Does the grey market explain money velocity decline?

Here is Jonathan Ashworth and Charles A.E. Goodhart doing real economics, actual good stuff, not the hand wave.

http://www.voxeu.org/article/trying-glimpse-grey-economy
Despite the growth of online and card payments, the ratio of currency to GDP in the UK has been rising. This column argues that rapid growth in the grey economy has been a key cause. The authors estimate that the grey economy in the UK could have expanded by around 3% of UK GDP since the beginning of the Global Crisis.

We use the currency demand approach to estimate the likely increase in the size of the grey economy. The currency demand approach has historically been one of the main methods for estimating the size of the ‘shadow economy’ (grey plus black economy).1 The basic idea is that, since tax evasion is illegal, almost all grey (and black) economy transactions will be made in cash.2 For obvious reasons, cash is almost always anonymous, whereas most other payment mechanisms leave a record. What one does, then, is to estimate how much of the currency-to-GDP ratio is due to incomes, interest rates, technological trends, and such other variables as theory or direct observation suggest (a standard currency demand regression). One can then either take the residuals from such an equation as an estimate of the shifting shape of the hidden economy, or, better, add additional variables that should be correlated with the grey economy, such as tax rates – especially VAT – and the ratio of the self-employed and unemployed to the total workforce. We did the latter/

There are, however, a couple of other factors that probably have raised currency holdings in recent years. The first is the decline in interest rates to nearly zero. If you cannot earn interest on a bank account, there is less incentive to put spare cash on deposit in a bank. We test for this effect in our empirical exercises and, like most other studies of this kind, we find that the demand for cash holdings is reduced if interest rates on bank deposits rise and vice versa (i.e. that the interest elasticity of cash holdings is negative), although the impact is relatively slight in terms of magnitude. (In this particular instance, however, the decline in interest rates was very large, meaning the overall effect was quite sizeable).

A 1.5% YoY growth in the grey economy puts the money velocities right on track for the USA.