The hardware and bandwidth for this mirror is donated by dogado GmbH, the Webhosting and Full Service-Cloud Provider. Check out our Wordpress Tutorial.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]dogado.de.

metafrontier

Analysis of Metafrontier Models for Efficiency and Productivity

Overview

metafrontier provides a unified R implementation of metafrontier production function models for estimating technical efficiencies and technology gaps across groups of firms operating under different technologies.

Estimation methods

• Deterministic metafrontier (Battese, Rao & O’Donnell, 2004) via constrained LP/QP optimisation
• Stochastic metafrontier (Huang, Huang & Liu, 2014) via second-stage SFA with Murphy-Topel corrected standard errors
• DEA-based metafrontier with CRS, VRS, DRS, and IRS technology assumptions
• Latent class metafrontier via EM algorithm with BIC-based class selection

Productivity analysis

• Metafrontier Malmquist TFP index (O’Donnell, Rao & Battese, 2008) with three-way decomposition (TEC x TGC x TC*)
• Panel SFA with time-varying inefficiency (BC92 and BC95 specifications)
• Directional distance functions for DEA-based efficiency measurement

Inference and diagnostics

• Bootstrap confidence intervals for TGR (parametric and nonparametric; percentile and BCa)
• Murphy-Topel variance correction for stochastic metafrontier standard errors
• Poolability tests (likelihood ratio) for common vs group-specific frontiers
• Half-normal, exponential, and truncated-normal inefficiency distributions

Visualisation

• Base R plot() with four plot types: TGR distributions, efficiency scatter, frontier decomposition, and frontier comparison
• ggplot2 integration via autoplot() methods for metafrontier, Malmquist, and bootstrap results

Interoperability

• Import pre-fitted models from sfaR, frontier, and Benchmarking via as_metafrontier_model()
• Formula interface with heteroscedastic SFA support (y ~ x1 + x2 | z1 + z2)
• Full S3 method suite: print, summary, coef, vcov, logLik, fitted, residuals, nobs, confint, predict, plot

Installation

Install the development version from GitHub:

# install.packages("devtools")
devtools::install_github("iik1/metafrontier")

Quick start

library(metafrontier)

# Simulate metafrontier data with two technology groups
sim <- simulate_metafrontier(n_groups = 2, n_per_group = 200, seed = 42)

# Estimate a deterministic SFA-based metafrontier
fit_det <- metafrontier(log_y ~ log_x1 + log_x2,
                        data = sim$data, group = "group")

# Estimate a stochastic metafrontier (with Murphy-Topel SEs)
fit_sto <- metafrontier(log_y ~ log_x1 + log_x2,
                        data = sim$data, group = "group",
                        meta_type = "stochastic")

# DEA-based metafrontier (requires level-scale inputs/outputs)
dat_lev <- within(sim$data, { y <- exp(log_y); x1 <- exp(log_x1); x2 <- exp(log_x2) })
fit_dea <- metafrontier(y ~ x1 + x2,
                        data = dat_lev, group = "group",
                        method = "dea", rts = "vrs")

# Inspect results
summary(fit_det)
tgr_summary(fit_det)
confint(fit_det)

Bootstrap confidence intervals

boot <- boot_tgr(fit_det, R = 999, seed = 1)
confint(boot)

# Parallel bootstrap
boot_par <- boot_tgr(fit_det, R = 999, ncores = 4, seed = 1)

Malmquist productivity index

# Simulate panel data
panel <- simulate_panel_metafrontier(n_groups = 3, n_firms_per_group = 50,
                                     n_periods = 5, seed = 42)

# Three-way Malmquist decomposition
malm <- malmquist_meta(log_y ~ log_x1 + log_x2,
                       data = panel$data, group = "group",
                       time = "year")
summary(malm)

Latent class metafrontier

# Automatic class selection via BIC (discovers groups endogenously)
lc <- latent_class_metafrontier(log_y ~ log_x1 + log_x2,
                                data = sim$data,
                                n_classes = 3)
summary(lc)

Visualisation

# Base R
plot(fit_det, which = "tgr")
plot(fit_det, which = "decomposition")

# ggplot2
library(ggplot2)
autoplot(fit_det)
autoplot(boot)
autoplot(malm)

Using pre-fitted models

library(sfaR)

# Fit group-specific SFA models externally
sfa_g1 <- sfacross(log_y ~ log_x1 + log_x2,
                   data = subset(sim$data, group == "G1"))
sfa_g2 <- sfacross(log_y ~ log_x1 + log_x2,
                   data = subset(sim$data, group == "G2"))

# Pass to metafrontier
fit <- metafrontier(models = list(G1 = sfa_g1, G2 = sfa_g2))

Vignettes

The package includes three vignettes:

• Introduction to metafrontier – end-to-end walkthrough covering estimation, inference, bootstrap CIs, panel SFA, latent class, and directional distance functions
• Metafrontier Malmquist Productivity Index – panel data productivity decomposition with worked examples
• Metafrontier Methods: Theory and Computation – mathematical details, comparison of deterministic/stochastic/DEA approaches, and Monte Carlo evidence

browseVignettes("metafrontier")

References

• Battese, G.E., Rao, D.S.P. and O’Donnell, C.J. (2004). A metafrontier production function for estimation of technical efficiencies and technology gaps for firms operating under different technologies. Journal of Productivity Analysis, 21(1), 91–103. doi:10.1023/B:PROD.0000012454.06094.29
• Huang, C.J., Huang, T.-H. and Liu, N.-H. (2014). A new approach to estimating the metafrontier production function based on a stochastic frontier framework. Journal of Productivity Analysis, 42(3), 241–254. doi:10.1007/s11123-014-0402-2
• O’Donnell, C.J., Rao, D.S.P. and Battese, G.E. (2008). Metafrontier frameworks for the study of firm-level efficiencies and technology ratios. Empirical Economics, 34(2), 231–255. doi:10.1007/s00181-007-0119-4

License

GPL (>= 3)

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.