🔗 Causal Impact

Causal Impact#

The estimated effect of an intervention, often via a counterfactual time-series model.

Important

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What it is#

Causal impact is the overall effect of an intervention — a campaign, launch or policy — on an outcome. In data science the term usually points to Google’s CausalImpact (Brodersen et al., 2015): a Bayesian structural time-series model that estimates what would have happened without the intervention and compares it to what actually did.

Why it’s needed#

In an RCT or A/B test the causal effect is easy — you have treatment and control groups. But in observational or time-series settings there may be no untreated control: run a nationwide ad campaign and there is no parallel country that didn’t see it. The fix is to model the counterfactual — the outcome you’d have seen without the intervention — and measure the gap.

The method and formula#

CausalImpact fits a model on the pre-intervention period (using historical data and control covariates), forecasts the counterfactual for the post period, and subtracts:

\[\text{Causal Impact} = Y_{\text{observed, post}} - Y_{\text{predicted, counterfactual}},\]

reporting the difference with Bayesian credible intervals rather than a single number.

Example#

A firm launches a TV campaign in July. Trained on January–June sales, the model forecasts a counterfactual of 50,000 units; actual sales come in at 60,000 — an estimated impact of +10,000 units, with a credible interval of roughly [7,000, 13,000].

Strengths, limits, and effect vs impact#

It handles time series naturally, yields full posterior distributions, uses covariates to sharpen accuracy, and needs no RCT — but it assumes the model captures the dynamics, is sensitive to the choice of controls, and wants a clear start date. Note the level distinction: the causal effect is micro (the change per unit — a drug lowers blood pressure 5 mmHg), while the causal impact is macro (the aggregate — a nationwide rollout prevents 10,000 hospitalisations).

Theme: Causal Inference & Uplift · All terminology

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Mind map — connected ideas

Treatment Effect · Causal Inference · Bayesian Time Series · Online Experimentation Platforms · A/B Testing · Counterfactual Explanations

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More in Causal Inference & Uplift

AUUC (Area Under the Uplift Curve) · Causal Effect · Causal Inference · Causal ML (Causal Machine Learning) · Causal Trees · Cumulative Incremental Gain (CIG) · Cumulative Uplift · Incremental Conversions · Incremental Gain · Incremental Recovery Rate (IRR) · Incremental Revenue · Incremental Sales · Qini Coefficient · Qini Curve