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From |
"David M. Drukker, StataCorp" <ddrukker@stata.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
RE: st: Problems Stochastic Frontier Analysis |

Date |
Tue, 03 Feb 2004 12:32:44 -0600 |

Erik Brouwer <erik.brouwer@nl.pwc.com> estimated a stochastic frontier model in Stata and obtained large z-statistics. Specifically, the estimation command . frontier lnTK lnZT, d(e) cost; produced Stoc. frontier normal/exponential model Number of obs = 15 Wald chi2(1) = 1.115e+12 Log likelihood = 8.5130782 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ lnTK | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- lnZT | 1.244566 1.18e-06 . 0.000 1.244563 1.244568 _cons | -4.327623 .0000181 . 0.000 -4.327659 -4.327588 -------------+---------------------------------------------------------------- /lnsig2v | -39.73655 977.6138 -0.04 0.968 -1955.824 1876.351 /lnsig2u | -3.135077 .5163978 -6.07 0.000 -4.147198 -2.122956 -------------+---------------------------------------------------------------- sigma_v | 2.35e-09 1.15e-06 0 . sigma_u | .2085579 .0538494 .1257324 .3459441 sigma2 | .0434964 .0224614 -.0005272 .08752 lambda | 8.87e+07 .0538494 8.87e+07 8.87e+07 ------------------------------------------------------------------------------ Likelihood-ratio test of sigma_u=0: chibar2(01) = 7.84 Prob>=chibar2 = 0.003 Some of the z-statistics are missing because their corresponding standard errors are so small. The pattern of extremely small and very large standard errors indicates that the Hessian is not well-conditioned at the point which the algorithm has converged. An ill-conditioned Hessian implies that the parameters are not well-identified by the data for this model. As discussed by Drukker and Wiggins (2004), Erik might want to begin dealing with this problem by checking that all of the variables are on about the same scale. Simply rescaling the variables could produce a better-conditioned Hessian and eliminate the problem of the missing z-statistics. However, the coefficients do not provide any clear indication of a scaling problem. Instead, if we accept the given solution point, the output indicates that there is very strong evidence against the presence of an inefficiency term in the model. This raises the possibility that the problems with numerically identifying the parameters of interest may be due to model misspecification. Finally, Erik asked how is it possible that two packages could produce very different Z-statistics when the parameter estimates are very similar. It might be that the different packages are using different estimators of the variance-covariance matrix. By default, -frontier- in Stata uses the inverse of the average of the Hessian at the point of convergence. It could be the other package is using another estimator, such as the inverse of the average outer product of the gradient (OPG) estimator. (See Wooldridge (2002) chapter 13 for a discussion of the different estimators.) --David ddrukker@stata.com References ---------- David M. Drukker and Vince Wiggins. 2004. "Verifying the solution from a Nonlinear Solver: A Case Study: Comment". American Economic Review, Forthcoming. Jeffry M. Wooldridge. 2002. Econometric Analysis of Cross Section and Panel Data. Cambridge, Mass: MIT Press. * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Problems Stochastic Frontier Analysis***From:*"Scott Merryman" <smerryman@kc.rr.com>

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