Problem: the ‘rational’ price of land is infinite; solution: abolish income tax
A simple equation involving price, rent, appreciation, interest and tax predicts that for realistic values of the parameters, the price of land should be infinite — or, if finite, far in excess of lenders' capacity to supply credit and of borrowers' capacity to service loans. In practice this means land prices will be bid upward until the financial system breaks, causing a credit crunch whose effects flow through to the rest of the economy. The associated “correction” in land prices, perhaps combined with financial reforms ostensibly designed to prevent any recurrence, eventually restores confidence. But unless the parameters in the equation are permanently changed, the recovery merely sets the stage for the next crash. The only parameters that can be permanently changed are those pertaining to tax. Paradoxically, the indicated tax reform would enrich property owners: by removing perverse incentives and encouraging investment in infrastructure, it would increase capacity to pay for land, so that the new (stable) price trajectory would be higher than the present (unstable) one. The alternative to such reform is a continuation of periodic financial crises and recessions.
1.1 Derivation from arbitrage
1.2 Derivation as present value of future rent
1.3 Effect of inflation
1.4 Effect of taxes4.1 Political constraints
4.2 Lower “rational” prices
4.3 Higher actual prices
4.4 Futility of financial regulation
1. The P/E formula
1.1 Derivation from arbitrage
Suppose that a site (a piece of land or associated airspace) has a price P and an annual rent E (for “Earnings”). Then the rental yield is
y = E/P(1)
and its reciprocal (1/y) is the P/E ratio (also known as the “years purchase”).
Suppose further that the site
- appreciates at an annual rate g (for “gain” or “growth”),
- can be borrowed against at an annual interest rate i, and
- is subject to a public holding charge or “tax” at an annual rate τ,
where all three variables, like y, are expressed as decimals (e.g. if g=0.07, the site appreciates at 7% per annum; and so on).
If buying is to be competitive with renting, the total return (that is, the rent earned or saved, plus the appreciation) must balance the total holding cost (the interest plus the holding “tax”). On a per-unit-price basis, this is written
y + g = i + τ ,(2)
1/y = 1 / (i+τ− g) .(3)
This is the P/E ratio, which one would think must be positive, so that the denominator on the right-hand side must also be positive. As that denominator approaches zero, the P/E ratio “approaches infinity”; that is, it increases without limit.
If the denominator in Eq.(3) is zero, any reduction in the interest rate or the holding charge or any increase in the appreciation rate will cause the denominator, hence the P/E ratio, to go negative. But any one of these changes would make one willing to pay more for the site, not less — as is clear if we substitute P/E for 1/y and rearrange as follows:
P = (E+ gP) / (i+τ) .(4)
It is as if negative prices were not less than zero, but greater than infinity!
Eq.(4) further indicates that if τ=0 (that is, if there is no holding charge), the price is the annual accrual (rent plus capital gain) divided by the interest rate, and that the holding “tax” affects the price like additional interest. All this could have been anticipated, in which case Eq.(4) would be an alternative derivation of Eq.(3).
The alternative interpretation of the denominator in Eq.(4) is that interest affects the price like another “land tax”. It should therefore be considered remarkable that while governments allow central banks to raise interest rates by many percentage points without consulting the voters, any proposal to increase “land tax”, even by a much smaller margin, is regarded as political suicide.
1.2 Derivation as present value of future rent
S = A + AR + AR2 + AR3 + AR4 + ...(5)
is called an infinite geometric series in which A is the first term and R is the common ratio (the ratio of each subsequent term to its predecessor).
If |R|<1, the sum is finite  and is given by
S = A / (1− R) .(6)
We can use this formula to find the P/E ratio of the aforesaid site, whose current price is P. In the first year the site will yield yP in rent and be liable for τP in “tax”, giving a net positive cash flow of (y−τ)P. If this cash flow occurs at the end of the year, its present value (discounted by one year at the interest rate i) is
A = (y−τ)P / (1+ i) .(7)
Imitating mainstream economists, let us now assume constant appreciation, constant yields and constant interest, so that in each subsequent year, the net cash flow increases by a factor (1+g) and is discounted by a further factor (1+i). Then the price P is an infinite geometric series whose first term is given by Eq.(7) and whose common ratio is
R = (1+ g) / (1+ i) .(8)
If g<i, this ratio will be smaller than 1, so that we can use Eq.(6): substituting Eqs.(7) and (8) into Eq.(6), renaming S as P, and simplifying, we get Eq.(3) again.
Having obtained Eq.(3) in two different ways and confirmed it through the interpretation of Eq.(4), we may regard it as reasonably robust.
1.3 Effect of inflation
The appreciation rate g and the interest rate i may be stated either in real terms (“constant dollars”) or in nominal terms (“current dollars”), provided that we are consistent. If any further explanation is needed, let the inflation rate be π (as is usual in economics), and let us temporarily use a prime (′) to denote a real quantity (with no prime for a nominal quantity). Then the relations between the nominal and real rates are roughly
g = g′ + π ,(9)
i = i′ + π .(10)
When these are substituted into Eq.(2), inflation cancels out. This “further explanation” is not exact, because Eqs.(9) and (10) are approximations that assume small values of the parameters. But, as none of the parameters in Eqs.(1) to (8) can be known exactly, there is no point in splitting hairs on Eqs.(9) and (10).
1.4 Effect of taxes
Recurrent property taxes are already taken into account in τ (the rate of the holding charge).
A broad-based consumption tax, in so far as it simply devalues the currency in which all values are measured, has no effect on the above analysis. In theory, because “investment” in land delays the opportunity to consume, a consumption tax may affect land prices if it is known to discriminate between current and future consumption, whether because the tax rate will change or because the items that will be consumed later (after selling the land) will be taxed more or less severely than the items that could be consumed now (instead of buying the land). But in practice such effects are unlikely to be known, or even guessed at, by market participants.
For convenience, let us define a neutral income tax as having a flat marginal rate, no discrimination between current income and capital gains, and full deductibility of interest and property taxes (that is, no quarantining of “negative gearing”). Under these conditions, the affected quantities are converted to their after-tax equivalents by multiplying by the scale factor (1−r), where r is the income-tax rate (e.g. r =0.3 for a 30% marginal rate). When this is done in Eq.(2) or (4), the factor (1−r) cancels out, so that Eqs.(3) and (4) remain valid. So a neutral income tax does not affect the P/E ratio.
In practice, however, income taxes can be highly non-neutral, so that conversion to after-tax equivalents involves different scale factors which do not cancel out. In particular:
- If capital gains are taxed at a lower rate than current income, their after-tax values are increased relative to current income, so that g is finally scaled by a factor greater than 1; let that factor be k.
- If we are working in real terms while the tax assesses nominal rather than real capital gains, the effect of inflation is to make the concession less generous and hence to reduce k (possibly to less than 1, if inflation is high).
- If deductibility of “negative gearing” is restricted in any way, interest becomes more expensive relative to rents and capital gains, and the effect may be approximated on the macro scale by multiplying i by a factor greater than 1; let that factor be h.
- If we are working in real terms while the tax system allows a deduction for nominal interest, then interest becomes less expensive, reducing h. In the absence of any restriction concerning negative gearing, h will then be less than 1.
So the P/E ratio given by Eq.(3) must be adjusted as follows:
P/E = 1 / (hi + τ − kg) .(11)
2. Putting in some numbers
2.1 Sanity in: insanity out
According to the Australian Bureau of Statistics (ABS), the nominal value of all land in Australia rose from $679.2 billion in June 1990 to $3152.2 billion in June 2008 , giving a nominal appreciation rate of 8.9% per annum between 1990 and 2008. Those years are chosen because they correspond to peaks in the total real land value, so that the average (compound) appreciation rate between those years can be taken as the appreciation rate over a representative cycle. The same appreciation rate is applicable to the average site in a fixed location . As the appreciation of a “home” (house-land package) is almost entirely due to the site, the appreciation of the “home” should be much slower in percentage terms than that of the site. Property promoters (“spruikers”) tell us that the nominal price of a typical home doubles every 7 to 10 years over the long term, in which case the home appreciates at 7% to 10% per annum. Having said this rate should be “much slower” than 8.9% per annum, we have reason to regard the more pessimistic “spruikers” as the more believable, but no reason to suspect the ABS figure of being excessive. So let us accept 8.9% per annum (g=0.089).
Having started in nominal terms, we continue in nominal terms. If the income tax rate is 30% for current income but 15% for nominal capital gains, the investor keeps 70% of current income but 85% of nominal capital gains, so that k=85/70.
In Australia, for a typical (i.e. small) property investor, rates and land tax would amount to less than 1% of the site value per annum. Being conservative (i.e. pessimistic, as seen by the investor), let us accept 1% per annum, so that τ=0.01.
In Australia, negative gearing is deductible provided that the property is at least “available” for rent; it need not be actually rented. That is not a strong argument for accepting any value of h other than 1.
Putting these values into Eq.(11), we get
P/E = 1 / (i − 0.098) ,(12)
indicating that it takes an expected nominal interest rate in excess of 9.8% per annum just to make the price finite! Mortgage interest rates in Australia have not been that high since 1996. The predicted P/E ratio is 100 for an expected interest rate of 10.8% per annum, or 50 for 11.8% per annum (a rate not seen in standard Australian variable-rate mortgages since 1992). Reasonable expectations on interest rates lead to infinite prices.
Now consider the viewpoint of owner-occupants rather than investors. In Australia, as owner-occupants do not pay tax on capital gains or imputed rents and do not claim interest or recurrent property taxes as deductions, the income tax is effectively neutral (at a rate of zero), so that h=k=1. As owner-occupants pay municipal rates but not state land taxes, let us take a lower value of τ — say τ=0.005, corresponding to a rate of 0.5% per annum on the site value. The appreciation rate g is unchanged. Putting the new values into Eq.(11), we get
P/E = 1 / (i − 0.084) .(13)
Now the expected nominal interest rate needed to make the price finite is “only” 8.4% per annum — a level exceed by actual mortgage rates for less than one year out of the last thirteen. Again, reasonable expectations on interest rates lead to infinite prices.
2.2 Pessimism in: optimism out
What if the above figures are “rubbery”? Even from the more pessimistic viewpoint of owner-occupants, if the rationally expected interest rate is 7% per annum (close to the average for the last decade), the “rubber” must yield another 1.4 percentage points of pessimism to make the “rational” P/E ratio finite, and then another 2 percentage points to bring the ratio down to 50, which is still outside Australian experience (remembering that E refers to gross rent).
What if we treat a home, comprising a site plus improvements, as a single asset? If appreciation is 7% per annum (at the pessimistic end of the promoters' range), and if we fail to reduce τ in response to the larger value base (again being pessimistic), the P/E ratios for investors and owner-occupants become, respectively,
P/E = 1 / (i − 0.075)(14)
P/E = 1 / (i − 0.065) .(15)
Assuming (pessimistically again) that the latter equation sets the price, and assuming 7% annual interest, we get a P/E ratio of 200. Actual ratios in Australian capital cities in 2009 were typically between 20 and 25.
On any of the above sets of inputs, the mystery is not why the actual prices of homes are so high, but why they are so low.
3.1 It's the debt, stoopid!
We must conclude that land prices are determined not in the property market, but in the financial market — not by any rational relationship between prices, rents, interest and capital gains, but by the capacity of the financial system to create credit against land. Given the propensity of financial institutions to lend first and attend to their reserves later, and of central banks to adjust reserve requirements accordingly, the capacity to create credit against land is determined by the capacity of buyers to service debts out of their current income, which is not necessarily derived from the property market.
3.2 Financial instability
If “rational” land prices were within the capacity of the financial system, we might hope that the growth in land prices would be orderly and would not cause financial crises. Given that “rational” prices are not within that capacity, the best we can hope for is that actual prices will rise to absorb that capacity. More realistically, given that
- access to land is essential for economic participation,
- people prefer to buy land rather than rent, in order to avoid rent increases,
- people buy as soon as they can, in order to avoid anticipated price increases,
- buyers will tend to believe in the greater fool, and
- lenders will take risks in pursuit of market share and market expansion,
we must conclude that prices will not only “absorb” the capacity of the financial system, but exceed it — with destructive results.
As real estate is the preferred form of collateral for private credit creation, the foregoing argument substantially confirms Minsky's Financial Instability Hypothesis, commonly paraphrased as “Stability is destabilizing.” In general, stability allows asset prices to seek their rational levels. But under current tax arrangements, land prices cannot find their rational levels, and the mere seeking breaks the financial system.
4. Policy responses
4.1 Political constraints
To avoid financial instability, “rational” land prices must be brought within reach of the financial system. But any policy that does this simply by reducing “rational” land prices will be unacceptable to property owners, who constitute a majority of voters. To be politically acceptable, the policy must also increase national income, hence the income available to service debts against land, hence the capacity of the financial system to create credit against land, so that lower “rational” prices meet higher actual prices.
4.2 Lower “rational” prices
To make “rational” land prices finite, one must increase the denominator in Eq.(11) so as to make it positive. This can be done by
(a) increasing after-tax interest rates (that is, increasing h or i),
(b) increasing holding charges on sites (that is, increasing τ), or
(c) increasing taxation of capital gains relative to current income (that is, increasing k),
or some combination thereof. Option (a) disqualifies itself on the grounds that (i) if monetary policy is sequestered for the purpose of containing prices of particular assets, it is unavailable for other purposes, (ii) high interest rates are politically odious, and (iii) artificially high interest rates strangle economic activity and therefore shrink the revenue base, so that the political odium cannot be offset by tax cuts.
Option (b) does not interfere with monetary policy, and its political costs, unlike those of option (a), can be compensated in some situations and avoided in others. They can be “compensated” in the sense that a site-holding charge raises revenue, which can be used to cut other taxes or charges. If it is used to cut taxes on current income but not capital gains, it increases k [as in option (c)] and thereby amplifies the desired effect on “rational” land prices. Political costs can be “avoided”, rather than compensated, in the following cases:
- Where land is subject to a mortgage, which obviously reduces the borrower's capacity to pay a holding charge, the mortgagor (borrower) and mortgagee (lender) should be treated as joint owners, so that the mortgagor and mortgagee share the holding charge in proportion to their equity in the land . The portion paid by the lender would, by itself, increase the interest-rate margin between deposits and loans. But this effect might be offset by removal of income tax on interest (as we shall see), and in any case would be taken into account by the central bank in setting monetary policy. So it would not necessarily increase i, and its main effect on “rational” land values would be through a compensating reduction in tax on current income, hence an increase in k.
- As the value of an owner-occupied residential site does not automatically yield a cash flow — except to a mortgage lender, and only in proportion to the amount owed — there would be overwhelming political pressure to exempt such sites from the holding charge. If that charge were shared between the mortgagee and the occupant as above, only the occupant's equity would need to be exempt. Thus the “joint owners” provision would minimize not only the political cost of the holding charge, but also the fiscal cost of the politically necessary exemption.
The exemption of residential owner-occupants' equity from option (b) makes it all the more necessary that residential owner-occupants contribute under option (c), in order to reduce “rational” land values as seen by them. For that purpose, option (c) requires that capital gains on land be taxed more heavily relative to current income from land — not necessarily all current income. Politically, however, introducing or increasing taxation of capital gains on the “family home” (genuflection) probably cannot be compensated by anything less than the complete abolition of tax on personal income other than capital gains. As any attempt to tax corporate income but not personal income would spawn avoidance schemes that turn the former into the latter, the prescription immediately expands to the complete abolition of tax on current income.
The challenge of replacing the revenue from taxation of current income can be met from within the framework of options (b) and (c), thus retaining the desired effect on “rational” land prices. In particular:
- The portion of the site-holding charge payable by the mortgagee could be expanded into a general tax on debt, to replace income tax on interest.
- The site-holding charge payable by mortgagors on their equity, and by unmortgaged owners, should not be applied to buildings or other improvements (because that would discourage construction), but could be applied at a lower rate to another sort of “equity”, namely shares in listed companies. In the latter form, it could be a tax on the total value of a company's shares, payable by the company, to replace income tax on retained and distributed profits; cf. .
- The tax on capital gains could be made quite general.
- If perchance the above three measures, at politically acceptable rates, do not yield enough revenue to replace the old tax on current income, then an increase in the rate of the broad-based consumption tax would yield additional revenue without increasing k, whereas any remaining tax on current income would increase k.
4.3 Higher actual prices
The higher capital gains tax and the holding charge on land values would partly capture increases in land values for public revenue, giving governments the ability and the incentive to do things that increase land values, including investing in public infrastructure. The additional infrastructure projects would cause additional uplifts in land values, and the “after-tax” portions of those uplifts would be an additional benefit for land owners.
On a local scale, better infrastructure means greater locational advantage, hence greater willingness and ability to pay for land in that location. On a national scale, better infrastructure means higher national income, hence more capacity to service loans. Either way, better infrastructure increases the maximum land values that the financial system can sustain. Meanwhile the abolition of tax on current income would remove disincentives on income-generating activities, further lifting the maximum sustainable land values. It is still necessary to reduce the “rational” values below the maxima; but, as we have seen, this can be done by the same kinds of tax reforms that increase the maxima.
As the increases in land values due to infrastructure reflect greater amenity — not higher prices for the same amenity — they are not incompatible with affordability. This conclusion is reinforced by the observation that the owner of a site subject to a heavy holding charge must either cover the holding charge by seeking tenants (and build such accommodation as may be needed for the purpose), or sell the site to someone who will. This pressure tends to increase the supply of accommodation and the availability of land for productive purposes.
4.4 Futility of financial regulation
The present financial crisis arose because the financial system (more specifically, borrowers) lacked the capacity to support land prices that are rational under current tax arrangements. In response, some commentators are calling for regulations that would curtail “irresponsible” lending and thereby further reduce the financial system's capacity to support prices. The introduction of such regulations, if badly timed, could easily trigger a price crash. Once in place, such regulations might merely shift the “greater fool” problem from the borrowers' side to the lenders' side: prices might crash when lenders lose faith in the intentions of other lenders, instead of when buyers lose faith in the intentions of other buyers.
Be that as it may, restrictions on lending are not politically sustainable, because they are too easily portrayed as locking prospective buyers out of the market, and because they can be repealed without any immediate adverse fiscal impact. In contrast, revenue measures that keep property prices within the capacity of a deregulated financial system do not lock out prospective buyers, and cannot be repealed without immediate (and lasting) fiscal pain.
We must conclude that tax-based remedies are both more effective and more permanent than regulatory remedies.
5.1 Tax the debt, not the interest
A broad-based tax on debt would not only replace income tax on interest, but also encourage lenders to write off or write down non-performing debts — because a tax on debt, unlike one on the interest, is payable on the face value of the debt whether it is “performing” or not. Faster clearance of dubious debt means faster restoration of financial clarity, hence earlier recovery from any sort of financial crisis.
Avoidance or evasion of a tax on debt would be minimal, because if a debt were not declared for tax purposes, it would simply not be enforceable. Informal loans between family members would presumably be in this category. There would be no need for a general ban on undeclared loans; the lack of enforceability would be enough to prevent such loans from becoming unduly common.
A tax on debt need not give rise to any cross-jurisdictional issues that do not exist in respect of the present income tax on interest.
5.2 Tax the land, not the rent
Tax on rental income can be avoided simply by failing to seek any rental income. It also reduces the marginal cost of such laziness. In contrast, a holding charge on the value of a site cannot be avoided by failing to seek rental income, but rather compels the seeking of rental income — and therefore the construction of such accommodation as may be necessary to obtain the rental income — as a means of defraying the charge. In other words, a holding charge on the value of a site is an economic stimulus. Of course the demands of industry lobbyists wishing to “stimulate” income-generation and capital-formation are always for subsidies and tax concessions, never for new or higher taxes or charges. But any old-school disciplinarian will confirm that the stick can stimulate at least as well as the carrot.
A holding charge on site values would not only help to bring “rational” prices of sites within reach of the financial system, but also tend to stabilize actual prices via negative feedback. A rising value would mean a rising holding charge, hence rising pressure to sell, hence downward pressure on the value; and a falling value would mean a falling holding charge, hence falling pressure to sell, hence upward pressure on the value. As property is the most important form of collateral for loans, and as fluctuations in property values mostly reflect fluctuations in site values, anything that stabilizes site values also stabilizes the financial system.
5.3 Tax the shares, not the dividends
Similarly, a holding tax on the value of corporate shares would tend to stabilize share prices. If the tax were payable by the company, investors and prospective investors in the company's shares would not feel the tax directly, but would know its implications for the company's cash flow and would react accordingly. To the (limited) extent that financial crises and recessions are caused by share-market crashes, they can be prevented by stabilizing share prices.
Such a tax would entirely avoid the complexities of income tax on distributed profits. As the tax would not be a marginal cost, it would have less effect on the prices of a company's products, hence less influence on locational decisions, than income tax on retained profits. It would also have lower compliance costs. On the downside, it would require a method of valuing local subsidiaries of multinational corporations for tax purposes ; but this difficulty can hardly be worse than that caused by transfer pricing under the present income tax.
5.4 Tax capital gains, not current income
The present practice of taxing current income more heavily than capital gains contributes to a high value of k, hence absurdly high “rational” land values, hence to financial instability. That alone is sufficient reason to reverse the practice. But there are others.
Most obviously, capital gains accrue to owners of appreciating assets, who tend to be at the high end of the income scale, so that taxing current income more heavily than capital gains is highly regressive.
The standard argument against taxation of assets, namely that it inhibits capital formation, is perfectly valid as regards taxation of current income from assets. But it is nonsense as regards taxation of “capital gains” because, in the long term, real capital doesn't gain. Real capital — the sort that needs “formation” — cannot increase in value without inducing “formation” of competing capital, which reduces values to normal. Therefore any assets that appreciate in the long term do so because they cannot be “formed” — that is, because they are in fixed supply, like land. It is perfectly inane to allege that a tax inhibits the “formation” of assets that cannot be “formed” at all. If the evangelists of “capital formation” were honest, they would advocate concessional rates for income from capital. That is not consistent with present practice, but perfectly consistent with what is advocated in this paper.
Critics of taxation of “capital gains” (which we now see to be a misnomer) further allege that one should not tax the appreciation of an asset that has been bought out of taxed current income, because this is “double taxation”. If that criterion has any merit, it is completely satisfied by retaining the tax on capital gains and abolishing the one on current income!
On the downside, a tax on capital gains causes a reluctance to realize gains: the lock-in effect. To keep this in perspective, one should note that a tax on the capital gain since the last transfer of an asset has far less lock-in effect than a tax on the whole transfer price. In the former case, the transfer does not create the tax liability, but merely realizes it, and transferring an asset more frequently divides the taxable gain into a larger number of smaller units. In the latter, the transfer indeed creates the tax liability, and an asset that is transferred more frequently pays more tax. Those who oppose lock-in effects should be more concerned about taxes of the latter kind — which are overwhelmingly common, even on that most sacred “family home”.
To prevent a capital-gains tax from being branded a “death tax”, an inheritance should not be deemed to realize a gain; rather, the tax on an inherited asset should be payable on the first sale after the inheritance, and the taxable gain should be calculated since the last sale before the inheritance.
5.5 Avoiding a deflationary shock
In employers' accounts, personal income tax looks much like payroll tax, which is partly shifted into prices. As normal profit, on the macro-economic scale, is a cost of production, corporate income tax raises prices to some extent. For these reasons, abolition of income tax would cause a deflationary shock: a one-off fall in prices. Anticipation of this fall would cause a consumption hiatus, which would be better avoided. A certain increase in the general consumption tax would compensate for the deflationary effect. As this effect would not be universally understood, a somewhat smaller increase in the consumption tax would compensate for the deflationary expectation and thereby avoid the hiatus in consumption.
A non-inflationary increase in the consumption tax would be doubly useful if the holding charges on debt, shares and land, at rates that were high enough to stabilize asset values but low enough to be politically acceptable, did not yield sufficient revenue to replace tax on current income.
These observations should be interpreted in context — as a solution to a particular problem, and not as an endorsement of consumption taxes per se. In the long term, given sufficient political will, expansion of the revenue base due to economic growth would allow consumption taxes to be phased out — gradually, so as to avoid deflationary shocks.
5.6 Sample rates for Australia
The following calculations are of the “ballpark” or “back-of-envelope” variety, and are intended only to establish the feasibility of the suggested reform. Some readers, drawing on their particular expertise, may wish to rework certain parts more accurately. Others may wish to make corresponding estimates for other countries.
Debt: In December 2009, Australia's household debt amounted to about $1.2 trillion. If this is a reasonable estimate of the debt within reach of Federal tax collectors, and if it is taxed at 2.5% per annum, it yields $30 billion per annum.
Land: As at June 2009, Australia's land was valued at $3012 billion, of which $2215 billion was residential, $592 billion commercial or rural, and $205 billion “other” . To be conservative, let us exclude the “other”. Taking a third of the residential land (by value) as non-owner-occupied, and adding the commercial and rural values, we get $1330 billion. If a quarter of this is mortgaged (hence taken into account under “Debt”, above), the remaining “taxable” value is near enough to $1 trillion. As this does not represent land plus buildings, but only land, the rate of the holding charge can be somewhat higher than that on debt — say 3.5% per annum. This would yield $35 billion per annum.
Shares: The total value of shares listed on the ASX has been somewhat variable over the last two years. But $1.2 trillion is within the range. If this value is taxed at 2.5% per annum, it yields $30 billion per annum.
Capital gains: Suppose that real gains are taxed at a rate of 50%. It is noted above that the nominal appreciation of land over the last cycle was about 8.9% per annum. A conservative estimate of the corresponding real rate would be 6% per annum, corresponding to a doubling every 12 years. Suppose that the stock of land also turns over about once every 12 years, and that a twelfth of it (by value) is sold each year. If this year's total value is $3 trillion, a twelfth of that will sell for $250 billion, yielding a real capital gain of $125 billion, on which the revenue will be $62.5 billion. In the share market, where turnover is much faster, we may assume that capital gains are continuously realized. Suppose that in terms of capital gains, shares are competitive with improved property (land plus buildings), for which we have previously used a nominal appreciation of 7% per annum, corresponding to a real appreciation of about 4.5% per annum. For a current total share value of $1.2 trillion, this yields a real capital gain of $54 billion per annum, on which the revenue is $27 billion per annum. The sum of the two revenue figures is near enough to $90 billion per annum. This sum is conservative as it does not allow for capital gains on government-created licences and privileges other than land titles.
Total: The above revenue figures (in bold type) add up to $185 billion per annum, which is near enough to the present revenue from Federal income tax, personal and corporate, on current income and capital gains. Any desired increase in the GST rate (for the purpose of avoiding deflationary expectations) can be compensated by a reduction in one or more of the above rates.
Growth dividend: The above revenue figures are conservative because they fail to account for growth in economic activity, hence asset values, due to investment in infrastructure and abolition of tax on income from productive activities.
Effect on “rational” land values: With the above rates, for a site appreciating at a real rate of 6% per annum, the parameter values are h=1, τ=0.035, k=0.5 and g=0.06. Considering the viewpoint of property investors, we can allow for municipal rates and “land tax” by increasing τ to (say) 0.045, so that Eq.(11) becomes
P/E = 1 / (i + 0.015) .(16)
At a real interest rate of 4.5% per annum, this gives a P/E ratio of 16.7; at 6.5% per annum, it gives 12.5. Considering the viewpoint of residential owner-occupants, we can allow for municipal rates and the holding-charge exemption by reducing τ to (say) 0.005, so that Eq.(11) becomes
P/E = 1 / (i − 0.025) .(17)
At a real interest rate of 4.5% per annum, this gives a P/E ratio of 50; at 6.5% per annum, it gives 25. That these ratios are higher for owner-occupants than for investors implies, for the first time in this paper, that it makes more sense to buy one's own place of residence than to invest in someone else's.
These results do not account for the effect of infrastructure on the appreciation rate. Nor do they consider that E would be competed upward because tenants would no longer pay income tax, while debt-servicing capacity would likewise increase because buyers would no longer pay income tax.
5.7 Alternative rates, with different treatment of home owners
One might argue that different P/E estimates for investors and owner-occupants are distorting and should be avoided. The difference is caused by the exemption of owners' equity in owner-occupied residential sites from the site-holding charge. An alternative to this “politically necessary exemption” is to allow an automatic right to defer the site-holding charge until the site is next sold (not bequeathed), and to cap the deferred component to some fraction of the real capital gain, so that the deferred component can be no worse than a surcharge on the capital-gains-tax rate. The figures in the preceding subsection may then be modified as follows.
Debt: No change. A rate of 2.5% per annum yields revenue of $30 billion per annum.
Land: The total land value excluding “other” is about $2800 billion. If a quarter of this is mortgaged, the remaining “taxable” value is about $2100 billion, of which $1100 billion is due to the inclusion of owner-occupied residential land. Hence a holding charge at a rate of 2.5% per annum yields $52.5 billion per annum, of which $27.5 billion is deferable.
Shares: No change. A rate of 2.5% per annum yields revenue of $30 billion per annum.
Capital gains: If a rate of 50% yields revenue of $90 billion per annum, then cutting the rate to 40% reduces the revenue to $72 billion per annum, and a “surcharge” of 20% is more than enough to capture the deferred component of the land-holding charge provided that sites appreciate uniformly.
Total: The above revenue figures (in bold type) add up to $184.5 billion per annum, which is near enough to the previous total. The new total is conservative in that it neglects the growth dividend, but optimistic in that it neglects any leakage through the defer-and-cap mechanism.
Effect on “rational” land values: With the above rates, for a site appreciating at a real rate of 6% per annum, the parameter values are h=1, τ=0.025, k=0.5 and g=0.06. Considering the viewpoint of property investors, we can allow for municipal rates and “land tax” by increasing τ to (say) 0.035, so that Eq.(11) becomes
P/E = 1 / (i + 0.005) .(18)
At a real interest rate of 4.5% per annum, this gives a P/E ratio of 20. For residential owner-occupants, τ might be reduced by half a percentage point, raising the P/E ratio to about 22.
Governments could bring “rational” land prices within the capacity of the financial system, and simultaneously increase that capacity, by
- abolishing taxation of income, including interest and income from assets,
- increasing taxation of capital gains,
- introducing broad-based holding charges on debt, shares, and land values (either excluding owners' equity in owner-occupied residential land, or deferring the charge thereon), and
- increasing consumption taxes, but only enough to avoid deflationary expectations due to abolition of income tax.
The effect would be to raise and stabilize the land-price trajectory, stabilize the financial system, and consequently avoid financial crises and the associated recessions. The appreciation of land would not damage affordability, because it would reflect increasing amenity and spending power, not speculative demand.
 If |R| is greater than 1, obviously the sum is infinite; it just keeps getting bigger as we keep adding terms. If |R| is equal to 1, successive terms do not get smaller, so the sum cannot “settle down”. But what if |R| is less than 1? First note that removing the first term is equivalent to multiplying each term, and hence the whole sum, by R; that is,
S − A = RS .(1n)
Then to remove the second term is to multiply the remaining sum by R, and so on. Then notice that because |R|<1, multiplying the sum by R means shrinking it, so that each successive removal shrinks the remaining sum by the same ratio. In other words, if we add the terms from left to right, each successive addition takes us closer to the sum S by the same ratio, which means that although there are infinitely many terms, the sum S is finite. To find that sum, we solve Eq.(1n) for S, obtaining Eq.(6). For alternative explanations, see Wikipedia under “Geometric series” and “Geometric progression”.
 The appreciation of a particular site is not to be confused with the increase in the median sale price or the mean sale price. As population increases and cities grow, the mean and median sales move further from city centres, so that the mean and median sale prices do not rise as fast as the price of a fixed site. It is therefore not valid to cite mean or median prices against any claim concerning the likely rate of appreciation of a particular property.
 This obvious concession, which is conspicuously and inexcusably missing from modern “land taxes” and municipal rates, was recommended by Henry George as early as 1885. See “Land and Taxation: A Conversation between David Dudley Field and Henry George”, North American Review, July 1885; reprinted in (e.g.) The Complete Works of Henry George (New York: Doubleday Page & Co., 1904), vol. 8 (“Our Land and Land Policy, Speeches, Lectures and Miscellaneous Writings”), pp. 219–239.
 G. R. Putland, “Tax relief for listed companies”, archive.grputland.com, Sep.12, 2005. References to franking credits, which assume the continued existence of personal income tax, are superfluous in the present context.
‡ Version 2010.01.13 was the original. Version 2010.01.13a made a correction concerning the effect of income tax on prices.
Version 2010.01.15 switched the “temporary” notations in Eqs.(9) and (10), justified the choice of time base for estimating the appreciation rate of land, and considered more pessimistic inputs into the price/earnings calculation [Eqs.(14) and (15)].
Version 2010.01.22 interchanged the names of “option (b)” and “option (c)”, added the subsection on financial regulation and the section on implementation and, in so doing, more thoroughly considered the effect of a holding charge payable by a mortgagee. Version 2010.01.22a recalculated the P/E ratio under the proposed reform, considering investors and home owner-occupants separately and allowing for existing rates and “land tax”. Version 2010.01.22b added the section on alternative rates with different treatment of home owners, and corrected an editing error (the assumed real appreciation rate for a site is 6% per annum, not 4.5%).
Version 2010.01.31 added an estimate of the “surcharge” on the rate on capital gains, and corrected a “typo” in the version numbers!
Version 2011.02.18 qualified the “Futility of financial regulation”.
(Version numbers are dates in the form YYYY.MM.DD, with alphabetical suffixes for revisions on the same day. Non-substantive textual improvements are not necessarily enumerated in detail.)
∗ This document is published as a “working paper” so that other authors have the earliest possible opportunity to cite its results in their own works (approvingly or otherwise), or to offer feedback (publicly at the Forum, or privately to the author).