Can tax and subsidy incidence really be negative?

Imagine a country where shoes cannot be imported and furthermore the elasticity of supply of shoes is very low. Imagine that the government in this country subsidises shoes. The person on the street who doesn't understand tax incidence might think that this policy lowers the price of shoes by the amount of the subsidy. An economist, however, would be likely to point out that, because supply is fairly unresponsive to price, the subsidy mostly results in an increase in the before-subsidy price to the seller.    In our jargon, he would be saying that most of the incidence of the subsidy would be on sellers and only a bit on buyers.

So far so good, but what if that economist now explained that removing the subsidy would make shoes cheaper to consumers, by stopping buyers from bidding up the price. This would seem to now be claiming that the incidence of the subsidy on buyers would be negative. Sure removing the subsidy would reduce the price to sellers but it would be a very strange model that would have the price falling by more than the reduced subsidy. In fact, it would seem to require that the supply curve be downward-sloping. 

And now, imagine that the economist further claimed that removing the subsidy would be good, as it would result in investors switching from investing in shoe production to investing in productive assets. This would go beyond strange. Sure the subsidy might have been diverting assets to having too much shoe production and not enough other stuff, but in what sense would we say that producing shoes is unproductive? And, how is it consistent to argue at the same time that removing the subsidy would lead to less investment in shoe production at the same time as arguing that it would result in lower shoe prices for consumers? 

O.K. this country, this policy, and this economist are fictitious. But if we change "country" to "New Zealand", "shoes" to "housing", "subsidy" to "tax exemption", and "economist" to "Gareth Morgan", you pretty much get this blog piece from Gareth on Tuesday. 

Gareth argues, correctly, that owner-occupied housing receives a favourable tax treatment relative to other investment since we are not charged income tax on the implicit rental payments we receive from ourselves. But he then goes on to argue that removing this exemption would "bring affordability within reach of many more families". This is an argument I have commented on before; it really looks like arguing that tax incidence can be negative: If housing is effectively subsidised by the tax system, we can't expect removing the subsidy to make it more affordable. 

And he then says that our tax treatment of housing has "discriminated against productive investment in favour of property speculation". Now if he means that we have invested too much in building houses and other kinds of investment, then we have to ask: In what sense is it unproductive to build houses that provide housing services to people that they value enough to pay for? And, how is it possible that curtailing such investment would "bring affordability within reach of many more families"? If, in contrast, he means diverting investment resources from building new equipment to buying existing houses as speculation, I have my perennial concern that this line or argument fails to note that buying existing houses for speculation or other reasons is not "investment" at all, and the assumptions you have to make to conclude that such behaviour diverts resources away from productive investment are a stretch to say the least.  

One final curious seeming contradiction in Gareth's post. At the start, he notes "When, not if, interest rates increase, this illusion that housing is `affordable' will burst....house prices will adjust". But later he suggests that if we don't remove the tax-favoured treatement of housing, he should "go out and buy another three houses now and just wait for the rest of you to bid the prices up". Why would that be good personal investment advice if, as he says, house prices are sure to fall? What am I missing?