Kajian Robust Stochastic Frontier Dengan Fat-Tailed Distribution Untuk Pendugaan Efisiensi Teknis Usaha Tani Padi

Abstract

Pencilan merupakan permasalahan statistika yang menyebabkan galat tidak lagi simetris dan memiliki sebaran yang sangat menjulur. Penelitian ini dilatarbelakangi oleh permasalahan kehadiran amatan pencilan pada pemodelan stochastic frontier analysis (SFA). Pencilan dapat mengganggu performa model SFA baik dari sisi pendugaan fungsi frontir maupun pendugaan efisiensi itu sendiri. Model SFA banyak digunakan untuk mengukur efisiensi. Model SFA yang secara spesifik mengukur efisiensi teknis disebut dengan model stochastic production frontier (SPF). Pada model SPF, sisaan didekomposisi menjadi noise dan inefisiensi teknis yang masing-masing memiliki sebaran. Model konvensional SPF, noise-nya berdistribusi normal dan inefisiensinya berdistribusi half normal. Model ini memiliki keterbatasan jika terdapat pencilan dalam data amatan. Hasil dugaan efisiensi akan cenderung melebar. Penelitian ini mengajukan model SPF yang berdistribusi fat-tailed pada sisaannya. Model SPF alternatif yang diajukan yaitu berdistribusi normal-Rayleigh, normal-Weibull, dan Cauchy-half normal Ketiga model tersebut dikaji dengan membandingkannya terhadap model SPF konvensional normal-half normal dalam menduga parameter model dan efisiensi teknis. Kajian dilakukan pada data simulasi dan data riil. Berdasarkan hasil kajian data simulasi dengan 12 skenario simulasi menunjukkan model SPF konvensional normal-half normal memberikan kinerja yang paling baik dibandingkan model SPF fat-tailed distribution saat data amatan tidak mengandung pencilan. Namun ketika data terkontaminasi pencilan model SPF konvensional normal-half normal menjadi tidak akurat dalam menduga fungsi frontir produksi dan tidak efisien dalam menduga inefisiensi dan efisiensi teknis. Model SPF fat-tailed Cauchy-half normal menjadi model alternatif yang paling kekar dibandingkan model lainnya pada berbagai kondisi pencilan dan berbagai jumlah amatan. Model SPF Cauchy-half normal mampu menduga fungsi frontir produksi lebih akurat dibandingkan model SPF normal-half normal dan SPF normal-Rayleigh. Model SPF Cauchy-half normal juga menghasilkan dugaan inefisiensi dan efisiensi teknis paling efisien dibanding model lainnya. Selanjutnya, model SPF Cauchy-half normal digunakan untuk menduga nilai efisiensi teknis produksi padi di Kalimantan Tengah. Hasil kajian menunjukkan bahwa luas panen, bibit, pupuk, dan pekerja mempengaruhi produksi padi di Kalimantan Tengah. Rata-rata nilai efisiensi teknis yang dihasilkan petani tanaman padi dalam mengelola faktor input tersebut adalah sebesar 52,72%. Diperkirakan baru ada sekitar 24,60% rumah tangga sampel pertanian padi yang sudah dikategorikan efisien.

Outliers are statistical problems that cause the error to be no longer symmetrical and have a very prominent spread. This research is motivated by the concern of outlier observations in the stochastic frontier analysis (SFA) modelling. Outliers can interfere with the SFA model's performance in estimating the frontier function and the efficiency itself. The SFA model is widely used to measure efficiency. The SFA model that specifically measures technical efficiency is called the stochastic production frontier (SPF) model. In the SPF model, the residuals are decomposed into noise and inefficiencies, each has its own distribution. In the conventional SPF model, the noise is normally distributed, and the inefficiency is half normally distributed. This model has limitations if there are outliers in the observed data. The results of efficiency estimates will widen. This study proposes SPF model with fat-tailed distribution. The alternative SPF models proposed are normal-Rayleigh, normal-Weibull, and Cauchy-half normal distributions. The three models are studied by comparing them to conventional models normal-half normal in estimating parameters and technical efficiency. The study was carried out on simulated data and actual data. Based on the results of a study of simulation data with 12 simulation scenarios, the conventional normal-half normal SPF model gives the best performance compared to the fat-tailed distribution SPF model when the observed data does not contain outliers. However, when the data is contaminated with outliers, the normal-half normal conventional SPF model becomes inaccurate in estimating the function of the production frontier and inefficient in estimating inefficiency and technical efficiency. The fat-tailed Cauchy-half normal SPF model is the most robust alternative model compared to other models in various outlier conditions and various number of observations. The Cauchy-half normal SPF model is able to estimate the production frontir function more accurately than the normal-half normal SPF and normal-Rayleigh SPF models. The Cauchy-half normal SPF model also produces the most efficient estimates of technical inefficiency and efficiency compared to other models. Furthermore, the Cauchy-half normal SPF model is used to estimate the value of technical efficiency of rice production in Central Kalimantan. The results of the study show that harvested area, seeds, fertilizers, and workers affect rice production in Central Kalimantan. The average value of technical efficiency produced by rice farmers in managing these input factors is 52.72%. It is estimated that only around 24.60% of rice farming sample households have been categorized as efficient.