<p>Neglecting technology parameters and assuming constant returns to scale, the parameters <span class="math-container">$\sigma$</span> and <span class="math-container">$\gamma$</span> are jointly estimable via dynamic (least squares) programming.
See <a href="https://arxiv.org/pdf/1902.01052.pdf" rel="nofollow noreferrer">this paper</a>.</p>

CC BY-SA 4.0
2019-03-31T12:00:58.717Z
I cannot ignore the technology parameters. Thanks.
london
CC BY-SA 4.0
2019-03-27T01:15:55.327Z
2019-03-27T01:15:55.327Z
Kazuhiko Nishimura
<p>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: $$Y_t=(A_lL^{\gamma}+[A_kK_t^{\sigma} +A_xX_t^{\sigma}]^\frac{\gamma}{\sigma})^{\frac{1}{\gamma}}  $$</p>

<p>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.</p>

CC BY-SA 3.0
2016-05-01T16:24:02.693Z
This is related to the [question](http://economics.stackexchange.com/questions/10586/ces-production-function-estimation) I asked. The linked reference therein estimates a normalized nested CES production function. Might be of interest.
Graeme Walsh
CC BY-SA 3.0
2017-02-25T15:20:10.737Z
Possible duplicate of [CES production function estimation](http://economics.stackexchange.com/questions/10586/ces-production-function-estimation)
luchonacho
CC BY-SA 3.0
2017-02-27T13:08:28.787Z
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.
BKay
<elasticity><production-function><elasticity-of-substitution>
Estimating elasticity of substitution in nested CES functions
london
# Estimating elasticity of substitution in nested CES functions

(Asked by: username_0 on 2016-05-01)

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.

**Tags:** elasticity, production-function, elasticity-of-substitution

> **Comments:**
> **username_1**: This is related to the [question](http://economics.stackexchange.com/questions/10586/ces-production-function-estimation) I asked. The linked reference therein estimates a normalized nested CES production function. Might be of interest.  
> **username_2**: Possible duplicate of [CES production function estimation](http://economics.stackexchange.com/questions/10586/ces-production-function-estimation)  
> **username_3**: 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.  

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## 1 answers

### Answer by username_4 on 2019-03-27. Score: 1

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](https://arxiv.org/pdf/1902.01052.pdf).

> **Comments:**
> **username_0**: I cannot ignore the technology parameters. Thanks.  

---

