This paper begins by discussing some of the problems frequently encountered in obtaining demand elasticity estimates. To these problems is added that associated with inaccuracy in the measurement of the dependent variable and one or more of the independent variables that impact upon the quantity demanded. Two diagnostics - the regression coefficient bounds and the bias correction factor - are introduced to assess the effect that such a measurement error has on the estimated coefficients of demand relationships. Use of these diagnostics aids in assessing the integrity of the estimates obtained. In considering the demand for electricity for irrigation and the demand for electricity for other (non-irrigation) uses by farmers in the USA, both the quantity demanded and the unit price data available for demand model estimation purposes contain measurement errors. The regression coefficient bounds diagnostic is used to indicate a range over which the true price responsiveness of farmers to changes in energy prices lies. The results suggest that each 1% increase (decrease) in the price of energy will result in between a 0.51 and 0.35% decrease (increase) in the quantity of electricity demanded for irrigation and between a 0.43 and 0.17% decrease (increase) in the quantity of electricity demanded for other uses. The bias correction factor is computed to evaluate the magnitude of the under-estimation of the responsiveness of the quantity of electricity demanded for irrigation and electricity for other uses to a change in the number of acres irrigated and the number of acres planted. For electricity for irrigation, the under-estimation was 14.1% while, for electricity for other uses, it was 13.9%.