Our model of inflation  allows replacing price index with the cumulative growth of labor force. The biggest world developed economies all fit our model, as Figures 1 through 6 demonstrate (all borrowed from ). Moreover, the difference between observed and predicted cumulative inflation is a I(0) process, i.e. all observed/predicted pairs should be cointegrated. This allows linear regression, which is characterized by the goodness of fit above 0.99 for all presented cases: the USA, Austria, Canada, France, Germany, and Japan.
All observed curves have well predicted points of inflection. The most striking case is Japan, where the decline in labor force observed since the late 1990s manifests itself in deflation and cumulative curves (predicted and observed) have synchronized peak points.
We are going to consider each case in details, but it is crystal clear that the relative error of the proposed replacement (i.e. the prediction of cumulative inflation or price index) decreases with time and what one needs is a projection of labor force not all these forecasts of inflation. The former is usually is much more accurate than the latter.
Figure 1. USA
Figure 2. Austria
Figure 3. Canada
Figure 4. France
Figure 5. Germany
Figure 6. Japan