Suppose that an endogenous variable yt is related to two exogenous shocks:
where alpha and beta are positive parameters and ε_t~iidN(μ_ε,σ^2_ε)/ η_t~iidN(μ_η,σ^2_η)
cov(ε_t, η_t)=0. eqsilon and eta are unobservable.
(1) are all the parameters(alpha, beta, mus, sigmas) identified?
(2) suppose that alpha=beta=1 and that we can observe another variable x_t=η_t.
can we identify the remaining parameters?
(3) suppose that y is not observed. with the information in (2), what is E(y|x)?