<p>To elaborate on my comment above, whether there's a "restriction" on the possible values of <span class="math-container">$a$</span> depends on your assumptions about the production function.</p>

<p>If you assume that all inputs into the production function contribute positively to the final output, then it must be that <span class="math-container">$a \in (0, 1)$</span>.</p>

<p>Since you estimated the parameter, you might want to check the confidence interval of the estimated parameter. You can do a one-sided test if <span class="math-container">$a &lt; 1$</span>, for example.</p>

CC BY-SA 4.0
2019-05-30T09:53:44.070Z
So it is an odd result. Thank you Art.
indigo_luc
CC BY-SA 4.0
2019-05-30T08:40:55.377Z
2019-05-30T08:40:55.377Z
Art
<p>I estimated the CES function (<a href="https://en.wikipedia.org/wiki/Constant_elasticity_of_substitution" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Constant_elasticity_of_substitution</a>) using national accounts data for France. I got (using notation in wikipedia):</p>

<p>a = 1.19
r = -0.48</p>

<p>so the term next to capital is negative (-0.19). Is this possible? What does it mean? I don't see anywhere in that website a restriction on the sign of "a". My textbook does not state restrictions either. Is it fine? Or is it a problem?</p>

<p>Any thoughts on the issue?</p>

CC BY-SA 4.0
2019-05-28T20:07:25.730Z
"I got" How did you get this numbers? Exercise, regression on data? What data?
Giskard
CC BY-SA 4.0
2019-05-29T04:15:04.960Z
Just imagine that you have some amount $L$ of labor. As you increase capital, you get less output.
Art
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2019-05-29T07:31:46.407Z
I estimated them, using data from national accounts.
indigo_luc
CC BY-SA 4.0
2019-05-29T10:37:00.153Z
I updated the question.
indigo_luc
<production-function><structural-estimation>
Can a CES parameter be negative?
indigo_luc
# Can a CES parameter be negative?

(Asked by: username_0 on 2019-05-28)

I estimated the CES function (<https://en.wikipedia.org/wiki/Constant_elasticity_of_substitution>) using national accounts data for France. I got (using notation in wikipedia):

a = 1.19
r = -0.48

so the term next to capital is negative (-0.19). Is this possible? What does it mean? I don't see anywhere in that website a restriction on the sign of "a". My textbook does not state restrictions either. Is it fine? Or is it a problem?

Any thoughts on the issue?

**Tags:** production-function, structural-estimation
> **Comments:**
> **username_1**: "I got" How did you get this numbers? Exercise, regression on data? What data?  
> **username_2**: Just imagine that you have some amount $L$ of labor. As you increase capital, you get less output.  
> **username_0**: I estimated them, using data from national accounts.  
> **username_0**: I updated the question.  

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## 1 answers

### Answer by username_2 on 2019-05-30. Score: 0 | Accepted answer

To elaborate on my comment above, whether there's a "restriction" on the possible values of $a$ depends on your assumptions about the production function.

If you assume that all inputs into the production function contribute positively to the final output, then it must be that $a \in (0, 1)$.

Since you estimated the parameter, you might want to check the confidence interval of the estimated parameter. You can do a one-sided test if $a < 1$, for example.

> **Comments:**
> **username_0**: So it is an odd result. Thank you Art.  

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