data.gen.p: Generate Panel Data for Stochastic Frontier Analysis

In sfa: Stochastic Frontier Analysis

Generate Panel Data for Stochastic Frontier Analysis

Description

data_gen_p generates simulated panel data for estimating various panel stochastic frontier models, including the Generalized True Random Effects (GTRE), True Random Effects (TRE), Pooled Cross-Section (PCS), and True Fixed Effects (TFE) models. The function returns the data as a pdata.frame. All variants are produced so that the user can select those that they want.

Usage

data_gen_p(t, N, rand, sig_u, sig_v, sig_r, sig_h, cons, tau = 0.5, mu = 0, beta1, beta2)

Arguments

t	The number of time periods.
N	The number of individuals.
rand	A seed for the random number generator to ensure reproducibility.
sig_u	The standard deviation (\sigma_u) for the one-sided error component (u_{it}).
sig_v	The standard deviation (\sigma_v) for the two-sided error component (v_{it}).
sig_r	The standard deviation (\sigma_r) for the two-sided individual effect (r_i).
sig_h	The standard deviation (\sigma_h) for the one-sided individual effect (h_i).
cons	The constant term (\beta_0) for the frontier models.
tau	The dependence parameter (\tau) used for the y_tfe (TFE) model formulation, default is 0.5. See Chen, Schmidt, and Wang (2014, Journal of Econometrics).
mu	The mean parameter (\mu) used for the Truncated-Normal (TN) component of the y_fd model with default set to 0. See Wang and Ho (2010, Journal of Econometrics).
beta1	The coefficient for the x1 variable (\beta_1).
beta2	The coefficient for the x2 variable (\beta_2).

Details

A pdata.frame object with N \times t observations, containing the following columns:

• name Individual identifier.

• year Time period identifier.

• cons The constant term used in the data generation.

• x1, x2 Explanatory variables generated from a log-uniform distribution.

• x1_w, x2_w Explanatory variables with dependence parameter \tau and linkage with r_i, used for the TFE model.

• u, v, r, h The generated error and individual effect components.

• y_gtre, y_tre, y_pcs, y_tfe Output variables for the Production Frontier models, including the constant.

• y_gtre_nc, y_tre_nc, y_pcs_nc Output variables for the Production Frontier models, excluding the constant.

• c_gtre, c_tre, c_pcs, c_tfe Output variables for the Cost Frontier models, including the constant.

• c_gtre_nc, c_tre_nc, c_pcs_nc Output variables for the Cost Frontier models, excluding the constant.

• y_fd Output variable for the first difference model (see Wang and Ho, 2010).

• x_fd Explanatory variable for the y_fd model.

• u_fd_star, z_fd, r_fd, u_fd Components used to generate y_fd.

• u_gtre, z_gtre, y_gtre_z, y_tre_z Variables for models with heteroskedastic inefficiency (\sigma_{u,i} = \exp(0.9 + 0.6 Z_{i})).

The data is generated based on standard Stochastic Frontier Analysis (SFA) formulations, primarily for a **Production Frontier** where the one-sided error component u_{it} is subtracted:

• y_gtre: GTRE model: y_{it} = \beta_0 + \beta_1 x_{1,it} + \beta_2 x_{2,it} + r_i - h_i + v_{it} - u_{it}

• y_tre: TRE model: y_{it} = \beta_0 + \beta_1 x_{1,it} + \beta_2 x_{2,it} + r_i + v_{it} - u_{it}

• y_pcs: PCS model: y_{it} = \beta_0 + \beta_1 x_{1,it} + \beta_2 x_{2,it} + v_{it} - u_{it}

• y_tfe: TFE model: y_{it} = \beta_1 x_{1,it}^w + \beta_2 x_{2,it}^w + r_i + v_{it} - u_{it}

• y_gtre_z: GTRE with Heteroskedastic u_{it}: \sigma_{u,i} = \exp(0.9 + 0.6 Z_i).

For **Cost Frontier** models, the one-sided error component u_{it} is added (e.g., c_gtre).

The error terms are generated as:

• r_i \sim N(0, \sigma_r^2) (individual two-sided effect)

• h_i \sim |N(0, \sigma_h^2)| (individual one-sided effect)

• v_{it} \sim N(0, \sigma_v^2) (two-sided noise)

• u_{it} \sim |N(0, \sigma_u^2)| (one-sided inefficiency)

The First-Difference estimation model (y_fd) uses a variation where r_{i,fd} \sim U(0,1) and u_{it,fd} is generated using a heteroskedastic truncated-normal structure, reflecting an alternative model type.

Value

A pdata.frame object containing N \times t observations suitable for Stochastic Frontier Analysis (SFA).

Author(s)

David Bernstein

References

Chen, Y., Schmidt, P., & Wang, H. (2014). Consistent estimation of the fixed effects stochastic frontier model. Journal of Econometrics, 181(2), 65-76.

Filippini, M., & Greene, W. H. (2016). Persistent and transient productive inefficiency: a maximum simulated likelihood approach. Journal of Productivity Analysis, 45, 187-196.

Wang, H., & Ho, C. M. (2010). Estimating fixed-effect panel stochastic frontier models by model transformation. Journal of Econometrics, 157(2), 286-296.

See Also

data_gen_p, to see all the data generating processes

Examples

library(sfa) 
# Generate a dataset 
data_trial <- data_gen_p(t=10, N=100, rand = 100, 
                       sig_u = 1,  sig_v = 0.3, 
                       sig_r = .2, sig_h = .4, 
                       cons = 0.5, tau = 0.5,
                       mu= 0.5, beta1 = 0.5,
                       beta2 = 0.5)
 # See the first few rows 
 head(data_trial)

sfa documentation built on Jan. 22, 2026, 1:08 a.m.