# IV with heterogeneous treatment effects and causal mechanisms

> One thread of 6 from the "instrumental variable" map, covering the 12 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: High-dimensional and sparse IV methods, Nonparametric and semiparametric IV models.

This line extends IV beyond homogeneous treatment effects to estimate heterogeneous impacts, local average treatment effects, and treatment effect heterogeneity using Bayesian methods and causal forests. It addresses compliance variability, nonseparability, and personalized treatment allocation, incorporating machine learning for flexible effect estimation.


**Instrumental Variable Bayesian Model Averaging via Conditional Bayes Factors** (2012) \cite{karl2012instrumental}

> “We consider the problem of incorporating instrument and covariate uncertainty into the Bayesian estimation of an instrumental variable (IV) regression system.”
>
> ✓ verified: found word for word in the paper's own text


**Instrumental Variables Estimation of a Generalized Correlated Random Coefficients Model** (2013) \cite{masten2013instrumental}

What it did: Extended IV identification to discrete instruments in random coefficients  *(the tool's reading)*

Built on classical IV methods by allowing binary or discrete instrumental variables in correlated random coefficients models, relaxing prior requirements for continuous instruments and enabling identification of average treatment effects.  *(the tool's reading)*

> “Concerns about endogeneity are widespread in economic applications and are often addressed by using the variation of an instrumental variable, Z, that is plausibly independent (or uncorrelated) with (B_0, B_1), but correlated with X.”
>
> ✓ verified: found word for word in the paper's own text


**Instrumental Variable Estimation When Compliance is not Deterministic: The Stochastic Monotonicity Assumption** (2014) \cite{small2014instrumental}

What it did: Relaxed monotonicity assumption from deterministic to stochastic form  *(the tool's reading)*

Introduced stochastic monotonicity as a weaker condition than deterministic monotonicity, requiring only that the monotonic relationship hold across subjects within strata rather than universally.  *(the tool's reading)*

> “The instrumental variables (IV) method is a method for making causal inferences about the effect of a treatment based on an observational study in which there are unmeasured confounding variables. The method requires a valid IV, a variable that is independent of the unmeasured confounding variables and is associated with the treatment but which has no effect on the outcome beyond its effect on the treatment.”
>
> ✓ verified: found word for word in the paper's own text


**Sharp Bounds and Testability of a Roy Model of STEM Major Choices** (2017) \cite{mourifie2017sharp}

What it did: Applied stochastically monotone IVs to Roy selection models  *(the tool's reading)*

Extended stochastically monotone instrumental variables to Roy models of occupational choice, using selection shifters that affect potential outcomes monotonically rather than requiring full independence.  *(the tool's reading)*

> “There exists a vector Z of observable random variables, such that (Y_0,Y_1)⊥⊥ Z. Such variables are akin to typical instrumental variables, and examples within Roy models in the existing literature include parental education in […], distance to a college in […] and attendance in a Catholic high school in […].”
>
> ✓ verified: found word for word in the paper's own text


**Instrumental variables estimation with competing risk data** (2018) \cite{martinussen2018instrumental}

> “This is a variable which is (a) associated with the exposure, (b) has no direct effect on the outcome other than through the exposure, and (c) whose association with the outcome is not confounded by unmeasured variables (see e.g. Hernán and Robins, 2006).”
>
> ✓ verified: found word for word in the paper's own text


**Heterogeneous causal effects with imperfect compliance: a Bayesian machine learning approach** (2019) \cite{bargaglistoffi2019heterogeneous}

What it did: Combined IV with Bayesian machine learning for heterogeneous effects  *(the tool's reading)*

Developed BCF-IV algorithm integrating instrumental variables with Bayesian Causal Forests to discover and estimate heterogeneous causal effects under imperfect compliance.  *(the tool's reading)*

> “In these cases, researchers can make use of a secondary treatment or instrument (i.e., being eligible for additional funding) to isolate the causal effects of the primary treatment (i.e., actually receiving the funding) on the outcome of interest.”
>
> ✓ verified: found word for word in the paper's own text


**A Correlated Random Coefficient panel model with time-varying endogeneity** (2020) \cite{laage2020correlated}

What it did: Generalized control function IV for random coefficients without joint restrictions  *(the tool's reading)*

Extended control function IV approach to allow random coefficients without restricting the joint distribution of instruments and coefficients, broadening the applicability of IV-based control variable methods.  *(the tool's reading)*

> “To identify structural parameters of models with endogenous regressors, two well-known approaches are the instrumental variable approach and the control function approach.”
>
> ✓ verified: found word for word in the paper's own text


**Identification of Incomplete Preferences** (2021) \cite{rigotti2021identification}

> “We define an instrument as a random variable that is independent of preferences but correlated with choice; in particular, the fraction of individuals who choose an alternative changes for each realization of the instrument while preference characteristics do not.”
>
> ✓ verified: found word for word in the paper's own text


**Difference-in-Differences Estimators for Treatments Continuously Distributed at Every Period** (2022) \cite{dechaisemartin2022difference}

What it did: Applied IV framework to continuous-treatment difference-in-differences  *(the tool's reading)*

Adapted instrumental variable logic to difference-in-differences with endogenous continuous treatments by imposing parallel-trends assumptions on the instrument rather than the treatment.  *(the tool's reading)*

> “First, we consider an instrumental-variable (IV) setting in which the parallel-trends assumption is made with respect to an instrument rather than the treatment. For instance, when estimating the price elasticity of demand, prices may respond to demand shocks, violating parallel trends; taxes can instead serve as an instrument.”
>
> ✓ verified: found word for word in the paper's own text


**RobustIV and controlfunctionIV: Causal Inference for Linear and Nonlinear Models with Invalid Instrumental Variables** (2023) \cite{koo2023robustiv}

What it did: Developed robust inference for possibly invalid instrumental variables  *(the tool's reading)*

Created software packages implementing robust causal inference methods that accommodate possibly invalid instrumental variables in both linear and nonlinear models.  *(the tool's reading)*

> “The validity of IV methods relies on that the constructed IVs satisfy the following three assumptions simultaneously […]: conditioning the measured covariates, (A1) the IVs are associated with the treatment; (A2) the IVs are independent with the unmeasured confounders; (A3) the IVs have no direct effect on the outcome.”
>
> ✓ verified: found word for word in the paper's own text


**Sensitivity Analysis in Unconditional Quantile Effects** (2023) \cite{martineziriarte2023sensitivity}

> “Identification relies on the a separable threshold model for the selection equation, and the availability of a continuous instrumental variable. In this setting, the proportion of treated individuals is changed by manipulating the instrumental variable. Our analysis does not make any assumptions on the selection equation. We do not require an instrumental variable either.”
>
> ✓ verified: found word for word in the paper's own text


**IV Regressions without Exclusion Restrictions** (2023) \cite{gao2023regressions}

> “where the instrumental variable Z_i, exc is required to be exogenous with respect to ϵ_i, relevant for X_i, and excluded from the regression model […].”
>
> ✓ 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.

- **High-dimensional and sparse IV methods** → **IV with heterogeneous treatment effects and causal mechanisms** (2019): Machine learning heterogeneous effects
- **Nonparametric and semiparametric IV models** → **IV with heterogeneous treatment effects and causal mechanisms** (2018): Semiparametric structural models