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# st: Stochastic frontier model_ constraining coefficients

 From Declan.Curran@dcu.ie To statalist@hsphsun2.harvard.edu Subject st: Stochastic frontier model_ constraining coefficients Date Thu, 16 Sep 2010 21:03:22 +0100

```Hello, I hope you can help me:

I am running a time varying decay (panel) stochastic frontier model for a
translog production function. The model converges but my capital and labour
coefficients are -0.52 and 1.52, respectively (see output below). So, they
add to 1 (constant returns) but they are not between 0-1.

I try to constrain their values to 0-1 using the following constraints:

constraint define 4 _b[capstock] >0
constraint define 5 _b[capstock] <1
constraint define 6 _b[emp] >0
constraint define 7 _b[emp] <1

Unfortunately, I then get a (green) error message r111 and the model converges
but again yields capital and labour coefficients of -0.52 and 1.52.
(note: constraint number 4 caused error r(111))
(note: constraint number 5 caused error r(111))
(note: constraint number 6 caused error r(111))
(note: constraint number 7 caused error r(111))

I would be very grateful for any suggestions as to how I can solve this problem.

thanks!

Declan

Time-varying decay inefficiency model Number of obs =
551
Group variable: countryid Number of groups =
19

Time variable: year Obs per group: min =
29
avg =
29
max =
29

Wald chi2(6) = 7294.61
Log likelihood = 801.04002 Prob > chi2 = 0.0000

( 1) [gdp]capstock + [gdp]emp = 1
( 2) [gdp]t_emp + [gdp]t_capstock = 0
( 3) - [gdp]h_emp2 + [gdp]h_capstock2 = 0
------------------------------------------------------------------------------

&#8195;
gdp | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
capstock | -.5211088 .1083487 -4.81 0.000 -.7334683 -.3087494
emp | 1.521109 .1083487 14.04 0.000 1.308749 1.733468
t | .0422084 .0039268 10.75 0.000 .034512 .0499047
h_t2 | -.0000759 .0000767 -0.99 0.322 -.0002262 .0000744
t_emp | .004327 .0006317 6.85 0.000 .003089 .0055651
t_capstock | -.004327 .0006317 -6.85 0.000 -.0055651 -.003089
h_emp2 | .0316302 .0182119 1.74 0.082 -.0040645 .067325
h_capstock2 | .0316302 .0182119 1.74 0.082 -.0040645 .067325
emp_cap | .0281684 .0186388 1.51 0.131 -.0083629 .0646998
_cons | 3.272649 .3570213 9.17 0.000 2.5729 3.972398
-------------+----------------------------------------------------------------
/mu | -1.431065 5.785474 -0.25 0.805 -12.77039 9.908256
/eta | .0085057 .0018809 4.52 0.000 .0048192 .0121921
/lnsigma2 | -1.232547 3.305146 -0.37 0.709 -7.710515 5.245421
/ilgtgamma | 4.683227 3.336461 1.40 0.160 -1.856116 11.22257
-------------+----------------------------------------------------------------
sigma2 | .2915492 .9636126 .0004481 189.6957
gamma | .9908356 .0302963 .1351564 .9999866
sigma_u2 | .2888773 .9636131 -1.59977 2.177524
sigma_v2 | .0026719 .0001638 .0023508 .0029929
------------------------------------------------------------------------------

Dr. Declan Curran
Dublin City University
Dublin 9
Ireland

Email: declan.curran@dcu.ie
Tel: +353 (0)1 7006952

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```