You could call it a marital tiff.

A tax break for married couples is splitting the Coalition. Since it will probably amount to £150 a year, it's hardly likely to encourage a rush to the altar. After all, the eye-watering cost appears to be no deterrent to divorce.

But what about the principle? Do the private arrangements of individuals have anything to do with the state?

Plainly they do. Those who marry enter a contract approved by the state. Its details are logged and registered just like births and deaths. The state also decrees whom we may not marry. Close relations are debarred as are (for the moment) members of the same sex. Further, we may marry only one person at a time or we'll find ourselves in court accused of bigamy.

Marriage is a public statement and a matter of public record. Is it such a very big step to include it in the tax system?

The decision has repercussions. For example, it would surely be discriminatory to offer tax breaks for marriage while denying people who are gay the right to wed.

It has dangers too. It could add grist to the idea that there are two-tier families: that those with married parents are deemed superior. But maybe it's worth the risk. Marriage is a far from perfect institution but all the evidence points to it being better for society than the alternative, which is why it interests the state.

Nick Clegg accuses the Conservative Prime Minister of advocating, "a 1950s model of a suit-wearing, bread-winning dad and an aproned, home-making mother", of trying to set marriage in aspic.

I'd say David Cameron is motivated by a balance sheet. He is measuring the cost of educational failure, unemployability, state benefits and criminality. He is looking at statistics which show that the children of the married are more likely to be productive citizens. In short they cost less and contribute more. And he's thinking: let's encourage the rest to wed.

But are the figures all they seem to be? The Institute for Fiscal Studies (IFS) has looked into the matter at some depth and concluded that marriage is not a magic bullet.

It acknowledges the measurable difference in cognitive ability and socio-economic development between the children of married couples and those who co-habit. It concludes that this is because, by and large, those who marry are brighter, older and more successful than those who don't. They are more likely to stick together.

One third of cohabiting couples split up by the time their child is three years old and then the outcome for the child is poor. The report argues that money would be better spent on educating the parents of the future than on trying to encourage more to marry.

But reading the conclusions I couldn't help wondering whether the young parents with their poor cognitive development who choose not to marry had themselves grown up in unstable homes?

In a sense the IFS's argument was writ large in a recent Panorama programme about adoption. It portrayed parallel universes. On the one hand it showed children in foster homes which were warm and well-ordered. They were woken for breakfast, driven to school and arrived back to tea on the table.

The contrast with their birth parents' homes was stark. In each case the biological mothers had learning difficulties. They were poor, disorganised and self-focused. Their homes were bleak. One had seven children in care. Before she arrived to see her 10-year-old son he was told about the conditions into which he was born. He heard about the dirty dishes and dirty nappies and dangerous companions with whom his mother was associating.

We saw a well-meaning but inadequate mother fight in court to retrieve her four-year-old from the all-embracing foster family that had reared him since he was a baby and wanted to adopt him. His fate still hangs in the balance but few who saw the programme will be wishing his mother success.

I understand the IFS point: it is saying a marriage ceremony on its own wouldn't change the environment of the birth families. I wonder? Marriage has an effect on men and women as well as on children.

As a general rule of thumb those who marry may be older and better educated when they get together. But few long-term married couples will assert with confidence that they would still be together without the extra tie of marriage.

All mature couples talk about having lived through the better or worse they stated in their vows. "We've had our ups and downs," they will say or, "We've weathered the storms." Would that hold true of they'd simply been cohabiting?

Would 90% of them still be together when their child was three years old as opposed to the 66% of cohabitees?

Research shows that men's health is better when they are married. And for the majority of married women, marriage offers a welcome support system within which to raise a family – as well as affection and companionability.

At the moment there are too many women approaching 40 who haven't married or had children. Many are bright and successful and would like to raise a family but the fashion for remaining uncommitted has worked against them. I think it's a shame.

Mr Clegg says getting married was probably the best thing that ever happened to him. Vince Cable is a strong supporter of marriage. He has, after all, married twice.

I understand why they differentiate between making choices for themselves and seeming to steer clear of private decisions for other people. But the state already has that role in a number of areas. Take cigarettes, with health warnings on packets, smoking banned in public places and tax used as a disincentive.

If more couples can be coaxed into marriage and – because they are married – more stay together until their children are grown, fewer children will have poor outcomes and the spiral will begin to turn the other way.

It's a lot to ask of £150 per family per year. But since it costs so little and the stakes are so high, might it be worth a try?