Theta_tk coefficients = 0 in output-oriented tfdea models

[Aurora Ianello]

Hello everyone. I am experiencing some issue with tfdea (technology forecasting using Dea), and I would be grateful to anyone willing to help.

I am using tfdea on a dataset containing information on fighters (first flight date, max speed, climb ratio, range, engine's power-to-weight ratio).

My dmu is the fighter model; my year is the first flight year. Following the literature, I am specifying an output-oriented model, with variable returns to scale and constant inputs (=1 for every dmu). The outputs are max speed, climb ratio, range, engine's power-to-weight ratio.

Being an output-oriented model, I would expect theta_tk coefficients to be >=1 (=1 for the efficient dmu, >1 for inefficient dmu).
However, for two dmu in my dataset I get theta_tk=0.
How do I interpret that?
I looked at the features of those two specific fighters, and I couldn't notice anything strange or particular.

I get "normal" results (with theta_k>=1) if I don't include the engine's specific power in the model.

I am not posting specific commands or examples because everything seems to work fine; I'm just unable to interpret these results. However, if you need more info, I will provide them.


Thanks to anyone who might be able and willing to help.

[Choonjoo Lee]

Although quite some time has passed since this question was posted, the following may still be helpful if the issue remains unresolved.

A value of theta_tk = 0 should generally not be interpreted as a meaningful DEA efficiency score. In the TFDEA implementation, a missing or unsuccessful DEA/linear-programming result may be recorded as zero. Therefore, the two zero values are more likely to indicate that the corresponding DEA problems were not solved successfully than to represent genuine efficiency estimates.

The fact that the zero values disappear when the engine power-to-weight variable is omitted suggests that the issue may be related to that variable, the resulting technology set, numerical scaling, or infeasibility/unboundedness of the relevant linear programs. However, a more definitive diagnosis would require the exact dataset and the complete Stata command used in the analysis.

The Stata source code for tfdea, together with the dea package on which it relies, is available here:

https://sourceforge.net/p/deas/code/HEAD/tree/trunk/

If you still need assistance, please feel free to contact me. If you can share the exact command and a reproducible dataset, I would be happy to take a closer look and, if helpful, provide the relevant files and examples showing how to implement the analysis using the DEA commands in Stata.

Choonjoo