I am having some trouble trying to identify the parameters in the following structural model that I am trying to estimate.
$$ y = a'x_1 + \beta\eta + \epsilon_1 $$ $$ \eta = b'x_2 + \delta T+\epsilon_2 $$
$y$ is, say, any observable human behavior, $\eta$ is any unobservable human trait, $T$ is any treatment that affects the trait, $x_1,x_2$ are any individual-level covariates, and $\epsilon_1,\epsilon_2$ are errors. The reduced form of this model is $$ y = a'x_1+b'\beta x_2+\beta\delta T+ \epsilon_1 +\beta\epsilon_2 $$
The parameters I am interested in are $\beta,\delta,b'$, and I cannot figure out how I can identify them or estimate them.
I have been looking into Structural Equation Models (SEM), but was wondering if someone could direct me as to how to identify it or estimate this model.