Hi Babita,

what software did you use?

READING THE T-VALUE: The T-value calculated from the data set is called T(observed). The T(observed) is compared to the T(theoretical); the T(theoretical) is the value that is provided in the T-Table. Which T-table? There is only one T-table called Student T-Table.  However, T-value does not appear relevant to your search for test stistic for random stochastic frontier.

CAVEAT: The test statistic for stochastic production frontier is not based on t-test. We use moment analysis and judge the efficiency indication by the third moment of the data distribution. T-test from computer generated result may have referred to regression issues.

MOMENT: The interpretation of moment follows:

m1: First moment: mean of the data set

m2: Second moment: variance

m3: Third moment: skewness

m4: Fourth moment: kurtosis

TEST STATISTIC FOR STOCHASTIC MODEL: Coelli (1995) provides the test statistic for stochastic frontier as:

(1)   (bi)1/2 = m3 / (6m23 / N)1/2

... where N = number of observations' (6m23 / N) = variance of residual. The null hypothesis assumes that the frontier is efficiency, thus: H0: m3 = 0.

There is another method proposed by Schmidt and Lin (1984). The test statistic for stochastic frontier may be given by:

(2)   (bi)1/2 = m3 / m23/2

... where mi = moment of the empirical residual; m3 = third moment of distributed ui. The decision rule follows: m3 < 0 evidence of inefficient; and m3 > 0 the model is misspecified. The null hypothesis says: m3 = 0 assume evidence of efficiency.

Note in both methods (1) and (2), the T-table is not used. The conclusion of whether there is efficiency or inefficiency is achieved through m3 analysis.

REFERENCE: I provide download link to an article Mastromarco (2008). The language and explanation are quite accessible. It hope this is helpful Cheers.

https://drive.google.com/file/d/0B772RxSNNsoVT0k0Z3htZG5LeU0/view?usp=sharing

Using the p-value rule is easier...no need for tables.