Stata help for xtfrontier

 help xtfrontier dialog: xtfrontier also see: xtfrontier postestimation ------------------------------------------------------------------------------- 
 Title 
 [XT] xtfrontier -- Stochastic frontier models for panel data 
 
 Syntax 
 Time-invariant model 
 xtfrontier depvar [indepvars] [if] [in] [weight] , ti [ti_options] 
 
 Time-varying decay model 
 xtfrontier depvar [indepvars] [if] [in] [weight] , tvd [tvd_options] 
 
 ti_options description ------------------------------------------------------------------------- Model i(varname_i) use varname_i as the panel ID variable noconstant suppress constant term ti use time-invariant model; the default cost fit cost frontier model constraints(constraints) apply specified linear constraints 
 SE vce(vcetype) vcetype may be bootstrap or jackknife 
 Reporting level(#) set confidence level; default is level(95) 
 Max options ml_maximize_options control the maximization process; seldom used ------------------------------------------------------------------------- 
 tvd_options description ------------------------------------------------------------------------- Model i(varname_i) use varname_i as the panel ID variable t(varname_t) use varname_t as the time variable noconstant suppress constant term tvd use time-varying decay model cost fit cost frontier model constraints(constraints) apply specified linear constraints 
 SE vce(vcetype) vcetype may be bootstrap or jackknife 
 Reporting level(#) set confidence level; default is level(95) 
 Max options ml_maximize_options control the maximization process; seldom used ------------------------------------------------------------------------- 
 You must tsset your data before using xtfrontier; see tsset. depvars and indepvars may contain time-series operators; see tsvarlist. fweights and i weights are allowed; see weight. bootstrap, by, jackknife, statsby, and xi may be used with xtfrontier; see prefix. See xtfrontier postestimation for features available after estimation. 
 
 Description 
 xtfrontier fits stochastic production or cost frontier models for panel data. More precisely, xtfrontier estimates the parameters of a linear model with a disturbance generated by specific mixture distributions. 
 The disturbance term in a stochastic frontier model is assumed to have two components. One component is assumed to have a strictly non-negative distribution, and the other component is assumed to have a symmetric distribution. In the econometrics literature, the non-negative component is often referred to as the inefficiency term, and the component with the symmetric distribution as the idiosyncratic error. xtfrontier permits two different parameterizations of the inefficiency term: a time-invariant model and the Battese-Coelli parameterization of time-effects. In the time-invariant model, the inefficiency term assumed to have a truncated-normal distribution. In the Battese-Coelli parameterization of time effects, the inefficiency term is modeled as a truncated-normal random variable multiplied by a specific function of time. In both models, the idiosyncratic error term is assumed to have a normal distribution. The only panel-specific effect is the random inefficiency term. 
 
 Options for time-invariant model 
 +-------+ ----+ Model +------------------------------------------------------------ 
 i(varname_i); see estimation options. 
 ti specifies that the parameters of the time-invariant technical inefficiency model be estimated. 
 noconstant; see estimation options. 
 cost specifies the frontier model be fitted in terms of a cost function instead of a production function. By default, xtfrontier fits a production frontier model. 
 constraints(constraints); see estimation options. 
 +----+ ----+ SE +--------------------------------------------------------------- 
 vce(vcetype); see vce_option. 
 +-----------+ ----+ Reporting +-------------------------------------------------------- 
 level(#); see estimation options. 
 +-------------+ ----+ Max options +------------------------------------------------------ 
 ml_maximize_options: difficult, technique(algorithm_spec), iterate(#), [no]log, trace, gradient, showstep, hessian, shownrtolerance, tolerance(#), ltolerance(#), gtolerance(#), nrtolerance(#), nonrtolerance, from(init_specs); see ml and maximize. These options are seldom used. 
 
 Options for time-varying decay model 
 +-------+ ----+ Model +------------------------------------------------------------ 
 i(varname_i), t(varname_t); see estimation options. 
 noconstant; see estimation options. 
 tvd specifies that the parameters of the time-varying decay model be estimated. 
 cost specifies the frontier model be fitted in terms of a cost function instead of a production function. By default, xtfrontier fits a production frontier model. 
 constraints(constraints); see estimation options. 
 +----+ ----+ SE +--------------------------------------------------------------- 
 vce(vcetype); see vce_option. 
 +-----------+ ----+ Reporting +-------------------------------------------------------- 
 level(#); see estimation options. 
 +-------------+ ----+ Max options +------------------------------------------------------ 
 ml_maximize_options: difficult, technique(algorithm_spec), iterate(#), [no]log, trace, hessian, gradient, showstep, shownrtolerance, tolerance(#), ltolerance(#), gtolerance(#), nrtolerance(#), nonrtolerance, from(init_specs); see ml and maximize. These options are seldom used. 
 
 Examples 
 . xtfrontier lnv lnk lnl, i(id) t(t) tvd 
 . xtfrontier lnv lnk lnl, i(id) ti 
 . xtfrontier lnv lnk lnl, i(id) t(t) tvd cost 
 
 Also see 
 Manual: [XT] xtfrontier 
 Online: xtfrontier postestimation; frontier, regress, tsset, xtreg 

是回归方程中的non-negative residual

SFA中的殘差是被用來估計『技術進步』的用途。但由于一般殘差會是不偏的常態分配狀態，SFA將其殘差改成以U-V的形式出現。U為效率邊界，V則為技術無效率。

就這樣了