Causal Inference in Observational Data �— A Synthetic Difference-in-Differences Approach
Dr Yin Wang
Lecturer in Research Methods and AI Skills
National Centre for Research Methods (NCRM)
Department of Social Statistics and Demography
University of Southampton
email: yw14g25@soton.ac.uk 26/07/2026
Research Interests
I am interested in comparing data-driven and theory-driven approaches and examines how key features of complex survey data—such as clustering, sampling weights, and plausible values—can be incorporated into ML and AI-based analyses. The aim is to advance ML methods from individual-level pattern discovery towards population-level inference and policy-relevant evidence.
My research focuses on developing cognitive-computational models to explain and simulate creative processes. In particular, I use neuro-symbolic program synthesis approaches, such as DreamCoder, to investigate how cognitive mechanisms—including conceptual remapping, recursion, and overhypothesis formation—contribute to the generation and transformation of creative ideas.
My research examines how critical thinking and social network structures influence people’s ability to recognise and respond to dark ideas, including misinformation and conspiracy theories, across different national and cultural contexts.
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Aims：
To develop attendees’ understanding of:
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What is causality?
We are no strangers to causality. Causal questions are everywhere in our lives, and humans have long been fascinated by them—that is:
Causality refers to the idea that a change in one factor (the cause, X) produces a change in another (the effect, Y).
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How can we detect causal relationships?
To determine whether X causes Y, the most straightforward approach is to hold all other conditions constant and compare what happens to Y when X occurs with what happens when X does not occur.
Y(X=1) vs. Y(X=0)
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The fundamental problem of causal inference：
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Synthetic Difference-in-Difference:
Synthetic Difference-in-Differences (SDID) is a powerful quasi-experimental causal inference method that constructs a weighted synthetic control group to estimate the counterfactual outcome (Arkhangelsky et al., 2021).
Synthetic Difference-in-Differences = Difference-in-Differences + Synthetic Control
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What is Difference-in-Difference?
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Group | Before Intervention Implementation | After Intervention Implementation | Difference |
Treatment Group | | | |
Control Group | | | |
Difference | | | |
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Why is it a causal tool?
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Synthetic Control to Enhance the Parallel Trends Assumption
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Before SC
After SC
The “Smoking in California” case uses Synthetic Control to estimate the effect of a 1989 anti-smoking law by comparing post-policy cigarette sales in California to a weighted combination of other U.S. states that did not implement similar policies.
Weighting the control states does not necessarily produce a perfect pre-intervention match. SC also weights the pre-intervention time periods. Periods that provide more useful information about the post-intervention period receive greater weight and play a larger role in estimating the treatment effect.
Advantages of SDID for Intervention Evaluation �Using Observational Data
Because SDID constructs a counterfactual based on the characteristics and pre-treatment trends of the treatment group itself, the synthetic control is not a real historical group, but a hypothetical scenario derived from the treatment unit's own past and comparable units.
This means the estimated effect answers the question: What would have happened in this country (or region) had the policy not been implemented?
As a result, SDID estimates the impact within the same unit, without requiring direct cross-country or cross-region comparisons, making the findings highly relevant and credible for domestic policy debates.
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Unlike methods such as instrumental variables (IV), regression discontinuity designs (RDD), and propensity score matching (PSM), which often estimate local treatment effects by excluding units that don’t satisfy strict assumptions for counterfactual construction, SDID delivers a population-level average effect for the treated group over time.
This makes SDID particularly valuable for understanding broad, policy-relevant impacts rather than narrow local effects.
SDID is not limited to traditional panel data. It can also be applied to repeated cross-sectional datasets, such as PISA, PIRLS, or TIMSS. By combining synthetic control weights at the country or system level with student-level sampling weights, SDID enables causal inference even without individual-level tracking, as long as multiple pre-/post-time points exist at the aggregate level.
When using individual-level data, SDID can be extended to estimate heterogeneous treatment effects, allowing researchers to explore how the policy effect varies across subpopulations (e.g., low vs. high SES students, boys vs. girls) or across system-level features (e.g., countries with stronger governance or more equitable school systems).�This makes SDID especially valuable for nuanced policy insights beyond simple average effects.
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Robust Check of SDID
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Part 2: SDID in the R Software �Package
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Source/Editor pane (top-left) – Where you write and edit R scripts. It supports one-click execution of selected lines.
Console pane (bottom-left) – The live R interpreter. It shows immediate output from commands, error messages.
Environment/History pane (top-right) – Displays all active objects in memory, their types, and sizes, plus a searchable command history.
Files/Plots/Packages/Help/Viewer pane (bottom-right) – A multipurpose area: browse project files, view generated plots, manage installed packages, read built-in documentation, and preview web content without leaving RStudio.
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Extensions of the SDID Analysis
A country’s long-standing educational culture
A student's innate motivation or cognitive style
Regional infrastructure quality that hasn't changed over the study period
A change in international testing standards (e.g., PISA scoring framework update)
A worldwide economic crisis
Sudden curriculum reform applied nationwide
Further isolates causal effects by introducing a third dimension. Helps test heterogeneous treatment effects across subgroups.
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Thank you for your attention!
Please contact me at yw14g25@soton.ac.uk !
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