In my post yesterday I played around with some illustrative scenarios on the costs and benefits of the “insurance policy” the Reserve Bank Governor is proposing to impose on us: higher capital requirements for locally-incorporated banks will, on the Bank’s own estimates, impose an annual cost in the form of a modestly lower level of GDP each and every year, while in exchange there is the hope of averting some GDP costs from a rare but fairly severe financial crisis (perhaps in the form of several failures of large banks).

I used the Bank’s own estimate of the GDP cost (“up to 0.3 per cent per annum” – so used 0.25 per cent) and as a discount rate used either the current Treasury recommendation for regulatory proposals, or one a bit lower to take account of the sharp further fall in long-term interest rates this year. And to simplify things, I looked at various scenarios for the GDP cost of a financial crisis 75 years hence (the policy is supposed to ensure that New Zealand isn’t exposed to a crisis more than once in 200 years, so I used a 150 year time horizon to think about what benefits we might secure if the policy is adopted).

On those scenarios, the Bank’s proposal simply did not stack up. The costs far outweighed the benefits. If so, the insurance premium was not worth purchasing.

Last night a commenter pointed out, correctly, that my simplification (focusing on a single date – a crisis in 75 years time, halfway through the 150 years) probably wasn’t warranted, because the discount factor is non-linear. As it happens, so is the GDP cost (since real GDP itself is assumed to rise by – middle assumption – 2 per cent per annum.

There are two simple ways to overcome this. The simplest to illustrate is this one.

The Reserve Bank tells us it thinks the annual costs (to GDP) are around 0.25 per cent. And if, say, the GDP cost of the a crisis (three scenarios below, the third really as an illustrative extreme) once every 150 years is divided by 150, we get an estimated average annual GDP saving.

GDP effects per annum) | |||

Costs (RB assumption) | 0.25 | ||

Benefits: GDP saved | |||

Equal annual probability of crisis over 150 years | |||

10% | 0.067 | ||

20% | 0.133 | ||

30% | 0.200 |

It would take averted crisis costs – simply from the bank failures, not from the prior misallocation of resources in the poor lending/investing – well in excess of 30 per cent of for the expected benefits to equal the expected costs. Alternatively, the Bank’s estimate of the costs – itself conservative in some respects – would have to be revised down quite materially.

That particular approach isn’t dependent on an assumption about discount rates at all. But to continue the approach in my post yesterday, here was the table (from that post) of the estimated present value of the costs of the policy (the 0.25 per cent per annum capitalised) on various trend growth and discount rate assumptions.

Present value cost ($bn), 150 years of 0.25% annual GDP loss | ||||

Real GDP growth | ||||

1.5 | 2.0 | 2.5 | ||

Real discount rate | 5% | 21.60 | 25.20 | 29.90 |

6% | 16.90 | 19.10 | 21.80 |

The middle column is my baseline scenario (perhaps 1 per cent annual population growth and 1 per cent annual productivity growth).

So what if, instead of focusing on a crisis in 75 years time, we assign an equal probability of a crisis to each of the next 150 years, using that baseline scenario (2 per cent per annum real GDP growth)?

Or if we simply focus on the offical Treasury discount rate guidance (6 per cent) here is table of the savings under various trend growth and crisis loss assumptions.

Present value of GDP benefits of averting a crisis (probability spread evenly over 150 years) 6% disc rate | ||||

Trend GDP growth | 10 | 20 | 30 | |

1.5 | 4.5 | 9 | 13.5 | |

2 | 5.1 | 10.2 | 15.3 | |

2.5 | 5.8 | 11.6 | 17.5 |

In none of these scenarios do the savings equal the cost of the policy. My own central scenario would be 2 per cent trend GDP growth and a 10 per cent GDP loss (perhaps 2 per cent a year over five years) purely from a financial crisis. With a 6 per cent discount rate, the costs over 150 years are around $19 billion amd the benefits perhaps $5 billion.

And, as I noted yesterday, all this assumes the policy can be committed to for 150 years. Realistically, the current Governor can’t commit much beyond his term, and the probability of severe crisis in the next decade or so looks – on the Bank’s own analysis and stress tests – very very low.

Of course, all of this is only illustrative, but in a sense that is the point. We need the Reserve Bank to do what it has not yet done – and tells us it won’t do until the final decision is made – and lay out their assumptions, how sensitive their results are to various different assumptions, and some assessment of the reasonableness or otherwise of those assumptions.

One could play around with all sorts of additional assumptions (including weighting the savings – in the midst of a period of difficult economic times) – more highly than the costs. But unless the Bank itself is materially overestimating the expected “insurance premium” it is hard to see how the benefits of what they propose are likely to exceed the costs.

And that, of course, was the gist of a recent paper, taking a quite different (and more high tech) approach and not focused on New Zealand, done by a group of experts at the BIS.