content_image/298211.jpg content_image/298212.jpg
function that satisfies the equation 

<img src='content_image/298211.jpg'>

We can show that the function ˜ κ$_{k}$ is uniquely determined in the class of continuous functions on W by the equation (20) . Proof is identical to the proof in part (a) for equation ((19)) . Next we show that φ is then uniquely determined on W. Indeed, the continuous function 

<img src='content_image/298212.jpg'>

is the unique solution to ˜ φ (0) = 1 , ˜ φ − 1 k ˜ φ ′ = κ$_{k}$ ; then since κ$_{k}$ (= φ ′ $_{k}$φ − $^{1}$) is uniquely determined on W, so is φ on W where it coincides with ˜ φ. 

By Theorem 2, then γ is then uniquely defined on W. Then in S ∗ g = F t − $^{1}$( γ ) is uniquely defined. 

This Theorem extends the identification results of Schennach (2007) and Zinde-Walsh(2009) to the multivariate case and to the case when γ rather than φ is continuously differentiable (part (a) of this Theorem), and extends the identification result of Cunha et al (2011) by showing that in the model with several measurements considered there identification additionally holds with the requirement of continuous differentiability of φ replacing the re- quirement that γ be continuously differentiable (part (b)). 

