IV validity, violations, and sensitivity analysis

The paper identifies average treatment effect bounds derived from instrumental variable restrictions as a leading example of intersection bounds addressed by their methodology.

“Examples include average treatment effect bounds from instrumental variable restrictions […], bounds on the distribution of treatment effects in a randomized experiment […], treatment effect bounds from nonparametric selection equations with exclusion restrictions […], monotone instrumental variables and the returns to schooling […]”◌ not checked against the paper’s text as it now stands

The paper contrasts its nonparametric approach with AS's method that transforms conditional restrictions into unconditional ones using instrument functions.

“Whereas we treat the problem with fundamentally nonparametric methods, AS provide inferential statistics that transform the model's conditional restrictions to unconditional ones through the use of instrument functions.”◌ not checked against the paper’s text as it now stands

The paper notes that its method is applicable to instrumental variable (IV) and monotone instrumental variable (MIV) bounds even when covariates are continuously distributed, similar to recent work by other authors.

“with the exception of the recent work by […] in the context instrumental variable (IV) and monotone instrumental variable (MIV) bounds, and that of […], which extends methods developed in AS to this case.”◌ not checked against the paper’s text as it now stands

The paper defines instrumental variable validity formally using potential outcomes and a parameter π* that captures violations of the exclusion restriction and no-confounding assumptions.

“We say that instrument j = 1,…,L is valid if π_j^* = 0 and invalid if π_j^* ≠ 0.”◌ not checked against the paper’s text as it now stands

It proposes a general confidence interval construction method for causal effects that is robust to some instrumental variables being invalid, without knowing which ones a priori.

“We propose a simple and general confidence interval procedure that theoretically guarantees the correct coverage rate in the presence of invalid instruments and can easily be used with traditional instrumental variables methods.”◌ not checked against the paper’s text as it now stands

The paper proves that its confidence interval, formed by taking unions over subsets of instruments, maintains correct coverage even when instrumental variable assumptions are violated.

“Suppose model […] holds and s < U. Given α, consider any test statistic T(β_0,B) with the property that for any B^* ⊆ B, T(β_0,B) has size at most α under the null hypothesis H_0: β^* = β_0. Then, C_1 - α(Y,D,Z) in […] always has at least 1 - α coverage even with invalid instruments.”◌ not checked against the paper’s text as it now stands

The paper proposes a new statistical test (NPS test) that combines existing necessary tests with a novel Bayesian marginal likelihood comparison to probabilistically assess the validity of an instrumental variable from observed data.

“Combining the above approach with necessary tests proposed in past work leads to a Necessary and Probably Sufficient (NPS) test for instrumental variables.”◌ not checked against the paper’s text as it now stands

It formalizes valid and invalid instrumental variable causal models as classes of Bayesian generative models and computes the ratio of their marginal likelihoods given observed data to judge instrument validity.

“Specifically, let Valid-IV refer to the class of all causal models that yield a valid instrument and Invalid-IV to the class of causal models that yield an invalid instrument. Given an observed data distribution P(X, Y, Z), the proposed method computes the ratio of marginal likelihoods for Valid-IV and Invalid-IV models.”◌ not checked against the paper’s text as it now stands

The paper extends Bonet's necessary test for instrumental variables by incorporating the monotonicity assumption and provides a practical, efficient implementation for discrete variables with arbitrary numbers of levels.

“In this paper, therefore, we extend Bonet's work by incorporating monotonicity and present a practical method for testing IVs when variables can have arbitrary number of discrete levels.”

The paper addresses conditional moment restriction models where instrumental variables serve as conditioning instruments and some may be weak or irrelevant, without requiring prior knowledge of which ones are weak.

“We introduce a novel inference method without any prior information about which conditioning instruments are weak or irrelevant.”◌ not checked against the paper’s text as it now stands

The paper contrasts its approach with earlier work that extended Bierens' test to parametric IV regression settings with nonparametric IV alternatives.

“[…] is perhaps the first to extend […]'s integrated conditional moment (ICM) statistic to test a null of a parametric IV regression E[Y-f(X,θ_0)|W]=0 (with X≠ W) against a nonparametric IV regression alternative.”◌ not checked against the paper’s text as it now stands

The paper applies its method to an empirical example estimating the elasticity of intertemporal substitution, showing that an uninformative confidence interval based on unconditional instruments becomes informative using conditional instrumental variables.

“First, as our main example, we revisit […] and find that an uninformative confidence interval (resulting from unconditional moment restrictions) for the elasticity of intertemporal substitution, based on annual US series (n ≈ 100 and p = 4), can turn into an informative one.”◌ not checked against the paper’s text as it now stands

The paper treats the IV exclusion restriction as a belief that can be violated and studies how much instrument invalidity is compatible with data and other beliefs.

“The instrumental variables exclusion restriction, for example, represents the belief that the instrument has no direct effect on the outcome of interest.”◌ not checked against the paper’s text as it now stands

It derives the sharp identified set jointly characterizing instrument invalidity, treatment endogeneity, and measurement error in a linear IV model.

“we first characterize the joint restrictions relating instrument invalidity, treatment endogeneity, and non-differential measurement error in a workhorse linear model, showing how beliefs over these three dimensions are mutually constrained by each other and the data.”◌ not checked against the paper’s text as it now stands

The paper formalizes the instrument relevance and validity conditions (correlation with treatment and exogeneity) as explicit assumptions in its model.

“z is relevant for T^*: π≠ 0;”◌ not checked against the paper’s text as it now stands

It shows that even with a potentially invalid instrument, the framework can still be used to conduct Bayesian partial identification inference for the treatment effect by allowing correlation between the instrument and the structural error.

The paper's automatic robustness metric (Approximate Maximum Influence Perturbation) is designed to be automatically computable for Instrumental Variables (IV) estimators, among others.

“Our metric, the “Approximate Maximum Influence Perturbation,” is based on the classical influence function, and is automatically computable for common methods including (but not limited to) OLS, IV, MLE, GMM, and variational Bayes.”◌ not checked against the paper’s text as it now stands

The authors explicitly list IV as one of the common estimators for which their fast approximation to the Maximum Influence Perturbation works.

“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).”◌ not checked against the paper’s text as it now stands

The paper notes that exactly identified IV regression is a Z-estimator that does not optimize any objective function, showing the Z-estimator framework used for their method is more general than M-estimation and covers IV.

“However, some Z-estimators, such as exactly identified IV regression or GMM, do not optimize any particular empirical objective function, so the notion of Z-estimator is in fact more general than that of an M-estimator.”

The paper formally develops a two-stage instrumental variable estimation procedure generalizing 2SLS to handle spatial confounding and spatially-correlated errors.

“We use a 2-stage estimation procedure which generalizes the 2-stage least squares (2SLS) of […] and […].”◌ not checked against the paper’s text as it now stands

The paper establishes an identification result showing that a valid instrumental variable independent of the confounder and error terms recovers the true causal treatment effect despite unmeasured spatial confounding.

“This section establishes that with a valid instrument Z, we can recover the true treatment effect δ_1 even when A and Y are confounded by an unmeasured confounder U.”◌ not checked against the paper’s text as it now stands

The paper conducts extensive simulations comparing local (non-spatial) versus spatially-dependent instrumental variables and finds that local IVs generally reduce bias and variance more effectively than spatial IVs when the instrument is valid.

“We find that local instrumental variables tend to provide more information with which to remove confounding bias, than those with spatial dependence. This suggests that local instruments are more effective at reducing confounding and isolating causal effects of treatment.”◌ not checked against the paper’s text as it now stands

The paper conducted simulation studies comparing estimation procedures under IV identification, examining mean bias and standard deviation of estimators.

“[…] plot the mean bias and standard deviation of the estimation procedures in the case of IV identification. The relative ranking of the various estimation procedures is essentially the same as in the median bias and interquartile range plots presented in our main analysis in […].”◌ not checked against the paper’s text as it now stands

The paper showed that SVAR-IV median bias is particularly elevated when the degree of invertibility is small, confirming theoretical predictions.

“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.”◌ not checked against the paper’s text as it now stands

The paper examined median bias of estimation procedures for IV identification across DGPs with the smallest and largest degrees of invertibility.

“[…] show the median bias of our estimation procedures, but now for the 10 percent of DGPs with the smallest and largest degrees of invertibility, respectively.”◌ not checked against the paper’s text as it now stands

The paper identifies invoking an instrumental variable assumption for survey selection as an existing method to point-identify treatment effects on 'always buyers' in the literature.

“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.”◌ not checked against the paper’s text as it now stands

The paper explicitly contrasts its own identification strategy with prior instrumental-variable-based approaches, noting that it does not rely on an instrumental variable assumption but instead exploits a unique survey feature.

“In contrast to these previous studies, the approach in this paper point-identifies the treatment effect by exploiting the rather unique survey feature that customers were asked about their behavior in the absence of the discount, which under monotonicity permits identifying the principal stratum of always buyers directly in the data.”◌ not checked against the paper’s text as it now stands

The paper shows that pre-treatment outcomes act like proxy/regressor variables that are endogenous due to shared error components, motivating the need for an instrument-like solution.

“This is analogous to the well-known problem of error-in-variable regressions, where using proxy variables in place of unobserved true variables as regressors leads to coefficient estimates with nonvanishing bias […].”◌ not checked against the paper’s text as it now stands

The paper resolves the endogeneity problem by using post-treatment outcomes as moment conditions to identify the bridge function parameters, functioning analogously to instrumental variables.

“Although bridge functions are defined in terms of unmeasured confounders, we can learn them by using moment equations based on post-treatment observations under an additional serial independence assumption and use them to learn average causal effects.”◌ not checked against the paper’s text as it now stands

The paper connects its bridge function approach, which relies on instrument-like post-treatment variables, to the negative control framework in the causal inference literature.

“connect this paper to the negative control framework proposed in recent literature […].”◌ not checked against the paper’s text as it now stands

The paper uses variation in county-level prescription practices across 21 Swedish county councils as an instrumental variable for treatment choice between abiraterone acetate and enzalutamide.

“The design explicitly make use of differences in prescription practices across 21 Swedish county councils for the estimation of the two drugs comparative effectiveness on overall mortality, pain and skeleton related events.”◌ not checked against the paper’s text as it now stands

The paper formally states the two core instrumental variable assumptions of relevance and exclusion required for the county factor to serve as a valid IV.

“The design requires that the county factor: (1) affects the probability to be treated (i.e. being prescribed abiraterone acetate instead of enzalutamide) but (2) is not otherwise correlated with the outcome.”◌ not checked against the paper’s text as it now stands

The paper empirically validates the relevance assumption of the instrument by showing the county factor significantly predicts treatment assignment via a first-stage probit regression with a strong F-statistic.

“An overall test of relevance of the county factor is displayed in Table […]. The F-statistic is 16.22 with a p-value close to zero. In traditional IV analysis the rule of thumb for the relevance of IV is that the F-statistic should be above 10, […].”◌ not checked against the paper’s text as it now stands

The paper shows that with micro data, valid instruments are only needed for prices rather than for all prices and quantities as required with market-level data.

“With market-level data, nonparametric identification typically requires instruments for all quantities and prices […]. With micro data, we find that the only essential instruments are those for prices.”◌ not checked against the paper’s text as it now stands

The paper demonstrates that using micro data cuts the number of required instruments in half and avoids reliance on BLP-type instruments (characteristics of competing products).

“This cuts the number of required instruments in half and avoids the necessary reliance on so-called “BLP instruments” (characteristics of competing products).”◌ not checked against the paper’s text as it now stands

The paper shows that demand elasticities can sometimes be identified using price instruments even when non-price product characteristics are endogenous and unistrumented, provided the price instruments remain valid conditional on those characteristics.

“This requires that instruments for prices remain valid when conditioning on the endogenous observed product characteristics, and we illustrate through simple causal graphs how different cases do or do not satisfy this requirement.”◌ not checked against the paper’s text as it now stands

The paper uses the commodity price of barley as an instrumental variable for beer price to address endogenous variation in prices and quantity.

“A popular instrument in the estimation of beer demand is the commodity price for barley, one of the product's main ingredients, see e.g. […].”◌ not checked against the paper’s text as it now stands

The paper reports IV estimates of the demand elasticity and notes they are negative but imprecise due to the instrument only varying over time.

“IV estimates show demand is strongly negatively elastic (-3.39), however, estimates are very imprecise. This could be because the instrument only varies over one dimension, time, or, e.g., because prices of other inputs are also highly variable so the instrument does not explain much price variation.”◌ not checked against the paper’s text as it now stands

The paper diagnoses the weakness of the barley instrument by examining its correlation with beer price at different levels of aggregation, finding it is highly correlated only when beer price is aggregated to the monthly level.

“In this dataset, correlation between the price of barley, which varies over only month, every second t, and price of beer depends on how beer price is first aggregated. If beer price is first integrated over i, j, and to the monthly level, such that it only varies over every second t, then it is highly correlated with the price of barley, at 0.79. However, if beer price is not aggregated at all it is only correlated at 0.001.”◌ not checked against the paper’s text as it now stands

The paper proposes a novel instrumental variable that uses ALMP policy mix implemented in areas outside a local labour market but within overlapping employment agencies.

“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.”◌ not checked against the paper’s text as it now stands

The paper argues this instrument addresses the simultaneity problem between ALMP and labour market outcomes at the regional level.

“We propose a novel identification strategy to overcome the simultaneity of ALMP and labour market outcomes at the regional level.”◌ not checked against the paper’s text as it now stands

The paper contrasts its instrumental variable approach with prior weaker attempts such as lagged policy variables used as instruments, claiming its instruments are less endogenous.

“Previous attempts to mitigate the simultaneity problem use transformations of policy variables such as ratios […], lagged policy variables […], or lagged measures as instrumental variables […].”◌ not checked against the paper’s text as it now stands

The paper states that its instruments rely on imperfect overlap between local labour markets and administrative regions, making them less likely to be endogenous compared to alternatives.

The paper distinguishes two distinct reasons an instrumental variable can be invalid—acting as a confounder (violating exclusion) or as a collider (violating exogeneity)—showing this distinction matters for identification results built on instruments.

“An invalid instrument may act as a confounder, violating the exclusion restriction through a direct effect on the outcome, or as a collider, when the instrument instead is influenced by the error term.”◌ not checked against the paper’s text as it now stands

The paper shows that having at least one valid and relevant instrumental variable is necessary but treatment of the other invalid instruments must match their true violation type for the falsification adaptive set to be guaranteed to contain the true treatment effect.

“we show that if there is a valid and relevant IV, the FAS is guaranteed to contain the true treatment effect parameter β only if the invalid IVs are treated according to their true violation type.”◌ not checked against the paper’s text as it now stands

The paper derives a generalized falsification adaptive set as the union of pattern-specific sets across combinations of instrumental variable violations, guaranteeing inclusion of β if at least one instrument is valid and relevant, without needing to specify each instrument's violation type in advance.

“Second, we derive a pattern-specific FAS for each possible combination of exclusion and exogeneity violations across instruments, and propose the generalized FAS as their union. If at least one instrument is valid and relevant, the generalized FAS is guaranteed to contain β without requiring the researcher to specify the violation type of each instrument ex ante.”

The survey notes that instrumental variables are one of several shock-based designs used in prior causal inference research in finance and accounting to address selection bias.

“To handle these issues, various shock-based designs such as difference in differences (DiD), event studies (ES), instrumental variables (IV) etc., were proposed handling the selection bias.”◌ not checked against the paper’s text as it now stands

The survey classifies instrumental variables as one of the fundamental causation concepts, distinguishing it from mere associational notions.

“Causation fundamentals include randomization, impact, effect, confounding, “holding constant,” disturbance, error terms, structural coefficients, spurious correlation, faithfulness/stability, instrumental variables, intervention, explanation, and attribution (Pearl, 2010).”◌ not checked against the paper’s text as it now stands

The paper used the term 'instrumental variables' as one of the keywords/approaches to filter and identify relevant causal inference articles for inclusion in the survey.

The paper uses all exogenous variables as instrumental variables in the first stage of its two-stage variational Bayesian algorithm to compute predicted values of the dependent variable for each unit.

The paper explicitly frames its two-stage procedure as analogous to two-stage least squares, where predicted values from instrumented endogenous variables are substituted into the second-stage equation.

“In essence, those two stages are similar to the two-stage least squares (2LSL) in which the parameters can be estimated equation by equation.”◌ not checked against the paper’s text as it now stands

The paper lists 'Instrumental Variables' as one of its keywords, signaling the centrality of this technique to the proposed method.

“Keywords: Panel Spatial Autoregressive Models, Unrestricted Weighting Matrix, Instrumental Variables, Variational Bayes, Large Data”◌ not checked against the paper’s text as it now stands

The paper implements the instrumental-variable-based algorithm as a formal two-stage procedure, running the first stage in parallel across units to predict endogenous spatial variables before estimating each row of the spatial weights matrix in the second stage.

The paper proposes a new categorical instrumental variable (CIV) estimator designed for settings with a large number of categorical instruments and few observations per category.

“This paper proposes a new optimal instrumental variable estimator for settings with a large number of categorical instruments.”◌ not checked against the paper’s text as it now stands

It shows that when the number of support points of the optimal instrument is known, CIV achieves the same asymptotic variance as the oracle IV estimator and is semiparametrically efficient under homoskedasticity.

“In asymptotic regimes that allow the number of observations per category to grow at arbitrary small polynomial rate with the sample size, I show that when the cardinality of the support of the optimal instrument is known, CIV is root-n asymptotically normal, achieves the same asymptotic variance as the oracle IV estimator that presumes knowledge of the optimal instrument, and is semiparametrically efficient under homoskedasticity.”◌ not checked against the paper’s text as it now stands

The paper demonstrates that under-specifying the number of support points of the instrument reduces efficiency but still preserves asymptotic normality.

“Under-specifying the number of support points reduces efficiency but maintains asymptotic normality.”◌ not checked against the paper’s text as it now stands

The paper introduces instrumental variable analysis as a novel causal inference method in the sabermetrics literature to study the infield shift.

“In particular, we use an instrumental variables analysis, a method which, to the best of our knowledge, is novel to sabermetrics.”◌ not checked against the paper’s text as it now stands

The paper selects the fielding team's season-to-date propensity to shift as the instrumental variable, reasoning that it affects the outcome only through treatment and is not tied to team success.

“The fielding team's propensity for shifting was considered as an instrument, as teams with high shift rates are not necessarily the most winning teams (this choice is discussed in more detail in Section […]).”◌ not checked against the paper’s text as it now stands

The paper contrasts IV methods with balancing methods, noting that IV methods allow for unmeasured confounding while requiring assumptions about instrument validity.

“We employed two approaches to estimate the ETT: balancing methods and instrumental variable (IV) methods. Balancing methods seek to adjust for measured confounding, whereas IV methods control for unmeasured confounding.”◌ not checked against the paper’s text as it now stands

The paper applies the instrumental variable method alongside matching and IPTW to estimate the causal effect of the shift on run expectancy, separately for batter-handedness subgroups.

The paper contrasts its analytic bias correction with existing instrumental variable approaches that use further lags of outcomes as instruments.

“The exact bias correction approach has some appealing characteristics in comparison to alternative corrections, which are based on instrumental variables […]. The instrumental variable methods are based on using further outcome lags as instruments for outcome lags.”◌ not checked against the paper’s text as it now stands

It argues that instrumental variable methods suffer from unclear instrument choice and weak instrument problems.

“The correct choice of instrument is often unclear and can lead to problems caused by weak instruments.[Problems caused by weak instruments are discussed by […].]”◌ not checked against the paper’s text as it now stands

The paper shows via simulation that its analytical solution yields smaller standard errors than instrumental variable methods while maintaining proper coverage.

“In simulations, I find that my analytical solution keeps standard errors as small as the original linear regressions and maintains proper coverage, as compared to instrumental variable methods which lead to larger standard errors.”◌ not checked against the paper’s text as it now stands

The paper reviews the instrumental variables literature (Arellano-Bond and related) as one of two main approaches for dealing with Nickell bias in fixed-T settings, noting its sensitivity to instrument choice and vulnerability to weak instruments with many time periods.