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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?

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    $\begingroup$ "I got" How did you get this numbers? Exercise, regression on data? What data? $\endgroup$ – Giskard May 28 '19 at 20:07
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    $\begingroup$ Just imagine that you have some amount $L$ of labor. As you increase capital, you get less output. $\endgroup$ – Art May 29 '19 at 4:15
  • $\begingroup$ I estimated them, using data from national accounts. $\endgroup$ – indigo_luc May 29 '19 at 7:31
  • $\begingroup$ I updated the question. $\endgroup$ – indigo_luc May 29 '19 at 10:37
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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.

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  • $\begingroup$ So it is an odd result. Thank you Art. $\endgroup$ – indigo_luc May 30 '19 at 9:53

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