Instrumental Variables
Instrumental Variables (IV) is a causal inference approach used when an explanatory variable is endogenous—that is, when it is associated with factors that also affect the outcome, making an ordinary observed association potentially misleading. IV methods attempt to isolate a source of variation in the treatment or exposure that is sufficiently independent of those confounding influences to support a more credible causal comparison.
An instrumental variable, usually represented as Z, is a variable that changes or predicts the treatment or exposure X but does not affect the outcome Y through another pathway and does not share uncontrolled causes with the outcome. These requirements are commonly expressed through three core assumptions: relevance, independence and exclusion restriction.
The attraction of IV is important: unlike methods that depend on measuring and adjusting for all important treatment-outcome confounders, a valid instrument can sometimes support causal inference despite unmeasured confounding. The price for that advantage is a demanding set of assumptions about the instrument itself. Some of these assumptions cannot generally be verified from the observed data alone.
On this page:
- Instrumental Variables Explained Simply
- What Are Instrumental Variables?
- Why Endogeneity Creates a Problem
- How Instrumental Variables Work
- The Three Core IV Assumptions
- Instrument Relevance and Weak Instruments
- Independence
- Exclusion Restriction
- Two-Stage Least Squares
- What Effect Does IV Estimate?
- Dudovskiy Instrument Validity Assessment Framework
- Application of Instrumental Variables: an Example
- Advantages and Limitations of Instrumental Variables
- Common Mistakes When Using Instrumental Variables
- Instrumental Variables in Business Research
- Instrumental Variables in the Age of AI and Digital Research
- When to Use Instrumental Variables
- Dissertation Example
- Exam Tip
| Question | Instrumental Variables |
|---|---|
| Main methodological problem | Endogeneity and confounding in causal estimation |
| Basic idea | Use variation in treatment generated by a credible instrument |
| Instrument | Z |
| Treatment/exposure | X |
| Outcome | Y |
| Core assumptions | Relevance, independence and exclusion restriction |
| Important advantage | Can sometimes address causal inference despite unmeasured treatment-outcome confounding |
| Major challenge | Finding and defending a genuinely valid instrument |
| Common estimation approach | Two-Stage Least Squares (2SLS) for linear models |
| Major statistical risk | Weak instruments |
| Major conceptual risk | Assuming that correlation between Z and X is sufficient for instrument validity |
Instrumental Variables Explained Simply
Imagine that researchers want to determine whether participation in an optional professional certification programme increases employees’ subsequent earnings. Simply comparing participants with non-participants is problematic because employees decide whether to participate. Ambition, career planning and ability could influence both participation and future earnings.
Suppose, however, that the programme is offered through employers and some offices happen to be located much closer to the training centre than others. Distance may influence the likelihood of participation because employees working nearby find attendance easier. The researchers might therefore consider distance as a potential instrument for programme participation.
The logic would be:
Distance to training centre (Z) → Programme participation (X) → Subsequent earnings (Y)
Distance would be useful as an instrument only if a credible argument could be made for all the necessary assumptions. It must meaningfully influence participation. It must not be systematically related to other causes of subsequent earnings. Most importantly, distance must not affect earnings through another pathway independent of programme participation.
That final requirement immediately shows why finding an instrument is difficult. Offices near the training centre might also be concentrated in major commercial districts where salaries and promotion opportunities are higher. If so, distance could influence earnings through labour-market location rather than exclusively through programme participation, undermining the proposed instrument.
IV therefore does not solve an endogeneity problem merely because researchers find another variable correlated with treatment. The credibility of IV comes from the causal argument supporting the instrument.
What Are Instrumental Variables?
An instrumental variable provides a source of variation in an endogenous treatment or exposure that can, under appropriate assumptions, be used to estimate its causal effect on an outcome. The method has long been associated with econometrics but is now used across a wide range of observational research settings where conventional adjustment for measured confounders may be inadequate.
Consider the following basic causal structure:
Z → X → Y
where:
Z = instrumental variable
X = treatment or endogenous explanatory variable
Y = outcome
The problem becomes more interesting when an unmeasured factor U influences both X and Y:
U → X
U → Y
This creates confounding in the observed relationship between X and Y. IV analysis attempts to use the variation in X associated with Z rather than all observed variation in X. If Z satisfies the necessary assumptions, that variation can provide causal leverage even though U has not been completely observed.
The method therefore differs fundamentally from simply adding another control variable to a regression. The instrument plays a specific causal role. Its validity depends on why it changes treatment, why it should be sufficiently independent of confounding influences, and why it should not affect the outcome through another route.
Why Endogeneity Creates a Problem
Endogeneity occurs when an explanatory variable is correlated with the error term in a regression model. In substantive research terms, this means that the variable whose effect researchers are trying to estimate is related to other influences on the outcome that the model has not adequately separated.
Several processes can create endogeneity. Omitted variables arise when a factor influences both the explanatory variable and the outcome but is absent or inadequately measured. Reverse causality occurs when the presumed outcome also influences the explanatory variable. Measurement error can produce another form of endogeneity. Selection processes and simultaneous relationships can create additional complications.
These problems are particularly important in management research because many organisational decisions are endogenous. Firms choose whether to internationalise, invest in technology, borrow money or appoint particular executives. Employees choose whether to undertake training or change jobs. Customers choose products, channels and subscription plans. The determinants of those choices may also influence the outcomes researchers subsequently observe. Methodological research in management has consequently treated endogeneity as a significant threat to causal claims.
Suppose innovative firms are more likely to adopt an advanced technology and subsequently become more productive. A regression showing higher productivity among adopters cannot by itself establish that adoption caused the difference. Pre-existing innovative capability may influence both adoption and productivity.
Controlling for measured innovation indicators may help, but researchers cannot necessarily observe every relevant aspect of organisational capability. IV offers a different strategy: find variation in technology adoption generated by a variable that meets the requirements for a valid instrument.
How Instrumental Variables Work
The logic of IV can be understood as isolating a particular source of variation in treatment.
Suppose researchers want to estimate:
X → Y
but unobserved confounding creates:
U → X
U → Y
The ordinary relationship between X and Y now combines the causal effect of X with variation associated with U.
A proposed instrument Z introduces another source of variation:
Z → X → Y
For IV reasoning to work, Z should not share the problematic confounding relationship with Y and should not independently cause Y. Researchers can then use the component of variation in X associated with Z to estimate the effect of X on Y.
This explains both the power and fragility of IV. Researchers no longer need to claim that they have measured every cause of both X and Y. Instead, they need to make a different causal argument about Z. If that argument is wrong, the IV estimate can also be wrong—and in some circumstances more biased than estimates obtained using alternative approaches. (PubMed Central (PMC))
The central methodological question is therefore not:
“Is Z correlated with X?”
It is:
“Why should the variation in X associated with Z provide a credible source of causal identification?”
The Three Core IV Assumptions
A proposed instrument is conventionally evaluated against three fundamental requirements.
| Assumption | Core question |
|---|---|
| Relevance | Does Z meaningfully predict or influence X? |
| Independence | Is Z sufficiently independent of uncontrolled causes of Y? |
| Exclusion restriction | Does Z affect Y only through X? |
These assumptions describe different properties and should not be collapsed into a single statistical test. Relevance can be assessed empirically through the relationship between instrument and treatment. Independence and exclusion restriction rely much more heavily on substantive knowledge, research design and causal reasoning, although empirical evidence can sometimes reveal violations or make the assumptions less plausible.
A statistically powerful relationship between Z and X therefore establishes only part of the argument. An instrument can be extremely strong statistically and still be invalid because it directly affects the outcome or is related to another determinant of that outcome.
Instrument Relevance and Weak Instruments
The relevance assumption requires the instrument to be associated with the endogenous treatment or exposure. If changes in Z produce no meaningful variation in X, Z provides little or no leverage for estimating the causal effect of X.
Consider research using eligibility for a government subsidy as an instrument for receiving the subsidy. Eligibility would be relevant if becoming eligible substantially increases the probability of receiving support. If eligibility makes almost no difference to actual receipt, it would provide a weak basis for IV estimation.
Instrument strength matters because weak instruments can produce biased estimates and unreliable statistical inference. Stock and Yogo developed formal approaches for assessing weak instruments based on the consequences for IV bias and hypothesis testing.
The familiar idea that a first-stage F-statistic above 10 automatically establishes an acceptable instrument should therefore be treated cautiously. The value of 10 is a commonly encountered rule of thumb in particular settings rather than a universal validity threshold. Appropriate diagnostics depend on the model, number of instruments, number of endogenous variables and inferential problem.
More fundamentally:
Instrument strength ≠ instrument validity.
A powerful predictor of treatment can still violate independence or exclusion restriction. Researchers therefore should not allow a strong first-stage result to substitute for a causal justification of the proposed instrument.
Independence
The independence assumption requires the proposed instrument not to share uncontrolled causes with the outcome. It is also described in parts of the methodological literature as exchangeability or an absence of confounding in the instrument-outcome relationship.
Suppose geographic proximity to a specialist business-support centre is proposed as an instrument for receiving consultancy support. Proximity may strongly predict programme participation, satisfying relevance. However, firms located close to the centre might also operate in economically stronger regions with better infrastructure, financing and labour markets.
The problem can be represented as:
Regional economic strength → Proximity to centre
Regional economic strength → Firm performance
Proximity would then share a cause with the outcome, weakening the independence argument.
Researchers should consequently investigate the institutional or behavioural mechanism generating the proposed instrument. A variable does not become plausibly independent simply because it appears external to the company, employee or consumer being studied.
Independence is especially demanding because it generally cannot be conclusively verified from the observed data. Researchers can investigate observable differences, conduct falsification exercises and develop evidence against plausible violations, but failure to detect a problem does not prove the absence of all unmeasured common causes.
Exclusion Restriction
The exclusion restriction requires the instrument to affect the outcome only through the treatment or exposure being studied.
The desired pathway is:
Z → X → Y
The problematic structure is:
Z → X → Y
Z → Y
or any alternative pathway through which Z influences Y without operating through X.
Suppose researchers use the introduction of faster broadband infrastructure as an instrument for firms’ adoption of cloud computing and then estimate the effect of cloud adoption on productivity. Broadband availability may strongly increase cloud adoption. Yet broadband infrastructure could also improve communication, enable remote work, facilitate e-commerce or affect access to digital services independently of cloud adoption.
Those alternative pathways would threaten the exclusion restriction.
This assumption is often the most difficult aspect of an IV argument because it is fundamentally about the absence of relevant alternative causal pathways. It cannot generally be proven from the observed dataset. Subject-matter knowledge, institutional detail, theory, negative controls, falsification exercises and sensitivity analyses can strengthen or weaken the case, but a non-significant statistical test cannot transform an implausible exclusion restriction into a credible one.
Two-Stage Least Squares
Two-Stage Least Squares (2SLS) is one of the most familiar estimation procedures for linear instrumental-variable models.
In simplified form, suppose X is endogenous, Z is the instrument and Y is the outcome.
The first stage estimates the relationship between Z and X:
X = α₀ + α₁Z + controls + error
This produces the component of X predicted by the instrument.
The second stage uses instrument-induced variation in X to estimate its relationship with Y:
Y = β₀ + β₁X̂ + controls + error
where X̂ represents the component of X associated with the instrument within the 2SLS procedure.
This two-stage representation is valuable pedagogically because it shows that IV is not using all observed variation in X in the same way as an ordinary regression. The causal estimate is driven by variation associated with the instrument.
However, successful execution of 2SLS does not demonstrate that the instrument is valid. Statistical software can estimate an IV model using a substantively indefensible instrument just as easily as it can estimate one using a credible instrument. The causal interpretation still comes from the identification assumptions.
This distinction is particularly important in dissertations. 2SLS is an estimation procedure; IV validity is a research-design argument.
What Effect Does IV Estimate?
Students sometimes interpret an IV coefficient as automatically representing the average causal effect for the entire population. That interpretation can be incorrect.
Under additional assumptions, including a form of monotonicity, a binary instrument in common IV settings can identify a Local Average Treatment Effect (LATE): the average treatment effect for individuals whose treatment status is changed by the instrument, commonly called compliers. Methodological discussions therefore sometimes introduce monotonicity as an additional assumption needed for this particular interpretation.
Suppose eligibility for a programme increases participation. Some people would participate whether eligible or not, while others would never participate. The IV estimate may primarily identify the effect among those whose participation actually changes because eligibility changes.
This matters for external validity. An IV estimate generated by a particular institutional rule or source of variation should not automatically be generalized to every member of the population. Researchers need to ask:
Whose treatment behaviour is actually changed by this instrument?
The answer helps define the population for whom the estimated causal effect is meaningful.
Dudovskiy Instrument Validity Assessment Framework
The Dudovskiy Instrument Validity Assessment Framework provides a structured process for evaluating whether an instrumental-variable analysis can support the causal claim being proposed. It synthesizes established IV principles into a practical research decision framework rather than proposing a new statistical theory.
Causal Question → Endogeneity Problem → Candidate Instrument → Relevance → Independence → Exclusion Restriction → Instrument Strength → Sensitivity/Falsification Evidence → Identified Population → Defensible Causal Claim
1. Causal Question
Begin by specifying the causal relationship of interest. Researchers should identify the treatment or exposure, outcome, target population and effect they intend to estimate before searching for an instrument.
2. Endogeneity Problem
Explain why conventional estimation may not identify the desired causal effect. Is the problem omitted-variable bias, reverse causality, measurement error, selection or another source of endogeneity? The choice of IV should respond to an identified causal problem rather than being added mechanically because endogeneity is considered possible.
3. Candidate Instrument
Identify a variable that generates potentially useful variation in the endogenous treatment. The mechanism connecting the candidate instrument to treatment should be explicit and substantively plausible.
4. Relevance
Determine whether the candidate instrument meaningfully changes or predicts treatment. Evidence should show that the instrument provides enough treatment variation to contribute to identification.
5. Independence
Investigate whether the instrument could share causes with the outcome. Researchers should use contextual knowledge to identify plausible variables or processes that could influence both the proposed instrument and the outcome.
6. Exclusion Restriction
Map the plausible pathways from the instrument to the outcome. If a credible route exists that bypasses the treatment, the exclusion restriction becomes difficult to defend.
7. Instrument Strength
Evaluate whether the relationship between instrument and treatment is sufficiently strong for reliable estimation and inference. Appropriate weak-instrument diagnostics should be reported rather than relying solely on statistical significance.
8. Sensitivity/Falsification Evidence
Search actively for evidence that could undermine the IV argument. Depending on the research design, this might include placebo outcomes, pre-treatment outcomes, covariate-balance examinations, alternative specifications, negative controls or sensitivity analyses. Such evidence can reveal problems, but passing these exercises should not be interpreted as definitive proof of validity.
9. Identified Population
Determine whose causal effect is being estimated. If the instrument changes treatment only for a particular group, interpretation should reflect that population rather than automatically extending the estimate to everyone.
10. Defensible Causal Claim
The final claim should be no stronger than the identification strategy permits. Instrument strength, assumption plausibility, sensitivity evidence and the population represented by the estimate should all inform the conclusion.
The central principle of the framework is:
An instrument is credible because the causal argument supporting its assumptions is credible—not simply because the first-stage regression is statistically significant.
Application of Instrumental Variables: an Example
Consider a study investigating whether access to external business finance causes manufacturing firms to increase capital investment. Directly regressing investment on borrowing may produce a misleading estimate. Firms with stronger growth opportunities may simultaneously seek more finance and invest more, while financially distressed firms may borrow for entirely different reasons. Growth expectations, managerial quality and risk preferences may not all be adequately observed.
Suppose a policy changes the lending capacity of particular local banks for reasons unrelated to individual firms’ investment opportunities. Firms have established banking relationships, so exposure to the policy varies according to their pre-existing primary bank. The researcher considers this policy-induced change in credit availability as a candidate instrument for external borrowing.
The first question is relevance. The researcher demonstrates that firms exposed to affected banks experience a meaningful change in access to external finance. However, that result alone is insufficient. The independence argument requires evidence that exposure to the affected banks was not itself systematically associated with unobserved determinants of future investment.
The exclusion restriction requires even closer attention. If the banking policy could affect firms through services other than credit availability—for example, payment facilities, financial advice or risk-management services—the pathway from instrument to investment may not operate exclusively through borrowing. The researcher would need to examine these possibilities using institutional knowledge and supporting empirical evidence.
After assessing instrument strength and conducting appropriate robustness and falsification analyses, the IV estimate could be used to examine the effect of finance generated by this particular source of variation. The final interpretation would specify the firms and financing behaviour represented by the instrument rather than claiming that the estimate necessarily describes the effect of every form of borrowing for every company.
Advantages and Limitations of Instrumental Variables
The major attraction of IV is its ability, under appropriate assumptions, to support causal inference when important treatment-outcome confounders are unobserved. Conventional regression adjustment and propensity-score approaches rely heavily on sufficiently measuring the confounding structure. IV replaces part of that requirement with assumptions about an external or quasi-external source of treatment variation. This can make IV particularly valuable when unmeasured confounding is a serious and unavoidable concern.
IV can also provide a powerful way to exploit naturally occurring institutional variation. Policy rules, eligibility thresholds, historical allocations, geographic variation and other mechanisms can sometimes create changes in treatment that are more plausibly separated from individual choice than the treatment itself. In such cases, understanding how the real-world assignment mechanism operates can provide stronger causal leverage than simply adding more control variables to a regression.
The difficulty is that credible instruments are rare. A variable that strongly predicts treatment may also be related to the outcome through confounding or alternative causal pathways. Independence and exclusion restriction cannot generally be established simply by inspecting a regression table, which means IV studies often depend on substantial institutional knowledge and theoretical reasoning.
Weak instruments introduce another vulnerability. If the instrument generates little meaningful treatment variation, IV estimates and conventional inference can behave poorly. Adding instruments indiscriminately is not necessarily a solution, and researchers need diagnostics appropriate to the specific IV specification.
Interpretation can also be narrower than researchers initially expect. In settings where IV identifies a local treatment effect, the resulting estimate may apply to the group whose treatment changes because of the instrument rather than to the entire population. A design can therefore have strong internal causal logic while supporting a comparatively bounded substantive conclusion.
Common Mistakes When Using Instrumental Variables
Searching for an instrument only after discovering an endogeneity problem can encourage researchers to select whichever available variable produces a convenient first-stage relationship. A credible instrument requires a substantive explanation of the mechanism generating treatment variation. Statistical availability is not itself a causal justification.
Treating relevance as equivalent to validity ignores two of the central IV requirements. A candidate instrument can strongly predict treatment while sharing causes with the outcome or affecting it through another pathway. The first-stage relationship therefore addresses relevance, not the entire validity question.
A first-stage F-statistic should not become a binary certificate of instrument quality. Weak-instrument diagnostics are important, but a familiar cutoff does not establish independence or exclusion restriction and may not even be the appropriate weak-instrument diagnostic for every specification. (National Bureau of Economic Research)
Control variables cannot automatically repair an implausible instrument. Adjustment may make some IV assumptions more plausible conditional on observed characteristics, but researchers need a clear causal argument explaining why remaining pathways and common causes are sufficiently addressed.
Passing a falsification test does not prove the exclusion restriction. Falsification exercises are valuable because they may reveal evidence inconsistent with the IV assumptions. Failure to detect a violation, however, is not evidence that every possible alternative pathway has been eliminated.
Interpreting every IV coefficient as a population-wide average treatment effect can overstate what the design identifies. Researchers should establish the estimand and consider whether the instrument identifies an effect for a particular subgroup.
Presenting 2SLS output without explaining the causal identification strategy reverses the methodological priority. The equations and regression results are the implementation of the IV design. The validity of the design comes from the argument about why the instrument provides appropriate variation in treatment.
Instrumental Variables in Business Research
Instrumental Variables are especially relevant to business research because many important explanatory variables are products of managerial, organisational or consumer choice. Capital structure, international expansion, executive appointments, digital adoption, corporate governance, employee training and strategic alliances are not usually randomly assigned.
Strategic-management researchers have consequently used IV methods to address endogeneity in observational data, while methodological work has emphasized that identifying the source of endogeneity and selecting the appropriate response are integral to credible empirical research. (Sage Journals)
Consider research examining whether international expansion improves firm profitability. Firms entering foreign markets may already possess stronger management, better products, more financial resources and superior growth opportunities. Some characteristics can be measured and controlled, but others may remain unobserved. A credible source of variation affecting foreign-market entry while otherwise remaining sufficiently separated from profitability could potentially provide an IV strategy.
The word credible is decisive. Management research has also raised concerns about treating instrumental-variable modelling as a routine remedy for omitted-variable bias, given the challenges involved in finding instruments that satisfy the required assumptions.
IV should therefore not be interpreted as the statistically sophisticated option researchers select whenever they want to make a stronger causal claim. In business research, its value depends particularly on understanding institutions, policies, organisational processes and decision mechanisms well enough to explain why the proposed instrument generates plausibly exogenous treatment variation.
Instrumental Variables in the Age of AI and Digital Research
AI changes the technical environment in which IV analysis is conducted but does not remove its fundamental identification problem. Machine-learning methods can help model complex first-stage relationships, explore heterogeneous effects and analyse high-dimensional data. Generative AI can also assist researchers in mapping possible causal pathways, identifying candidate threats to an instrument and producing code for IV estimation and diagnostic procedures.
These capabilities create an important danger. Finding variables that predict treatment is becoming progressively easier, but predictive relevance is only one component of instrument validity. An algorithm searching thousands of variables may identify exceptionally strong predictors of treatment while providing no credible reason to believe that those variables satisfy independence and exclusion restriction.
Generative AI can make this problem more subtle by producing plausible-sounding justifications for an instrument. A fluent explanation that “geographic distance is exogenous” or “policy timing is externally determined” is not evidence that the claim is true in a particular institutional setting. Researchers need to investigate how locations were selected, how policies were implemented, who anticipated the changes and what other pathways could connect the proposed instrument with the outcome.
AI is potentially more valuable when used adversarially. Instead of asking only “Why is this a valid instrument?”, researchers can use AI-supported exploration to ask “Through what pathways could this instrument affect the outcome without operating through the treatment?” and “What could jointly determine the instrument and outcome?” Those questions help expose assumptions that require empirical or institutional investigation.
The AI-era principle is therefore straightforward: better prediction can strengthen the first stage, but it cannot manufacture exogeneity.
When to Use Instrumental Variables
Instrumental Variables may be appropriate when:
- the research question is causal rather than purely descriptive or predictive;
- an important explanatory variable is endogenous;
- random assignment is unavailable;
- unmeasured confounding makes conventional covariate adjustment questionable;
- a theoretically and institutionally credible candidate instrument exists;
- the instrument meaningfully predicts the endogenous treatment or exposure;
- independence can be plausibly defended;
- the exclusion restriction can be plausibly defended;
- instrument strength can be evaluated appropriately;
- the population and causal effect identified by the instrument are relevant to the research question;
- sensitivity, robustness or falsification evidence can be used to investigate plausible threats to the IV argument.
IV should not be used simply because a researcher suspects endogeneity. If no defensible instrument exists, acknowledging the limitation or using another research design can be methodologically stronger than constructing an IV analysis around a convenient but implausible instrument.
Dissertation Example
A dissertation titled “The Impact of Employee Training on Labour Productivity in Manufacturing Firms” may face endogeneity because firms decide how much training to provide. Companies with better management, stronger finances or more productive employees may invest more heavily in training, meaning that a conventional regression could incorrectly attribute pre-existing performance differences to the training itself.
Suppose a government programme provides training subsidies according to an administrative eligibility rule that substantially affects firms’ training expenditure. The methodology chapter could investigate programme eligibility as a candidate instrument. The researcher would first explain the endogeneity problem and why conventional adjustment may not capture every factor influencing both training and productivity. The causal mechanism connecting eligibility to actual training would then establish the relevance argument.
The methodology would need to devote considerably more attention to independence and exclusion restriction than simply reporting the first-stage regression. The researcher would examine whether eligibility is related to firm characteristics that independently influence productivity and whether the subsidy programme provides any benefits capable of affecting productivity other than through employee training. Appropriate first-stage diagnostics and supporting falsification or robustness analyses would also be reported.
If the instrument remained defensible, the dissertation could estimate the effect of instrument-induced variation in training on productivity using an appropriate IV procedure such as 2SLS. The interpretation would specify the assumptions under which the estimate is causal and consider which firms’ training decisions were actually affected by eligibility. This would make the methodological justification part of the causal argument rather than treating IV as merely an advanced regression technique.
Exam Tip
If asked why you used an instrumental variable, do not answer simply that “IV solves endogeneity.” Explain what created the endogeneity problem in your research and why your particular instrument provides a potentially credible source of variation in the endogenous variable.
You should then be able to defend three separate propositions: why the instrument affects treatment, why it is sufficiently independent of uncontrolled causes of the outcome, and why it should not affect the outcome through another pathway. A strong first-stage relationship supports the first proposition but does not establish the other two.
If an examiner asks whether your instrument is proven to be valid, a more defensible response is that the assumptions have different empirical status. Relevance can be directly investigated, while independence and exclusion restriction generally require substantive justification and can sometimes be challenged through falsification or sensitivity evidence rather than conclusively verified.
The principle worth remembering is:
A strong instrument predicts treatment. A credible instrument also survives a serious causal argument about why it should not otherwise determine the outcome.
Need to determine whether Instrumental Variables are appropriate for your dissertation—and whether your proposed instrument can support the causal claim you want to make?
Use Dudovskiy Research Assistant to develop a methodology tailored to your research topic, with clear academic justification for the research design, data analysis and methodological choices.
References
Angrist, J.D., Imbens, G.W. and Rubin, D.B. (1996) ‘Identification of causal effects using instrumental variables’, Journal of the American Statistical Association, 91(434), pp. 444–455.
Angrist, J.D. and Pischke, J.-S. (2009) Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton, NJ: Princeton University Press.
Bascle, G. (2008) ‘Controlling for endogeneity with instrumental variables in strategic management research’, Strategic Organization, 6(3), pp. 285–327. (Sage Journals)
Hill, A.D., Johnson, S.G., Greco, L.M., O’Boyle, E.H. and Walter, S.L. (2021) ‘Endogeneity: A review and agenda for the methodology-practice divide affecting micro and macro research’, Journal of Management, 47(1), pp. 105–143. (Sage Journals)
Stock, J.H. and Yogo, M. (2005) ‘Testing for weak instruments in linear IV regression’, in Andrews, D.W.K. and Stock, J.H. (eds.) Identification and Inference for Econometric Models. Cambridge: Cambridge University Press, pp. 80–108. (National Bureau of Economic Research)
Swanson, S.A. and Hernán, M.A. (2018) ‘The challenging interpretation of instrumental variable estimates under monotonicity’, International Journal of Epidemiology, 47(4), pp. 1289–1297.
Davies, N.M., Holmes, M.V. and Davey Smith, G. (2018) ‘Reading Mendelian randomisation studies: a guide, glossary, and checklist for clinicians’, BMJ, 362, k601.