Oil palm production is an important income source for millions of smallholder farmers in the tropics. Oftentimes, yields in smallholder systems are low, entailing larger area requirements and higher than necessary rates of deforestation. Smallholder performance differs spatially, even within countries and provinces. A better understanding of this spatial variation can help to design more effective support programs to preserve forestland and foster sustainable economic development. Here, we use survey data from smallholder oil palm producers in Sumatra, Indonesia, to identify spatial variation in yields, input use, and output prices by employing structured additive regression models with nonlinear spatial effects, so-called geosplines. Our results confirm large spatial differences. Some of these differences can be explained. For instance, possession of land titles and proximity to urban centers are positively associated with oil palm productivity. However, much of the spatial variation cannot be explained by variables typically included in socioeconomic studies. The geosplines help to control for possible bias even when the identified spatial variation cannot be fully explained. From a policy perspective, knowing where regions with high and low yields and input intensities are located can help to geographically target suitable support programs. From a research perspective, more work on trying to explain spatial heterogeneity in smallholder production is needed, possibly combining quantitative and qualitative approaches.

油棕生产是热带地区数百万小农的重要收入来源。通常，小农系统的产量很低，需要更大的面积和高于必要的森林砍伐率。小农的表现在空间上存在差异，即使在国家和省份内也是如此。更好地了解这种空间变化有助于设计更有效的支持计划，以保护林地和促进可持续经济发展。在这里，我们使用来自印度尼西亚苏门答腊岛小农油棕生产商的调查数据，通过采用具有非线性空间效应的结构化加性回归模型（所谓的geosplines）来识别产量、投入使用和产出价格的空间变化。我们的结果证实了巨大的空间差异。其中一些差异是可以解释的。例如，拥有土地所有权和靠近城市中心与油棕生产力呈正相关。然而，大部分空间变化不能用社会经济研究中通常包含的变量来解释。即使无法完全解释已识别的空间变化，地理样条也有助于控制可能的偏差。从政策的角度来看，了解产量和投入强度高、低的地区的位置有助于在地理上针对合适的支持计划。从研究的角度来看，需要更多的工作来解释小农生产中的空间异质性，可能结合定量和定性方法。