Are there two inflation regimes?

Arnold Kling tentatively postulates that central banks can, at most, select between a low-stable inflation regime and a high-variable inflation regime. Bryan Caplan proposes a quick test, which I hereby supply. Below are some scatterplots of inflation variance versus inflation means for 176 countries. The data is from the World Bank, which gets it from the IMF (gated). The data begins in 1961 for some countries, but later in others. If we observe two clusters, then that is strong evidence for Kling’s hypothesis.

The first scatterplot uses all available data.

It’s clear that there is a strong correlation between inflation means and variances (r=0.77, in fact) and an even stronger one, r=0.92, for means and standard deviations (see how the data appears to be quadratic?). But I don’t observe any evidence of clustering.

Because most of the data appears on the lower left, it may be helpful to zoom in. I repeat the plot for those countries where the mean is less than 150 percent. I also exclude the countries that have less than 15 observations.

Once again, there don’t appear to be discrete clusters. Just to make sure, let’s zoom in one more time on the lower left.

While Caplan’s proposed test does not support the Kling hypothesis, I am not sure that it effectively captures what Kling is postulating. For one, what counts as high and variable in the US is not the same as what counts as high and variable in Israel, Chile, Russia, or Zimbabwe. Secondly, if central banks have a choice between the two regimes as Kling postulates, then countries that spend time in both regimes are going to appear on the scatterplot in between the two hypothetical clusters (is this what we observe?). You can’t use a scatterplot of aggregated data to detect structural breaks. I’ll leave it to someone else (maybe one of my commenters?) to propose a better test.

Update: At Bryan’s request, here are three more graphs, zoomed in further on the lower left.