summary {ssfa}

SSFA summaries

Description

The function print.ssfa is used to display the values of SFA and SSFA estimated coefficients. In particular:

- for SFA the function displays the Intercept, the regressors beta coefficients, the inefficiency variance sigmau2, the stochastic error variance sigmav2 and the total variance sigma2;
- for SSFA the function displays, in addition, the decomposition of the inefficiency variance into sigmau2_dmu and sigmau2_sar, respectively the part of inefficiency variance due to DMU's specificities and to the spatial dependence, and finally, the spatial lag parameter rho.

The function summary.ssfa is used to display the summary results of SFA and SSFA. In particular:

- for SFA the summary shows the estimation of SFA coefficients (Intercept, beta coefficients, sigmau2 and sigmav2) and others useful information as the total variance sigma2, the inefficiency parameter Lambda (sigmau/sigmav), the Moran I statistic, the mean of efficiency, the LR-test and the AIC values;
- for SSFA the summary shows, in addition, the decomposition of the inefficiency variance into sigmau2_dmu and sigmau2_sar and the spatial lag parameter rho.

Usage

## S3 method for class 'ssfa'
print(x, ...)
## S3 method for class 'ssfa'
summary(object, ...)

Arguments

x

an object of class ssfa.

object

an object of class ssfa.

...

further arguments for methods.

Note

Please note that the classical SFA inefficiency variance sigmau2, in the SSFA, is decomposed into sigmau2_dmu and sigmau2_sar, respectively the part of inefficiency variance due to DMU's specificities and to the spatial dependence, i.e. sigmau2 = sigmau2_dmu + sigmau2_sar and consequently the total variance is given by sigma2 = sigmau2_dmu + sigmau2_sar + sigmav2.

References

Anselin, L. (1995). Local indicators of spatial association, Geographical Analysis, 27, 93-115.

Fusco, E. and Vidoli, F. (2013). Spatial stochastic frontier models: controlling spatial global and local heterogeneity, International Review of Applied Economics, 27(5) 679-694.

Fusco, E. (2020). Spatial Dependence in Efficiency Parametric Models: A Generalization and Simulation Studies, "Scienze Regionali, Italian Journal of Regional Science" Speciale/2021, 595-618.

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

Examples

library(ssfa) 
data(SSFA_example_data)
data(Italian_W)
ssfa <- ssfa(log_y ~ log_x, data = SSFA_example_data, 
             data_w=Italian_W, form = "production", par_rho=TRUE)

print(ssfa)
summary(ssfa)