Gavin R. Putland,  BE PhD

Friday, December 23, 2011 (Comment)

How tax causes financial crises and unaffordable housing

If you want to model the economy through the bubble-burst-recession cycle, as Steve Keen is trying to do, the math gets complicated. But if you only want to find some sufficient conditions for financial instability (or, on the contrary, necessary conditions for financial stability), the math is dead easy: you assume financial stability and look for conditions under which that assumption leads to an absurdity or a contradiction. The conditions relate to taxation of property, and can be represented by means of a “contour map” on which you can locate our tax system to see whether it is compatible with financial stability. And it isn't.

The property market, being the biggest “physical” asset market and the market in which acquisitions are most dependent on debt, is the most obvious place to look for financial instability.

First we define our symbols. Suppose that a property has a gross annual rental yield y, appreciates at an annual “growth” rate g, can be mortgaged at an effective annual interest rate i, and is subject to a public holding charge or “land tax” at an annual rate τ, where all four variables are expressed as decimals; e.g., if y=0.04, the yield is 4% per annum, and so on.

The “effective” interest rate is the appropriately weighted average of interest paid and interest forgone — that is, the interest paid on the debt-funded part of the purchase price plus the interest forgone on the remainder, all divided by the price.

In the case of an improved property (e.g. a property including a building), τ is expressed in terms of the improved value for present purposes (even if the rate defined by legislation is levied on the land value alone — as it should be, to avoid penalizing construction).

The applicable appreciation rate is that of a fixed address — not to be confused with that of the average property or the median property. As cities grow, average and median properties move further from city centres, so that their prices do not grow as fast as those of particular properties.

Now we invoke the assumption of financial stability. The weakest form of that assumption is that lending and servicing of loans can continue under the most favourable circumstance, namely equilibrium — not in the sense that prices are constant (which would mean g=0), but rather in the sense that y, g, i and τ are constant.

When the market reaches equilibrium, buying must be competitive with renting. Hence the total return (that is, the rent saved or earned, plus the appreciation) must balance the total holding cost (the interest paid or forgone, plus the holding charge). On a per-unit-price basis, this is written

y + g = i + τ .

Then we consider how taxes modify the equation. Recurrent property taxes are already included in τ. An indirect tax, in so far as it simply devalues the currency in which all values are measured, has no effect. The problem concerns income tax in its various forms.

In Australia, for owner-occupied homes, imputed rents and capital gains are not taxable, while interest and property taxes are not deductible, so all four terms in the equation are unaffected. But for investment homes, rent is taxable, and forgone interest means avoided tax, while interest and property taxes paid are deductible at the same marginal rate even if they exceed the rent (negative gearing); but capital gains are usually taxed less, so that a dollar in capital gains is usually worth more after income tax than a dollar in rent, interest or property taxes. To allow for this effect in the above equation, we multiply g by a scale factor k, which we shall call the capital gain preference. So the equation becomes

y + gk = i + τ .

For owner-occupied housing, k=1. For investment housing, k is usually greater than 1, indicating that capital gains are more attractive (taxed less) than rental income. If k were less than 1, it would mean that capital gains were taxed more severely than rental income. If k were zero, it would mean capital gains were confiscated.

(This analysis assumes short-term appreciation. If deductibility of negative gearing is restricted, the effect is equivalent to increasing i for the affected owners; but that is not applicable in Australia. Capital gains and interest have been taken as nominal, in accordance with the Australian practice of assessing nominal (not real) capital gains and allowing deductions for nominal interest. Other situations can be represented by adjusting k and/or i.)

What about conveyancing stamp duty? From the viewpoint of someone who buys a property and re-sells it, the stamp duty is equivalent to a holding tax at a rate inversely proportional to the time for which the asset is held. In a rising market, it is alternatively equivalent to a capital gains tax (which reduces k) at a rate inversely related to the time for which the asset is held. Thus it can be represented through a time-dependent adjustment of τ or k. Either way, it tends to impose a lower limit on the holding time, but has little effect on buyers who intend to hold for long periods.

The last equation can be rearranged as

1/y = 1 / (i+τ-gk) .

Of course 1/y is the P/E (price/earnings) ratio. Because the denominator on the right-hand side is a difference, it can approach zero. As it does so, a small increase in τ or a small reduction in k can produce an arbitrarily large reduction in the price. And conveyancing stamp duty can be represented by an increase in τ or a reduction in k. So this simple theory is good enough to explain the following counter-intuitive observation on p.16 of a paper by Andrew Leigh:

Across all neighbourhoods, the short-term impact of a 10 percent increase in the tax rate is to lower house prices by 1–2 percent.... Since stamp duty averages only 2–4 percent of the value of the property, these results imply that the economic incidence of the tax is entirely on the seller... Indeed, the house price results are in some sense “too large”, in that they imply a larger reduction in sale prices than the value of the tax.

In practice, the P/E ratio must be positive, so that the denominator in the above equation must also be positive. As that denominator approaches zero, the P/E ratio “approaches infinity” — that is, increases without limit. Hence if the denominator goes negative, the resulting negative P/E ratio is, as it were, not less than zero, but greater than infinity.

But of course that's absurd. In reality, the P/E ratio must be finite. Thus we have found a condition under which the assumption of financial stability (or of equilibrium) leads to an “absurdity”.

In reality, P/E ratios must be finite because prices must be finite, and prices must be finite because buyers have limited capacity to service loans. Even if buyers plan to pay interest out of capital gains, their capacity to service loans is limited by the economy's capacity to realize capital gains. If the capacity to service loans is exceeded, there will be a financial crisis (which in turn will cause disequilibrium). Thus we have found a condition under which the assumption of financial stability (or of equilibrium) leads to a “contradiction” — a condition under which “Stability is destabilizing.”

Let's represent that condition graphically. The last equation (or the one before) can be rearranged in the form

gk = τ + i-y ,

which shows that the graph of gk vs. τ is a straight line, with unit slope and an intercept of i-y on the “gk axis”. Each value of y gives a different line, so that each line can be understood as a contour in a graph of y vs. gk and τ. Because the intercept (i-y) is a linear function of y, equally spaced values of y give equally spaced contours.

The most interesting contours are y=0, for which the intercept is i, and y=i, for which the intercept is 0. From these we may deduce the regions for which y>i (positive gearing for 100% LVR), 0<y<i (negative gearing for 100% LVR), and y<0 (guaranteed financial instability), as shown in the graph (larger version / hi-res version).

Financial Stability Contour Map

Experience teaches us to fear an imminent crash when the yield gets down to half the interest rate — that is, when y=i/2. The contour for y=i/2 is in the middle of the amber “negative gearing” band. Hence, if the tax system places us closer to the red region of the contour map than the green region, it invites a strong suspicion that the tax system is incompatible with long-term financial stability. If the tax system places us in the red region (infinite P/E), suspicion gives way to certainty.

The one case in which an infinite P/E ratio does not require infinite capacity to service loans is the case of unoccupied and unavailable properties, for which E is zero but P is positive. Such are the vacant lots and boarded-up houses held by speculators for capital gains alone; they are portents of financial doom.

If the tax system causes the “equilibrium” rental yield to be unsustainably low, prices will rise until the financial system collapses, then fall until the bad debts are somehow worked out, then rise again, and so on. At any stage of the cycle, the price of a property will be determined by what one can borrow against it. Arguments about supply and demand will still be relevant to rents, but prices will be decoupled from rents. Vacant lots and boarded-up houses, held by speculators for capital gains alone, are the ultimate examples of this decoupling.

So where are we on the contour map? In Australia, over the long-term, the appreciation rate is similar to the interest rate. For residential owner-occupants, k=1, so gk is roughly i; and the property tax rate is a small fraction of i. That places us close to the red region — too close for financial stability. For other classes of property owners, k is higher, and the total property tax rate is also higher, but probably by an insufficient margin to compensate for the higher k, in which case the destabilizing tendency is even greater than that from ordinary home owners.

Financial stability can be restored by higher “land tax” and/or higher taxation of capital gains relative to current income, including at least income from assets. At present, capital gains are taxed less than income from assets. If it were the other way around, financial crises would be less likely.

In lieu of tax reforms that limit “rational” property prices and hence the demand for credit, one might try to limit the supply of credit by means of regulations that restrict lending against property. But this policy, by definition, can “succeed” only if prospective buyers' capacity to borrow is limited by the regulations rather than by their capacity to service loans. In other words, it can succeed only if some people who are financially capable of becoming home owners are “locked out of home ownership” by the regulations, in which case the political pressure for deregulation will be irresistible. So the regulations will be relaxed until credit is limited on the demand side.

Now consider the implications for the affordability of home ownership. On a per unit-price-basis, the initial annual cost of owning (if we include only interest on the price, and the holding tax) is i+τ, while the annual cost of renting is y; and an expression for y can be obtained from any of the last three equations. Thus we find that the initial ratio of the annual cost of owning to the annual cost of renting is \[\frac{i+\tau}{y}=\frac{i+\tau}{i+\tau-gk}.\] (Enable JavaScript™ to see the equation.) If the market is rising (g>0) and capital gains are not completely confiscated (k>0), this ratio will be greater than 1 (that is, owning will be more expensive than renting). But higher “land tax” (bigger τ) and/or and higher taxation of capital gains relative to current income (smaller k) will increase i+τ relative to gk and therefore make the ratio closer to 1 (smaller).

How can an increase in the holding tax rate make it cheaper to buy and hold the property, relative to renting? Obviously by reducing the price/rent ratio, which in turn affects not only the holding tax bill but also the interest bill.

Conclusion: For given rent, higher “land tax” and/or and higher taxation of capital gains relative to income from assets would improve financial stability and make home ownership more affordable.

[Last modified Apr.17, 2012. Used for MathJax testing, Sep.1, 2013.]

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