*! version 1.1.2 14may2009
help sfcross postestimation also see: sfcross

Title

sfcross postestimation -- Postestimation tools for
sfcross

Description

The following postestimation commands are available for sfcross:

command description

predict predictions, residuals, influence statistics, and other diagnostic measures

Syntax for predict

predict [type] newvar [if] [in] [, statistic]

predict [type] {stub*|newvar_xb newvar_v newvar_u} [if] [in], scores

statistic

Main
xb linear prediction; the default

stdp standard error of the prediction

u estimates of (technical or cost) inefficiency via E(u|e) (Jondrow et al., 1982)

m estimates of (technical or cost) inefficiency via M(u|e)

jlms estimates of (technical or cost) efficiency via exp[-E(u|e)]

bc estimates of (technical or cost) efficiency via E[exp(-u)|e] (Battese and Coelli, 1988)

ci estimates of confidence interval for (technical or cost) inefficiency/efficiency

marginal marginal effects of the exogenous determinants on the unconditional mean and variance of the inefficiency (Wang, 2002)

scores calculates score variables

These statistics are only available for the estimation sample.

Options for predict

Main

xb, the default, calculates the linear prediction.

stdp calculates the standard error of the linear prediction.

u produces estimates of (technical or cost) inefficiency via E(u|e) using the Jondrow et al. (1982) estimator.

m produces estimates of (technical or cost) inefficiency via M(u|e), the mode of the conditional distribution u|e. This option is not allowed when the estimation is performed with the distribution(gamma) option.

jlms produces estimates of (technical or cost) efficiency via exp[-E(u|e)].

bc produces estimates of (technical or cost) efficiency via E[exp(-u)|e] using the Battese and Coelli (1988) estimator. This option is not allowed when the estimation is performed with the distribution(gamma) option.

ci computes confidence interval using the approach proposed by Horrace and Schmidt (1996). It can be used only when u or bc is specified.
The default confidence level is 95, meaning a 95% confidence interval.
If the option level(#) is used in the previous estimation command, the confidence interval will be computed using the # level.
This option creates two additional variables: newvar_LBcilevel
and newvar_UBcilevel, the lower and the upper bound, respectively. This option cannot be used if the estimation
is performed with distribution(gamma).

marginal calculates the marginal effects of the exogenous determinants on E(u) and Var(u) using the approach proposed by Wang (2002).
The marginal effects are observation-specific and are saved in the new variables varname_m_M and varname_u_V, the marginal effects on the unconditional mean and variance of inefficiency, respectively.
varname_m and varname_u are the names of each exogenous determinants specified in options emean(varlist_m [,noconstant])
and usigma(varlist_u [,noconstant]).
marginal can be used only if the estimation is performed with distribution(tnormal).
When they are both specified, varlist_m and varlist_u must contain the same variables in the same order.
This option can be specified in two ways: i) together with either u, m, jlms or bc; ii) alone without specifying newvar.

scores calculates score variables. When the argument of the option distribution() is hnormal, tnormal, or exponential scores are defined as the derivative of the objective function with respect
to the parameters.
When the argument of the option distribution() is gamma scores are defined as the derivative of the objective function with respect to the coefficients.
This difference is due to the different moptimize() evaluator type used to implement the estimators (See mata moptimize()).

Remarks

When the sfcross command is used to estimate production frontiers, predict will provide the post-estimation of technical (in)efficiency,
while when the sfcross command is used to estimate cost frontiers, predict will provide the post-estimation of cost (in)efficiency.
It is worth noting that sfcross and the related predict command follow the definitions of technical and cost (in)efficiency given in Kumbhakar and Lovell (2000).

Examples

Setup production SF model

. webuse greene9, clear

. sfcross lnv lnk lnl, vsigma(lnk)

Linear prediction

. predict xb

Technical inefficiency

. predict ineffmean, u

. predict ineffmode, m

Technical efficiency

. predict jlms, jlms

Technical efficiency/inefficiency confidence intervals

. predict ineffmean, u ci

. predict bc, bc ci

. predict jlms, jlms ci

Non-monotonic marginal effects

. webuse frontier1, clear

. sfcross lnoutput lnlabor lncapital, d(tn) emean(lnlabor, nocons) usigma(lnlabor, nocons) difficult

. predict, marg

Equation-level score variables

. predict score*, scores

Authors

Federico Belotti

Centre for Economic and International Studies, University of Rome Tor Vergata

Rome, Italy

federico.belotti@uniroma2.it

Silvio Daidone

Centre for Health Economics, University of York

York, UK

silvio.daidone@york.ac.uk

Vincenzo Atella

Centre for Economic and International Studies, University of Rome Tor Vergata

Rome, Italy

atella@uniroma2.it

Giuseppe Ilardi

Economic and Financial Statistics Department, Bank of Italy

Rome, Italy

giuseppe.ilardi@bancaditalia.it

Also see

Help: sfcross, sfpanel.