marginal: Compute marginal effects of the inefficiency drivers in...

In sfaR: Stochastic Frontier Analysis using R

Compute marginal effects of the inefficiency drivers in classic or latent class stochastic models

Description

This function returns marginal effects of the inefficiency drivers from classic or latent class stochastic frontier models estimated with sfacross or lcmcross.

Usage

## S3 method for class 'sfacross'
marginal(object, ...)

## S3 method for class 'lcmcross'
marginal(object, ...)

Arguments

object	A classic or latent class stochastic frontier model returned by sfacross or lcmcross.
...	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_{(m)u}}) and the marginal effects on the variance of inefficiency (\frac{\partial V[u]}{\partial Z_{(m)u}}).

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

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_") is returned.

In the case of the latent class model (LCM), each variable terminates with "_c#" where "#" is the class number.

Author(s)

K Hervé Dakpo, Yann Desjeux and Laure Latruffe

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.

lcmcross, for the latent class stochastic frontier analysis model fitting function.

Examples

## 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 (DGP)
# LCM Cobb Douglas (production function) half normal distribution
cb_2c_h <- lcmcross(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)

sfaR documentation built on May 3, 2022, 3 p.m.