# Identification assumptions and causal relationships

I'm new to econometrics and I'm having a hard time answering if the following statement is true or false:

"In regression studies, making adequate identification assumptions is sufficient for identifying causal relationships between the variables of interest"

-Strucutural conditional expectation allows us to draw a causal inference

-If we cannot collect data on some variables, we can use identification assumptions to recover the structural conditional expectation

-So, if we make the adequate identification assumptions, we can draw a causal inference -> the statement is true.

Could someone please shed some light on this?

• Commented May 8, 2020 at 17:26

E.g., when you think the causal effect of $X$ on $Y$ is a constant $\beta$, one may identify it with $cov(X, Y)/(var(X))$, the coefficient of a linear regression of Y on X, assuming $E[\epsilon|X]=0$, where $\epsilon$ is the structural error representing all other causes of Y other than X.
Or, when you define the causal parameter in potential outcomes, for example as the ATE $E[Y^{1} - Y^{0}]$, then you sometimes can identify it as $E[Y|X = 1] - E[Y|X = 0]$, assuming $E[Y^{x}|X] = E[Y^{x}]$ for $x \in {1,2}$. The latter assumption is a generalization of the error term assumption: $X$ should be mean-independent from all variables that affect $Y$ save for $X$.