Description Details Author(s) References

This package provides a variety of tools for nonparametric and parametric efficiency measurement.

The nonparametric models in `npsf`

comprise nonradial efficiency measurement (`tenonradial`

), where non-proportional reductions (expansions) in each positive input (output) are allowed, as well as popular radial efficiency measurement (`teradial`

), where movements to the frontier are proportional.

Using bootstrapping techniques, `teradialbc`

, `tenonradialbc`

, `nptestrts`

, `nptestind`

deal with statistical inference about the radial efficiency measurement. `nptestind`

helps in deciding which type of the bootstrap to employ. Global return to scale and individual scale efficiency is tested by `nptestrts`

. Finally, `teradialbc`

and `tenonradialbc`

, performs bias correction of the radial Debrue-Farrell and nonradial Russell input- or output-based measure of technical efficiency, computes bias and constructs confidence intervals.

Computer intensive functions `teradialbc`

and `nptestrts`

allow making use of parallel computing, even on a single machine with multiple cores. Help files contain examples that are intended to introduce the usage.

The parametric stochastic frontier models in `npsf`

can be estimated by `sf`

, which performs maximum likelihood estimation of the frontier parameters and technical or cost efficiencies. Inefficiency error component can be assumed to be have either half-normal or truncated normal distribution. `sf`

allows modelling multiplicative heteroskedasticity of either inefficiency or random noise component, or both. Additionally, marginal effects of determinants on the expected value of inefficiency term can be computed.

For details of the respective method please see the reference at the end of this introduction and of the respective help file.

All function in `npsf`

accept formula with either names of variables in the data set, or names of the matrices. Except for `nptestind`

, all function return `esample`

, a logical vector length of which is determined by `data`

and `subset`

(if specified) or number of rows in matrix `outputs`

. `esample`

equals `TRUE`

if this data point parted in estimation procedure, and `FALSE`

otherwise.

Results can be summarized using `summary.npsf`

.

Oleg Badunenko, <oleg.badunenko@brunel.ac.uk>

Pavlo Mozharovskyi, <pavlo.mozharovskyi@telecom-paris.fr>

Yaryna Kolomiytseva, <kolomiytseva@wiso.uni-koeln.de>

Maintainer: Oleg Badunenko <oleg.badunenko@brunel.ac.uk>

Badunenko, O. and Kumbhakar, S.C. (2016), When, Where and How to Estimate Persistent and Transient Efficiency in Stochastic Frontier Panel Data Models, *European Journal of Operational Research*, **255**(1), 272–287, doi: 10.1016/j.ejor.2016.04.049

Badunenko, O. and Mozharovskyi, P. (2016), Nonparametric Frontier Analysis using Stata, *Stata Journal*, **16**3, 550–89, doi: 10.1177/1536867X1601600302

Badunenko, O. and Mozharovskyi, P. (2020), Statistical inference for the Russell measure of technical efficiency, *Journal of the Operational Research Society*, **71**3, 517–527, doi: 10.1080/01605682.2019.1599778

Bartelsman, E.J. and Gray, W. (1996), The NBER Manufacturing Productivity Database, *National Bureau of Economic Research*, Technical Working Paper Series, doi: 10.3386/t0205

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Battese, G., Coelli, T. (1992), Frontier production functions, technical efficiency and panel data: With application to paddy farmers in India. *Journal of Productivity Analysis*, **3**, 153–169

Charnes, A., W. W. Cooper, and E. Rhodes. 1981. Evaluating Program and Managerial Efficiency: An Application of Data Envelopment Analysis to Program Follow Through. *Management Science* **27**: 668–697

Caudill, S., Ford, J., Gropper, D. (1995), Frontier estimation and firm-specific inefficiency measures in the presence of heteroscedasticity. *Journal of Business and Economic Statistics*, **13**, 105–111

Debreu, G. 1951. The Coefficient of Resource Utilization. *Econometrica* **19**: 273–292

Färe, R. and Lovell, C. A. K. (1978), Measuring the technical efficiency of production, *Journal of Economic Theory*, **19**, 150–162, doi: 10.1016/0022-0531(78)90060-1

Färe, R., Grosskopf, S. and Lovell, C. A. K. (1994), *Production Frontiers*, Cambridge U.K.: Cambridge University Press, doi: 10.1017/CBO9780511551710

Farrell, M. J. 1957. The Measurement of Productive Efficiency. *Journal of the Royal Statistical Society. Series A (General)* **120**(3): 253–290

Heston, A., and R. Summers. 1991. The Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950-1988. *The Quarterly Journal of Economics* **106**: 327–368

Horrace, W. and Schmidt, P. (1996), On ranking and selection from independent truncated normal distributions. *Journal of Productivity Analysis*, **7**, 257–282

Jondrow, J., Lovell, C., Materov, I., Schmidt, P. (1982), On estimation of technical inefficiency in the stochastic frontier production function model. *Journal of Econometrics*, **19**, 233–238

Kneip, A., Simar L., and P.W. Wilson (2008), Asymptotics and Consistent Bootstraps for DEA Estimators in Nonparametric Frontier Models, *Econometric Theory*, **24**, 1663–1697, doi: 10.1017/S0266466608080651

Koetter, M., Kolari, J., and Spierdijk, L. (2012), Enjoying the quiet life under deregulation? Evidence from adjusted Lerner indices for U.S. banks. *Review of Economics and Statistics*, **94**, 2, 462–480

Kumbhakar, S. (1990), Production Frontiers, Panel Data, and Time-varying Technical Inefficiency. *Journal of Econometrics*, **46**, 201–211

Kumbhakar, S. and Lovell, C. (2003), *Stochastic Frontier Analysis.* Cambridge: Cambridge University Press, doi: 10.1017/CBO9781139174411

Restrepo-Tobon, D. and Kumbhakar, S. (2014), Enjoying the quiet life under deregulation? Not Quite. *Journal of Applied Econometrics*, **29**, 2, 333–343

Simar, L. and P.W. Wilson (1998), Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models, *Management Science*, **44**, 49–61, doi: 10.1287/mnsc.44.1.49

Simar, L. and P.W. Wilson (2000), A General Methodology for Bootstrapping in Nonparametric Frontier Models, *Journal of Applied Statistics*, **27**, 779–802, doi: 10.1080/02664760050081951

Simar, L. and P.W. Wilson (2002), Nonparametric Tests of Return to Scale, *European Journal of Operational Research*, **139**, 115–132

Wang, H.-J. (2002), Heteroskedasticity and non-monotonic efficiency effects of a stochastic frontier model. *Journal of Productivity Analysis*, **18**, 241–253

Wilson P.W. (2003), Testing Independence in Models of Productive Efficiency, *Journal of Productivity Analysis*, **20**, 361–390, doi: 10.1023/A:1027355917855

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