Comparing parametric and non-parametric efficiency measurement under data quality constraints: stochastic frontier and DEA evidence from smallholder sweet sorghum farms in Uzbekistan

Abstract

Agricultural economists must choose between stochastic frontier analysis (SFA) and data envelopment analysis (DEA) when assessing efficiency — the two methods treat measurement error differently, which matters greatly for smallholder survey data where reporting error is common. We test this on 98 sweet sorghum farms in Karakalpakstan, Uzbekistan. A Cobb-Douglas SFA model on four inputs (land, labor, seed, irrigation water) yields a plausible labor elasticity (0.428, p=0.002) and a large negative water elasticity (-2.744, p<0.001), but finds no meaningful inefficiency (gamma≈0.005; LR test p=0.545/1.000), with efficiency scores nearly identical across farms (mean 0.9916, SD 0.00016). A DEA model on the same data tells a different story: efficiency ranges from 0.567 to 1.000 (mean 0.883), and scale efficiency varies significantly with soil salinity (Kruskal-Wallis p=0.0007) — a relationship SFA could not detect. This gap follows mechanically from how each method handles noise: SFA attributes most variation to noise, while DEA treats every deviation as inefficiency. A smaller 16-farm sample further shows DEA loses discriminatory power as unit count shrinks. We close with practical recommendations for working with imperfect field data.