Estimation Overview

Consider a typical stochastic frontier model,

\[ \begin{aligned} y_i = f(x_i; \beta) + v_i - u_i(z_i), \end{aligned}\]

where $v_i$ and $u_i(z_i) >0$ are both stochastic.

SFrontiers provides utilities to estimate the model using the maximum likelihood approach.

1. Specify the model using sfmodel_spec()

• a cross-sectional (the default) or a panel data (require tags) model
• a production or a cost type of model
• distribution assumptions on $u_i$
• names of variables for $y_i$, $x_i$, and $z_i$ (if any)

2. (optional) Provide initial values using sfmodel_init()

• initial values for the maximum likelihood estimation
• a full list or a partial list for some of the equations

3. (optional) Provide parameters for numerical maximization and other controls using sfmodel_opt()

• algorithms (e.g., Nelder-Mead, BFGS, Newton, etc.)
• maximum iteration number
• convergence criterion
• information to print on screen
• whether calculating inefficiency index, marginal effect, etc.

4. Start the Numerical Maximization Process using sfmodel_fit()

• name of the dataset

5. Conduct Post-Estimation Analysis

• hypothesis testing
• the inefficiency index of Jondrow et al. (1982) or the efficiency index of Battese and Coelli (1988)
• marginal effect of the inefficiency determinants