The Choice Between Multiplicative and Additive Output Uncertainty

When modeling output uncertainty, the multiplicative specification is consistently chosen over the additive form, despite the latter being arguably intuitively more obvious. The rationale for this seems to be that when production risk is the only source of uncertainty, additive uncertainty does not reduce output below the certainty level, while multiplicative uncertainty does. We show that, regardless of the specification of output uncertainty, if hedging is absent and there is simultaneous price and output uncertainty, output is always lower than the situation in which one or both sources of uncertainty are absent. Thus, both models yield qualitatively identical results, i.e., adding a source of uncertainty reduces expected output. Therefore, additive uncertainty is indeed a reasonable a priori method of modeling production uncertainty