Wheeler gets criticised for the four official cash rate hikes he dispensed between March and July 2014. They were, with the benefit of hindsight, unnecessary and he had to set about reversing them within a year. But the intervening year was marked by a collapse in oil prices and a drop in the terms of trade from what had been 40-year highs.
Such shocks are one of the things that make doing monetary policy really hard, especially in a small, open economy whose people have a low propensity to save.
Wheeler has had to operate in a world economy with strong deflationary forces running - industrial over-capacity and an over-reliance on monetary policy to haul economies out of the crevasse of the global financial crisis. A world, in short, awash with cheap money. These factors affect tradables prices (nearly half the CPI) and banks' funding costs.
It has been a period when any number of central banks have undershot their inflation targets.
Another constant challenge for the Reserve Bank is that its interest rate decisions have to be based on forecasts derived from economic modelling that quantifies relationships between key variables based on past experience.
But they are not dealing with immutable laws of nature. The strength of these relationships can change over time.
So they might have expected the strong employment growth we have seen in recent years to flow through to more wage inflation than has eventuated.
Part of the explanation for that is the unexpected strength of net immigration. Part is a rise to record rates of labour force participation. And part may be underlying structural changes in the labour market such as increases in casualisation and the "gig" economy.
Similarly, in light of the mid-2000s boom, the bank might well have expected the wealth effect from runaway house price inflation - where home-owners spend some of the increase in their equity - to show through sooner and stronger than it has.
The point is that the central bank's interest rate decisions have to be based on expectations of the future guided by the past, and that guidance can be unreliable.
Under Wheeler, the bank has moved to a more formally collegial process for making decisions, with a governing committee of the governor, two deputy governors (Grant Spencer and Geoff Bascand) and assistant governor John McDermott.
The governor retains the final word and the statutory responsibility, but this has been a significant move towards the more internationally normal practice of making monetary policy decisions by committee.
But the big innovation of Wheeler's tenure has been the foray into macro-prudential regulation, specifically loan-to-value ratio (LVR) curbs on bank lending into the residential property market.
It has provided an alternative way of hosing down an overheated housing market without pushing up interest rates, with the consequences that would have had for an already overvalued exchange rate.
Wheeler was living in the United States when its housing market crashed. He saw, up close, what it does when one mortgage in four is under water, with the loan worth more than the property. It evidently made a deep impression on the man.
Measures to reduce the risk of that are not just about ensuring banks' balance sheets are sturdy enough to survive a property crash. They are not just about averting a systemic failure of the banking system. They are about borrowers and the potential for blighted lives.
Like any exercise in risk mitigation, the LVR regime comes at a cost and it is not until disaster strikes that its value can be appreciated and its efficacy appraised.
But Wheeler surely deserves the benefit of the doubt at this stage.
The ratios of house prices to income and household debt to income are very stretched.
The statisticians tell us that one household in six is spending more than 40 per cent of its pre-tax income on housing.
That includes 99,000 owner-occupied households, even at a time when mortgage rates have been at multi-decade lows and are now starting to rise. And it includes even more renting households.
The incomes out of which mortgage and rents have to be paid are vulnerable to an international shock. As it is nine years since the GFC, one is probably overdue.
Should one hit before Wheeler's term ends in September, or in the following six months when Grant Spencer fills in, we will be in good hands.
