Spatial autoregressive stochastic frontier model with application to Indonesia’s aquaculture

Abstract

Stochastic frontier analysis (SFA) is one of the popular methods for measuring efficiency and productivity. SFA generally assumes that decision making units are independent. However, this assumption may be inappropriate since decision making units are probable interdependent depending on their spatial proximities. This paper aims to incorporate spatial lag into standard SFA model. The performance of spatial autoregressive stochastic frontier model (SAR-SFA) is compared to standard SFA using simulation and real data. Simulation study is undertaken using various degrees of spatial autocorrelation. Furthermore, SAR-SFA is applied to estimate technical efficiency of aquaculture in Indonesia. Simulation results showed that the SAR-SFA generally produces better performance than the standard SFA. If spatial dependencies are significant, then the estimation of production frontier from standard SFA could be misleading. It affects the distribution of technical efficiency and its ranking. Moran’s I test indicated that Indonesia’s aquaculture has significant positive spatial autocorrelation. If standard SFA is applied to estimate technical efficiency of Indonesia’s aquaculture, then the resulted technical efficiency is implausible. This issue is well handled by the SAR-SFA model. Moreover, SAR-SFA model serves procedure to estimate efficiency spillovers.