Emi Nakamura and Jon Steinsson ask exactly that question:
Figure 2 plots a typical price series for a grocery product in the United States. This figure illustrates a central issue in thinking about price rigidity for consumer prices: Does this product have an essentially flexible price, or is its price highly rigid? On the one hand, the posted price for this product changes quite frequently. There are 117 changes in the posted price in 365 weeks. The posted price thus changes on average more than once a month. On the other hand, there are only 9 regular price changes over a roughly 7 year period. Which of these summary measures of price rigidity is more informative?
Here is their new paper (pdf), which is an excellent survey of what we know about price (as opposed to wage) stickiness.
You will note is that we know more about price stickiness in times of inflation rather than deflation, if only because we have more of the former. Intuitively, one might expect greater flexibility of prices in the downward direction, for prices that is. Why are bosses afraid to cut nominal wages? It will disrupt worker morale and prompt shirking and sabotage. Why might suppliers be reluctant to raise prices? They might not wish to upset long-term relationships and expectations with customers. But customers would love nominal price declines, or so it would seem.
Less-than-fully-flexible nominal prices may follow from sticky nominal wages, to be sure. But absolutely sticky nominal prices? The supplier still can cut price by a bit. By construction of the problem, these are sectors which are not perfectly competitive and thus we are not at P = MC. If demand goes down, and one of your main costs is sticky, you still can shade price a bit rather than say raising it. Since “menu costs” appear refuted by the data, small price changes should not be so costly.
Yet, in reality, we don’t actually know much about what happens and why.