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| RE: Definition of elasticity [ Reply ] By: Arne Henningsen on 2013-07-14 08:23 | [forum:39714] |
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Dear Lukas The elasticity of substitution is always defined as sigma = ( d ( x_1 / x_2 ) / d ( MP_2 / MP_1 ) ) * ( ( MP_2 / MP_1 ) / ( x_1 / x_2 ) ), where x_k is the quantity of the k-th input and MP_k is the marginal product of the k-th input. If you derive this elasticity of substitution from a two-input CES function as defined as defined in [1], you get sigma = 1 / ( 1 + rho ). Sato (1967) writes that rho = ( 1 - sigma ) / sigma (equation 5); solving this equation for sigma, you also get sigma = 1 / ( 1 + rho ). You correctly note that rho is in the interval (-1, infinity) so that sigma is in the interval (0, infinity). In the two-input case, the two inputs cannot be complements -- no matter which functional form you use (as long as the monotonicity condition is fulfilled). Therefore, it is not surprising that sigma is non-negative. [1] http://EconPapers.repec.org/RePEc:foi:wpaper:2011_9 Best regards, Arne |
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| Definition of elasticity [ Reply ] By: Lukas Recka on 2013-06-27 16:33 | [forum:39702] |
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Dear Arne, I would like to ask one more question. I dont understand why you define the elasticity of substituion as sigma=1/(1+rho) and not like Sato (1967) sigma=1/(1-hro), while the domain of rho has similar dimenstion (-1 to infintiy). I your case the domain of sigma is [0, infinity). That means we cannot have negative elasticity even for AES which allows negative values for complements. As a result, we cannot see if product of the nest and the third output are subtitutes of complements. Maybe I am wrong or missed some explanation but I don't see why it is so. Thank you very much for your explanation. Best regards, Lukas |
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| RE: micEconCES [ Reply ] By: Lukas Recka on 2013-04-24 20:54 | [forum:39543] |
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Dear Arne, thank you very much for your help. Now, it is already clear :) I should study the papers and documentation more carefully next one. My best, Lukas |
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| RE: micEconCES [ Reply ] By: Arne Henningsen on 2013-04-23 21:14 | [forum:39537] |
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Hej Lukas Thank you for providing a reproducible example. This enabled me to identify the problem: some of your input quantities are zero. For simplicity, I explain this for the CES function with two input quantities but it is basically the same for the other CES functions. I will refer to the equation numbers in our paper that describes the micEconCES package [1]. The partial derivative of the CES function (1) with respect to rho (18) includes the terms ln(x1) and ln(x2) so that this derivative is undefined if either x1 or x2 is zero. If the partial derivative of the CES function (1) with respect to rho (18) is undefined, also the partial derivative of the sum of squared residuals (RSS) with respect to rho (24) is undefined. As derivative-based optimisation algorithms usually do not work if some of the derivatives are undefined, the minimisation of RSS does not work in the presence of zero input quantities. You might try to use optimisation algorithms that do not use partial derivatives but they are usually very slow. Furthermore, I am not sure whether it makes sense at all to use a CES production function with zero input quantities, e.g. because a CES function with zero input quantities is only defined for -1 < rho < 0. [1] http://EconPapers.repec.org/RePEc:foi:wpaper:2011_9 Best regards, Arne |
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| RE: micEconCES [ Reply ] By: Lukas Recka on 2013-04-23 14:45 | [forum:39532] Estimation.rar (37) downloads
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Dear Arne, thank you very much. But unfortunatelly it didn't help. I have to say I am not very experienced in R, so maybe I do some elementary mistake and I would like to apologize for that. But if I use the same code as you in your WP, I only change name of data and name of variables. With "GermanIndustry" it works well but not with mine. Therefore I am confused. I attach with part of my code and data. Thank you very much for your time and help. I will definitely cite micEconCES. With best regards, Lukas |
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| RE: micEconCES [ Reply ] By: Arne Henningsen on 2013-04-21 21:37 | [forum:39527] |
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Dear Lukas cesEst() always assumes that you have pooled data. There could be many reasons for NA/NaN values in the gradients. You might try to specify starting values using argument "start" and/or use another optimisation method. If this does not help, you could post here a (simplified) reproducible example so that I or others can take a deeper look at the reasons for the NA/NaN values in the gradients. Please do not forget to cite micEconCES in your publications. Best regards, Arne |
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| micEconCES [ Reply ] By: Lukas Recka on 2013-04-19 15:29 | [forum:39521] |
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Hello every one, If I use the cesPort1 in order to estimate elasticity of substitution on a pooled data (one sector, 27 countries, 15 yeas), it yield the following error in nlminb: cesPort1 <-cesEst("Y",c("K","E","empe"),tName="time",data=Textil,method="PORT",control=list(iter.max=1000,eval.max=2000)) Error in nlminb(start = start, objective = cesRss, gradient = cesRssDeriv, : NA/NaN gradient evaluation Should I specify somehow that I have pooled data? Could you advice me how? Thank you very much in advance. Lukas |
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