Re: st: Estimating the CES-Translog Production Function

[Charles Koss <hqtiger@gmail.com>]

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?


Charles

-- 
Charles Koss
http://charlesonnet.blogspot.com

On Sat, Mar 26, 2011 at 11:29 PM, Dawei Zhang <dz.calgary@gmail.com> 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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