Does Calvo Meet Rotemberg at the Zero Lower Bound?

This paper compares the Calvo model with the Rotemberg model in a fully nonlinear dynamic new Keynesian framework with an occasionally binding zero lower bound (ZLB) on nominal interest rates. Although the two models are equivalent to a first-order approximation, they generate very different results regarding the policy functions and the government spending multiplier based on nonlinear solutions. The multiplier in the Calvo model is less than one for low persistence of the government spending shock and rises above one as the persistence increases, but eventually decreases with the persistence and falls below one for sufficiently high persistence. In addition, the multiplier increases with the duration of the ZLB. By contrast, the multiplier in the Rotemberg model is less than one and decreases with the persistence. Surprisingly, it also decreases with the duration of the ZLB.