vcov.metafrontier: Variance-Covariance Matrix for Metafrontier Coefficients

In metafrontier: Analysis of Metafrontier Models for Efficiency and Productivity

Variance-Covariance Matrix for Metafrontier Coefficients

Description

Returns the variance-covariance matrix of the Stage 2 (metafrontier) coefficients, or, with which = "group", the per-group matrices from the Stage 1 maximum likelihood fits. NULL is returned when no Stage 2 Hessian exists: the deterministic metafrontier is fitted by LP/QP optimisation and has no sampling variance in this framework, so which = "meta" returns NULL with a warning; with which = "group", list entries are NULL for groups without a stored Hessian (e.g. externally fitted models). DEA-based metafrontiers are nonparametric and vcov() signals an error; use boot_tgr for inference instead.

Usage

## S3 method for class 'metafrontier'
vcov(
  object,
  correction = c("none", "murphy-topel"),
  which = c("meta", "group"),
  extraPar = FALSE,
  ...
)

Arguments

object	a "metafrontier" object.
correction	character. "none" (default) returns the Stage 2 variance-covariance matrix. "murphy-topel" applies the Murphy and Topel (1985) correction for first-stage estimation uncertainty (the generated-regressor problem). Only available for stochastic metafrontiers.
which	character. "meta" (default) returns the metafrontier (Stage 2) variance-covariance matrix; "group" returns a named list with one full variance-covariance matrix per group (from the inverse negative Hessian of the group MLE), with NULL entries for groups without a stored Hessian.
extraPar	logical. If TRUE and which = "meta", the full Stage 2 matrix is returned, including the rows and columns for the auxiliary parameters (raw MLE parameterisation, e.g. log_sigma_v); the default returns only the block for the frontier coefficients.
...	additional arguments (currently unused).

Value

A variance-covariance matrix (which = "meta"), a named list of matrices (which = "group"), or NULL if unavailable.

References

Murphy, K.M. and Topel, R.H. (1985). Estimation and inference in two-step econometric models. Journal of Business & Economic Statistics, 3(4), 370–379.

Examples

sim <- simulate_metafrontier(n_groups = 2, n_per_group = 50, seed = 42)
fit <- metafrontier(log_y ~ log_x1 + log_x2, data = sim$data,
                    group = "group", meta_type = "stochastic")
vcov(fit)

vcov(fit, correction = "murphy-topel")

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