covariates are required.

minor comments (2)
  1. [Abstract] Abstract: the phrase 'the weights on some conditional LATEs are negative' would benefit from a one-sentence parenthetical indicating that this occurs only under the weaker (cell-specific) monotonicity, not under the standard global monotonicity.
  2. [Application] The application section would be strengthened by reporting the first-stage F-statistics for the interacted instruments alongside the jackknife results to allow direct comparison of strength.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive and accurate summary of our paper and for recommending minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central derivation applies the standard IV weighting formula (from external citations to Angrist and Imbens 1995 and Imbens and Angrist 1994) to show that linear IV can produce negative weights on conditional LATEs when monotonicity is permitted to flip sign across covariate cells. This is an algebraic consequence of the first-stage and reduced-form misspecification under omitted interactions; the interacted specification is invoked from the same external 1995 reference rather than any self-citation. No step reduces a prediction to a fitted parameter by construction, renames a known result, or imports a uniqueness theorem from the author's prior work. The argument remains self-contained against the external benchmark of classical IV theory.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on standard econometric assumptions for IV identification and LATE without introducing new free parameters or invented entities.

axioms (1)
  • domain assumption Standard IV assumptions including relevance, exclusion restriction, and some form of monotonicity hold in the setup.
    These are invoked to derive the conditions under which the linear IV estimand fails to be interpretable as a causal effect.

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Reference graph

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