Why this section matters

Chapter 1 highlights endogeneity, dynamics, and spillovers. Section 2.1 provides the formal language to state causal questions clearly and to see which assumptions an estimator needs.

The panel setup

We observe $N$ units over $T$ periods. Outcomes are $Y_{it}$ and treatments are $D_{it}$. For now, think of $D_{it}$ as binary (treated vs not). The central causal object is a potential outcome that says what would happen under a specified treatment.

Two notations for potential outcomes

  1. Contemporaneous notation: $Y_{it}(d)$ depends only on current treatment in period $t$. This is convenient but assumes no anticipation and no carryover.
  2. Path-dependent notation: $Y_{it}(\mathbf{d}_{it})$ depends on the whole treatment history $\mathbf{d}_{it}=(d_{i1},\ldots,d_{it})$. This is the right object when dynamics, habit formation, or strategic responses matter.

Marketing settings often require the path-dependent form because campaigns build stock, loyalty effects accumulate, and competitors react over time.

Key assumptions and what they buy you

  • Assumption 1 (No anticipation): future treatments do not affect current outcomes. Violations show up as pre-trends in event studies.
  • Assumption 2 (No carryover): past treatments do not affect current outcomes. Violations imply that $Y_{it}(d)$ is too simple.
  • Assumption 3 (SUTVA for panels): outcomes depend only on a unit’s own treatment history and treatment versions are consistent. In marketing, interference and version differences are common, so this assumption must be defended or relaxed.

When Assumptions 1 and 2 hold, you can work with $Y_{it}(d)$ and static DiD-style estimands. When they fail, you need dynamic specifications, distributed lags, or explicit spillover models.

Why assignment matters

Even with correct potential outcomes, identification depends on the assignment mechanism $\Pr(D \mid Y(\cdot), X)$. Marketing treatments are strategic and often depend on past outcomes. That is why design-based arguments (experiments, staggered rollouts, synthetic control, instruments) are essential.

Takeaway

Potential outcomes provide the language for causal questions in panels. The simple notation is useful, but marketing almost always demands the richer path-dependent framework and explicit attention to anticipation, carryover, and interference.

References

  • Shaw, C. (2025). Causal Inference in Marketing: Panel Data and Machine Learning Methods (Community Review Edition), Section 2.1.
  • Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology.