How do you estimate an effect with difference-in-differences?
Difference-in-differences compares change in a treated group with change in an untreated group. Identification relies on credible parallel trends without treatment.
Scientific editorial team : Marketing Science Center
Direct answer
Estimate an ATT for groups and periods covered by the design.
Difference-in-differences compares change in a treated group with change in an untreated group. Identification relies on credible parallel trends without treatment.
Hernán & Robins, Causal Inference: What IfArnold et al., 2020
01
Operational summary
Scientific question and scope
How do you estimate an effect with difference-in-differences?
Supported
Estimate an ATT for groups and periods covered by the design.
Forbidden
Prove future parallel trends from pre-period data alone.
02
Three reading levels
- 01
Decision-maker — Connect the result to a declared decision, useful threshold and error cost.
- 02
Practitioner — Fix population, unit, horizon, available variables and analysis rule before calculation.
- 03
Analyst — Reproduce the calculation, quantify uncertainty and document diagnostics, failures and sensitivities.
03
Concrete marketing situation
Difference-in-differences compares change in a treated group with change in an untreated group. Identification relies on credible parallel trends without treatment.
04
Scientific question and scope
How do you estimate an effect with difference-in-differences?
ATT in a two-group, two-period design
Required data
unit × group × period
Population, unit of analysis, origin date and horizon must be declared in the deliverable. Without them, the estimand silently changes.
05
Why a simple analysis can fail
- Prove future parallel trends from pre-period data alone.
- Pre-trends
- Anticipation
- Use group-time ATT for staggered adoption
06
Method intuition
The method does not automatically turn an association into evidence. It links a declared question to an estimand, specification, compatible data and a bounded interpretation rule.
ATT in a two-group, two-period design
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Required data
Scientific symbol dictionary
Y_T_post- Mean outcome for treated-group units after intervention. Unit:
outcome· Type:number· Role:input Y_T_pre- Mean outcome for the same treated group in the declared pre-period. Unit:
outcome· Type:number· Role:input Y_C_post- Mean outcome for the declared comparison group in the post-period. Unit:
outcome· Type:number· Role:input Y_C_pre- Mean outcome for the same comparison group in the pre-period. Unit:
outcome· Type:number· Role:input z- Two-sided normal critical value for the declared confidence level. Unit:
dimensionless· Type:positive number· Role:parameter cluster_SE- Externally supplied cluster-robust standard error for the DiD contrast in this sealed illustration. Unit:
outcome· Type:positive number· Role:input ATT_DiD- Two-period difference-in-differences contrast, interpreted causally only under the declared identification assumptions. Unit:
outcome· Type:number· Role:output CI- Normal interval based on the supplied cluster-robust standard error. Unit:
outcome· Type:ordered pair· Role:output
Exact sealed engine inputs
treated_pre- Value:
100· Unit:index· Type:number· Data status:synthetic treated_post- Value:
120· Unit:index· Type:number· Data status:synthetic control_pre- Value:
90· Unit:index· Type:number· Data status:synthetic control_post- Value:
98· Unit:index· Type:number· Data status:synthetic standard_error- Value:
4· Unit:index· Type:number· Data status:synthetic z_critical- Value:
1.95996398454· Unit:dimensionless· Type:number· Data status:parameter
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Formal model
Formal model
att_did = (treated_post − treated_pre) − (control_post − control_pre); CI = att_did ± z_critical × standard_errorEvidence claims: MSC-P015-C01 · MSC-P015-C02 · MSC-P015-C03 · MSC-P015-C04 · MSC-P015-C05 · MSC-P015-C06
Scientific question and scope
ATT in a two-group, two-period design
09
Declared calculation
- 01
Lock treated and comparison groups, timing, outcome definition and the supplied cluster-robust uncertainty specification.
- 02
Compute each group’s change, subtract the comparison change from the treated change, and form the declared interval.
- 03
Interpret as ATT only if parallel trends, no anticipation, overlap and valid comparison timing are defensible.
10
Numerical example or application case
Worked example — synthetic data or declared parameters; no real observations
Sealed inputs
treated_pre=100 [index]treated_post=120 [index]control_pre=90 [index]control_post=98 [index]standard_error=4 [index]z_critical=1.95996398454 [dimensionless]
Reproducible results
ATT_DiD=12CI95=[4.160144; 19.839856]
Verified dossier: claims are linked to passage-level sources, the Python/R calculation is reproduced, limits are explicit, and independent scientific review is complete.
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Validity assumptions
- Are pre-treatment trends credible for the chosen comparison group?
- Could units anticipate treatment or change composition before adoption?
- For staggered adoption, is group-time ATT used instead of an invalid two-way fixed-effects aggregation?
12
Diagnostics and uncertainty
Diagnostics and uncertainty
Pre-trends · Anticipation · Use group-time ATT for staggered adoption · Clustered uncertainty
Bounded diagnostic
Interpretation still requires parallel trends, no anticipation and an appropriate clustered variance design.
Explicit uncertainty contract · quantified_conditional
Method : Deterministic reference-engine calculation on the sealed input slice.
Target : Uncertainty of the difference-in-differences ATT illustration.
Engine evidence : metric.ci_lower= · metric.ci_upper=
Interpretation : The interval is conditional on the supplied cluster-robust standard error and does not establish parallel trends.
Stop when
Prove future parallel trends from pre-period data alone.
13
Result interpretation
- Estimate an ATT for groups and periods covered by the design.
- The result is conditional on the declared population, horizon, specification and diagnostics. It must not be extended to another decision without new justification.
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Supported and forbidden conclusions
Supported
Estimate an ATT for groups and periods covered by the design.
Forbidden
Prove future parallel trends from pre-period data alone.
15
Possible marketing decision
- 01
Estimate an ATT for groups and periods covered by the design.
- 02
The result is conditional on the declared population, horizon, specification and diagnostics. It must not be extended to another decision without new justification.
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When to use — when to stop
Use when
Estimate an ATT for groups and periods covered by the design.
unit × group × period
Stop when
Prove future parallel trends from pre-period data alone.
Methodological alternatives
- Estimate group-time ATT with not-yet-treated or never-treated controls for staggered adoption.
- Use an event-study design to expose dynamic effects and pre-trend diagnostics.
- Prefer randomized rollout when intervention timing can be assigned.
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Reproducibility contract
Python and R are the executable references. SPSS and SAS remain secondary syntaxes until checked on the same data, specification and diagnostics.
The engine selects only this page’s explicit slice and branch. Its hash, outputs, and diagnostics remain sealed in the atomic dossier; no generic fallback branch is allowed.
Slice fingerprint: 928e93319b64e017684dad7e878d79a85a38b2296a0925cc3597773489b3fc56
Available asset · MSC-005
Promotion incrementality
Available asset · MSC-T02
DiD calculator
CSV · CC0
msc-validation-inputs-v1.csv ↓Python · MIT
msc-validation-reference-v1.py ↓R · MIT
msc-validation-reference-v1.R ↓SPSS / SAS · MIT · inspection only
SPSS ↓SAS ↓Formal model
att_did = (treated_post − treated_pre) − (control_post − control_pre); CI = att_did ± z_critical × standard_errorVerified dossier: claims are linked to passage-level sources, the Python/R calculation is reproduced, limits are explicit, and independent scientific review is complete.
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Expected final deliverable
- 01
How do you estimate an effect with difference-in-differences? —
unit × group × period - 02
Y_T_post · Y_T_pre · Y_C_post · Y_C_pre · z · cluster_SE · ATT_DiD · CI
- 03
att_did = (treated_post − treated_pre) − (control_post − control_pre); CI = att_did ± z_critical × standard_error - 04
Pre-trends · Anticipation · Use group-time ATT for staggered adoption · Clustered uncertainty
- 05
Estimate an ATT for groups and periods covered by the design. / Prove future parallel trends from pre-period data alone.
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Scientific sources and evidence status
Verified dossier: claims are linked to passage-level sources, the Python/R calculation is reproduced, limits are explicit, and independent scientific review is complete.
MSC-P015-C01— The causal target contrasts mean potential outcomes under two defined interventions.MSC-P015-C02— Consistency links the observed outcome to the potential outcome under the assigned policy.MSC-P015-C03— Fitting a regression does not itself establish a causal design.MSC-P015-C04— Identification requires explicit parallel-trends and no-anticipation assumptions.MSC-P015-C05— The framework distinguishes common and staggered adoption designs.MSC-P015-C06— Covariate adjustment depends on the identification design.
Dataset · Tool
Method connections