A spatial stochastic frontier model including both frontier and error-based spatial cross-sectional dependence

ABSTRACT

Spatial dependence in stochastic frontier models is usually handled by modelling the frontier function or the inefficiency error term through the introduction of some spatial components. The model proposed in this paper (SDF-CSD) combines the two different modelling approaches, obtaining a full comprehensive specification that introduces four different sources of spatial cross-sectional dependence. The most appealing feature of the model is that it allows capturing global and local spatial spillover effects while controlling for spatial correlation related to firms’ efficiency and to unobserved but spatially correlated variables. Moreover, it can be estimated using maximum likelihood techniques. Finally, some Monte Carlo simulations were run to test the final sample properties of the new spatial estimator and an application to the Italian agricultural sector is provided.

KEYWORDS:

• spatial stochastic frontier models
• spillover effects
• Italian agricultural sector

JEL:

• C21
• C23
• D24
• L25

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the author.

Notes

1 Matlab codes are available from the author upon request.

2 In Italy, the minimum threshold for the inclusion in the RICA observation sample corresponds to a minimum standard gross income of €8000.

3 A second-order matrix compared with a first-order one allows one to consider more complex spatial structures and better identify spatial clusters. Moreover, this matrix minimizes the log-likelihood function. Some robustness checks using different spatial weight matrices are provided afterwards.