Estimating elasticity of substitution in nested CES functions I have aggregate data on $L_t, K_t$ and $X_t$, and want to estimate elasticity of substitution parameters, $\gamma$ and $\sigma$ for these factors. Assuming the production function takes the following form: $$Y_t=(A_lL^{\gamma}+[A_kK_t^{\sigma} +A_xX_t^{\sigma}]^\frac{\gamma}{\sigma})^{\frac{1}{\gamma}}  $$

Technology parameters, $A$s are not observable and hence need to be controlled for in an econometric specification. I am thinking of first estimating the parameter, $\sigma$, on the inner CES function combining $K$ and $X$. Then I should be able to estimate the outer CES parameter, $\gamma$. In a way, the two parameters are not jointly estimated. Would this method be valid, I mean, in statistical sense? Will I get consistent and unbiased estimates? 
I've read papers on non-linear regression methods, but was wondering if this simple approach is feasible. 
Thanks.
Neglecting technology parameters and assuming constant returns to scale, the parameters $\sigma$ and $\gamma$ are jointly estimable via dynamic (least squares) programming.
See this paper.