The impact of measurement error on estimating the demand for diesel fuel by farmers in the United States

This paper deals with two diagnostics that are useful in evaluating regression results when one of the explanatory variables contains either random or systematic measurement error. The two diagnostics discussed are regression-coefficient bounds and the bias correction factor. The first is useful because such bounds indicate the impact on the estimated regression coefficients not only of the random component in the dependent variable but also of the random component of the explanatory variable (that contains the measurement error). The bias correction factor is useful because, depending on the type of measurement error present, it will indicate the extent of the difference between the true population parameter and the estimated value of the parameter. In an application of the two diagnostics, the demand for diesel fuel by farmers in the United States is explored. Given that the data on the price of diesel fuel contain random measurement error, it is illustrated that the responsiveness of the quantity of diesel fuel demanded by farmers ranges between -1.77 and -0.26% for each 1% change in the price of diesel fuel. In terms of bias arising from measurement error, the responsiveness of the quantity of diesel fuel demanded due to a change in the number of acres planted is under-estimated by 36%. The responsiveness of the quantity demanded due to a change in precipitation is under-estimated by 63%.