Zeroporfit condition and calibration


I have a simple CES function with capital and total hours worked (h*L). When I follow the standard calibration, I do not end up with 0 dividends.

CES: Y = (share_k*(K)*((siggma-1)/siggma)+(1-share_k)*(h*L)*((siggma-1)/siggma))^(siggma/(siggma-1))

Calibration: share_k= 1/(1+(w/r)*(h*L/K)^(1/siggma)).

What am I missing?

Thank you
ZEROPROFIT.xlsx (13.2 KB)

That looks like a numerical overflow due to your numbers being to big and disparate in size. Zero profits is a result of constant returns to scale and competitive factor markets.

@jpfeifer thank you, that was my first hint. I actually have a way bigger model with different industries, and more inputs (energy, materials). All inputs are very different in size, which ultimately lead to Dividends being non zero. I departed from a super simple model, and had the same because of this size problem.

I actually do not mind having dividends. Since I cannot just simply resolve the problem, I was careful in adding the dividends to the budget constraint of households owning the firms.

Thank you again

That is not valid. These dividends result purely from numerical error. You need to appropriately normalize your model variables to circumvent this issue.

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Thank you @jpfeifer . But how exactly do I do that ?

I already reparametrized the parameters to be consistent with Cantore and Levine, but I might have done some mistakes. i’m gonna check again.

But how do you end up with values like

K_f_nondurable                  		 1.48429e+07
KL_nondurable                   		 809249

? With the usual scaling to technology, you should not get such large values.

What I did is simply parametrize the parameter shares from national account data for capital, labor etc following Cantore and Levine reparametrization:

If then, I multiply the per capital value of K by total labor, I end up with the right value for K used in this sector. But I just spotted an issue in the calibration. In resolving this issue, I end up finally with zero profit. However, I’ll still get at SS the value for K_f and KL that you just mentionned.

But that should allow you to normalize. You can measure capital in dollar or millions of dollars. Similarly, you can measure hours in hours or in thousands of hours.

Ok I’ll try recalibrating carefully this week, and will get back to you.

Thanks very much for the help

One question @jpfeifer , even if the production system is normalized in my model, what about my exogenous variables ?

I cannot normalize them and their size would inevitably be high compared to normalized production/consumption variables. For example :

  • I have Investment in housing that enters the model as a per capita value
  • Investments in power system that also enters in per capita value

The size of these two, if I divide the investments found in national account by the population would still be big…

How do I treat these exogenous variables for normalization ? They end up in the resource constraint

What do you mean with big? You could even just normalize GDP per capita to 1 and work with shares of total GDP for other data. Total investment per capita would then be about 0.2.

Ah just got it :grin:

Thanks !

@jpfeifer Hi,

Regarding the Cantore and Levine reparametrization of CES consumption functions, the distribution parameters add up to 1, while for production functions they do not restrict the distribution parameters to add up to 1.

Can I do the same thing for CES consumption function with different goods, where I do not restrict the distribution parameters to equal to 1 ?

Thank you

My understanding is that, if done correctly, the two versions are identical.