Update: Here is a paper on this topic by Adam Ozimek using US metro data Population Growth and Inflation



"Overall, these results suggest that slowing population growth can be a headwind for inflation and help explain why inflation has remained stubbornly weak in some places."

If we look at the annual change in the prime working age population, there is one other period similar to the current situation - the early-to-mid 60s.

…

The key is the prime working age population was declining in the early part of this decade and has only started increasing again recently.



This is very similar to what happened in the 60s.



In the early 60s, there was a slow increase in the prime working age population until the baby boomers started pouring into the labor force.



[This] graph shows the unemployment rate and year-over-year change in inflation in the 1960s.



In the 1960s, inflation didn't pickup until the unemployment rate had fallen close to 4%. There could be several demographics reasons for the low inflation (in addition to policy reasons). As an example, maybe older workers were being replaced by younger workers who made less (just like today), and maybe the slow increase in the prime working age population put less pressure on resources.

Demographic shifts, such as population ageing, have been suggested as possible explanations for the past decade’s low inflation. We exploit cross-country variation in a long panel to identify age structure effects in inflation, controlling for standard monetary factors. A robust relationship emerges that accords with the lifecycle hypothesis. That is, inflationary pressure rises when the share of dependants increases and, conversely, subsides when the share of working age population increases. This relationship accounts for the bulk of trend inflation, for instance, about 7 percentage points of US disinflation since the 1980s. It predicts rising inflation over the coming decades.

emphasis added

Most euro area countries have entered an unprecedented ageing process: life expectancy continues to rise and fertility rates have declined, while retirement age in the last twenty to thirty years hardly increased. This implies an ever smaller fraction of the working age population in total population, leading to changes in consumption and saving behaviours and having an important impact on the macroeconomy. In this paper we focus on the relationship between demographic change and inﬂation. We ﬁnd that based on a cointegrated VAR model there is a positive long-run relationship between inﬂation and the growth rate of working-age population as a share in total population in the euro area countries as a whole, but also in the US and Germany. We also ﬁnd that this relation is mitigated by the eﬀect of monetary policy, which we account for by including the short-term interest rate in our analysis. One caveat of the analysis could be that the empirical relationship as found does not suﬃciently take into account changes in policy settings following the high inﬂation experiences in the 1970s. Our ﬁndings support the view that demographic trends are among the forces that shape the economic environment in which monetary policy operates. This is particularly relevant for countries, like many in Europe, that face an ageing process.

In early 2015, I wrote about the possible relationship between Demographics, Unemployment Rate and Inflation. An excerpt (at that time the unemployment rate was at 5.7%):Recently there has been more research on this topic. From Mikael Juselius and Előd Takáts at the BIS, May 2018: The enduring link between demography and inflation And from Elena Bobeica, Eliza Lis, Christiane Nickel, Yiqiao Sun at the ECB January 2017: Demographics and inflation Note: For some different views, see the comments in this post by Tyler Cowen at Marginal Revolution: Does demography predict inflation?