The output from frontier includes estimates of the standard deviations of the two error components,sigma (v) and sigma(u), which are labeled sigma v and sigma u, respectively. In the log likelihood, they are parameterized as ln2v and ln2u, and these estimates are labeled /lnsig2v and /lnsig2u in the output. frontier also reports two other useful parameterizations. The estimate of the total error variance, 2S = 2v + 2u, is labeled sigma2, and the estimate of the ratio of the standard deviation of the inefficiency component to the standard deviation of the idiosyncratic component, = u=v, is labeled lambda.
At the bottom of the output, frontier reports the results of a test that there is no technical inefficiency component in the model. This is a test of the null hypothesis H0 : 2u = 0 against the alternative hypotheses H1 : 2u
> 0. If the null hypothesis is true, the stochastic frontier model reduces to an OLS model with normal errors. However, because the test lies on the boundary of the parameter space of 2u, the standard likelihood-ratio test is not valid, and a one-sided generalized likelihood-ratio test must be constructed; see Gutierrez, Carter, and Drukker (2001). For this example, the output shows LR = 0.43 with a p-value of 0.256 for the half-normal model and LR = 1.21 with a p-value of 0.135 for the exponential model. There are several possible reasons for the failure to reject the null hypothesis, but the fact that the test is based on an asymptotic distribution and the
sample size was 25 is certainly a leading candidate among those possibilities.
more detail
Run stata11/help frontier
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