## Thursday, 12 February 2009

### Illiquidity measures

Continuing the discussion of a few days ago, Nick Rowe joins in correcting Niall Ferguson's "average debt" logic. Maybe we should give the guy a break - he is only a historian, not an economist. No doubt whenever a historian writes a book about the history of [X], they get brickbats from all the practitioners of [X]. But then that's the price of intellectual engagement.

The comments on Nick's post set me thinking about better ways to measure the total impact of debt in the economy. One commenter (Patrick) reminded me of the issue of debt maturity mismatch, which seems to have been a major contributor to of the current financial crisis (aside from the effect on the real economy). Here's the response I posted there:

It sounds attractive that there would be some meaningful measure that at least partly captures the way in which debt influences the economy. We could certainly build models where a large amount of gross debt has almost no effect at all (e.g. A owes B, B owes C and C owes A an identical fixed amount with identical fixed repayments, and each debt secured on the next), so it can't simply be the quantity of gross debt.

To adjust Declan's example, the 10% interest rate should be there to compensate for the fact that one or two of Harry's friends will default on their loan; this reduces the accumulation of money in FI. But without quibbling on the details, there is definitely less "stability" in that system than in one with no debt at all.

Patrick pointed out the issue of liquidity, or more generally the length of maturity of debt; although by the same logic as the original argument, the net amount of debt at any given maturity is also zero.

One could generate a measure reflecting the amount of short-term liabilities held by entities who have lent long. This would be appropriately asymmetrical, because we don't care about those who have borrowed long and lent short (except that their short borrowers may be unable to repay! but that is captured in the original measure anyway).

More precisely, we could draw a maturity graph for each entity, showing the debt they are due to repay in each period net of the assets they are due to collect (including their money holdings). This illiquidity measure (IM) at any given time t would be the integral of that curve between 0 and t.

The appropriate aggregate measure would be the sum of all positive IMs, ignoring negative ones, for a given period. So you could generate an one-year IM for the whole economy, or a one-month IM or a ten-year IM.

What does this tell us? I don't know exactly, but a lot more than "average debt". I imagine it could offer guidance for the appropriate size of central bank liquidity measures such as the Bank of England's SLS and the Fed's money market purchases.

Update: Enrico Perotti and Javier Suarez have a proposal for mandatory liquidity insurance at VoxEU.