{smcl}
{* *! version 1.1.2 14may2009}{...}{cmd:help sfcross postestimation} {...}
{right:also see: {help sfcross}}
{hline}
{title:Title}
{p2colset 5 32 38 2}{...}
{p2col :{hi:sfcross postestimation} {hline 2}}Postestimation tools for
sfcross{p_end}
{p2colreset}{...}
{title:Description}
{pstd}
The following postestimation commands are available for {opt sfcross}:
{synoptset 11}{...}
{p2coldent :command}description{p_end}
{synoptline}
INCLUDE help post_estat
INCLUDE help post_estimates
INCLUDE help post_lincom
INCLUDE help post_linktest
INCLUDE help post_lrtest
INCLUDE help post_margins
INCLUDE help post_nlcom
{synopt :{helpb sfcross postestimation##predict:predict}}predictions, residuals, influence statistics, and other diagnostic measures{p_end}
INCLUDE help post_predictnl
INCLUDE help post_test
INCLUDE help post_testnl
{synoptline}
{p2colreset}{...}
{marker predict}{...}
{title:Syntax for predict}
{p 8 16 2}{cmd:predict} {dtype} {newvar} {ifin} [{cmd:,} {it:statistic}]
{p 8 16 2}{cmd:predict} {dtype} {c -(}{it:stub*}{c |}{it:newvar_xb} {it:newvar_v} {it:newvar_u}{c )-} {ifin}{cmd:,} {opt sc:ores}
{synoptset 15 tabbed}{...}
{synopthdr :statistic}
{synoptline}
{syntab :Main}
{synopt :{opt xb}}linear prediction; the default{p_end}
{synopt :{opt stdp}}standard error of the prediction{p_end}
{synopt :{opt u}}estimates of (technical or cost) inefficiency via {it:E}(u|e) (Jondrow et al., 1982){p_end}
{synopt :{opt m}}estimates of (technical or cost) inefficiency via M(u|e){p_end}
{synopt :{opt jlms}}estimates of (technical or cost) efficiency via exp[-E(u|e)]{p_end}
{synopt :{opt bc}}estimates of (technical or cost) efficiency via E[exp(-u)|e] (Battese and Coelli, 1988){p_end}
{synopt :{opt ci}}estimates of confidence interval for (technical or cost) inefficiency/efficiency{p_end}
{synopt :{opt marginal}}marginal effects of the exogenous determinants on the unconditional mean and variance of the inefficiency (Wang, 2002){p_end}
{synopt :{opt scores}}calculates score variables{p_end}
{synoptline}
{p2colreset}{...}
{p 4 6 2}
These statistics are only available for the estimation sample.
INCLUDE help menu_predict
{title:Options for predict}
{dlgtab:Main}
{phang}
{opt xb}, the default, calculates the linear prediction.
{phang}
{opt stdp} calculates the standard error of the linear prediction.
{phang}
{opt u} produces estimates of (technical or cost) inefficiency via E(u|e) using the Jondrow et al. (1982) estimator.
{phang}
{opt 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 {opt distribution(gamma)} option.
{phang}
{opt jlms} produces estimates of (technical or cost) efficiency via exp[-E(u|e)].
{phang}
{opt 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 {opt distribution(gamma)} option.
{phang}
{opt ci} computes confidence interval using the approach proposed by Horrace and Schmidt (1996). It can be used only when {opt u} or {opt bc} is specified.
The default confidence level is 95, meaning a 95% confidence interval.
If the option {cmd:level(#)} is used in the previous estimation command, the confidence interval will be computed using the {it:#} level.
This option creates two additional variables: {it:newvar_LBcilevel}
and {it:newvar_UBcilevel}, the lower and the upper bound, respectively. This option cannot be used if the estimation
is performed with {cmd:distribution(gamma)}.
{phang}
{opt 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 {it:varname_m_M} and {it:varname_u_V}, the marginal effects on the unconditional mean and variance of inefficiency, respectively.
{it:varname_m} and {it:varname_u} are the names of each exogenous determinants specified in options {cmd:emean(}{help varlist:varlist_m} [,{opt noconstant}]{cmd:)}
and {cmd:usigma(}{help varlist:varlist_u} [,{opt noconstant}]{cmd:)}.
{opt marginal} can be used only if the estimation is performed with {cmd:distribution(tnormal)}.
When they are both specified, {it:varlist_m} and {it:varlist_u} must contain the same variables in the same order.
This option can be specified in two ways: i) together with either {opt u}, {opt m}, {opt jlms} or {opt bc}; ii) alone without specifying {it:newvar}.
{phang}
{opt scores} calculates score variables. When the argument of the option {opt distribution()} is {opt hnormal}, {opt tnormal}, or {opt exponential} scores are defined as the derivative of the objective function with respect
to the {help mf_moptimize##def_parameter:parameters}.
When the argument of the option {opt distribution()} is {opt gamma} scores are defined as the derivative of the objective function with respect to the {help mf_moptimize##def_K:coefficients}.
This difference is due to the different {opt moptimize()} {it:evaluator type} used to implement the estimators (See {help mata moptimize()}).
{title:Remarks}
{pstd}When the {cmd:sfcross} command is used to estimate production frontiers, {cmd:predict} will provide the post-estimation of technical (in)efficiency,
while when the {cmd:sfcross} command is used to estimate cost frontiers, {cmd:predict} will provide the post-estimation of cost (in)efficiency.
It is worth noting that {cmd:sfcross} and the related {cmd:predict} command follow the definitions of technical and cost (in)efficiency given in Kumbhakar and Lovell (2000).{p_end}
{title:Examples}
{pstd}Setup production SF model{p_end}
{phang}{cmd:. webuse greene9, clear}{p_end}
{phang}{cmd:. sfcross lnv lnk lnl, vsigma(lnk)}{p_end}
{pstd}Linear prediction{p_end}
{phang}{cmd:. predict xb}
{pstd}Technical inefficiency{p_end}
{phang}{cmd:. predict ineffmean, u}{p_end}
{phang}{cmd:. predict ineffmode, m}{p_end}
{pstd}Technical efficiency{p_end}
{phang}{cmd:. predict jlms, jlms}{p_end}
{pstd}Technical efficiency/inefficiency confidence intervals{p_end}
{phang}{cmd:. predict ineffmean, u ci}{p_end}
{phang}{cmd:. predict bc, bc ci}{p_end}
{phang}{cmd:. predict jlms, jlms ci}{p_end}
{pstd}Non-monotonic marginal effects{p_end}
{phang}{cmd:. webuse frontier1, clear}{p_end}
{phang}{cmd:. sfcross lnoutput lnlabor lncapital, d(tn) emean(lnlabor, nocons) usigma(lnlabor, nocons) difficult}{p_end}
{phang}{cmd:. predict, marg}{p_end}
{pstd}Equation-level score variables{p_end}
{phang}{cmd:. predict score*, scores}{p_end}
{title:Authors}
{pstd}Federico Belotti{p_end}
{pstd}Centre for Economic and International Studies, University of Rome Tor Vergata{p_end}
{pstd}Rome, Italy{p_end}
{pstd}federico.belotti@uniroma2.it{p_end}
{pstd}Silvio Daidone{p_end}
{pstd}Centre for Health Economics, University of York{p_end}
{pstd}York, UK{p_end}
{pstd}silvio.daidone@york.ac.uk{p_end}
{pstd}Vincenzo Atella{p_end}
{pstd}Centre for Economic and International Studies, University of Rome Tor Vergata{p_end}
{pstd}Rome, Italy{p_end}
{pstd}atella@uniroma2.it{p_end}
{pstd}Giuseppe Ilardi{p_end}
{pstd}Economic and Financial Statistics Department, Bank of Italy{p_end}
{pstd}Rome, Italy{p_end}
{pstd}giuseppe.ilardi@bancaditalia.it{p_end}
{title:Also see}
{psee}
{space 2}Help: {help sfcross}, {help sfpanel}.
{p_end}