4  Causality for Decisions

4.1 Why “causal effect” is not the end goal

In practice, you rarely do causal inference to admire an estimate. You do it to make a choice:

  • Should we expand a program?
  • Which policy should we adopt?
  • What price change should we implement?
  • Which intervention is worth funding?

A causal estimate is an input to a decision, not the decision itself.

This chapter builds a simple bridge:

Causal inference tells you what would happen under different actions.
Decision-making tells you which action to take given goals, costs, uncertainty, and constraints.

Even a perfectly identified causal effect can be irrelevant if it is not the effect you need for the decision at hand. (shmueli2010?)

4.2 Step 1: Make the decision explicit

Start by writing the decision in a form like:

  • Action set: \(\mathcal{A} = \{a_0, a_1, \dots\}\) (do nothing, do something, choose intensity, choose timing)
  • Target population: who is affected?
  • Outcome(s): what matters (often multiple: benefits, harms, equity, budget)
  • Time horizon: short run vs long run
  • Constraints: budget, capacity, political feasibility, legal restrictions

If you can’t state these, you are not ready to pick an estimand.

4.3 Step 2: Pick the estimand that matches the decision

Causal inference is full of estimands. The best estimand depends on what you will do.

4.3.1 Common estimands

  • ATE: average effect if everyone were treated vs not treated
  • ATT: average effect for those who actually got treated
  • LATE: effect for compliers (often in IV settings)

In potential outcomes notation, with treatment \(D \in \{0,1\}\):

\[ \text{ATE} = \mathbb{E}\!\left[ Y(1) - Y(0) \right]. \]

\[ \text{ATT} = \mathbb{E}\!\left[ Y(1) - Y(0) \mid D = 1 \right]. \]

\[ \text{LATE} = \mathbb{E}\!\left[ Y(1) - Y(0) \mid \text{compliers} \right]. \]

These are not interchangeable. (imbensrubin2015?)

4.3.2 Decision mapping examples

  • Scaling a program nationwide: ATE is often closer to the policy question than ATT.
  • Improving a program already running for participants: ATT may be more relevant.
  • Policy lever that shifts participation at the margin (e.g., eligibility, encouragement): LATE may be relevant (and also limited in scope). (angristpischke2009?)

Rule: If you can’t explain in one sentence why your estimand matches your decision, you probably have the wrong estimand.

4.4 Step 3: Convert effects into value (benefits, costs, and trade-offs)

Most decisions require you to translate outcomes into some measure of value.

A simple template is net benefit (or net present value):

  • \(B(a)\) = expected benefits under action \(a\)
  • \(C(a)\) = expected costs under action \(a\)

Choose the action that maximizes expected net benefit:

\[ a^* = \arg\max_{a \in \mathcal{A}}\; \mathbb{E}\!\left[ B(a) - C(a) \right]. \]

This sounds obvious, but it forces clarity about what you value and what you count as a cost.

4.4.1 A minimal “treatment decision” example

Suppose action \(a_1\) is “treat” and \(a_0\) is “do not treat.” Let:

  • outcome \(Y\) = benefit metric (e.g., earnings, health, productivity)
  • per-unit treatment cost = \(c\) (in same units, or monetized)

Treat if the expected causal effect exceeds cost:

\[ \mathbb{E}\!\left[ Y(1) - Y(0) \right] > c. \]

This is a decision rule, not an estimation procedure.

4.5 Step 4: Uncertainty matters—don’t collapse it too early

A single point estimate is not enough to decide responsibly. For decisions, you care about:

  • uncertainty in the effect estimate
  • uncertainty in costs
  • uncertainty in implementation (compliance, spillovers)
  • uncertainty in external validity (transportability)

4.5.1 “Statistical significance” is not the decision criterion

A \(p\)-value answers a narrow question about sampling variation under a null hypothesis. Many decisions are better framed as:

  • What is the probability the effect is positive?
  • What is the probability the effect exceeds a policy-relevant threshold?
  • What is the worst-case plausible effect given threats to identification?

This is why intervals, sensitivity analyses, and robustness checks are central in applied causal work. (hernanrobins2024?)

4.5.2 A threshold framing you can actually use

Let \(\tau\) be the effect and \(\tau_0\) a “break-even” threshold (e.g., cost per unit). A decision-relevant quantity is:

\[ \Pr(\tau > \tau_0 \mid \text{data, assumptions}). \]

Even without full Bayesian machinery, you can approximate this idea with confidence intervals plus a threshold test:

  • If the entire interval is above \(\tau_0\): strong case to act.
  • If the interval overlaps \(\tau_0\): decision depends on risk tolerance and value of more information.
  • If the entire interval is below \(\tau_0\): strong case not to act.

4.6 Step 5: Heterogeneous effects—who benefits, who is harmed?

Average effects can hide distributional realities.

Two interventions can have the same ATE but very different implications:

  • one helps everyone a little
  • another helps a minority a lot and harms others

Decision-making often requires targeting: - Who should receive the intervention? - Under what conditions? - At what intensity?

4.6.1 A targeting view

Let \(X\) be covariates (needs, risk, baseline status). The decision might be a rule \(g(X)\) determining treatment:

  • treat if \(g(X)=1\)

The causal target becomes conditional effects like:

\[ \tau(x) = \mathbb{E}\!\left[ Y(1) - Y(0) \mid X=x \right]. \]

You rarely identify \(\tau(x)\) perfectly, but even coarse heterogeneity (by subgroup) can radically improve decisions.

Warning: Subgroup analysis is a bias magnet if done casually. Treat it as a design problem, not a fishing expedition.

4.7 Step 6: External validity is part of the decision

Even if your effect is internally valid, the decision is about your context:

  • a different population
  • a different time period
  • a different implementation capacity
  • different prices, incentives, or equilibrium responses

So you should always say:

  • What exactly is the population and intervention I identified?
  • How different is the target setting from the study setting?
  • What mechanisms might change the effect when scaled?

A useful practice is to separate claims:

  1. Identified effect (study context): what you can defend strongly
  2. Transported effect (target context): what you can defend with additional assumptions and evidence

4.8 Step 7: The value of information (VOI) and “should we learn more first?”

Sometimes the right decision is not “treat” or “don’t treat,” but:

  • run a pilot
  • collect better data
  • wait for another policy cycle
  • change measurement
  • test implementation logistics

The decision depends on the value of reducing uncertainty.

4.8.1 Intuition (no heavy math)

You can think of VOI as:

How much better would our decision be if we had better information, compared to acting now?

If decisions are high-stakes and uncertainty is large, learning is valuable. If decisions are low-stakes or uncertainty won’t change the decision, learning is not worth it.

A practical heuristic:

  • If your current evidence leaves you genuinely torn between two actions, consider a pilot or better identification.
  • If every plausible effect estimate points to the same choice, act (and monitor).

4.9 A reusable “Causal → Decision” template

When you finish an analysis, write a short decision memo with:

  1. Decision: what action is being considered?
  2. Estimand: what causal effect is relevant, and why?
  3. Identification: why you believe the estimate is causal (assumptions + threats)
  4. Magnitude: best estimate + interval
  5. Decision threshold: what effect size justifies action?
  6. Risks: key failure modes (bias, spillovers, scaling issues)
  7. Recommendation: act / pilot / gather more evidence

This is how causal work becomes operational.

4.10 Exercises

  1. Estimand alignment You are advising a city on expanding a job training program that currently serves volunteers.
    • What is the decision?
    • Which estimand is most relevant (ATE, ATT, something else)?
    • What would make your chosen estimand misaligned with the decision?
  2. Decision threshold Suppose your program increases earnings by an estimated \(\hat\tau = 800\) per year, with a 95% CI of \([100, 1500]\). The program costs \(c = 600\) per participant per year.
    • How would you reason about acting vs piloting?
    • What additional information would be most valuable?
  3. Heterogeneity and targeting Imagine the program works mostly for participants with low baseline earnings.
    • Write a simple targeting rule in words.
    • What data and assumptions would you need to evaluate it causally?

4.11 Further reading