5
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ This is related to the question I asked. The linked reference therein estimates a normalized nested CES production function. Might be of interest. $\endgroup$ – Graeme Walsh May 1 '16 at 16:24
  • 2
    $\begingroup$ Possible duplicate of CES production function estimation $\endgroup$ – luchonacho Feb 25 '17 at 15:20
  • $\begingroup$ Doesn't look like a duplicate. That linked question is a two input production function and the above is a three input production function that is nested. $\endgroup$ – BKay Feb 27 '17 at 13:08
1
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ I cannot ignore the technology parameters. Thanks. $\endgroup$ – london Mar 31 at 12:00

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.