<p>I have empirically estimated the elasticity of substitution parameter in the following model: 
<span class="math-container">$$Y_t=[(A_1L_tK_{t})^{\rho} +(A_2M_{t})^{\rho}]^\frac{1}{\rho}  $$</span></p>

<p>here, <span class="math-container">$Y_t$</span> is output, <span class="math-container">$A_i$</span> is a factor-augmenting technology index, <span class="math-container">$K, L$</span> and <span class="math-container">$M$</span> are factors of production and the elasticity of substitution is <span class="math-container">$\sigma = 1/(1 - \rho)$</span>. I estimated <span class="math-container">$\rho$</span> combining the logorithmised form of the above function and its FOC conditions in a system of nonlinear equations. </p>

<p>I am getting <span class="math-container">$\rho&gt;1$</span> which gives a negative elasticity of subsitution, <span class="math-container">$\sigma&lt;0$</span>. 
I am now struggling to put a plausible interpretation on this result; theoretically, the lower bound for <span class="math-container">$\sigma$</span> is 0. </p>

<p>I am guessing that I could still interpret the negative <span class="math-container">$\sigma$</span> as an evdience that factors are strong complements. Would this be a correct interpretation?</p>

CC BY-SA 4.0
2020-04-27T17:02:44.953Z
In my models, I assume $0<\rho<1$ so I'm shocked :) I guess you double-checked your estimations and calculations. In this paper, https://link.springer.com/article/10.1007/s13209-019-00205-0 they interpret $σ<0$ as strong complementarity.
emeryville
CC BY-SA 4.0
2020-04-27T18:02:35.467Z
I am afraid, I cannot assume it away. I have to estimate it :(. Why do you ussume $0<\rho<1$. It can be negative and still be theoretically plausible.
london
CC BY-SA 4.0
2020-04-27T18:54:50.073Z
I assume the products to be somewhat sustitutes with $\sigma>1$.
emeryville
CC BY-SA 4.0
2020-04-27T19:47:01.160Z
Please could you define the terms of the function?
emeryville
CC BY-SA 4.0
2020-04-28T09:57:42.367Z
@emeryville, yes $\sigma>1$ implies gross substitutability between the factors. However, my empirical estimates give $\sigma<0$ which is theoretically implausible.
london
<production-function><regression><elasticity-of-substitution><ces-function>
Negative elasticity of substitution in a CES production function
london
# Negative elasticity of substitution in a CES production function

(Asked by: username_0 on 2020-04-27)

I have empirically estimated the elasticity of substitution parameter in the following model:
$$Y\_t=[(A\_1L\_tK\_{t})^{\rho} +(A\_2M\_{t})^{\rho}]^\frac{1}{\rho} $$

here, $Y\_t$ is output, $A\_i$ is a factor-augmenting technology index, $K, L$ and $M$ are factors of production and the elasticity of substitution is $\sigma = 1/(1 - \rho)$. I estimated $\rho$ combining the logorithmised form of the above function and its FOC conditions in a system of nonlinear equations.

I am getting $\rho>1$ which gives a negative elasticity of subsitution, $\sigma<0$.
I am now struggling to put a plausible interpretation on this result; theoretically, the lower bound for $\sigma$ is 0.

I am guessing that I could still interpret the negative $\sigma$ as an evdience that factors are strong complements. Would this be a correct interpretation?

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

> **Comments:**
> **username_1**: In my models, I assume $0<\rho<1$ so I'm shocked :) I guess you double-checked your estimations and calculations. In this paper, https://link.springer.com/article/10.1007/s13209-019-00205-0 they interpret $σ<0$ as strong complementarity.  
> **username_0**: I am afraid, I cannot assume it away. I have to estimate it :(. Why do you ussume $0<\rho<1$. It can be negative and still be theoretically plausible.  
> **username_1**: I assume the products to be somewhat sustitutes with $\sigma>1$.  
> **username_1**: Please could you define the terms of the function?  
> **username_0**: @username_1, yes $\sigma>1$ implies gross substitutability between the factors. However, my empirical estimates give $\sigma<0$ which is theoretically implausible.  

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## 0 answers

