Stata 15 help for frontier

[R] frontier -- Stochastic frontier models


frontier depvar [indepvars] [if] [in] [weight] [, options]

options Description ------------------------------------------------------------------------- Model noconstant suppress constant term distribution(hnormal) half-normal distribution for the inefficiency term distribution(exponential) exponential distribution for the inefficiency term distribution(tnormal) truncated-normal distribution for the inefficiency term ufrom(matrix) specify untransformed log likelihood; only with d(tnormal) cm(varlist[, noconstant]) fit conditional mean model; only with d(tnormal); use noconstant to suppress constant term

Model 2 constraints(constraints) apply specified linear constraints collinear keep collinear variables uhet(varlist[, noconstant]) explanatory variables for technical inefficiency variance function; use noconstant to suppress constant term vhet(varlist[, noconstant]) explanatory variables for idiosyncratic error variance function; use noconstant to suppress constant term cost fit cost frontier model; default is production frontier model

SE/Robust * vce(vcetype) vcetype may be oim, robust, cluster clustvar, opg, bootstrap, or jackknife

Reporting level(#) set confidence level; default is level(95) nocnsreport do not display constraints display_options control columns and column formats, row spacing, line width, display of omitted variables and base and empty cells, and factor-variable labeling

Maximization maximize_options control the maximization process; seldom used

coeflegend display legend instead of statistics ------------------------------------------------------------------------- * vce(robust) and vce(cluster clustvar) may not be specified with distribution(tnormal). indepvars and varlist may contain factor variables; see fvvarlist. bootstrap, by, fp, jackknife, rolling, and statsby are allowed; see prefix. Weights are not allowed with the bootstrap prefix. fweights, iweights, and pweights are allowed; see weight. coeflegend does not appear in the dialog box. See [R] frontier postestimation for features available after estimation.


Statistics > Linear models and related > Frontier models


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 nonnegative and symmetric distribution, respectively. frontier can fit models in which the nonnegative distribution component (a measurement of inefficiency) is assumed to be from a half-normal, exponential, or truncated-normal distribution. See Kumbhakar and Lovell (2000) for a detailed introduction to frontier analysis.


+-------+ ----+ Model +------------------------------------------------------------

noconstant; see [R] estimation options.

distribution(distname) specifies the distribution for the inefficiency term as half-normal (hnormal), exponential, or truncated-normal (tnormal). The default is hnormal.

ufrom(matrix) specifies a 1 x K matrix of untransformed starting values when the distribution is truncated-normal (tnormal). frontier can estimate the parameters of the model by maximizing either the log likelihood or a transformed log likelihood (see Methods and formulas). frontier automatically transforms the starting values before passing them on to the transformed log likelihood. The matrix must have the same number of columns as there are parameters to estimate.

cm(varlist [, noconstant]) may be used only with distribution(tnormal). Here 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 varlist. Specifying noconstant suppresses the constant in the mean function.

+---------+ ----+ Model 2 +----------------------------------------------------------

constraints(constraints), collinear; see [R] estimation options.

By default, when fitting the truncated-normal model or the conditional mean model, frontier maximizes a transformed log likelihood. When constraints are applied, frontier will maximize the untransformed log likelihood with constraints defined in the untransformed metric.

uhet(varlist [, noconstant]) specifies that the technical inefficiency component is heteroskedastic, with the variance function depending on a linear combination of varlist_u. Specifying noconstant suppresses the constant term from the variance function. This option may not be specified with distribution(tnormal).

vhet(varlist [, noconstant]) specifies that the idiosyncratic error component is heteroskedastic, with the variance function depending on a linear combination of varlist_v. Specifying noconstant suppresses the constant term from the variance function. This option may not be specified with distribution(tnormal).

cost specifies that frontier fit a cost frontier model.

+-----------+ ----+ SE/Robust +--------------------------------------------------------

vce(vcetype) specifies the type of standard error reported, which includes types that are derived from asymptotic theory (oim, opg), that are robust to some kinds of misspecification (robust), that allow for intragroup correlation (cluster clustvar), and that use bootstrap or jackknife methods (bootstrap, jackknife); see [R] vce_option.

vce(robust) and vce(cluster clustvar) may not be specified with distribution(tnormal).

+-----------+ ----+ Reporting +--------------------------------------------------------

level(#); see [R] estimation options.

nocnsreport; see [R] estimation options.

display_options: noci, nopvalues, noomitted, vsquish, noemptycells, baselevels, allbaselevels, nofvlabel, fvwrap(#), fvwrapon(style), cformat(%fmt), pformat(%fmt), sformat(%fmt), and nolstretch; see [R] estimation options.

+--------------+ ----+ Maximization +-----------------------------------------------------

maximize_options: difficult, technique(algorithm_spec), iterate(#), [no]log, trace, gradient, showstep, hessian, showtolerance, tolerance(#), ltolerance(#), nrtolerance(#), nonrtolerance, and from(init_specs); see [R] maximize. These options are seldom used.

Setting the optimization type to technique(bhhh) resets the default vcetype to vce(opg).

The following option is available with frontier but is not shown in the dialog box:

coeflegend; see [R] estimation options.


--------------------------------------------------------------------------- Setup . webuse greene9

Cobb-Douglas production function with half-normal distribution for inefficiency term . frontier lnv lnk lnl

Cobb-Douglas production function with exponential distribution for inefficiency term . frontier lnv lnk lnl, dist(exponential)

--------------------------------------------------------------------------- Setup . webuse frontier1

Cobb-Douglas production function with size as explanatory variable in variance function for idiosyncratic error . frontier lnoutput lnlabor lncapital, vhet(size)

--------------------------------------------------------------------------- Setup . webuse frontier2

Cost frontier model with truncated-normal distribution for inefficiency term . frontier lncost lnp_k lnp_l lnout, dist(tnormal) cost ---------------------------------------------------------------------------

Stored results

frontier stores the following in e():

Scalars e(N) number of observations e(df_m) model degrees of freedom e(k) number of parameters e(k_eq) number of equations in e(b) e(k_eq_model) number of equations in overall model test e(k_dv) number of dependent variables e(chi2) chi-squared e(ll) log likelihood e(ll_c) log likelihood for H_0: sigma_u=0 e(z) test for negative skewness of OLS residuals e(sigma_u) standard deviation of technical inefficiency e(sigma_v) standard deviation of V_i e(p) p-value for model test e(chi2_c) LR test statistic e(p_z) p-value for z e(rank) rank of e(V) e(ic) number of iterations e(rc) return code e(converged) 1 if converged, 0 otherwise

Macros e(cmd) frontier e(cmdline) command as typed e(depvar) name of dependent variable e(function) production or cost e(wtype) weight type e(wexp) weight expression e(title) title in estimation output e(chi2type) Wald; type of model chi-squared test e(dist) distribution assumption for U_i e(het) heteroskedastic components e(u_hetvar) varlist in uhet() e(v_hetvar) varlist in vhet() e(vce) vcetype specified in vce() e(vcetype) title used to label Std. Err. e(opt) type of optimization e(which) max or min; whether optimizer is to perform maximization or minimization e(ml_method) type of ml method e(user) name of likelihood-evaluator program e(technique) maximization technique e(properties) b V e(predict) program used to implement predict e(asbalanced) factor variables fvset as asbalanced e(asobserved) factor variables fvset as asobserved

Matrices e(b) coefficient vector e(Cns) constraints matrix e(ilog) iteration log (up to 20 iterations) e(gradient) gradient vector e(V) variance-covariance matrix of the estimators e(V_modelbased) model-based variance

Functions e(sample) marks estimation sample


Kumbhakar, S. C., and C. A. K. Lovell. 2000. Stochastic Frontier Analysis. Cambridge: Cambridge University Press.

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