Third, assume that the government chooses between a system where interest on housing is deductible from taxable income (as in (24)), and a system without deductions (i.e. the budget constraint reads c-wi- r(X – X) – T(w£)). Which system is preferable from a welfare point of view? Interest deductions stimulates the housing consumption of high-income earners, which makes the allocation of housing consumption more uneven across income groups than it would otherwise have been.
This could imply a welfare loss – but a loss that could be outweighed by an efficiency gain from lower marginal tax rates on the labor income of high-wage individuals. Thus, the common view that tax arbitrage is costly for society is not necessarily correct; depending on the curvature of the tax function, and on the form of the utility function, it could actually be welfare-enhancing. This was true in our simple model of costless paper transactions in section 3, but even in the present model, where deductions lead to a distorted consumption pattern, we can not rule out that arbitrage creates an efficiency gain. Whether this is the case in reality is of course an open question.
Finally, we have assumed that everyone consumes the same type of housing. In reality, people also make a tenure choice decision: low-income earners tend to consume rental housing, while high-income earners tend to live in their own houses. This suggests an arbitrage mechanism reminiscent of the simple model of section 3. In that model, low-income earners issue tax-exempt claims and hold taxable ones, while high-income earners hold tax-exempt claims and issue taxable ones.
In a housing market with tenure choice, a typical low-income earner pays a non-deductible rent to a landlord and has some taxable savings in the bank. The typical landlord is a high-income earner who has borrowed (tax-deductible) money from the bank in order to buy an apartment house, the income of which is in general favorably taxed. The payment streams are thus very similar: in both cases, low-income earners pay nondeductible and non-taxable (or lightly taxed) money to high-income earners, while high-income earners pay tax-deductible and taxable money to low-income earners.