📄 frontier.hlp
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{smcl}
{* 08mar2005}{...}
{cmd:help frontier}{right:dialog: {bf:{dialog frontier}}{space 15}}
{right:also see: {help frontier postestimation}}
{hline}
{title:Title}
{p2colset 5 21 23 2}{...}
{p2col :{hi:[R] frontier} {hline 2}}Stochastic frontier models{p_end}
{p2colreset}{...}
{title:Syntax}
{p 8 17 2}
{cmd:frontier}
{depvar}
[{indepvars}]
{ifin}
{weight}
[{cmd:,} {it:options}]
{synoptset 31 tabbed}{...}
{synopthdr}
{synoptline}
{syntab :Model}
{synopt :{opt nocons:tant}}suppress constant term{p_end}
{synopt :{cmdab:d:istribution(}{opt h:normal)}}half-normal distribution for the
inefficiency term{p_end}
{synopt :{cmdab:d:istribution(}{opt e:xponential)}}exponential distribution for the inefficiency term{p_end}
{synopt :{cmdab:d:istribution(}{opt t:normal)}}truncated-normal distribution for the inefficiency term{p_end}
{synopt :{opt uf:rom(matrix)}}specify untransformed log-likelihood; only with
{cmd:d(tnormal)}{p_end}
{synopt :{cmd:cm(}{it:{help varlist}}[{cmd:,} {opt nocons:tant}]{cmd:)}}fit
conditional mean model; only with {cmd:d(tnormal)}; use {opt noconstant} to
suppress constant term{p_end}
{syntab :Model 2}
{synopt :{cmdab:const:raints(}{it:{help estimation options##constraints():constraints}}{cmd:)}}apply specified linear constraints{p_end}
{synopt :{cmdab:u:het(}{it:{help varlist}}[{cmd:,} {opt nocons:tant}]{cmd:)}}explanatory
variables for technical inefficiency variance function; use {opt noconstant}
to suppress constant term{p_end}
{synopt :{cmdab:v:het(}{it:{help varlist}}[{cmd:,} {opt nocons:tant}]{cmd:)}}explanatory
variables for idiosyncratic error variance function; use {opt noconstant}
to suppress constant term{p_end}
{synopt :{opt cost}}fit cost frontier model; default is production frontier
model{p_end}
{syntab :SE/Robust}
{synopt :{opth vce(vcetype)}}{it:vcetype} may be {opt oim},
{opt opg}, {opt boot:strap}, or {opt jack:knife}{p_end}
{syntab :Reporting}
{synopt :{opt l:evel(#)}}set confidence level; default is
{cmd:level(95)}{p_end}
{syntab :Max options}
{synopt :{it:{help frontier##maximize_options:maximize_options}}}control the maximization process; seldom used{p_end}
{synoptline}
{p2colreset}{...}
{p 4 6 2}
{opt bootstrap}, {opt by}, {opt jackknife}, {opt rolling}, {opt statsby}, and
{opt xi} are allowed; see {help prefix}.{p_end}
{p 4 6 2}
{opt fweight}s, {opt iweight}s, and {opt pweight}s are allowed;
see {help weight}.{p_end}
{p 4 6 2}
See {help frontier postestimation}
for features available after estimation.{p_end}
{title:Description}
{pstd}
{opt frontier} fits stochastic production or cost frontier models; the default
is a production frontier model. It provides estimators for the parameters of
a linear model with a disturbance that is assumed to be
a mixture of two components, which have a strictly
non-negative and symmetric distribution, respectively.
{opt frontier} can fit models in which the non-negative distribution component
(a measurement of inefficiency) is assumed
to be from a half-normal, exponential, or truncated-normal distribution.
{title:Options}
{dlgtab:Model}
{phang}
{opt noconstant}; see {help estimation options}.
{phang}
{opt distribution(distname)} specifies the
distribution for the inefficiency term
as half-normal ({opt hnormal}), {opt exponential}, or truncated-normal
({opt tnormal}). The default is {opt hnormal}.
{phang}
{opt ufrom(matrix)} specifies a 1 X K matrix of
untransformed starting values when the distribution is
truncated-normal ({opt tnormal}). {opt frontier} can
estimate the parameters of the model by maximizing either the log likelihood
or a transformed log-likelihood.
{opt frontier} automatically transforms the starting values before passing
them on to the transformed log-likelihood. The matrix must have exactly the
same number of columns as there are parameters to estimate.
{phang}
{cmd:cm(}{varlist} [{cmd:,} {opt noconstant}]{cmd:)}
may only be used with {cmd:distribution(tnormal)}.
In this case, {opt frontier} will fit a conditional
mean model in which the mean of the truncated-normal distribution is modeled
as a linear function of the set of covariates specified in {it:varlist}.
Specifying {opt noconstant} suppresses the constant in the mean function.
{dlgtab:Model 2}
{phang}
{opt constraints(constraints)}; see {help estimation options}.
{pmore}
By default, when fitting the truncated-normal model or the conditional mean
model, {opt frontier} maximizes a transformed log-likelihood. When
constraints are applied, {opt frontier} will maximize the untransformed
log-likelihood with constraints defined in the untransformed metric.
{phang}
{cmd:uhet(}{it:varlist} [{cmd:, noconstant}]{cmd:)}
specifies that the technical inefficiency component is heteroskedastic,
with the variance function depending on a linear combination of
{it:varlist_u}. Specifying {opt noconstant} suppresses the
constant term from the variance function. This option may not be specified
with {cmd:distribution(tnormal)}.
{phang}
{cmd:vhet(}{it:varlist} [{cmd:, noconstant}]{cmd:)}
specifies that the idiosyncratic error component is heteroskedastic,
with the variance function depending on a linear combination of
{it:varlist_v}. Specifying {opt noconstant} suppresses the
constant term from the variance function. This option may not be specified
with {cmd:distribution(tnormal)}.
{phang}
{opt cost} specifies that {opt frontier} fit a cost frontier model.
{dlgtab:SE/Robust}
{phang}
{opt vce(vcetype)}; see {it:{help vce_option}}.
{dlgtab:Reporting}
{phang}
{opt level(#)}; see {help estimation options}.
{marker maximize_options}{...}
{dlgtab:Max options}
{phang}
{it:maximize_options}:
{opt dif:ficult},
{opt tech:nique(algorithm_spec)},
{opt iter:ate(#)},
[{cmdab:no:}]{opt lo:g},
{opt tr:ace},
{opt hess:ian},
{opt grad:ient},
{opt showstep},
{opt tol:erance(#)},
{opt ltol:erance(#)},
{opt gtol:erance(#)},
{opt nrtol:erance(#)},
{opt nonrtol:erance},
{opt from(init_specs)};
see {help maximize}.
These options are seldom used.
{title:Examples}
{phang}{cmd:. frontier lnv lnk lnl}{p_end}
{phang}{cmd:. frontier lnv lnk lnl, d(e)}{p_end}
{phang}{cmd:. frontier lnv lnk lnl, cost}{p_end}
{phang}{cmd:. frontier lnv lnk lnl, vhet(capital)}{p_end}
{phang}{cmd:. frontier lnv lnk lnl, d(t) cm(z)}{p_end}
{title:Also see}
{psee}
Manual: {hi:[R] frontier}
{psee}
Online: {help frontier postestimation};{break}
{helpb constraint},
{helpb regress},
{helpb xtfrontier}
{p_end}
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