technology_gap_ratio: Extract Technology Gap Ratios

In metafrontier: Analysis of Metafrontier Models for Efficiency and Productivity

Extract Technology Gap Ratios

Description

Extracts the technology gap ratios (TGR) from a fitted metafrontier model. The TGR measures how close a group's production frontier is to the global metafrontier at each observation's input mix.

Usage

technology_gap_ratio(object, by_group = TRUE, ...)

Arguments

object	a fitted "metafrontier" object.
by_group	logical. If TRUE (default), returns a named list of TGR vectors, one per group. If FALSE, returns a single numeric vector.
...	additional arguments (currently unused).

Details

The technology gap ratio is defined as:

TGR_i = \frac{f(x_i; \hat\beta_j)}{f(x_i; \hat\beta^*)}

for the deterministic SFA metafrontier, and

TGR_i = \frac{TE^*_i}{TE^{group}_i}

for DEA-based metafrontiers. Under the stochastic metafrontier of Huang, Huang, and Liu (2014) the Stage 2 model is \ln f(x_i; \hat\beta_j) = x_i'\beta^* + v^*_i - u^*_i, and the TGR is the conditional expectation

TGR_i = E[\exp(-u^*_i) \mid \varepsilon^*_i]

(Battese and Coelli, 1988), so the noise v^*_i is not part of the technology gap.

In all cases TGR lies in (0, 1].

A TGR of 1 means the group frontier coincides with the metafrontier at that input mix. Values less than 1 indicate a technology gap. Since each group technology is a restricted subset of the common metatechnology (Battese, Rao and O'Donnell, 2004), the gap reflects the restrictions a group faces (regulation, environment, endowments) rather than a fundamentally different technology.

Value

If by_group = TRUE, a named list of numeric vectors. If by_group = FALSE, a numeric vector of length nobs(object).

See Also

metafrontier, efficiencies.metafrontier

Examples

set.seed(42)
sim <- simulate_metafrontier(n_groups = 2, n_per_group = 100)
fit <- metafrontier(log_y ~ log_x1 + log_x2,
                    data = sim$data, group = "group")
tgr <- technology_gap_ratio(fit)
lapply(tgr, summary)

metafrontier documentation built on Oct. 28, 2026, 5:13 p.m.