- 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."

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."

Theoretical Estimand vs. Empirical Estimand

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."

University of Michigan - Ann Arbor

"The estimand is the target quantity—the purpose of the statistical analysis ... the thing we are estimating" " that connects statistical evidence to theory."

It refers "to both the theoretical and the empirical estimands."

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

Theoretical Estimand

"We make only one point in this article. Every quantitative study must be able to answer the question: what is your estimand? The estimand is the target quantity—the purpose of the statistical analysis. Much attention is already placed on how to do estimation; a similar degree of care should be given to defining the thing we are estimating. We advocate that authors state the central quantity of each analysis—the theoretical estimand—in precise terms that exist outside of any statistical model. In our framework, researchers do three things: (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; and (3) learn from data. Adding precise estimands to research practice expands the space of theoretical questions, clarifies how evidence can speak to those questions, and unlocks new tools for estimation. By grounding all three steps in a precise statement of the target quantity, our framework connects statistical evidence to theory."

"Each theoretical estimand is linked to an empirical estimand involving only observable quantities (e.g., a difference in means in a population) by assumptions about the relationship between the data we observe and the data we do not. These identification assumptions can be conveyed in a Directed
Acyclic Graph (DAG. i.e., a causal diagram)."

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