to the model in 4 with x − z playing the role of z, u$_{x}$ playing the role of x $^{∗}$, − u playing the role of u, and x ∗ playing the role of u$_{x}$. The additional convolution equations arising from the extra independence conditions provide extra equations and involve the unknown density f$_{u}$$_{x}$. This representation leads to a generalization of Kotlyarski’s identification result similar to that obtained by Evdokimov (2011) who used the joint characteristic function. The equations in 4a make it possible to identify f$_{u}$, f$_{u}$$_{x}$ ahead of f$_{x}$ ∗ ; for identification this will require less restrictive conditions on the support of the characteristic function for x $^{∗}$. Consider a model ˜ z = AU, with A a matrix of known constants and ˜ z a m × 1 vector of observables, U a vector of unobservable variables. Usually, A is a block matrix and AU can be represented via a combination of mutually independent vectors. Then without loss of generality consider the model where ˜ A is a m × d known matrix of constants, ˜ z is a m × 1 vector of ob- servables, unobserved x ∗ is d × 1 and unobserved ˜ u is m × 1 . If the model (2) can be transformed to model 3 considered above, then x ∗ will be identi- fied whenever identification holds for model 3. Once some components are 19 ˜ z = ˜ Ax ∗ + ˜ u, (2) 2.2.3 Some extensions A. Common factor models.