Child poverty and social inequality is a big problem in the UK. And according to the report published last month by the poverty Tsar, Alan Milburn, the private rented sector is partly to blame.

Mr Milburn and the commission he leads have worthy goals but tragically misdiagnose the problems in the sector, focusing on nebulous short term costs of renting and all but ignoring the much more worrying generation gap.

First off, he argues that renting is more expensive than paying a mortgage. To a renter like myself with one eye on one buying a place, this is (to put it politely) simply untrue. The report compares rental costs (£163 per week) to interest only mortgages (£149) and ignores the more common repayment mortgages (£154). This weekly figure is still less than private renting, but not by much. More misleading is that they ignore the cost (and opportunity cost) of raising a deposit to buy, which is prohibitive.

  The report states that owners have been cushioned by low interest rates, compared with renters who have not. The report fails to mention that owners are more exposed to the effects of an eventual interest rate rise and that (if they were sensible) they should be saving to cover their extra costs. The Office for Budget Responsibility has driven the point home, highlighting the crippling effect that even a small interest rate rise could have.

  Mr Milburn also argues that because renting is more expensive than owning (which it isn’t), the risk of children growing up in poverty (44% for renters) is higher than owner occupiers (13%). This apparently very alarming statistic has the causation back to front. It is (fairly obviously) precisely because buying is more expensive that homeowners are likely to be richer than renters in the first place.

  Which points to the biggest missed opportunity of the report. A house is valuable asset which can be passed to the next generation, which lifelong renters will simply never own. The report touches on this but does not run with that argument. The real risk is that renters will, over a generation, have less capital.

Now I have yet to meet anyone who has actually read Thomas Piketty’s Capital in the Twenty First Century, but I understand it’s pretty good if you like that sort of thing. As Wikipedia explains, the central thesis is that “when the rate of return on capital is greater than the rate of economic growth over the long term, the result is concentration of wealth, and this unequal distribution of wealth causes social and economic instability.” This central thesis has been hailed by both The Economist and Paul Krugman, so there must be something in it.

  If you’re ever going to reduce inequality, Piketty’s thesis would suggest that you either have to heavily tax the return on capital (Piketty’s ultimate conclusion) or increase growth rates, or (perhaps more realistically) a combination of the two.

  Either way, concentrating homeownership in the hands of the few will concentrate the return of capital over time. And it doesn’t take a genius to work out that the way to spread homeownership is… to supply more homes thus reducing house prices. Investment in house building would also have the knock on effect of, well, increasing economic growth, also helping to reduce inequality.

  If Mr Milburn wants to save the next generation of Tiny Tims, he should simplify his message: build homes and go for growth.