# How to define Unit-specific quantity of the effect of a continuous variable on another continuous one?

Recently Lundberg, 2021 [1] emphasized the necessity to define a unit-specific quantity, target population, and causal diagram, to clarify the theoretical and empirical estimands of any quantitative study. The state "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." However, almost all the examples I see compare the aggregate (usually average) unit-specific quantity across two groups of a dichotomous variable, such as males vs. females, treated vs. control, ... I found no single example of analyzing the correlation between two continuous variables or the causal effect of one continuous variable on another one.

Please give me such an example or explain how one can formulate the unit-specific quantity for the causal effect of one continuous variable on another one.

References:

[1] 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.

• Can you describe what you mean by "unit-specific"? Do you mean individual treatment effects? We generally can't estimate those with any certainty regardless of the treatment type. Average treatment effects may be identified but individual treatment effects are not. There are average treatment effects for continuous treatments, though; are those what you are asking about?
– Noah
Jan 9, 2022 at 0:03
• Please check out the cited paper. They've fully explained it. Jan 9, 2022 at 16:34