Cagan's paradox revisited

Data from 20 hyperinflations - from the French Revolution to Venezuela's 2018 episode - provide nearly no evidence of a Laffer curve for seignorage. Rather, in nearly all cases, the relationship between the inflation tax and inflation has been either positive at all inflation rates, or initially positive and then flattening out towards the end of the hyperinflation. Consistent with this, econometric evidence shows that the preferred money demand specification at very high inflation rates is not Cagan's (1956) "semi-log", which automatically imposes a Laffer curve upon the data: rather, it is either Meltzer's (1963) "loglog" - for which the inflation tax is monotonically increasing in inflation - or a more general functional form making log real money balances a linear function of the Box-Cox transformation of expected inflation (of which the "log-log" is a special case), which allows the inflation tax to flatten out at high inflation rates. My results suggest that the paradox first highlighted by Cagan - of policymakers seemingly inflating in excess of the revenue-maximizing rate during hyperinflations - is the product of the literature's predominant focus on the semi-log specification.