poolability_test: Test Poolability of Group Frontiers

In metafrontier: Analysis of Metafrontier Models for Efficiency and Productivity

Test Poolability of Group Frontiers

Description

Tests the null hypothesis that all groups share a common frontier (i.e., the metafrontier coincides with all group frontiers) against the alternative that group-specific frontiers differ. For SFA-based metafrontiers a likelihood ratio test is used; for DEA-based metafrontiers a permutation test is used.

Usage

poolability_test(object, B = 199, seed = NULL, ...)

Arguments

object	a fitted "metafrontier" object with method = "sfa" or method = "dea".
B	integer. Number of permutation replicates for the DEA permutation test (default 199). Ignored for SFA objects.
seed	integer or NULL. Random seed for the DEA permutation test, for reproducibility. Ignored for SFA objects.
...	additional arguments (currently unused).

Details

Likelihood ratio test (SFA). The LR statistic is:

LR = -2 [LL_{pooled} - \sum_j LL_j]

where LL_{pooled} is the log-likelihood of the pooled (single frontier) model and LL_j are the group-specific log-likelihoods. Under H0, the statistic follows a chi-squared distribution with degrees of freedom equal to df = k_{groups} - k_{pooled}, where k_{groups} is the total number of parameters across all group-specific models and k_{pooled} is the number of parameters in the pooled model. For J groups each with p frontier parameters plus distributional parameters, this equals (J - 1) \times p_{total} where p_{total} includes frontier coefficients, \sigma_v, and \sigma_u (and \mu for truncated-normal). This test requires a likelihood and is therefore only available for SFA-based metafrontiers.

Permutation test (DEA). DEA has no likelihood, so the poolability hypothesis is assessed by a permutation test. Under the null of a single pooled technology, group labels are exchangeable: reassigning observations to groups at random should not systematically change the distance between the group frontiers and the metafrontier. The observed statistic is the mean technology gap, S_{obs} = \mathrm{mean}(1 - TGR_i), and its null distribution is approximated by refitting the metafrontier on B random permutations of the group labels. The p-value is (1 + \#\{S_b \ge S_{obs}\}) / (B + 1), following the aggregate-efficiency inference logic of Simar and Zelenyuk (2007). The smoothed subsampling approach of Kneip, Simar, and Wilson (2016) is the asymptotically rigorous alternative for testing hypotheses in nonparametric production models; the permutation test offered here is a computationally simple approximation. The default B = 199 is a pragmatic choice; p-values have resolution 1/(B + 1), so increase B for finer resolution.

Value

A list of class "htest" with components:

statistic

the test statistic (LR statistic for SFA; the mean technology gap, \bar{S} = \mathrm{mean}(1 - TGR), for DEA)

parameter

degrees of freedom (SFA) or the effective number of permutation replicates (DEA)

p.value

p-value of the test

method

description of the test

References

Simar, L. and Zelenyuk, V. (2007). Statistical inference for aggregates of Farrell-type efficiencies. Journal of Applied Econometrics, 22(7), 1367–1394. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/jae.991")}

Kneip, A., Simar, L. and Wilson, P.W. (2016). Testing hypotheses in nonparametric models of production. Journal of Business & Economic Statistics, 34(3), 435–456. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/07350015.2015.1049747")}

Examples

set.seed(42)
sim <- simulate_metafrontier(n_groups = 2, n_per_group = 200,
                             tech_gap = c(0, 0.5))
fit <- metafrontier(log_y ~ log_x1 + log_x2,
                    data = sim$data, group = "group")
poolability_test(fit)


# DEA permutation test
fit_dea <- metafrontier(log_y ~ log_x1 + log_x2,
                        data = sim$data, group = "group",
                        method = "dea")
poolability_test(fit_dea, B = 99, seed = 1)

metafrontier documentation built on Aug. 19, 2026, 5:08 p.m.