Institute for Transport Studies (ITS)

Benchmarking and Efficiency Analysis Resources

This page serves as a repository for various outputs, mainly working papers and code, relating to efficiency and productivity analysis research undertaken by several researchers at the University of Leeds, including Phill Wheat and Alex Stead.

Working Papers

Stata Code

To install automatically:

Enter the relevant net install command shown below.

To install manually: 

  1. Download the zipped folder for the relevant package and extract the files.
  2. Go to your personal directory for Stata (you can find this by entering the command personal).
  3. Paste each file in the downloaded package into a subfolder named for the first letter of that file, e.g. paste tregress.ado into the …/personal/t. If this folder does not exist, you will need to create it.
  4. The package is ready to use. Enter help followed by the name of the package to get started, e.g. help tregress.


rfrontier - robust stochastic frontier models

net install rfrontier, all from(

    This package enables the estimation of stochastic frontier models with Student's t, logistic, or Cauchy distributed noise terms via maximum simulated likelihood.


    cnsf - Contaminated normal-half normal stochastic frontier model

    net install cnsf, all from(

    This package enables the estimation of a stochastic frontier model in which the noise term follows a scale contaminated normal distribution and the inefficiency term follows a half normal distribution.


    tregress - Student’s t regression model

    net install tregress, all from(

    This package enables the user to estimate a regression model in which the errors follow a non-standard Student’s t distribution with a scaling parameter.

    Panel data stochastic frontier models with firm-specific, deterministically time-varying efficiency trends

    (N.B. This code comes in .do files rather than .ado files. To install them, download the .do file and run it in Stata. This must be repeated at the start of each session.)

    The file enables the estimation of the firm-specific, time-varying random effects stochastic frontier model of Cornwell, Schmidt, and Sickles [see:  Cornwell, C., Schmidt, P., and Sickles, R.C. 1990. Production frontiers with cross-sectional and time-series variation in efficiency levels. Journal of Econometrics. 46 (1990) 185-200].

    The file enables the estimation of a panel data stochastic frontier model with firm-specific time trends proposed by Cuesta. Inefficiency in this case is modelled as a random variable which is scaled by a (firm-specific) deterministic function of time [see: Cuesta, R.A. 2000. A production model with firm-specific temporal variation in technical inefficiency: with application to Spanish dairy farms. Journal of Productivity Analysis. 13(2) 139-158]. Note that this command requires sfpan package to be installed [see: Kumbhakar, S.C., Wang, H.-J., and Horncastle, A.P. 2015. A Practitioner's Guide to Stochastic Frontier Analysis Using Stata. Cambridge University Press.]