The shoe-leather cost of inflation is minimal

One popular way to justify the introduction of monetary frictions in macroeconomic models is to assume that there is some cost associated to changing cash holdings, ATM fees or more generally "shoe-leather" cost. Whether these cost matter at all is controversial and settling this requires a two-pronged approach: first find empirically how large these costs are, and second demonstrate that the costs are large enough to matter in a reasonable model.

Alessandro Calza and Andrea Zaghini estimate the shoe-leather cost for the US. This is by far not the first time this is performed, by it can be worth it as data change, and in this case one can suspect that transaction costs indeed have gone down over a few decades. But there is one critical aspect that they take into account: most on US M1 is not held domestically, and this share has increased to currently 60%. Ignoring this seriously biases estimates, first because it overstates domestic demand and second because the shoe-leather cost stemming from inflation is largely borne by foreigners. At an inflation rate of 10%, the cost amounts to negligible 0.05% of total income. At lower inflation rates, it is even negative thanks to foreigners giving up real resources to acquire US money. In other words, you cannot build a monetary theory on this,