A quick addition to the previous results. If we look at the bi-weekly St Louis Adjusted Monetary Base (seasonally adjusted) data, and measure the slope over the previous 20-weeks for each date, we find that the average slope (monetary base growth rate) was about $6.5\%$ (before 2008). If the information transfer index is (as determined in the previous results) $1/\kappa \approx 1.31$, then $i = 0.065 \times (1.31 - 1) \approx 2.0 \%$. This is the de facto inflation target over the past few decades.
A low $1/\kappa$ (i.e. high $\kappa$) is a way of obtaining a lower inflation rate for any given monetary base growth rate. Additionally, $\kappa$ is slow to react to changes in MB and NGDP growth rates (since it depends on the rates only in the long run as $t \rightarrow \infty$; it depends on the absolute magnitude in the short run), but $i$ can change immediately to changes in $r_0$. The growth rate of the price level will follow the change in $r_0$ in the short run. However, while increasing $r_0$ will cause $i$ to increase in the short run, it can cause $i$ to decrease in the long run as $1/\kappa$ decreases.
The trend has been towards $1/\kappa$ decreasing since the 1970s in the US, which leads to a disinflationary trend. This trend may well be due to the long run effect on $1/\kappa$ from an increased MB growth rate $r_0$, which went from $\sim 2-3\%$ in the 1960s to $\sim 6.5\%$ since the 1970s until the 2000s.