Technical efficiency estimated using a quantile regression

[TomasHlavsa]

Hi all,

I am trying to develop some model estimating technical efficiency. I can use Cobb-Douglas function and translog production function, both using PROC QLIM.

I want to build another model for technical efficiency - the quantile model. I found multiple papers on how to use quantile regression in SAS (PROC QUANTREG, QUANTSELECT...) but none was focused on quantile regression for calculation technical efficiency (not only calculating the prediction of the target variable but also calculation the score of technical efficiency).

Any SAS users here experienced with it?

Thank you,

Tomas

[sbxkoenk]

If I hear about "technical efficiency" I think about DEA.

To estimate the technical efficiency, the production function frontier is usually estimated by using a non-parametric approach (data envelopment analysis (DEA)) or a parametric approach (stochastic frontier analysis (SFA)).

Here is some info about DEA in SAS:

• SAS/OR® 15.2 User's Guide: Mathematical Programming Examples
  Efficiency Analysis: How to Use Data Envelopment Analysis to Compare Efficiencies of Garages?
  https://go.documentation.sas.com/doc/en/ormpex/15.2/ormpex_ex22_toc.htm
• SAS Global Forum 2011 -- Operations Research -- Paper 198-2011
  The Final Frontier: A SAS® Approach to Data Envelopment Analysis
  Sabah Sadiq, Institute for Advanced Analytics, North Carolina State University, Raleigh, N.C.
  https://support.sas.com/resources/papers/proceedings11/198-2011.pdf

Do you have any reference where an author explains how quantile regression would help in estimating technical efficiency?

Br, Koen

[TomasHlavsa]

Thank you for your reply.

Yep, technical efficiency can be estimated using DEA or SFA. I follow the SFA approach (Cobb-Douglas, translog production function, well explained in SAS documentation or in Applied Econometrics with SAS by Goodwin, Ramsey, and Chvosta). 

Then I found a paper written by Kaditi and Nitsi (Applying regression quantiles to farm efficiency estimation), where they develop quantile production function (file attached). That is what I would like to develop in SAS.

Tomas

[sbxkoenk]

I am sorry. I do not have any experience with the Quantile Regression approach to this topic.

But, after a quick Google search,

... quantile regression indeed seems to be an alternative approach that has been investigated at numerous occasions.

Like here:
The quantile regression approach to efficiency measurement: insights from Monte Carlo Simulations
Health, Econometrics and Data Group (HEDG)
The University of York
https://www.york.ac.uk/media/economics/documents/herc/wp/07_14.pdf

Br, Koen

[TomasHlavsa]

Thank you, I will check it.
Best, Tomas

[gunce_sas]

Hi Tomas,

Yes, quantile regression can be a nice alternative to the DEA and SFA methods as a semiparametric method for estimating production function. However, when it comes to the performance of technical efficiency measure obtained from this method, it may not be as good as those obtained from DEA and SFA. (see https://www.york.ac.uk/media/economics/documents/herc/wp/07_14.pdf)

To my knowledge, in SAS, there is no procedure that outputs technical efficiency measure when a production function is estimated by using quantile regression, as in PROC QLIM or PROC FRONTIER. However, the output from PROC QUANTREG or QUANTSELECT can be used to calculate technical efficiency based on its definition, which can be found here or in the reference you linked.  

Best regards,

Gunce

[TomasHlavsa]

Hi Gunce, 

thanks a lot for your comment and valuable suggestions. Yep, you are right, it is meaningful to estimate the production using PROC QUANTREG and then separately calculate the scores of technical (in)efficiency. I will check the approaches and the literature.

Best

Tomas