# IV validity, violations, and sensitivity analysis

> One thread of 6 from the "instrumental variable" map, covering the 21 papers in it. The other threads are not represented here.
>
> Every quotation was copied word for word from the paper's own text, and
> checked against that text. Quotes marked *inferred* failed that check and
> must be re-checked before use. Quotes marked *not re-checked* have not been
> matched against the paper's text as it now stands, so they carry no current
> verification either. Lines labelled *the tool's reading* are
> model judgment, not quotation, and carry no verification.
>
> **This is a scaffold, not prose.** The citations, quotes and structure are
> real; the argument is yours to write.

> Connects to: Classical IV foundations and refinement, Specialized IV applications and domain extensions.

Emerging work on necessary and possibly sufficient tests for instrument validity, sensitivity to invalid/weak instruments, and bounds under partial violations of exclusion restrictions. This line develops methods that relax deterministic monotonicity, accommodate possibly correlated instruments, and quantify inference robustness when assumptions fail.


**Intersection Bounds: Estimation and Inference** (2009) \cite{chernozhukov2009intersection}

What it did: Reformulated IV validity as intersection bounds problem  *(the tool's reading)*

Treated instrumental variables as exclusion and monotonicity restrictions on auxiliary variables, showing that IV validity constraints could be formulated within the intersection bounds framework rather than as isolated assumptions.  *(the tool's reading)*

> “If V is an instrument satisfying E[ Y( t) |X,V] =E [ Y( t) |X], then for any fixed x, bounds on θ^∗:= θ^∗(x):= E[ Y( t) |X=x] are given by sup_v∈𝒱θ ^l(x,v) ≤θ^∗(x) ≤inf_v∈𝒱θ ^u(x,v),”
>
> ✓ verified: found word for word in the paper's own text


**Robust inference on average treatment effects with possibly more covariates than observations** (2013) \cite{farrell2013robust}

> “Second, the covariates may, in general, include instruments for treatment status, but they are not known as such. This is standard, but left implicit, in discussions of ignorability. If instruments are present, and selected for estimation, efficiency suffers but unbiasedness is not harmed. Efficiency bounds in this context typically (implicitly) assume there are no instruments in X.”
>
> ✓ verified: found word for word in the paper's own text


**A simple and robust confidence interval for causal effects with possibly invalid instruments** (2015) \cite{kang2015simple}

What it did: Formalized three-part validity definition with confidence intervals  *(the tool's reading)*

Explicitly defined IV validity through three assumptions (relevance, exclusion restriction, exogeneity) within linear structural models, then developed methods for confidence intervals when candidate instruments may violate these assumptions.  *(the tool's reading)*

> “Informally speaking, the method relies on having instruments that are (A1) related to the exposure, (A2) only affect the outcome by affecting the exposure (no direct effect), and (A3) are not related to unmeasured confounders that affect the exposure and the outcome (see Section […] for details).”
>
> ✓ verified: found word for word in the paper's own text


**Necessary and Probably Sufficient Test for Finding Valid Instrumental Variables** (2018) \cite{sharma2018necessary}

What it did: Proposed testable necessity and sufficiency conditions  *(the tool's reading)*

Combined Pearl-Bonet necessary tests with Bayesian marginal-likelihood comparison to assess whether instruments satisfy both necessary and probable sufficiency conditions for validity.  *(the tool's reading)*

> “To be a valid instrument, however, Z should satisfy three conditions […]. First, Z should have a substantial effect on X. That is, Z causes X (Relevance). Second, Z should not cause Y directly (Exclusion); the only association between Z and Y should be through X. Third, Z should be independent of all the common causes U of X and Y (As-if-random).”
>
> ✓ verified: found word for word in the paper's own text


**Inference for parameters identified by conditional moment restrictions using a generalized Bierens maximum statistic** (2020) \cite{chen2020inference}

> “This happens when the set of instrumental variables W contains redundant elements.”
>
> ✓ verified: found word for word in the paper's own text


**A Framework for Eliciting, Incorporating, and Disciplining Identification Beliefs in Linear Models** (2020) \cite{ditraglia2020framework}

What it did: Extended validity analysis to allow partially invalid instruments  *(the tool's reading)*

Derived partial identification results for settings where the standard exclusion restriction may be invalid, allowing measurement error and treatment endogeneity to coexist with invalid instruments.  *(the tool's reading)*

> “The instrumental variables exclusion restriction, for example, represents the belief that the instrument has no direct effect on the outcome of interest.”
>
> ✓ verified: found word for word in the paper's own text


**An Automatic Finite-Sample Robustness Metric: When Can Dropping a Little\n Data Make a Big Difference?** (2020) \cite{broderick2020automatic}

What it did: Introduced finite-sample sensitivity metric for violation assessment  *(the tool's reading)*

Developed an automatically-computable, finite-sample sensitivity metric (AMIP) applicable to IV and other Z-estimators, quantifying robustness to assumption violations without prior knowledge of violation magnitude.  *(the tool's reading)*

> “We propose a fast approximation that works for common estimators—including Generalized Methods of Moments (GMM), Ordinary Least Squares (OLS), Instrumental Variables (IV), Maximum Likelihood Estimators (MLE), Variational Bayes (VB), and all minimizers of smooth empirical loss (AMIP).”
>
> ✓ verified: found word for word in the paper's own text


**Instrumental variables, spatial confounding and interference** (2021) \cite{giffin2021instrumental}

What it did: Examined IV validity under spatial confounding structures  *(the tool's reading)*

Analyzed how IV validity assumptions perform specifically under unobserved spatial confounding, considering the spatial scale of instruments relative to treatment assignment.  *(the tool's reading)*

> “Z is independent of ϵ_1, ϵ_2, and U.”
>
> ✓ verified: found word for word in the paper's own text


**Local Projections vs. VARs: Lessons From Thousands of DGPs** (2021) \cite{li2021local}

> “As expected, the median bias for SVAR-IV is particularly elevated relative to other estimation methods if the degree of invertibility is small, as predicted by theory.”
>
> ✓ verified: found word for word in the paper's own text


**Business analytics meets artificial intelligence: Assessing the demand effects of discounts on Swiss train tickets** (2021) \cite{huber2021business}

> “Alternatively, the treatment effect on always buyers is point-identified when invoking a selection-on-observables or instrumental variable assumption for selection into the survey, see for instance […], which requires sufficiently rich data on both survey participants and non-participants for modeling survey participation.”
>
> ✓ verified: found word for word in the paper's own text


**Controlling for Unmeasured Confounding in Panel Data Using Minimal Bridge Functions: From Two-Way Fixed Effects to Factor Models** (2021) \cite{imbens2021controlling}

> “Although this moment equation looks very similar to moment equations in instrumental variable estimation […], it is based on substantially different assumptions. Actually, post-treatment outcomes Y_𝚙𝚘𝚜𝚝 must not be valid instrumental variables, since below they are assumed to be strongly dependent with the unmeasured confounders.”
>
> ✓ verified: found word for word in the paper's own text


**A Study Protocol for an Instrumental Variables Analysis of the\n Comparative Effectiveness of two Prostate Cancer Drugs** (2021) \cite{johansson2021study}

> “The design is known as an Instrumental Variables (IV) design, where the county factor is the IV. It can be seen as a `natural experiment', that is we have IV that: (1) affect the probability of treatment (i.e. AA or ENZ) at the individual level, but (2) is not otherwise correlated with the outcome.”
>
> ✓ verified: found word for word in the paper's own text


**Nonparametric Identification of Differentiated Products Demand Using Micro Data** (2022) \cite{berry2022nonparametric}

> “such as that arising through instrumental variables, geographic boundaries, or repeated observations within a single economic unit.”
>
> ✓ verified: found word for word in the paper's own text


**Linear Multidimensional Regression with Interactive Fixed-Effects** (2022) \cite{freeman2022linear}

> “The classic instrumental variable approach is to find a supply shifter that shifts the supply curve, allowing the econometrician to trace out the slope of the demand curve.”
>
> ✓ verified: found word for word in the paper's own text


**Macroeconomic Effects of Active Labour Market Policies: A Novel Instrumental Variables Approach** (2022) \cite{unterhofer2022macroeconomic}

> “Specifically, we instrument for the use of ALMP in a local labour market with the mix of ALMP implemented outside this market but in local employment agencies that partially overlap with this market.”
>
> ✓ verified: found word for word in the paper's own text


**The Generalized Falsification Adaptive Set for Violations of the Exclusion Restriction and Exogeneity** (2022) \cite{apfel2022generalized}

What it did: Distinguished confounder versus collider effects on validity assessment  *(the tool's reading)*

Showed that invalid instruments behave differently depending on whether they function as confounders or colliders, with important consequences for falsification-based validity testing approaches.  *(the tool's reading)*

> “Instrumental variables (IVs) are widely used in economics to estimate treatment effects. The key identifying assumptions are that the instruments affect the outcome only through the treatment (the exclusion restriction) and that they are uncorrelated with unobserved determinants of the outcome (exogeneity).”
>
> ✓ verified: found word for word in the paper's own text


**Causal Inference for Banking Finance and Insurance A Survey** (2023) \cite{kumar2023causal}

> “Instrument variable (IV) is used to identify the causal effect of X on Y. It satisfies conditions of independence from X and Y when controlled variables S are considered. This concept originates from econometrics and was initially employed to identify parameters in simultaneous equation models. By adjusting for the control variables, we can estimate the probabilities P (Y | do (I = i)) and P (X | do (I = i)) by using Eq. 8. The instrumental variable approach is useful in tracing the causal influence of I on Y through X (Pearl, 2009).”
>
> ✓ verified: found word for word in the paper's own text


**Identifying spatial interdependence in panel data with large N and small T** (2023) \cite{gefang2023identifying}

> “First, using all the exogenous (or predetermined) tx as instrumental variables to calculate the predicted values of nt y for 1,..., ; n N = Second, estimating the equation where ity is the dependent variable, by substituting jt y s, for {1,..., j N and j i , on the right-hand-side of the equation, by their predicted values derived in the first stage.”
>
> *(inferred: the check ran against the paper's text and could not find this passage, so re-check it before citing)*


**Optimal Categorical Instrumental Variables** (2023) \cite{wiemann2023optimal}

> “This paper discusses estimation with a categorical instrumental variable in settings with potentially few observations per category.”
>
> ✓ verified: found word for word in the paper's own text


**Causal effect of the infield shift in the MLB** (2024) \cite{markes2024causal}

> “Confounders are variables that affect both treatment and outcome, whereas instruments only affect the outcome through the treatment and are assumed to be independent of unmeasured confounding variables.”
>
> ✓ verified: found word for word in the paper's own text


**Dynamic Biases of Static Panel Data Estimators** (2024) \cite{klosin2024dynamic}

> “The instrumental variable methods are based on using further outcome lags as instruments for outcome lags. The correct choice of instrument is often unclear and can lead to problems caused by weak instruments.”
>
> ✓ verified: found word for word in the paper's own text


_[Your synthesis: what it enabled, what it left unsolved.]_


## Where this thread connects

Each crossing is where one line of work fed another. These are the tool's reading of
the corpus, not quotations.

- **Classical IV foundations and refinement** → **IV validity, violations, and sensitivity analysis** (2018): Testing instrument validity
- **IV validity, violations, and sensitivity analysis** → **Specialized IV applications and domain extensions** (2020): Weak instrument robustness