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Re: st: Estimating the CES-Translog Production Function

From   Dawei Zhang <>
Subject   Re: st: Estimating the CES-Translog Production Function
Date   Thu, 31 Mar 2011 22:53:25 -0600

Hi Charles,

Thanks for the advice. We tried really small steps (4e*10^-11), and also only imposed the constraints to make sure the log expression is valid and rho not equal to zero. However, we still couldn't get all the parameters to converge (sometimes rho, sometimes delta_Z). Actually, I am beginning the wonder what it means in stata if the estimation results for certain parameters are just "dots". Does this mean the parameters not converged? or the model is not identified? or singular matrix?..........


On 27/03/2011 7:02 AM, Charles Koss wrote:
Two ideas come to mind:

a) Try smaller step size between iterations.
b) Try different numerical optimization techniques

Can you describe the convergence without the constraints?


On Sat, Mar 26, 2011 at 11:29 PM, Dawei Zhang <> wrote:

>  Dear Statalist users,
>  I am having some convergence problems when estimating the CES-Translog
>  production function using the "nl" command in Stata. The program has
>  converged in terms of reaching a minimum residual sum of squares, however
>  not all of the parameters converged to steady values. The estimation form is
>  as following:
>  ln(Output) = {alpha}  -(1/{rho}) * ln[ {delta_Z} * Z^{-rho} + {delta_K} *
>  K^{-rho} + (1 - {delta_Z} - {delta_K}) * L^{-rho} ] + {beta_ZZ} * ln(Z)^{2}
>  + {beta_KK} * ln(K)^{2}
>                       + {beta_LL} * ln(L)^{2} + {beta_ZK} * ln(Z) * ln(K) +
>  {beta_LZ} * ln(L) * ln(Z) + {beta_LK} * ln(L) * ln(K) + epsilon   ,
>  where Output, Z, K, and L are the data. We have 10 parameters to be
>  estimated: alpha, rho, delta_Z, delta_K, beta_KK, beta_LL, beta_ZZ, beta_ZK,
>  beta_LZ, and beta_LK. We use re-parameterization (mainly using tanh() and
>  invlogit()) to impose interval constraints on the parameters: alpha in
>  (-5,5), rho in (-2,2) but not equal to 0, delta_Z in (0,1), delta_K in
>  (0,1), 1 - delta_Z - delta_K>0 (we use multinomial logit to reparameterize
>  this constraint), and all the rest parameters in (-1,1).
>  After trying 2000 sets of starting values randomly selected from the
>  intervals mentioned above, we could not have all 10 parameters converge at
>  the same time, especially for the two parameters: delta_Z and rho. We tried
>  a few different datasets and this problem persists. Any suggestions on how
>  we can solve this problem?
>  Thank you,
>  Dawei
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