"The unit-specific quantity clarifies whether the research goal is causal, and if so, what counterfactual intervention is being considered." It "involves a substantive question: what factual or counterfactual thing would we like to know for each unit in the population?"

Unit-specific Quantity of Theoretical Estimand

The target Population specifies "over whom or what do we aggregate that unit-specific quantity?"

Target Population of Theoretical Estimand

1- **Estimated Rate**:
$$\frac{1}{n} \sum_{i=1}^n Y_{i}$$
- **Target population**: Mean over every *i* among U.S. adults
- **Unit-specific quantity ($Y_{i}$)**: Whether each *i* is employed

2- **Causal question**: How would the probability of employment differ if we enrolled a randomly chosen individual in job training or not?
$$\frac{1}{n} \sum_{i=1}^n \left( Y_{i}(1) - Y_{i}(0) \right)$$
- **Target population**: Mean over every *i* among U.S. adults
- **Unit-specific quantity**: Whether each *i* is employed
   - **$Y_{i}(1)$**: Employment if enrolled in job training
   - **$Y_{i}(0)$**: Employment if not enrolled in job training


Components of Theoretical Estimand - Example: Employment Rate Among U.S. Adults

- Unit-specific quantity
- Target population

"The goal is often a quantity involving two components: a unit-specific quantity subscripted by i aggregated over a target population of units."

University of Michigan - Ann Arbor

Theoretical estimand "sets the targets of inference" and defines the estimand "outside of any statistical model ... like an average causal effect or a population mean..., clearly connecting this quantity to theory" through argument.

"The unit-specific quantity and target population combine to define the theoretical estimand: the thing we would like to know if we had data for the full
population in all factual or counterfactual worlds of interest. A paper may have multiple theoretical estimands."

Theoretical Estimand

Lundberg, I., Johnson, R., & Stewart, B. M. (2021). What is your estimand? Defining the target quantity connects statistical evidence to theory. American Sociological Review, 86(3), 532-565.
https://journals.sagepub.com/doi/pdf/10.1177/00031224211004187?casa_token=kd-8FImHZ90AAAAA:jzdKy6ZOAbd6PmxW2sXQG3CwYeSScDGeNKRJkPI0yGRzTBr2j7dUw384Bgg3Fihk9TiVLnOOUL81L4E

What Is Your Estimand? Defining the Target Quantity Connects Statistical Evidence to Theory

Components of Theoretical Estimand

1- "Set a **theoretical estimand**, clearly connecting this quantity to theory"

2- "Link to an **empirical estimand**, which is informative about the theoretical estimand under some identification assumptions"

3- Use "an **estimation strategy** to learn the empirical estimand (e.g., a regression model) ... from data."

Three Critical Choices in Causal Inference

1- "The former may involve unobservable quantities such as counterfactuals, whereas the latter involves only observable data."

2- "The choice of theoretical estimands requires substantive argument about the theory and goals; the choice of empirical estimands requires conceptual argument about unobserved data."

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