st: Estimating the CES-Translog Production Function

[Dawei Zhang <dz.calgary@gmail.com>]

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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