STATISTICAL METHOD
Instrumental Variable Analysis
Statistical Consulting for Causal Estimation
We apply the method within your study design, arguing the instrument's exclusion and independence, reporting first-stage diagnostics and two-stage least squares estimates with 95% confidence intervals, and stating whom the effect describes.
No Commitment Required
Strictly Confidential
In-House PhD-Level Statisticians
Fixed Project Fee
Same-Day Response
METHOD OVERVIEW
What Is Instrumental Variable Analysis?
An instrumental variable design estimates the causal effect of an exposure on an outcome when unmeasured factors confound the exposure, by using an instrument that shifts the exposure but affects the outcome only through it. The instrument must be associated with the exposure, be independent of the unmeasured confounders and have no direct path to the outcome. Estimation is usually by two-stage least squares. When effects differ between people, and the instrument moves exposure in one direction only, the estimate is a local average effect for compliers, not for everyone. OnlineSPSS, a specialist statistical consultancy for academic, clinical and professional research, provides instrumental variable analysis within your study design, with the relevant checks, effect estimates, uncertainty measures, interpretation and publication-ready reporting.
WHEN TO ENGAGE
When Is an Instrumental Variable Approach Appropriate?
The method fits an exposure whose effect is confounded in ways the data cannot adjust for, and these are the situations in which researchers most often ask us to apply or confirm it.
Unmeasured Confounding Suspected Who receives a treatment depends on factors the data do not record, so adjusting for measured covariates is unlikely to remove the bias.
A Candidate Instrument Exists Distance to a provider, a prescriber's habits or a policy rule shifts exposure, and the researcher must judge whether it can be defended as an instrument.
Non-Adherence in a Randomized Trial Participants did not all take the treatment assigned, and randomization is used as the instrument for the treatment actually received.
Reviewing a Completed IV Analysis A two-stage estimate has been reported and a reviewer has questioned the instrument. Independent Statistical Review re-examines the assumptions and the output.
ANALYTICAL APPROACH
How We Apply Instrumental Variables
Within the family of Clinical, Survival & Epidemiological, an instrument is accepted only after its assumptions have been argued from the design, not from the output alone.
Relevance and First Stage We report the first-stage F-statistic. Weak instruments make estimates unstable and biased toward the confounded result, and a significant first stage alone does not prove validity.
Exclusion and Independence These cannot be proved from the data. We argue them from subject knowledge, name each plausible path that would violate them, and treat overidentification tests as limited evidence.
Estimand and Monotonicity With heterogeneous effects, the estimate is a local average effect among compliers, which needs monotonicity. We describe the compliers and never present it as the effect for everyone.
Estimation and Outcome Type We fit two-stage least squares with robust or clustered standard errors. For a binary outcome, a logistic second stage on fitted values is biased, so we estimate a risk difference.
DELIVERABLES
What You Receive
As part of our Quantitative Data Analysis service, the instrumental estimate is delivered with the diagnostics, arguments and files needed to report and defend it.
Data & Variable Review Exposure, outcome and instrument definitions, their timing and measurement, missing data and the structure of any clusters are reviewed before estimation.
Method-Specific Checks First-stage strength with the F-statistic, weak-instrument robust intervals where needed, and overidentification tests with their limits stated, if several instruments exist.
Statistical Results The reduced-form and two-stage least squares estimates with 95% confidence intervals, the ordinary regression result for comparison and the first-stage results.
Publication-Ready Tables & Figures Tables of first-stage, reduced-form and second-stage results, prepared in line with the journal's requirements or STROBE-style reporting, ready to insert.
Interpretation The estimate is read for the complier population, with each assumption written out in plain language and the strongest threat to the instrument discussed.
Reproducible Analysis Files R scripts, Stata do-files or Python code for every stage are provided where applicable, so each reported value can be traced and rerun if the data change.
ALTERNATIVE METHODS
When Another Method May Be More Appropriate
An instrument is rare and its assumptions are demanding. These methods fit better when confounders are measured, when treatment follows a threshold or when outcomes are observed over time.
01
Propensity Score Matching (PSM)
If the important confounders were measured and no defensible instrument exists, matching or weighting on them is the more direct route, with its own untestable assumption.
02
Regression Discontinuity (RD)
When a rule assigns treatment at a cutoff on a score, comparing units just either side of it can identify an effect without a separate instrument.
03
Difference-in-Differences (DiD)
When some units adopt a policy and others do not, DiD relies on parallel trends before and after the change, which is often easier to defend than an exclusion restriction.
04
Logistic Regression
For a binary outcome with plausible measured confounding only, an adjusted logistic model reports a conditional odds ratio and avoids the demands an instrument makes.
CASE EXAMPLE
How We Work in Practice
An illustration of how an instrumental estimate moves from a defended instrument to a result that states whom it describes.
ILLUSTRATIVE EXAMPLE · MEDICAID PROGRAM EVALUATION · UNITED STATES
A state Medicaid office wanted to know whether enrolling in a care coordination program reduced emergency department visits among eligible adult members with chronic conditions.
Members chose whether to join, and those who did were probably sicker, so a direct comparison was confounded. The office had mailed invitations to a randomly chosen subset, which gave a candidate instrument. Before outcomes were examined, we fixed the analysis plan: the invitation’s effect on visits, the first stage with its F-statistic and the two-stage estimate. We discussed whether the letter could change visits other than through enrollment, for example by prompting a clinic visit. Because the invitation changed enrollment for only some members, we stated that the estimate describes members who enroll only when invited, not all enrollees.
Outcome: The office received the effect of the invitation, the two-stage estimate with its 95% confidence interval, the first-stage results, a written exclusion argument and the analysis code.
This example does not describe a real client or project. We never share details of actual client work, in line with the confidentiality we promise every researcher. This illustrative example is included to show the type, scope, and standard of work involved in this kind of analysis.
SOFTWARE
Statistical Software for Instrumental Models
Two-stage least squares and first-stage diagnostics are run in the statistical software researchers already use, with syntax or scripts provided where applicable.
RESEARCH DISCIPLINES
Instrumental Methods Across Research Fields
Instrumental variable designs are used across research fields, each with its own sources of exogenous variation, confounders and reporting conventions.
A Defined Process for Your Analysis
We review your dataset, research question and design before any work begins, so the scope, deliverables, timeline and fixed project fee are clear from the outset.
01
Share Your Research Materials
Send your dataset, research question, study design and any existing analysis plan or output. We will let you know if anything else is needed to assess the project.
02
Receive Your Assessment
Your statistically trained Research Coordinator reviews the project and confirms the required analysis, deliverables, timeline and fixed project price before work begins.
03
Analysis & Delivery
Once you confirm the scope, an in-house statistician completes the agreed analysis and delivers the outputs, interpretation and reporting files.
RESEARCHER VOICE
What Researchers Say
Feedback from a policy researcher who wanted a second review of whether the instrument was relevant and defensible.
“I wanted a second set of statistical eyes on our Instrumental Variable Analysis, mainly because of whether the instrument was actually relevant and defensible. The review was practical and specific, and the final results were much easier to explain to the rest of the research team. The final reporting was much easier to use in the manuscript and in responding to reviewer comments.”
RESEARCH RESPONSIBILITY
Statistical Support Without Taking Over Your Research
We provide the statistical work for your instrumental analysis, and the study, its meaning and its authorship stay entirely with you.
Agreed Statistical Support We provide the agreed methodological, analytical and statistical reporting support for your instrumental variable work, within the scope confirmed before work begins.
No Intellectual Contribution OnlineSPSS claims no intellectual contribution to your research. Our work is statistical support, and authorship remains yours.
Your Research Decisions The choice of instrument, the research question and your conclusions remain with you, and our interpretation stays within what the estimates and the design support.
Confidential Handling Research data and project details are handled confidentially and are not published. An NDA is available where required, and can be arranged before sensitive materials are shared.
FREQUENTLY ASKED QUESTIONS
Questions About Instrumental Variables
Short answers to what researchers ask before using an instrument, from validity and weak instruments to confidentiality and the assessment process.
Is a significant first stage enough to show my instrument is valid?
No. A strong first stage shows relevance only, and the exclusion restriction and independence cannot be tested directly. They rest on subject-matter argument about how the instrument could reach the outcome by other routes. We set out those routes, discuss the most plausible one, and test sensitivity where a method for it exists.
Should I report the instrumental or the ordinary regression estimate?
Usually both, because they estimate different things. Ordinary regression gives an association adjusted for measured confounders across the whole sample, while the instrumental estimate targets the effect among compliers under the instrument’s assumptions, with wider intervals. A gap between them can reflect confounding, a different population or a weak instrument, so we interpret it rather than choose the estimate that looks better.
How do I know whether my instrument is too weak?
A first-stage F-statistic below about 10 is a common warning sign for one endogenous variable, but it is only a rough guide. Weak instruments bias estimates toward the ordinary regression result and distort intervals, so we report the F-statistic and use weak-instrument robust confidence sets, such as Anderson-Rubin, where strength is doubtful.
Can you review an analysis that has already been completed?
Yes, we can review a completed instrumental analysis before submission or a response to reviewers. We check the instrument’s argument, the first-stage diagnostics, any overidentification test and its limits, the estimand claimed and how the results were reported, and confirm what stands or needs to change.
How do you protect my dataset and research confidentiality?
Your dataset, output files and any protocol or analysis plan are handled confidentially, and project information is not published. An NDA is available where required and can be arranged before sensitive materials are shared. Read more about confidentiality and data security.
What happens when I request an assessment, and how long does it take?
You share your research question, design and relevant materials, and a statistically trained Research Coordinator reviews the request and responds the same day. The analysis, deliverables, timeline and one fixed project fee are then confirmed before any work begins, so the timeline follows from the agreed scope.
Still have a question? Find more answers in our full FAQ.
NEXT STEP
Need Support With an
Instrumental Variable Design?
Share your research question, candidate instrument and data. We assess whether the design supports the method and confirm the approach before any work begins.
No Commitment Required
Strictly Confidential
Fixed Project Fee
In-House PhD-Level Statisticians
Same-Day Response
Serving Researchers Since 2014