The repository of Stata command sftt. For details, see:

Lian, Y., Liu, C., & Parmeter, C. F. (2023). Two-tier stochastic frontier analysis using Stata. The Stata Journal, 23(1), 197–229. link, -PDF-

sftt fits two-tier stochastic frontier (2TSF) models with multiple model settings.

The 2TSF model consists of a linear model with a disturbance that is assumed to be a mixture of three components: two measures of inefficiency which are strictly nonnegative and nonpositive respectively, and a two-sided error term from a symmetric distribution.

sftt can fit 2TSF models with distributional assumption. When using distributional assumption mode, this command is applicable to estimate

• models in exponential/exponential/normal specification following Kumbhakar and Parmeter (2009)
• models in half-normal/half-normal/normal specification following Papadopoulos (2015).

This command also fits

• models with scaling property following Parmeter (2018).

Following Kumbhakar and Parmeter (2009), consider the 2TSF model

$$ \begin{aligned} & \mathbf{y}=\mathbf{X} \mathbf{\delta}+\varepsilon \\ & \varepsilon=\mathbf{v}-\mathbf{u}+\mathbf{w} \end{aligned} $$

where $\mathbf{y}$ is an $n \times 1$ vector containing observations of the outcome variable, $\mathbf{X}$ is an $n \times K$ matrix of covariates, $\delta$ is a $K \times 1$ vector of the coefficients, and $\mathbf{\varepsilon}$ is an $n \times 1$ vector of the composite error term, with $\mathbf{u}$ and $\mathbf{w}$ being two one-sided inefficiency terms and $\mathbf{v}$ capturing stochastic noise. These three components are assumed to be jointly independent. For each $i$, we have

$$ \begin{aligned} v_i & \sim \text { i.i.d. } N\left(0, \sigma_v^2\right) \\ u_i & \sim \text { i.i.d. } \text{Exp}\left(\sigma_u\right) \\ w_i & \sim \text { i.i.d. } \text{Exp}\left(\sigma_w\right) \end{aligned} $$

where i.i.d. stands for independent and identically distributed, $N(0, \sigma_v^2)$ denotes a normal distribution with mean 0 and variance $\sigma_v^2$, and $\text{Exp}(\sigma_z)$ denotes a random variable $z$ that is exponentially distributed with mean $\sigma_z$ and variance $\sigma_z^2$.

The model can be estimated using MLE, and $E\left(u_i \mid \varepsilon_i\right)$ and $E\left(w_i \mid \varepsilon_i\right)$ are estimated to measure inefficiency.

• sftt estimates two-tier SF models listed above.
• sftt sigs identifies the distribution of each component in the composite error term.
• sftt eff decomposes the residual and generate measures of inefficiency.

You can always type search sftt in Stata's command window to get access to package. Or, you can use the following commands to download it directly.

net install st0705.pkg, replace
net get     st0705.pkg, replace  // to get main.do file

Then you can read the help document to get more detailed information:

help sftt

First add directory to end of ado-path.

adopath + "./src"

Load the data used in Kumbhakar and Parmeter (2009) and replicate their results.

use "https://sftt.oss-cn-hangzhou.aliyuncs.com/kp09.dta", clear
sftt lwage iq educ educ2 exper exper2 tenure tenure2  ///
     age married south urban black sibs brthord meduc feduc

Finally, you can use the post-estimation commands sftt sigs and sftt eff to assist your efficiency analysis.

sftt sigs
sftt eff, replace

You can use help sftt to see more detailed instructions.

• ./mc_results stores the results generated by the Monte Carlo simulation using scaling_mc.do.
• ./output stores the results shown in Lian et al. (2022).
• ./src stores the source code of sftt.
• main.do provides example of the applications of sftt, the results will be saved in ./output.
• scaling_mc.do implements the Monte-Carlo simulation following Parmeter (2018), the results will be saved in ./mc_results.

• Kumbhakar, S. C., and C. F. Parmeter. 2009. The effects of match uncertainty and bargaining on labor market outcomes: Evidence from firm and worker specific estimates. Journal of Productivity Analysis 31: 1–14. https://doi.org/10.1007/s11123-008-0117-3.
• Papadopoulos, A. A. 2015. The half-normal specification for the two-tier stochastic frontier model. Journal of Productivity Analysis 43: 225–230. https://doi.org/10.1007/s11123-014-0389-8.
• Parmeter, C. F. 2018. Estimation of the two-tiered stochastic frontier model with the scaling property. Journal of Productivity Analysis 49: 37–47. https://doi.org/10.1007/s11123-017-0520-8.

We thank Dr. Jenkins and the anonymous reviewer for their valuable and insightful comments.

We also thank Alecos Papadopoulos for his helpful support.

• Yujun Lian (repo owner). Lingnan College, Sun Yat-sen University. Guangzhou, China. profile, blog
• Chang Liu. Lingnan College, Sun Yat-sen University Guangzhou, China.
• Christopher F. Parmeter. Department of Economics, University of Miami Miami, FL, USA. profile