Introduction
There are different ways of estimating the parameters of a production function. For example, single-equation and system equation techniques are both possible. Another difference among methods is that estimable forms may either involve direct or indirect estimation of the parameters. For instance, rather than estimate the production function as is, one may instead estimate the derived demand functions or, say, use other relations such as factor shares. Also to be considered are the underlying economic assumptions; such possibilities being perfect competition, constant returns to scale, profit maximization, etc.
Question
Bearing the above in mind, my question is what is the standard (accepted?) method of estimating normalized CES (constant elasticity of substitution) production functions?
For information, a normalized CES production function can be written as
$$ Y = Y_{0} \lbrace \pi_{0} K_{0}^{\frac{1-\sigma}{\sigma}}(K_{t}\cdot e^{\gamma_{K}(t-t_{0})})^{\frac{\sigma-1}{\sigma}} + (1-\pi_{0})N_{0}^{\frac{1-\sigma}{\sigma}}(N_{t}\cdot e^{\gamma_{N}(t-t_{0})})^{\frac{\sigma-1}{\sigma}}\rbrace $$
following the notation found in Klump, McAdam, and Willman (2011, p.22).
Importantly, what data is required to estimate the parameters of this particular production function? And, what is the exact procedure involved? Demonstrations and references are most welcome!
Reference:
Rainer Klump, Peter McAdam, and Alpo Willman, The normalized nested CES production function, theory and empirics, ECB Working Paper Series, No. 1294. (Feb., 2011), 2011.