Dynamic Fertilizer Nutrient Demands for Corn: A Cointegrated and Error‐Correcting System

Abstract

Past studies of the demand for fertilizer have typically been based on static models which assume that adjustments toward equilibrium are instantaneous. This article builds on past studies by developing a dynamic model of nutrient demands of corn. Unit root and cointegration tests demonstrate that fertilizer demands of corn are dynamic. Therefore, statistically correct estimates can be obtained using a dynamic model. A set of error-correction models for nitrogen, phosphate, and potash use in com production are estimated. Results provide strong statistical evidence that nutrient demands of corn are price inelastic both in the short and the long run.

Nutrient prices and concentrations in Midwestern agricultural watersheds

“…The elasticity estimate of nitrogen output from a watershed is consistent with the price elasticity of demand as an input into production found in the literature. Put another way, our negative sign is consistent with the negative relationship between nutrient prices and the quantity of nutrients used by farmers found in Denbaly and Vroomen (1993). The size of the elasticity is about the same as their estimated elasticity.…”

“…This 2 This yields a necessarily rough approximation of crop area, as county boundaries do not perfectly mirror watershed boundaries. is about the same size as the estimate in the nitrogen model and it is similarly consistent with estimates for input demand by Denbaly and Vroomen (1993). Corn prices have a strong positive effect on phosphorus outputs.…”

“…When farmers face a higher price for P, they will consume less of it. Based on Denbaly and Vroomen (1993), the farmers' price elasticity of phosphorus demand is −0.25, suggesting that a 25% increase in the phosphorus price will reduce phosphorus use by 6.25%. We cannot know the change in phosphorus inputs exactly because we do not know the farmer's initial inputs exactly, but we can estimate them based on estimates of the area of various crops planted and survey data that provides information on current phosphorus application rates (see USDA-ERS, 2012).…”

“…Given that the farmer demand function for nutrients is downward sloping, higher nutrient prices should lead to lower nutrient inputs and consequently emissions from farm fields. Economic studies have shown that the demand function for nutrients does indeed slope downwards, with input price elasticity for nutrients in the US around − 0.25 (Gunjal et al, 1980;Denbaly and Vroomen, 1993). Because much of the fertilizer used by farmers ultimately is taken up by crops and harvested, attached to soil, or taken up by other plants in the ecosystem, it is not clear whether this same elasticity estimate would apply to nutrient outputs from agricultural watersheds.…”

Estimation and inference in cointegrated demand systems: an application to Tunisian meat consumption

“…On the other hand, if the variables are cointegrated, the specification of a demand system in first differences is biased due to the misspecification of the long-run relationships. Thus, the estimation of cointegrated demand systems has become increasingly popular (see, for instance Denbaly and Vroomen, 1993;Balcombe and Davis, 1996;Attfield, 1997;and Chambers and Nowman, 1997).…”