Price Elasticity of Groundwater Demand: Attenuation and Amplification Bias Due to Incomplete Information

Measurement errors in both human and natural components of agricultural and environmental systems can be as much a source of estimation bias as omitted variables, selfselection, simultaneity, and reverse causality. Nonetheless, partly because of difficulties in obtaining data, there is less literature on measurement error problems than on other endogeneity problems. This article examines estimation bias in the price elasticity of groundwater consumption for irrigated agriculture on the intensive margin. The price at issue is for the energy used in pumping and pressurizing water for delivery. Lacking the precise unit irrigation cost, previous studies imputed irrigation costs. We first consider groundwater irrigation costs and identify factors that can cause measurement errors in the process of imputation under incomplete information about the determinants of irrigation costs. We follow this by systematically analyzing the potential bias caused by measurement errors, using econometric theory along with Monte Carlo simulations where appropriate. We then quantify actual measurement errors, making use of a unique dataset in which energy and groundwater consumption data are matched for individual observations. Finally, we compare regression results using exact irrigation costs as opposed to imputed ones. We find evidence of substantial measurement errors resulting in attenuation and amplification bias in the price elasticity of irrigation water consumption on the intensive margin. Our results indicate that measurement errors in irrigation costs can lead to misleading policy implications related to water and energy pricing as a tool to conserve water. We also show that estimating the energy price elasticity of groundwater use is not as straightforward as previously thought.