I suspect there are people within Treasury and Finance who think the answer's obvious: if the spending ain't working, give it the chop. Didn't you know we have a deficit problem?
But the gap between us is so wide in so many respects - life expectancy, health, income, employment, victimisation, incarceration and education - we couldn't in all conscience abandon our efforts to reduce it.
So I have a radical suggestion: why don't the people in charge of the government moneybags get off their backsides and put a hell of a lot more effort into ensuring taxpayers' funds are spent more effectively? Instead of wringing their hands, why don't they bring a bit of science to bear?
Last week Dr Rebecca Reeve, a senior research fellow of the Centre for Health Economics Research and Evaluation at the University of Technology, Sydney, outlined to a meeting of the Economic Society the results of her research evaluating the policies aimed at closing the gap.
She used econometric tools to analyse several surveys conducted by the Bureau of Statistics, noting that the nature of indigenous disadvantage and the best solutions to it may depend on where people are located.
It may surprise you that indigenous disadvantage isn't limited to people living in remote areas. And the majority of Aboriginal and Torres Strait islanders don't live in remote areas. Indeed, more live in NSW than other states or territories. Of those who do, 43 per cent live in major cities and another third live in inner regional areas. Reeve's studies focused on people in the major cities of NSW.
She found that rates of poverty were much higher for indigenous people, home ownership was lower, significantly fewer had completed year 12 and rates of employment were lower. The proportions reporting their health to be poor or fair were at least double those for other people. And the proportion who had been victims of assault was a lot higher.
Although indigenous people make up only about 3 per cent of the NSW population, they accounted for 23 per cent of prisoners. Young people are 26 times more likely to be in juvenile detention.
That's the gap. Reeve used sophisticated regression analysis to identify the key drivers of those gaps. She found that having been at school beyond year 10 made you more likely to be employed, as did participating in more than four types of social activity.
Being a lone parent, being a married female with children or being disabled made you significantly less likely to be employed.
The most significant predictors of having been a victim of physical or threatened violence in the past year were being disabled or having suffered stress from drug or alcohol use.
In this context, "disabled" means having a health problem lasting six months or more. Reeve found that by far the most significant predictor of being disabled was having been a victim of assault.
By far the most powerful predictor of being in jail was having been charged with some offence as a child. And by far the most powerful predictor of having been charged as a child was being male.
What these findings demonstrate is the interdependence of the various aspects of indigenous disadvantage. Problems such as involvement with the criminal justice system, long-term ill-health, victimisation and not having a job are all connected.
In a way, this is good news. It means targeting areas that are expected to reduce one or more of these problems should also mean improvements in other problems.
For instance, Reeve finds that an extra year of education should improve someone's employment prospects directly, but also improve them indirectly by reducing the likelihood of the person being in jail.
And get this one: her findings suggest that reducing drug and alcohol problems should reduce victimisation, which should reduce long-term health problems, which should increase employment, which should increase income.
The downside, however, is that failure to generate improvements in the key drivers of disadvantage will hinder progress in many areas.
The Council of Australian Governments' national indigenous reform agreement recognises the significance of interdependency: an improvement in one building block is reliant on improvements in other building blocks.
But though the COAG reform agenda aligns with Reeve's econometric evidence, the "close-the-gap report card" finds that targets have not been achieved in many areas. And in some areas gaps are widening.
A separate study by Reeve and colleagues on factors driving the gap in rates of diabetes also finds that, although programs are targeting the right areas, there's been no reduction in the high prevalence of diabetes among indigenous people.
I'd be surprised if Treasury and Finance have shown any interest in learning from Reeve's research. The usefulness of that research in showing "what works and what doesn't" seems to have been limited by the lack of detail in the existing official surveys it relied upon.
If we're to become better informed about why all the money we're spending isn't delivering better value we probably need to undertake more detailed, even purpose-built surveys, including longitudinal surveys that make it easier to distinguish between cause and effect.
But as we were reminded this week with all the problems the bureau has had with its jobs survey, successive governments have been reducing our statistical effort, not increasing it.
If Treasury and Finance warned the Abbott government that extracting yet more "efficiency dividends" from government agencies has become counterproductive - making government spending more wasteful in the name of making it less wasteful - there's been no whisper of it.
Reminds me of one of my father's sayings: too busy chopping wood to sharpen the axe.