sfaR (version 1.0.0)

marginal: Marginal effects of the inefficiency drivers in stochastic frontier models

Description

This function returns marginal effects of the inefficiency drivers from stochastic frontier models estimated with sfacross, sfalcmcross, or sfaselectioncross.

Usage

# S3 method for sfacross
marginal(object, newData = NULL, ...)
# S3 method for sfalcmcross
marginal(object, newData = NULL, ...)
# S3 method for sfaselectioncross
marginal(object, newData = NULL, ...)

Value

marginal returns a data frame containing the marginal effects of the \(Z_u\) variables on the expected inefficiency (each variable has the prefix 'Eu_') and on the variance of the inefficiency (each variable has the prefix 'Vu_').

In the case of the latent class stochastic frontier (LCM), each variable ends with '_c#' where '#' is the class number.

Arguments

object

A stochastic frontier model returned by sfacross, sfalcmcross, or sfaselectioncross.

newData

Optional data frame that is used to calculate the marginal effect of \(Z\) variables on inefficiency. If NULL (the default), the marginal estimates are calculated for the observations that were used in the estimation.

...

Currently ignored.

Details

marginal operates in the presence of exogenous variables that explain inefficiency, namely the inefficiency drivers (\(uhet = ~ Z_u\) or \(muhet = ~ Z_{mu}\)).

Two components are computed for each variable: the marginal effects on the expected inefficiency (\(\frac{\partial E[u]}{\partial Z_{mu}}\)) and the marginal effects on the variance of inefficiency (\(\frac{\partial V[u]}{\partial Z_{mu}}\)).

The model also allows the Wang (2002) parametrization of \(\mu\) and \(\sigma_u^2\) by the same vector of exogenous variables. This double parameterization accounts for non-monotonic relationships between the inefficiency and its drivers.

References

Wang, H.J. 2002. Heteroscedasticity and non-monotonic efficiency effects of a stochastic frontier model. Journal of Productivity Analysis, 18:241--253.

See Also

sfacross, for the stochastic frontier analysis model fitting function using cross-sectional or pooled data.

sfalcmcross, for the latent class stochastic frontier analysis model fitting function using cross-sectional or pooled data.

sfaselectioncross for sample selection in stochastic frontier model fitting function using cross-sectional or pooled data.

Examples

if (FALSE) {
## Using data on fossil fuel fired steam electric power generation plants in the U.S.
# Translog SFA (cost function) truncated normal with scaling property
tl_u_ts <- sfacross(formula = log(tc/wf) ~ log(y) + I(1/2 * (log(y))^2) +
log(wl/wf) + log(wk/wf) + I(1/2 * (log(wl/wf))^2) + I(1/2 * (log(wk/wf))^2) +
I(log(wl/wf) * log(wk/wf)) + I(log(y) * log(wl/wf)) + I(log(y) * log(wk/wf)),
udist = 'tnormal', muhet = ~ regu + wl, uhet = ~ regu + wl, data = utility, 
S = -1, scaling = TRUE, method = 'mla')
marg.tl_u_ts <- marginal(tl_u_ts)
summary(marg.tl_u_ts)

## Using data on eighty-two countries production (GDP)
# LCM Cobb Douglas (production function) half normal distribution
cb_2c_h <- sfalcmcross(formula = ly ~ lk + ll + yr, udist = 'hnormal',
    data = worldprod, uhet = ~ initStat + h, S = 1, method = 'mla')
  marg.cb_2c_h <- marginal(cb_2c_h)
  summary(marg.cb_2c_h)
  }