Capturing Household-Level Spatial Influence In Agricultural Management Using Random Effects Regression

Data on agricultural and natural resource management typically have spatial patterns related to the landscapes from which they came. Consequently, econometric models designed to explain the determinants of humans' natural resource management practices or their outcomes often have spatial structure that can bring bias or inefficiency to parameter estimates. Although econometric tools are available to correct for spatial structure, such tools are largely lacking for use with discrete dependent variable models. While one obvious solution would be to develop the necessary tools, an alternative is to identify conditions under which spatial dependency can be managed effectively without formal spatial autoregressive models. This study examines conditions under which spatial structure corresponds closely to defined agro-ecological zones, making it possible to model spatial effects by random effects regression. Using household survey data sampled along agro-ecological zone strata, this article develops two models of links between farmer assets and agricultural natural resource degradation in southern Peru. The first stage model looks at determinants of crop yield loss over time (an index of soil productivity), while the second stage model looks at determinants of the extent of fallow cycles in crop rotation, a key agricultural practice reducing crop yield loss. Diagnostic statistics for spatial dependency reveal spatial structure, particularly in the fallow model. This spatial dependency is eliminated in the ordinary least squares (OLS) models by inclusion of the agro-ecological zone random effects. In the spatially dependent fallow model, comparison of coefficient estimates between OLS and the spatial autoregressive maximum likelihood models showed OLS with random effects to give virtually identical results to the spatial autoregressive models, making the latter unnecessary. These results show that spatial structure in natural resource management models can sometimes be captured by zonal variables. When this occurs, random effects regression can largely eliminate spatial dependency. A necessary precondition for this approach with household survey data is prior sample stratification according to landscape characteristics. Where random effects models can effectively capture spatial structure, they may also offer analysts greater flexibility in analyzing models with limited dependent variables.