Estimating Farm Production Parameters with Measurement Error in Land Area

I provide a new method for correcting and assessing bias from measurement error in land area and apply it to estimating two important sets of parameters: the relationship between farm size and productivity and farm production function coefficients. Traditionally, researchers have measured area using farmer self-reporting, which is prone to (nonclassical) measurement error. In response, recent papers use area estimates from global positioning system (GPS) devices. However, GPS estimates may also have errors. I show that instrumenting GPS estimates with self-reported area resolves bias from measurement error in both measures, provided that (log) GPS estimates have classical measurement error. Applying this approach to data from Tanzania, I find that using either GPS estimates or self-reported area leads to bias, and the bias is actually worse when using GPS estimates. Measurement error in GPS-estimated area biases the farm size-productivity relationship by 22%–26% (4%–10% for self-reported), though the inverse farm size-productivity “puzzle” remains even when I correct this bias using my instrumental variables approach. In production function estimates, measurement error in GPS-estimated area biases the Cobb-Douglas coefficient on land down by 39% (27% for self-reported) and labor up by 44% (47% for self-reported). I show that the results also have implications for measuring misallocation.