The above chart compares the 2-yr annualized growth of productivity (to minimize the typical quarterly volatility of this series) to the year over year change in the GDP deflator, the broadest measure of inflation. There is a relative strong tendency for the two to be inversely correlated. Strong productivity tends to coincide with low inflation, and weak productivity gains with higher inflation. If the bloom is indeed off the productivity rose for the time being, then this chart suggests that we could see somewhat higher inflation in coming years.
Looked at another way, the decline in productivity means that unit labor costs are rising and could now begin to feed through to higher prices.