In DSGE models, to achieve sticky prices, there are two important mechanisms: Calvo pricing, and Adjustment Costs(Rotemberg?).
It’s known that with Calvo pricing there’s always a difference between the micro and macro estimates for price rigidity. A value for a higher rigidity is used for DSGE models than what the micro empirical studies advise.
I’m wondering if the same situation happens with the adjustment cost mechanism. Is there a dichotomy between what the micro studies estimate and the value used in macro dsge models?
Any help would be appreciated.
The question is ill-posed. Either micro-behavior is driven by time-dependent Calvo pricing or is subject to convex adjustment costs (or menu costs). It cannot be both. My reading of the literature is that it’s either Calvo pricing or menu costs or a mixture at the micro level. The reason many people use Rotemberg in macro models is that it is first-order equivalent to Calvo pricing and the algebra is easier.
At higher order, there is some evidence that Rotemberg fits the data better. See Richter, Alexander W. and Nathaniel A. Throckmorton (2016). “Is Rotemberg pricing justified by macro data?” Economics Letters 149, 44–48.
But in this case there is an obvious tension between the micro pricing and what is going on at the macro level.
Dear Jpfeifer,
I think I might not have expressed myself correctly. I understand that we either have one mechanism, not both, to create sticky prices.
I was interested in knowing if with adjustment costs, that tension between macro and micro estimates also existed.
The tension is, I think, well documented for calvo pricing, but I don’t know if it exists and has been studied for the Rotemberg mechanism.
I asked, since I’m looking for references to that tension with adjustment cost (Rotemberg) mechanism. Could you please supply some?
Thank you for your reply. It was much appreciated. 
To diagnose such a tension, we would need evidence on convex adjustment costs at the firm level. I am not aware of any studies that find these costs. So the chain of arguments is indirect. At first order, Calvo and Rotemberg are equivalent. So you will get the same slope the New Keynesian Phillips Curve. Because you get too high a value for macro Calvo price durations, the same will then apply to Rotemberg pricing. You might find some of the references in Born/Pfeifer (2018): The New Keynesian Wage Phillips Curve: Calvo vs. Rotemberg helpful
Thank you. It seems interesting. 
