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Abstract

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THE PROPERTY TAX AS A TAX ON VALUE:DEADWEIGHT LOSS

Richard Arnott and Petia PetrovaBoston College

April, 2002

Consider an atomistic developer who decides when and at what density to develophis land, under a property value tax system characterized by three time-invariant taxrates: , the tax rate on pre-development land value; , the tax rate on post-development residual site value; and , the tax rate on structure value. Arnott(2002) identi5ed the subset of property value tax systems which are neutral. Thispaper investigates the relative efficiency of four idealized, non-neutral property valuetax systems [i) 9Canadian: property tax system: ; ii) simple propertytax system: ; iii) residual site value tax system: ; iv)differentiated property tax system: ] under the assumption of aconstant rental growth rate.

JEL code: H2Keywords: property taxation, site value taxation, land taxation, deadweight loss

Corresponding authorrichard.arnott@bc.eduTel: 617 -551-3674; Fax: 617-552-1887;Department of Economics, Boston CollegeChestnut Hill, MA 02467, USA

2

1

2

developed

1 Introduction

The authors would like to thank Will Strange for proposing the topic of the paper, seminar participantsat the University of California, Berkeley, the European University Institute, GREQAM, QueenJs Universityand Syracuse University for helpful comments; Almos Tassonyi of the Department of Finance, Governmentof Ontario, Canada for calculating TorontoJs effective property tax rates for 1985; Ian Mead for bringingdata on effective property tax rates in the U.S. to our attention; Mark Liu for preparation of Figures 5 and7; and Shihe Fu for research assistance. The 5rst draft of the paper was written while Arnott was visitingthe Fisher Center at the University of California, Berkeley, the second while he was visiting GREQAM. Hewould like to thank both for their hospitality. We would like to dedicate the paper in memory of Louis-AndréGérard-Varet for his tireless efforts in encouraging the application of public economic theory to policy issuesin French local public 5nance.

This paper follows the literature in using 9property taxation: in two senses: as a generic term forthe wide variety of systems of taxing land and buildings, and for the speci5c form of taxation in which adeveloped property is taxed on the basis of its market value. Hopefully, the usage will be apparent fromthe context.

1

Through the centuries land and real property taxation have taken many forms. Land hasbeen taxed on the basis of area, foot frontage, and agricultural rent generated. And realproperty has been taxed on the basis of the number of windows, chimneys, or balconies,property rents, and estimated property values, among other things. A central tradeoffin the choice of how to tax land and structures is between efficiency and ease of taxcollection. Foot frontage is easy to measure but taxing foot frontage gives rise to long,narrow lots; taxing the number of windows is simple but leads to windows being brickedup in structures built before the tax was imposed, and to structures built subsequentlyhaving a small number of large windows; and so on.

In the Anglo-Saxon countries at least, the dominant debate today vis-à-vis land andreal property taxation concerns the choice between land/site value taxation, propertyvalue taxation, or some hybrid. The de5ning difference between these taxes concernsthe tax base of properties: under property taxation, the assessed market valueof the developed property is taxed; under site value taxation, the tax base subsequentto development is the imputed value of the land; under differentiated property taxation,the imputed values of land and structure are both taxed but at different rates. Thesame tradeoff occurs. Site value taxation in its purest form is non-distortionary, butsubsequent to development measuring such site value is fraught with difficulty. At theother extreme, property taxation is relatively easy to apply since property values can beestimated quite accurately from market transactions, but is distortionary P encouraginginefficiently low capital intensity in construction. Confronted with this tradeoff differentjurisdictions have made different choices. Property taxation is the norm in North America;in mainland China, site value taxation is employed; while Australia and New Zealand (andPittsburgh) have chosen differentiated property taxation.

An essential element of the debate entails quantifying the deadweight loss associatedwith the various forms of property taxation. The traditional analysis due to Cannan(1899, reprinted 1959) and Marshall (1961) has two distinctive features. First, it is partialequilibrium, analyzing the effects of taxing a single property in isolation. Land is treatedas being completely inelastic in supply, so its taxation is non-distortionary; a building

2

3

3

average

when

imputedresidual

raw

Hamilton (1975) introduces zoning into this model, and lays out a set of conditions under which theproperty tax becomes a non-distortionary bene5ts tax.

is treated as perfectly-elastically-supplied, so its taxation is distortionary. The seconddistinctive feature of the Marshallian analysis is that it treats the taxes as falling on rentsrather than P as is actually the case P on values. The deadweight loss generated bythe structure component of the property tax can then be portrayed diagrammatically asa conventional deadweight loss triangle.

One line of subsequent work (most notably, Mieszkowski (1972)) has analyzed propertytaxation from the perspective of static, general equilibrium theory à la Harberger. In thebasic variant of the model, the structure component of the property tax is viewed as a taxon capital in the building sector. A more sophisticated variant recognizes that differentjurisdictions tax property at different rates. The rate of the structure componentof the property tax is viewed as a tax on capital in the building sector, and jurisdiction-speci5c deviations in the tax rate from the average rate as generating excise tax effects.This branch of the literature continues in the Marshallian tradition by treating the taxesas falling on rents rather than on values.

Another line of subsequent work retains MarshallJs partial equilibrium perspective butemploys a dynamic analysis P speci5cally capital asset pricing theory P and treats thetaxes as falling on values rather than rents. Shoup (1970) investigated the effect of prop-erty taxation on a developerJs choice of to construct a 5xed project on a vacant lot,taking the time path of rents as given. Arnott and Lewis (1979) extended ShoupJs analysisto allow for variable building density. Capozza and Li (1994) subsequently investigatedhow these results are modi5ed by uncertainty, with rents being generated by an exoge-nous stochastic process. A closely related group of papers has focused on the neutrality ofsite value taxation. A neutral tax does not alter the developerJs choice of timing or den-sity, and therefore generates no deadweight loss. The 5rst three papers (Skouras (1978),Bentick (1979), and Mills (1981)) came to the unorthodox conclusion that site valuetaxation is distortionary. It was subsequently shown that this result hinges on how post-development site value is de5ned. Once an immobile and durable building is constructedon a site, the market provides a valuation for the property (site and building together)but not separate valuations for the site and the building. Thus, post-development sitevalue must be . Skouras, Bentick, and Mills all de5ned post-development sitevalue as property value minus structure value, which is now termed site value,and hence showed that residual site value taxation is distortionary, discouraging density.Tideman (1982), following Vickrey (1970), demonstrated that the orthodox conclusionthat site value taxation is neutral is restored if post-development site value is instead de-5ned as 9what the market value of the land would be if there were no building on the site(though in fact there is):; this alternative de5nition is termed site value. The policydebate these papers spawned (e.g., Netzer (1998), Tideman (undated), and Mills (1998))has concentrated on the practicability of employing either de5nition; in particular, howmight post-development residual site value and raw site value be estimated in practice,and how accurate would such estimates likely be? The majority view is that residual sitevalue could be more easily and accurately estimated than raw site value. Less accurate

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deadweightloss

property

Source: Calculated from Ontario Ministry of Municipal Affairs and Housing, Municipal Analysis andRetrieval System (MARS) Database.

Source: CMHC Rental Market Surveys. Over the period the rental growth rates on bachelor, one-bedroom, two-bedroom, and three-bedroom apartments were .84%, .90%, 1.00% and .93%.

Fisher and Peters (1998), Table 4.3, provides data on the lowest and highest effective property tax ratesin 1992 for a sample of cities within a state, for a selection of states. IndianaJs 5gures are 3.72%, 4.39%;IowaJs 4.23%, 4.68%; and MinnesotaJs 4.81%, 5.30%. Thus, the effective property tax rate for Toronto isby no means an outlier.

estimation would not only result in a tax system that was perceived as more capriciousand hence less fair, but would also likely lead to more corruption in assessment and morewasteful litigation in assessment appeals. Thus, the central tradeoff is between the greaterefficiency of the raw site value tax and the lower administrative costs (broadly speaking)of the residual site value tax. And the magnitude of the deadweight loss associated withresidual site value taxation is an essential element of the debate.

This paper contributes to this strand of the literature by investigating theassociated with alternative property tax systems, treating the taxes as taxes on values

rather than rents and in a partial equilibrium context. More precisely, it considers thesubset of property tax systems that can be characterized by three time-invariant tax ratesP one on pre-development land value, a second on post-development structure value,and a third on post-development residual site value. And for this subset of property taxsystems, it relates the deadweight loss from taxation applied to the single property to thethree tax rates, as well as to the time path of rents, the form of the structure productionfunction, and the interest rate. Particularly neat results are obtained for the 9Canadian:property tax system, which exempts land prior to development from taxation and thentaxes value subsequent to development (hence taxing post-development residualsite value and structure value at the same rate, ). Under the simplifying assumptionsthat agricultural rent is zero and that Uoor rent grows at a constant rate , it is shown thatthe present value of property tax revenues is maximized by setting the post-developmentproperty tax rate equal to the growth rate of Uoor rent; a higher property tax rate putstaxation on 9the wrong side of the Laffer curve:. The marginal deadweight loss associatedwith the revenue-maximizing tax rate is, of course, in5nity. At lower tax rates the marginaldeadweight loss is shown to be ; if therefore Uoor rent grows at two percent, theapplication of a one percent property tax (i.e., one percent of property value) generatesa 100% marginal deadweight loss P the marginal dollar of tax revenue collected has asocial cost of two dollars. In 1985, the average effective property tax rate in the Cityof Toronto for residential (six storeys or less) housing was 1.1% and for multi-familyresidential (more than six storeys) 4.2% , while the annual growth rate in real apartmentrents in the Toronto CMA between 1979 and 1989 was less than one percent. Theseobservations suggest that the Toronto property tax has been highly distortionary. Similarresults are obtained for many other jurisdictions.

Such back-of-the-envelope calculations are, of course, subject to numerous quali5ca-tions, but do indicate P as its critics have argued P that some forms of property taxationmay be very inefficient, and accordingly that switching to less distortionary but adminis-tratively more costly forms of property taxation merits serious policy consideration.

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We assume throughout that exogenous variables and parameter values are such that asset values are5nite.

Section 2.1 introduces the basic model in the absence of taxation. The rest of Section2 introduces property taxation, and derives the general formulae for the present valuesof tax revenue collected and of deadweight loss. Section 3 applies the results to fourbroad classes of property tax systems, employing numerical examples. Section 4 presentsquali5cations, discusses possible extensions, and concludes.

Since the theory is developed at length in a companion paper (Arnott [2002]), its presen-tation here will be compact.

The model is essentially that presented in Arnott and Lewis [1979]. An atomistic landownerowns a unit area of undeveloped land. He must decide when to develop the land and atwhat density (Uoor-area ratio). Once built, the structure is immutable; no depreciationoccurs and no redevelopment is possible. He makes his decisions under perfect foresight.To simplify even further, it is assumed that the interest rate, the price per unit of capital,and the structure production function are invariant over time, and also that land prior todevelopment generates no rent. The following notation is employed:

time ( today)development timecapital-land ratiostructure production function ( )rent per unit Uoor area at time P Uoor or structure rentinterest rateprice per unit of structure capital

The structure production function indicates how many units of structure are producedwhen units of capital are applied to the unit area of land. For concreteness, one maythink of as the number of units of rentable Uoor area per unit area of land (Uoor-arearatio), or less precisely but more intuitively as the number of storeys in the building (whichassumes an exogenous coverage ratio).

The developerJs problem in the absence of taxation is

(1)

The 5rst-order conditions are

(2)

(3)

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Figure 1: First-order conditions without taxation

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Eq.(2) states that, 5xed, development time should be such that the marginal bene5tfrom postponing construction one period (the one-period opportunity cost of constructionfunds) equal the marginal cost (the rent forgone). Eq.(3) states that, 5xed, capitalshould be added to the land up to the point where the increase in rental revenue due toan extra unit of capital, discounted to development time, equal the unit price of capital.

Figure 1 portrays the 5rst-order conditions in T-K space. Both 5rst-order conditionsare positively-sloped, and the second-order conditions for an interior maximum requirethat rents be growing at development time and that the 5rst-order condition for besteeper than that for (which, with a constant rate of rental growth, is equivalent to therequirement that the elasticity of substitution between land and capital in the productionof structure be less than one). Multiple local interior maxima are possible and mightindeed occur due to cyclical Uuctuations, but to simplify the analysis we assume thatthere is a unique interior maximum, which is the global maximum.

We shall have occasion to use several different asset values. To simplify notation,we write these values on the assumption that development takes place at the pro5t-maximizing development time and density; for example, we write for post-development

instead of .Post-development property value is

(4)

Some property tax systems (e.g., Australia, New Zealand and Pittsburgh) tax post-development structure value and post-development site value at different rates. Because of

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By de5nition, . With smoothly growing rents, if the land remains undeveloped after the pro5tmaximizing development time has passed , conditional on the land being undeveloped at time it ispro5t-maximizing to develop it right away, in which case . It is possible, however, that the housingmarket is in a slump at time so that even though the pro5t-maximizing development time has passed,conditional on the land being undeveloped at time it is pro5t maximizing to develop later, in which case

.

the spatial 5xity of structures, land and structure value are not separately observable afterdevelopment. Thus, post-development structure and site values are values. Theliterature on the neutrality of land value taxation has analyzed two different concepts forpost-development land or site value. The 5rst, , denoted by , equalsproperty value minus (depreciated P though here no depreciation is assumed) structurevalue:

(5)

The second site value, denoted by , is what the land would be worth at timewere it vacant, even though in fact it is developed:

(6)

where is the pro5t-maximizing development time conditional on the land beingundeveloped at time , and the corresponding pro5t-maximizing capital-land ratio.Since no depreciation is assumed, post-development is simply . Pre-development is

(7)

Because development occurs at the pro5t-maximizing time and density,

(8)

In what follows we ignore the taxation of raw site value since in our opinion the difficultyof estimating it would render its taxation impractical. We should, however, note thata hypothetical property tax system which taxes pre-development land value and (post-development) raw site value at the same rate, and exempts (post-development) structurevalue from taxation, is neutral P does not affect the developerJs choice of developmenttime and density, and hence entails no deadweight loss. Since the developerJs tax liabilityover time is independent of her choices, raw site value taxation is lump sum and so doesnot affect her decisions.

We restrict our analysis to the class of property tax systems characterized by threetime-invariant tax rates: the tax rate on pre-development land value, ; the tax rate onpost-development residual site value, ; and the tax rate on post-development structure

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Under the property tax systems in most Canadian provinces, pre-development agricultural land is taxedon the basis of what it would be worth if it were held in agricultural use forever. Under our assumptionthat land prior to development generates no rent, this corresponds to a zero tax rate on pre-developmentland value.

value, . We shall examine four different types of property tax systems. Under aproperty tax system, ; the tax rates on pre-development land valueand post-development residual site value and structure value are all the same. Undera property tax system, ; property is untaxed prior todevelopment , while after development property value is taxed, which is equivalent totaxing post-development residual site value and structure value at the same rate. Undera site value tax system , with ; pre-development landvalue and post-development residual site value are taxed at the same rate while post-development structure value is exempt from taxation. Finally, a propertytax system is like the common property tax system, except that the common tax rate onpre-development land value and post-development residual site value is higher than thaton post-development structure value: .

The rest of this section treats the general case. In the next section, we shall explorethe properties of the above four different types of property tax systems using numericalexamples.

We 5rst derive the asset valuation formulae and the corresponding 5rst-order condi-tions. Post-development residual site value is

(9a)

Differentiation with respect to yields

which has the solution

(9b)

Thus, the tax on structure value increases the cost of capital by the tax rate on structurevalue, while the tax on residual site value increases the post-development discount rateby the tax rate on residual site value. Pre-development land value equals

(9)

which, employing the procedure above and using (8), yields

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(11)

Figure 2: First-order conditions with taxation

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(10)

Hence, the pre-development land value tax increases the pre-development discount rateby the tax rate on pre-development land value.

The developer chooses and so as to maximize (10). The 5rst-order conditions are

(11)

(12)

Eq.(11) states that optimal development time occurs when the marginal bene5t frompostponing development one period equals the marginal cost. The marginal bene5t equalsthe savings from postponing construction cost one period, which equals construction coststimes the user cost of capital, , plus the savings in site/land value tax payments,

. The marginal cost equals the rent forgone. Eq.(12) states that capitalshould be added to the site up to the point where the discounted rent attributable to thelast unit of capital equals the discounted value of the user cost, with the discount rateequal to the interest rate plus the tax rate on post-development residual site value.

The effects of each of the three tax rates on pro5t-maximizing development time anddensity can be derived with the use of Figure 2 which is the same as Figure 1 except

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Note:*Building earlier at higher density can be ruled out.

This intuition is correct for the special case of a constant growth rate of rents, but not generally. See

for the presence of property taxation. We assume that rents are 9on average: rising overtimes. Under this assumption, the geometric implications of the second-order conditions

are qualitatively the same as for Figure 1. Consider 5rst . From (11),

; from (12), the assumption that rents are on average rising over

time implies that the denominator is positive. A rise in the pre-development land value

tax rate therefore causes (11) to shift up. From (12), . Thus, as intuition

suggests, a rise in the pre-development land value tax rate causes earlier development atlower density. These and the other comparative static results with respect to andare recorded in Table 1.

Comparative static effects of tax rates on development time and density

- ?* ?*- ?* ?*

Since the inefficiency due to a property tax derives from 9how far from neutral: theproperty tax system is, it is of interest to characterize neutral property tax systems. Formost of the paper, we shall focus on the special but central case where Uoor rent grows ata constant rate. For this case, Arnott (2002, Prop. 2) gives the result that: When Uoorrent grows at a constant rate , a neutral property tax system has the properties that

(13)

and provides two different intuitive explanations. The 5rst is casual, the second exact.A residual site value tax system has no effect on the developmenttiming condition (see (11)), but by increasing the discount rate causes the developmentdensity condition to shift down, resulting in earlier development at lower density. Takethis as the starting point and consider how , and should be modi5ed to restoreneutrality. First, capital should be subsidized to offset the depressing effect of residualsite value taxation on development density. But from (11), the subsidization of capitaladvances development by reducing the marginal bene5t from postponing development.The development timing condition, which was undistorted with residual site value taxa-tion, becomes distorted, leading to excessively early development. This can be correctedby setting the pre-development land value tax rate below the post-development site valuetax rate. This intuition suggests that a neutral property tax system has and

. The precise intuition is that the tax system described in (13) is equivalent to a

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site rent tax system with a timeWinvariant tax rate (post-development site rent is de5nedas rent net of amortized construction costs) which is neutral. Thus, how distortionary aproperty tax system is depends on how far it deviates from site rent taxation at a constantrate.

De5ne to be the discounted (and brought forward) social surplus from the site,evaluated at time . This equals the discounted social bene5t from the site, which equalsthe discounted revenue it generates, minus discounted construction costs. Thus,

(14)

Letting denote the pre-tax situation, the after-tax situation, and the deadweightloss from the site evaluated at time :

(15)

The social surplus from the site accrues to landowners, in the form of land value lessbrought-forward tax payments (before development) or property value less brought-forwardconstruction costs less brought-forward past tax payments (after development), , andto the government, in the form of discounted (and brought-forward) tax revenues, .Hence,

(16a,b)

(16c)

Eq. (16c) indicates that deadweight loss may be calculated as the loss in landownersurplus minus tax revenue.

With a tax on pre-development land value, the value of tax revenue collected dependson when the tax was 5rst imposed. Let and possibly represent this date, and

denote the value of tax revenue collected prior to development. Then

using from (10)

(17a)

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we examinethe effects of a property tax system applied to an undeveloped site from today on.

from today forward.

Let denote the value of the revenue collected after development. Then

using (9a)

using (14) and . (17b)

Also,

(17c)

The landownerJs pre- and post-tax present-value surpluses are

(18a)

and

(using (17a)). (18b)

In evaluating property tax systems, we assume that there is currently no prop-erty tax system in place and a choice is to be made concerning what property tax systemto apply from today forward. This choice would be uninteresting if the site is alreadydeveloped since property taxation would then have no real effects. Thus,

Thisconceptual excercise has two important implications. First, if the pro5t-maximizing de-velopment time computed per (11) and (12) is positive, then the pre-development landvalue tax is 5rst applied today, i.e. Second, if the pro5t-maximizing developmenttime computed per (11) and (12) is negative, then (11) is replaced by the condition thatdevelopment will occur at the most pro5table time

12

Suppose , is 5nite and . Then, from (17c) and (18b), and. If, furthermore, , , and are all small, then the government expropriates the entire

surplus from the site with no distortion. The 5rst result states that if the government initially imposesthe pre-development land tax in5nitely far into the past at a rate such that , it expropriatesthe entire surplus from the site. The second result indicates that this expropriation can be achieved withessentially no distortion if additionally the tax rates are sufficiently small. The practical relevance of thisneutrality result is open to question!

There is a problem with our conceptual exercise. Consider two property tax systems A and B. Choosingbetween the two tax systems today, A is preferred to B. However, if the choice were to be made ten years fromnow, B might be preferred to A. Such time inconsistency could arise if, for example, both tax systems yieldedthe same pro5t-maximizing development time and density, but tax system A generated more discountedrevenue than B from on while tax system B generated more discounted revenue from on.

′

′′

V V

V

V

V V

V

V

�

R � �

R �

R � �

L

L

�

R � �

R �

R � �

L

L

L

D � �R

R D

� � �

+ �

( + ) �

�

( + ) �

˜

˜

˜ ˜ ˜

+ ˜

( + ) ˜

˜

( + ) ˜

� � � ′

� ′

�

� ′

� ′

∞� �

� � � ′′

� ′′

� ′′

� ′′

� ′′

� � �� � � ��� �

� �� �

� �∫

� � �� � � ��� �

� �� �

� �

iT Ta

Ta

a iTa

a i Ta

a a

b iTb

b

a i Ta

a

T

iu iT

iT Ta

Ta

a iTa

a i Ta

a a

b iTb

b

a i Ta

a

b a

b a

TT

T > , t ,

V T e e V e

Y V T e

Y V T e Y V

V T e V

V T e V

T < , t ,

Y r u Q K e du pKe

V T e e V e

Y V T e

Y V T e Y V

V T e V

V T e V

T < , T .t T < T >

t t V

V V

V V ,

�˜ 0

� 0 = 0

(0) = ( �) 1 = (0) 1

(0) = (0) ( �)

(0) = (0) ( �) = (0) ( (0))

(0) = ( �) = (0)

(0) = ( �) = (0)

� 0 = 0

(0) = ( ) ( )

(0) = ( ˜) 1 = (0) 1

(0) = (0) ( ˜)

(0) = (0) ( ˜) = (0) ( (0))

(0) = ( ˜) = (0)

(0) = ( ˜) = (0)

� 0 ˜ = 0= 0 � 0 � 0

= 0 = 0 : (0) = (0)

(0) = (0) (0) (0)

(0) = (0) + (0) + (0)

The equations derived earlier in this subsection were general. We now particularizethem to the conceptual excercise we are performing. Let denote pro5t-maximizingdevelopment time computed per (11) and (12), and denote the pro5t-maximizingdevelopment time from today forward.

If the following system of equations applies: (14), (15), (16a,b,c) withand

(17a )

(17b )

(17c )

(18a )

(18b )

If the following system of equations applies: (15), (16a,b,c,) with and

(14 )

(17a )

(17b )

(17c )

(18a )

(18b )

In all the examples we shall consider, whenSince by assumption no tax revenue is raised before , whether or ,

landowner surplus at equals land value at . Thus, from (16c)

or

(19)

13

13

13

V

V

V

′

′

′

′

′

� �

� �

� �

b a b b

b a a a

� �

� �� �

� �L L R D L

L R D L

� �

� ��

� �

�

�

�

( + )( )

( + )( )

( + )( )

0

0

t t t t . V t t ,V t t t t . V ,

T

3 Four Property Tax Systems

( ) = ( ) + ( ) + ( ) ( ) = ( )( ) = ( ) + ( ) + ( ) (0) = (0)

= 0

a

T,K S

K

S

i T t

V

S

V K

S

i T t

S

K

S

i T t

V

V

V S K V

K S

S V

today

pro�t-maximizing structural densitydecreases with and is independent of and

� 0

( ) =max( ) ( )

+

+

+

:+

+( ) ( ) +

( + ) ( + )

( + )= 0

:( ) ( )

+

+

+= 0

( )

( )=

+

+

= ( )0 (0)

=1ln( + )( + )

( + ) ( ( ))

�

T <

V tr T Q K

i � �

i �

i �pK e .

Ti � �

i � �r T Q K

i � i �

i �pK e

Kr T Q K

i � �

i �

i �p e .

Q K

Q K K

i �

i � �.

QQ/Q K

� � � K K �K < . r r

T�

i � i � � p

i � r Q K �,

The general relationship is Also in general, so thatThus (19) applies when which holds since no tax revenue

is collected prior to .

which states that , immediately after the imposition of any form of property taxation,land value plus discounted tax revenue plus discounted deadweight loss equals land valueprior to taxation.

The analysis obtains the deadweight loss from applying alternative property tax sys-tems to a particular site in isolation. Extending the analysis to determine the efficiency ofalternative tax systems applied to an entire jurisdiction requires a fuller model which ac-counts for the heterogeneity of sites as well as (unless the jurisdiction is completely open)for the endogeneity of rents. Thus, the reader should be cautious not to over-interpretthe paperJs very partial equilibrium analysis.

Throughout this section we shall assume that structure rents grow at a constant rate overtime, which considerably simpli5es the analysis. To simplify the algebra, we ignore thecomplications which arise when ; we do, however, take account of these complicationsin our numerical examples. To further simplify notation, we omit the superscript onafter-tax variables, when there is no danger of ambiguity.

With this assumption, from (10):

(20)

The corresponding 5rst-order conditions are

(21)

(22)

Dividing the two 5rst-order conditions yields

(23)

By the second-order conditions, the elasticity of substitution of is less than one. Sinceis therefore increasing in K, (23) implies that

. Thus, we may writewith Letting , (21) and (23) imply

(24)

14

�

′′

VV

14

14

V S K c� � � � >( = 0 = 0)

�� �

� �

�

Proposition 1

� � � � ��

�� � � � �

� �

R � � � � �

D � � � � �

��

R � �

3.1 Canadian property tax system ,

K S

V

V S K S

K V

T

S

K

S

T iT

iTb

iT

V

a b c

ciT

c

0 0 1

= 0

(0) = ( ) ( )1

+1

+

+

(0) =( ) ( ) ( ) ( )

= 0

= +1ln

+

(0) =( ) ( )

( )( + )

This result was 5rst demonstrated in Arnott and Lewis (1979).

� �� � > Q < � <

� � � �� �

I

r T Q Ki �

e

i � �pK

i �

i �e e .

r T Q K

i �pK e

r T Q K

i �pK e .

�

T T�

i � �

i �.

r T Q K � e

i � i � �.

If the rate of rental growth is constant and if the second-order conditionsof the developer�s pro�t-maximization problem are satis�ed, then: i) development densityis decreasing in and independent of and ; ii) development time increases withand and and decreases with .

which indicates that pro5t-maximizing development time increases with and anddecreases with . The second-order conditions, , , and , guarantee thatthere is a unique maximum, which is interior. These results are of sufficient importancethat we record them in:

Following the discussion of the previous section, we shall take . Then from (17c),(14), and (20):

(25)

Finally, from (14) and (15):

(26)

We now consider four idealized property value tax systems. We start with what wehave referred to as the Canadian property tax system, since it is the neatest and easiestto analyze.

Many Canadian provinces and some U.S. states tax agricultural land on the basis of whatit would be worth if it were held in agriculture forever (Youngman and Malme (1993)).Since pre-development land rent in our model is zero, application of such a tax systemwould result in no tax liability prior to development, which corresponds to . Itcan be seen from (21) and (22) that this property tax system causes both the timing anddensity 5rst-order conditions to shift down, and from (23) in such a way that developmentoccurs at the same density as in the absence of taxation but at a later date P as displayedin Figure 3. That density is unaffected by the property tax system considerably simpli5esthe calculations. From (24):

(27)

From (25), the discounted revenue raised from the tax is

(28)

15

Figure 3: The Canadian property tax system

FOCTFOCT

FOCK

FOCK

b

b

a

a

K

T

2

� �

� �

i�

i�

i�

� � �

R ���

� � ���

D � ��

��

b iTb

iTb

b c

c

a

c

iT

c

iT

b

c

b c

c

�� � � � �

� �� �

� � � �� �� �

� � �� � )

(0) =( ) ( )

=( ) ( )

( )

(0) = (0)( ) +

(0) =( ) ( )

+=

( ) ( )

+

= (0)+

(0) = (0) 1+

( ) +

Vr T Q K

i �pK e

�r T Q K

i i �e .

Vi�

� i �

i �

i � �.

Vr T Q K

i � �pK e

r T Q K

i � �

�

ie

Vi �

i � �

V�i � i�

� i �

i �

i � �.

From (20) and (21):

(29)

Substituting (29) and (27) into (28) yields

(30)

From (20):

(using (21))

(using (27) and (29)). (31)

Then from (19):

(32)

Two results are of sufficient interest that we record them as:

16

�

′′

15

15

� �

0

+

0

00 0

0

cc

c

c

c

b b

b b

�

DR

L R R D

∞�

LR D �

Proposition 2

Table 2

A somewhat mechanical explanation is provided in Appendix 2.

� ��

� �

MDWL∂ /∂�

∂ /∂�.

K Qi . � . r . p .

T V .

� K T V MDWL

. . . . . .

. . . . .

. . . . . .

t V tV .

.

r

rr

�

r

r.

=

=(0)

(0)

= = 1= 03 = 02 = 024731 = 2 2408

= 50 (0) = 1

(0) = (0) (0) = (0) (0)0 1 50 1 0 0 001 1 84 7 354 530 116 1 002 1 104 9 192 577 23003 1 119 3 125 563 312 3 0

= 0 (0) = (0) = 0(0) + (0) + (0) 3 0

3 0

19% 23%

=2

1ln = 34 7

Under the Canadian property tax system:a) The revenue-maximizing tax

rate is . b) The marginal deadweight loss (MDWL) is .

Proof:a) Follows directly from (30).

b) The result then follows directly from (30) and (32).

Notes: i) recall that under our assumption that no tax revenue is collected priorto , ; ii) recall (19), that the imposition of taxation at doesnot change and; iii) a marginal deadweight loss of impliesthat as the tax rate is raised on the wrong side of the Laffer curve, a dollar reductionin revenue is associated with an increase in deadweight loss of .

The results are so simple that there should be a simple explanation of them; so far,however, an incisive explanation has eluded us.

Part a) of Prop. 2 is interesting since it suggests that jurisdictions in which the rentalgrowth rate is less than the property tax rate may be on the wrong side of the Laffer curve.Part b) suggests that the Canadian property tax system can be highly distortionary ateven modest tax rates.

We now present a numerical example. We choose units so that , assumethat and , and choose and so that development inthe no-tax situation occurs at and

Numerical example with Canadian property tax

Because pro5t-maximizing structural density is independent of the property tax rate,the above results hold independent of the form of the structure production function. Theresults, displayed in Table 2, indicate that the effects of the Canadian property tax aresubstantial. With the chosen parameters, a two-percent tax rate, for example, causes landvalue to fall to only of pre-tax value, generates a deadweight loss of of pre-taxvalue, and causes development of the land to be postponed 55 years!

If the tax is imposed at a location for which is lower, with the exogenous functionsand other exogenous parameters held 5xed, the only change is that everything occurs

later. If, for example, , everything occurs years later (see (24)).

17

Figure 4: The simple property tax system

FOCTa

FOCKa

FOCTb

FOCKb

K

T

�

s

s

� ��

�

�( + )

V K S s( = = 0)� � � � >

R � � �

�

iT s

s

T

s s

a

s s

i T

3.2 Simple property tax system

r T Q K e� �

i � i �

�e

i � � i �.

V�r T Q K

i � i � �e .

(0) = ( ) ( )+

( )( + ) ( + )( + )

(0) =( ) ( )

( + )( + )

It bears repeating that the above results describe the effects of imposing the propertytax on a single parcel of land. The general equilibrium effects, which could be examined ina growing, fully-closed monocentric city model, would be considerably more complicated.

We now consider a simple tax system in which the tax rates applied to pre-developmentland value and post-development property value are the same. This is the tax systemmost Americans would identify as 9the property tax:.

As displayed in Figure 4, the simple property tax system causes both the timingand density 5rst-order conditions to shift to the right (see (21) and (22)) such that: i)development density falls; and ii) development time may either be postponed or broughtforward, depending on parameter values and the form of the structure production function.

From (25) and (21):

(33)

From (20) and (21):

(34)

And then, from (29), (32) and (33):

18

� �

�

�

�

�

1

1 1

1

1

1

1

� �

��

′

� ′

� � ′

0 1

10

0 0

1

1

1

1 ( + )

1

�

��

��

��

�� s

��

s

��

D � R

� � �

�

�

� �

���

� ��

�

R � � � �

� �

D � � � �

� �

� � � �

� � � � ��� � �� �� ��

� � � �

� �

� � � �� �

� � � �

b a

iTb

s

s

iT

�

s s

s s

s

s s

s

s s

ss

s

iT s T

s

a

s s

i T

iTb

s

s

iT

(0) = (0) ( (0) + (0))

=( ) ( )

( )

( + ) ( ) ( )

( + )( )

( ) = (1 + )

=1

1

=+

( ) =+

=1ln

( + )+1

ln( + )

+

ln+

+1

ln( + )

+

1 0 ln+

ln+

( ) ( ) = ( + )+

(0) =+

+

+

(0) =( + ) +

(0) =( ) ( )

( )

( + )

+

V V

�r T Q K

i i �e

� � r T Q K

i � i �e .

Q K c c K ,

��

K�c

i � �Q K c

�

i �

T�

p i �

c r

�

�

c i �

i � �,

i �

i

�

�

i �

i

i �

i � �

� >i �

i�

i � �

i �.

r T Q K i � p�c

i � �.

p�c

i � �e

� �

i �

�e

i � �

V�p

i � �

�c

i � �e

�r T Q K

i i �e

� � p

i �

�c

i � �e .

(35)

Unfortunately, the results for this type of property tax system are not as neat as thosefor the Canadian property tax system because the tax alters structural density, whichcomplicates the algebra. We can, however, obtain some analytical results for the specialcase of CES production functions. We assume that

where in the elasticity of substitution between land and capital in the structure

production function. Then from (23):

and . (36a,b)

From (21):

(37)

from which it follows that development is postponed or brought forward according to

whether is greater or less than zero, or

since according to whether is greater or less than

And from (21) and (36a):

(38)

Inserting (38) into (33) W (35) yields

(33 )

(34 )

and

(35 )

19

1 1 1� � � �

� � �

′

Table 3

��

�� �

�

�

�

�

�

� �

b

a

s

s

s

�

s s s

(a) ,

(b) ,

(c) ,, , , ,

0 1

+

0

0

0

0 1

0

0 1 10 1 0

1

+ +

L R R R D

��

��

���

DR R � �

�R R R R �R

R RR

c cK Q

� . , . , .t V

� K Q T V MDWL.

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .� . c .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .� . c .

. . . . . . . . . .. . . . . . . .. . . . . . . .

� . c .Parameter values in all panels i . � . p . r . c .

T >T <

T KQ V

r Q K �

i � i � �,

Q K c c K K cc c r

p i � �.

� . ,� . , . � . , � . , . � . , � . ,

. .

Notes: 1. *The formulae presented in this subsection are for the case . Ifaccording to (37), development occurs today. The calculations are modi5ed

accordingly. (Eq. (21) does not apply and is set to . is then determined from(22) alone, from which follows. is then determined from (20), from

(26), and as a residual per (19) from (25). where

and ).

2. is calculated from (17a ), and as3. The revenue-maximizing tax rate and maximum revenue are:

= = 1= 25 5 75

= 50 = 1

(0) = (0) (0) (0) (0) (0)0 1 1 50 1 0 0 0 0 0 00

01 794 909 57 6 177 138 632 770 052 0 3902 693 843 65 7 039 105 721 826 135 3 4103 630 794 73 1 009 070 709 780 212 1 22

= 25 = 1 14471

01 500 750 44 1 192 106 597 703 105 1 3002 300 600 46 2 050 075 624 699 252 1 6503 250 500 50 0 014 048 563 611 375 1 13

= 50 = 1 5

01 125 422 3 56 243 009 503 512 245 4 9902 037 281 0 101 0 463 463 436 2 0703 016 208 0 051 0 386 386 563 1 41

= 75 = 3 375: = 03 = 02 = 2 2408 = 024731 = 5

� 0� 0

0(0) (0)

(0) (0) =( )

( ) ( + )

( ) = 1 + + =( + )

(0) (0) (0) = (0) (0)= 25

= 0176 (0) = 8286; = 5 = 0140 (0) = 725; = 75 = 00850(0) = 517

We shall now use these formulae in a numerical example. We employ the same para-meters as in the numerical example of the previous subsection, and choose and suchthat in the absence of taxation. We shall consider three values for the elas-ticity of substitution in the structure production function: . In the absenceof taxation the site is developed at and has . The results are displayed inTable 3.

Numerical example with simple property tax

With a low elasticity of substitution for the structure production function, the devel-oper responds to the tax by building somewhat later at slightly lower density. Compare

20

0.2 0.4 0.6 0.8R(0)

0.2

0.4

0.6

0.8

1

D (0)

τ s ,σ=0.75

τ s ,σ=0.5

τ s ,σ=0.25

τ c

Figure 5

D R

� .

� .

� .

� . .

� . , . , .

� . � .� . � . , .

= 25

= 25

= 75

6 7

(0) (0)= 25 5 75

= 25 = 5= 75 ( 5 75)

Table 2 with Table 3A. The relative efficiency of the Canadian tax system and the simpletax system with can be gauged by comparing the deadweight losses for a givenamount of revenue collected, or vice versa. Recall that with a constant rate of rentalgrowth, the tax rates for a neutral property tax system are given in (13). It is not obviouswhich of the Canadian or simple tax systems deviates more from the neutral tax system.But for the parameter values of the numerical example, with the simple tax sys-tem with is the more efficient. For intermediate values of the elasticity of substitution,the developer responds to the tax principally by building at moderately lower density,and for high values by building considerably earlier at considerably lower density. Thetax system becomes more distortionary the higher the elasticity of substitution, and for

the Canadian tax system is more efficient than the simple tax system. Based onempirical studies which estimate the elasticity of substitution between land and capitalin the structure production function (reviewed in McDonald(1981)), the current wisdomis that lies between and ; and in this range the efficiency of the two tax systems issimilar.

Figure 5 plots versus for the Canadian property tax system and the simpleproperty tax system with and . As noted above, the simple property taxsystem is more efficient the lower the elasticity of substitution between land and capitalin the structure production function. Furthermore, the Canadian property tax systemis less efficient than the simple property tax system with and but moreefficient with . Since empirical evidence suggests that lies in the range ,for the parameters of the example at least the Canadian and simple property tax systemsare comparable in efficiency.

21

FOCKa

FOCKb

Figure 6: Residual site value taxation

FOCT

K

T

�

r

r( + )

� �

� �

K V S r

��

�

� �

( = 0 = )� , � � �

R � � �

�

D � R

� � �

iT T

r r

a

r r

i T

b a

iTb

iT

3.3 Residual site value tax system

r T Q K e�

i � i

�e

i � i � �.

V�r T Q K

i � i � �e .

V V

�r T Q K

i i �e

�r T Q K

i i �e .

(0) = ( ) ( )( ) ( + ) ( + )

(0) =( ) ( )

( + ) ( + )

(0) = (0) ( (0) + (0))

=( ) ( )

( )

( ) ( )

( )

Residual site value taxation is employed in China (Wong(1999)) and in some Australianstates (Youngman and Malme (1993)). Residual site value taxation leaves unchanged theposition of the timing 5rst-order condition and causes the density 5rst-order condition toshift down P as displayed in Figure 6. As a result, as the tax rate rises developmentoccurs earlier and at a lower density.

From (25) and (21):

(39)

From (20) and (21):

(40)

And from (29), (39), and (40):

(41)

As with the simple property tax system, we assume that the structure productionfunction is CES. Then from (23):

22

�( = 0

)V S L K

��

�

� �

� �

�

�

�

�

1 1

1

1

1

1

� � � > , �

10

0 0

1

1

1

1 ( + )

1

��

��

��

�� r

��

r

��

�

� �

�

R � � � �

� �

D � � � �

rates

differentiated

� � � �

� � � � ��

� �

� � � �� �

� � � �

r r

r s

r

r

r

r

iT T

r r

a

r r r

i T

iTb

r

iT

3.4 Differentiated property tax systemunrestricted

=+

( ) =+

=1ln +

1ln

( + )

+

( ) ( ) =+

(0) =+ ( ) ( + ) ( + )

(0) =( + ) ( + ) +

(0) =( ) ( )

( ) +

K�c

i � �Q K c

�

i �,

� �

T�

ip

c r

�

�

c i �

i � �

r T Q K ip�c

i � �.

ip�c

i � �e

�

i � i

�e

i � i � �

V�ip

i � i � �

�c

i � �e

�r T Q K

i i �e

�p

i �

�c

i � �e .

and (42a,b)

which are the same expressions as for the simple property tax, but with replacing .From (21):

(43)

and

(44)

Then:

(45)

(46)

and

(47)

We now turn to the numerical example. The parameters are exactly the same as forcorresponding case for the simple property tax system example. The results are displayedin Table 4.

Comparing this table with Table 3, it is evident, for the example considered at least,that residual site value taxation is more efficient than simple property taxation. The onlydifference between the two tax systems is that residual site value taxation exempts struc-tures. The supplementary taxation of structures under the simple property tax system isso distortionary that in a number of the cases treated P those with higher rates of taxationand higher substitution elasticities P setting the tax equal, the revenue raised fromresidual site value taxation is higher than under simple property taxation. Put alterna-tively, holding the tax rate constant, revenue would be increased by exempting structuresfrom taxation.

There is potentially a considerable variety of hybrid property tax systems. One is theneutral property tax system discussed in Arnott (2000). Here we discuss the

23

+

16

16

�

�

�

�

Table 4

r r r

L

K

L

(a)

(b)

(c)

anticipated

L R R R D

�

��

R RR

� K Q T V MDWL.

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .� .

. . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .� .

. . . . . . . . .

. . . . . . . . .

. . . . . . . . .� .

T >T <

� . ,� . , . � . , � . , . � . , � . ,

. .

�

�

�

Notes: *1. The formulae presented in this subsection are for the case . Ifaccording to (43), development occurs today. The calculations are modi5ed

accordingly.2. The revenue-maximizing tax rate and maximum revenue are:

(0) = (0) (0) (0) (0) (0)0 1 1 50 1 0 0 0 0 0 00

01 794 909 43 2 237 128 608 736 028 0 1702 693 843 40 2 0833 103 744 847 070 1 1303 630 794 38 4 0351 076 780 856 109 4 14

= 25

01 500 750 29 7 256 089 574 663 081 0 7502 300 600 20 6 107 054 644 698 195 3 7703 250 500 15 3 0588 033 619 651 293 1 56

= 5

01 172 492 0 320 000 512 512 168 0 4202 132 433 0 180 000 596 596 216 1 2703 112 399 0 121 000 615 615 265 3 64

= 75

� 0� 0

= 25= 0267 (0) = 8574; = 5 = 0167 (0) = 7035; = 75 = 0415(0) = 619

There is a more basic logical Uaw in the standard rationale for a differentiated property tax system. Apure land value tax (tax on market land value prior to development and on raw site value after development),set at an in5nite rate, extracts a siteJs entire discounted surplus. No property tax system canraise more than this amount. To do so would require a negative landowner discounted surplus, which is notpossible with anticipation. Consider the effects of broadening the tax base to include structures. At lowtax rates, the addition of structures to the tax base does result in higher revenue. But above a certain taxrate, the revenue generated from structures is more than offset by the decline in revenue generated fromthe land deriving from the distortion caused by the taxation of structures.

Numerical example with residual site value taxation.

property tax system, employed in Australia, New Zealand, and Pittsburgh, under whichpre-development land value and post-development residual site value are taxed at thesame positive rate, and structure value at a different rate, where is the tax rate on9land value:. The standard rationale for this type of system goes as follows: Site valuetaxation is non-distortionary but does not raise sufficient revenue to 5nance the level ofpublic services demanded in a modern economy, and so is supplemented with distortionarystructure value taxation but at a lower tax rate. Since these jurisdictions measure post-development site value as residual site value, and since residual site value taxation isdistortionary, the standard rationale is Uawed. It is nonetheless of interest to enquire:Within this class of property tax systems, what ratio of is the most efficient and what

24

17

17

��

�

� �

�

�

1 1

1

1

3.4.1

10

0 0

1

1

1

��

��

�� L

��

�

� �

R � � � �

D � � �

efficiency locus

� � � �

� � � � ��

� � � �

� � � �

L L

K L

L

L

iT K T

K

L L

b K

L

iT

K L

L K

K L

It can however be shown that structure value should be taxed not subsidized P see Appendix 3.

� 0 � 0� 0

� 0; � 0= 0

� 0;

� 0

=+

( ) =+

=1ln

( + )+1

ln( + )

+

(0) =+

+ ( + )

( + ) ( + )

(0) = (0)+

+

( )

= 25= 0039 = 0251

862

T > T < .T >

T > T <T

T <

T >

K�c

i � �Q K c

�

i �.

T�

p i �

c r

�

�

c i �

i � �.

p�c

i � �e

� �

i �

e i � �

i � i � �

Y� �

i �p

�c

i � �e .

� , �

� . . � > � .� . � . ,

does this ratio depend on?The analysis is complicated by the presence of two regimes: and The way

we shall proceed is to: 5rst, examine the systems of equations that applies withwithout reference to the constraint that this system of equations applies when and onlywhen second, examine the systems of equations that applies with (and hence

) without reference to the constraint that this system of equations applies when andonly when and 5nally put the pieces together.

From (23), application of this differentiated property tax system results in constructionat lower than the efficient density. And since this tax system has the simple propertytax system and residual site value tax systems as special cases, it is clear from previousresults that its application may cause development to be either postponed or broughtforward. We continue to assume that structure production exhibits constant elasticity ofsubstitution. Thus, from (23):

(48a,b)

And then from (21):

(49)

From (25) and (21):

(50)

and

(51)

De5ne the to be the locus of that raise a given amount ofrevenue with minimum deadweight loss. Analytical characterization of the efficiency locusis algebraically messy. Consequently, we examine diagrammatically the efficiency locusfor the three examples considered in Tables 3 and 4.

Figure 7A displays iso-revenue contours, iso-deadweight-loss contours, and the corre-sponding efficiency locus for For all levels of revenue indicated, Therevenue-maximizing tax rates are and and the maximum revenueis . .

25

Efficiency Locus

Iso-DWL Curves

Iso-Rev Curves

Figure 7A: Efficient land/site and structure value tax rates: σ=.25

0.02 0.04 0.06 0.08τ K

0.02

0.04

0.06

0.08

0.1

0.12

τ L

Notes: What is labelled the "efficiency locus" is in fact the locus of tangency points of iso-revenue and iso-deadweight loss contours. The relevant portion of this locus runs from the origin to the maximum revenue point.

D R

K L

K

� � .

..

� .

.

=

0176829 (0) (0)

= 0

857

The simple property tax system is the same as the differentiated property system withthe constraint imposed that Thus, comparison of the differentiated and simpleproperty tax systems indicates the gains that can be achieved by taxing post-developmentresidual site value and structure value at different rates. With the corresponding simpleproperty tax system (from Table 3), the revenue-maximizing tax rate is and themaximum revenue . Plotting against for the differentiated property taxsystem and comparing the locus with the corresponding locus in Figure 5 for the simpleproperty tax system would indicate the proportional efficiency gain achievable at differentrevenue levels from employing differentiated rather than simple property taxation.

The residual site value tax system is the same as the differentiated property tax system,with the constraint imposed that Thus, comparison of the differentiated andresidual site value tax systems indicates the gain that can be achieved over residual sitevalue taxation by taxing structure value. The maximum revenue that can be achievedunder residual site value taxation is . Thus, for this example, the extra revenue thatcan be generated under the differentiated property tax system from being able to taxstructure value in addition to land value is quite modest.

26

0.02 0.04 0.06τK

-0.01

0.01

0.02

0.03

0.04

τL

Efficiency Locus

Iso-DWL Curves

Iso-Rev Curves

Figure 7B: Efficient land and structure value tax rates: σ=.5

Notes: What is labelled the "efficiency locus" is in fact the locus of tangency points of iso-revenue and iso-deadweight loss contours. The relevant portion of this locus runs from the origin to the maximum revenue point.

K

L

K L

K L

K L

� .� . � .

. � .� . . � . ,

. .

. .� . .

� . � . , ..

.. .

T > ,�,

� �

= 5= 0099 = 0150

728 = 5= 25 = 50140 725

0167 703= 75

= 0072 = 0229 5400122

499008 460

� 0

Figure 7B is the same as Figure 7A but is for (and the corresponding parametersfrom Table 3). The revenue-maximizing tax rates are and , and themaximum revenue is . Observe that is higher at the revenue maximum withthan with For the revenue-maximizing tax rate under the simple propertytax system is and the maximum revenue is . The improvement in efficiencyfrom being able to tax post-development site value and structure value at different ratesis small. Under the residual site value tax system, the revenue-maximizing tax rate is

and the maximum revenue is .Figure 7C is the same as Figures 7A and 7B but is for The revenue-maximizing

tax rates are and and the maximum revenue is . Under thesimple property tax system, the revenue-maximizing tax rate is and the maximumrevenue is , while under the residual site value tax system the corresponding 5guresare and .

These examples illustrate that, for residual site value taxation is more efficientthan simple property taxation for low levels of and less efficient for higher levels, whichis explained below. In all cases, the relative efficiency gains achieved from employingdifferentiated property taxation (with and set at optimal levels) rather than simpleor residual site value taxation appear quite modest; the robustness of the result is worthexamining. Finally, for the simple, residual, and differentiated property tax systems, thedeadweight loss due to property taxation appears to be more sensitive to the elasticity ofsubstitution between land and structures in the structure production function than to theform of property taxation employed, which points to the importance of obtaining moreaccurate estimates of this elasticity.

27

0.05 0.1 0.15 0.2

-0.01

-0.005

0.005

0.01

0.015

0.02

τK

τL Efficiency Locus

Iso-DWL Curves

Iso-Rev Curves

Figure 7C: Efficient land and structure value tax rates: σ=.75

Notes: What is labelled the "efficiency locus" is in fact the locus of tangency points of iso-revenue and iso-deadweight loss contours. The relevant portion of this locus runs from the origin to the maximum revenue point.

D R

��

∞

��

conditional on

V S K

a

KL

L

L L

K L

K

L K L

KL

L

3.4.2

3.4.3 Putting the pieces together

= 0

= 02) 577

� 0

0(0) (0) (0)

=+

= 0

=

� 0 ( )

= 50 ( ) = (0 0) � = 0� 0

� 0 � = 0

=+

� � > �

� . .

T <

. K QV

���

i � �, T

� �

T > . � , �T T �

� , T � , � , , TT >

T < T

���

i � �.

A differentiated Canadian property tax system under which andis possible. Indeed, the neutral property tax system identi5ed in (13) is an example,under which full surplus extraction with no deadweight loss is achievable. Recall that themaximum revenue with an undifferentiated Canadian property tax system (from Table 2,with is . Thus, for the Canadian property tax system differentiation of thepost-development tax rates generates signi5cant efficiency gains.

In this case, T is set to is then determined from (22) alone, from which follows.is then determined from (20), from (26) and as a residual per (19) from

(25). Since there are now two tax rates and only the capital 5rst-order condition, inthe light of the argument presented in Arnott(2002), it should not be surprising that by

setting revenue can be raised without distortion,

with the amount rising with until with full surplus extraction is achieved.

Turn to Fig. 7A, which applies to the case This case applies when aresuch that in (49) is greater than or equal to zero. Since in (49) is increasing inand decreasing in and since with is a positively-slopedlocus lying above the origin. Below the locus, the equations for apply, and abovethe locus those for apply. Below the locus, the efficiency locus is positively-

sloped; above the locus, it is given by Thus there is a discontinuity in

28

�

�

�

�

Table 5

� ∞

� ∞

R R∞ �∞ �∞ �

∞

� ∞

K L

K L

K L

L K L K

L

K

K

L

L K

K L

Local maximum 1 Local maximum 2

coincide,

T T

T

� , � �, TT� , � T

� , � �, T .

T < T >� � � K Q � � K Q T. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .

�

T > ,�

�� .

�� .

� �

T < T ,

� .

T

� . � . � ,

Notes: 1. Parameter values are the same as for the corresponding case of inTables 3 and 4.

2. indicates the global-maximizing set of tax rates and revenue.

� = 0 � = 0

� = 0

( ) = ( ); = 0= 50( ) � = 0

( ) = ( ) = 0

� 0 � 0(0) (0)

25 02 554 593 761 0251 0039 862 658 817 45 3950 02 753 410 676 0150 0099 728 399 666 38 6975 02 892 298 632 0092 0229 540 188 513 28 04

� 0

= 0= 0

=

� 0 = 0

1

= 0

= 0 02 = = 0

the efficiency locus as it crosses the locus; below the locus, the efficiencylocus takes into account that a rise in tax revenue affects two margins, timing and density,while above the locus, the efficiency locus takes into account that there is only thedensity margin.

Now consider determination of the revenue-maximizing tax rate. There are two localrevenue maxima. The 5rst is at here, timing is distorted withinstead of , but density is efficient conditional on timing. The second is the revenue-maximizing below or on the locus. If it is on the locus, it is dominated by

since that pair of tax rates is efficient conditional on If it isbelow the locus, there are two local maxima which must be compared; the former entailsdistortion on only the timing margin, the latter less distortion on the timing margin butmore on the density margin.

The numerical results are displayed in Table 5.

Numerical example with differentiated property value taxation.Revenue-maximizing tax rates.

A pattern is evident. For as the elasticity of substitution increases, the max-imum surplus extraction and at the revenue maximum fall. To understand these

results, consider 5rst the extreme case of Density is unaffected by taxation, andefficient timing can be maintained by setting (see (49)), with full surplus ex-traction being achieved by setting In this extreme case, therefore, residual sitevalue taxation is non-distortionary, while simple property taxation is distortionary. As theelasticity of substitution increases, both timing and density, and hence deadweight loss,become relatively more sensitive to than to (see (48), (49) and (51)) implying thatsimple property taxation increases in efficiency relative to residual site value tax system.For and in contrast, as the elasticity of substitution increases the maxi-mum surplus extraction rises and the revenue-maximizing tax rates remain unchanged.To understand the former result, consider 5rst the limiting case as approaches Thetiming and density 5rst-order conditions then almost implying that almost thesame surplus can be achieved at and an appropriately reduced density as at theno-tax optimum, and the appropriately reduced density is achieved with full surplus ex-traction with and At the other extreme with construction

29

inter alia

4 Concluding Comments

occurs at the same density as at the no-tax optimum but 5fty years earlier, which entailsconsiderable distortion.

This paper examined the deadweight loss due to the property tax when the property taxis realistically modeled as a tax on value rather than as a tax on rent. The analysis waspartial equilibrium, examining the effects of the property tax when it is applied to a single,small parcel of land, and paying no attention to the disposition of the tax revenue raised.To keep the algebra manageable, a number of simplifying assumptions were made. Mostnotably, the extreme case of in5nitely durable structures was considered. The landownerdecides when to build a structure on his vacant land and at what density, and subsequentlythat structure remains on the site forever with no depreciation. Thus, the deadweight lossdue to the property tax derives from its changing the timing and density of construction.

The property tax was modeled as a triple of time-invariant tax rates, the 5rst applied topre-development land value, the second to post-development (residual) site value (de5nedas property value minus construction costs), and the third to structure value (measuredby construction costs). A number of variants of the property tax were examined: i) the9Canadian: property tax system under which property value is taxed after development,with pre-development land value exempt from taxation; ii) the simple property tax systemunder which pre-development land value and post-development property value are taxedat the same rate; iii) the residual site value tax system under which pre-development landvalue and post-development residual site value are taxed at the same rate, with structurevalue exempt; and iv) the differentiated property tax system, which is like the residualsite value tax system except that structure value is taxed but at a different rate. Thepaper focused on the special case where the rate of rental growth is constant.

All four tax systems are distortionary (Arnott (2002) derives the property tax sys-tem that is neutral in the context of the model). The Canadian property tax systemcauses later development at unchanged density; the simple and differentiated propertytax systems have an ambiguous effect on development time but unambiguously discour-age density; and the residual site value tax system results in earlier development at lowerdensity. For the Canadian property tax system, the revenue-maximizing tax rate equalsthe growth rate of rents and the marginal deadweight loss equals the tax rate divided bythe growth rate of rents less the tax rate. The corresponding results for the other propertytax systems are not as neat, depending on the current level of rents and theelasticity of substitution between land and capital in the structure production function.For each of the property tax systems considered, for a set of plausible parameter valueswe computed deadweight loss as a function of the tax rate. Two results were particularlystriking. First, in all the numerical examples, the revenue-maximizing tax rate was lowerthan the actual effective property tax rate employed in many jurisdictions, suggestingthat some jurisdictions may be 9on the wrong side of the Laffer curve: with respect toproperty taxation. Second, in all the examples except for the Canadian property taxsystem, deadweight loss was strongly positively related to the elasticity of substitution

30

,

and

18

19

18 19

between land and capital in the production of structures, and the revenue-maximizing taxrate strongly negatively related to it, which points to the importance for policy analysisof precise estimation of this elasticity.

In the course of our analysis, we encountered a general conceptual issue of how tocompare the efficiency of two interWtemporal tax systems. Though doing so entails timeinconsistency, we compared their efficiency from today forward.

In the paper, we provided a reasonably thorough analysis of the efficiency effectsof a variety of idealized property tax systems, but in the context of a speci5c, partialequilibrium model. It remains to be seen how robust our results are. There are severalimportant issues for future research:

1. We modeled the property tax as applying to a single, atomistic property. Howshould the model be generalized to a metropolitan area or to an entire country, and howwill this generalization affect the results?

2. We assumed that structures are completely immalleable. Does introducing depre-ciation and property rehabilitation and redevelopment signi5cantly alter the results?

3. We made a number of simplifying assumptions: no technical change, a constant

31

An appealing way to address this question would be to analyze the effects of alternative propertyvalue tax systems in the context of a model of growing, monocentric city with completely durable housingmodel in which developers have perfect foresight (Fujita (1976), Arnott (1980), and Wheaton (1982)). Ouranalysis generalizes straightforwardly to an open city since equilibrium housing rents are then unaffectedby property taxation. In a closed city, however, housing rents are affected by property taxation, whichconsiderably complicates the analysis.In a growing monocentric city with completely durable housing different locations have different devel-

opment times, which complicates the comparison of property tax systems to be implemented today. Forproperties that have already been developed, the (unanticipated) imposition of a property tax from todayforward entails no distortion; for properties that will be developed far off into the future, the bulk of thepresent value of revenue collected from the tax will be collected prior to development. Thus, a tax systemthat is relatively efficient at some locations may be relatively inefficient at others, and the overall efficiencyof a tax system entails averaging over locations.

Think of the standard partial equilibrium tax analysis. The deadweight loss for a given tax rate or agiven amount of tax revenue is higher, the larger are the demand and supply elasticities. Looking at a singleproperty for which rent is 5xed is analagous to assuming a perfectly elastic demand curve. Thus, it is naturalto conjecture that the deadweight loss from a given property tax system, whether for a particular propertytax rate or for a given amount of tax revenue collected, is lower the less elastic is demand. Accordingly,looking at a single property with exogenous rent tends to overstate the deadweight loss due to propertytaxation.This intuition can be formalized by considering a growing closed (exogenous population) monocentric

city in which demand is such that housing unit size is 5xed the elasticity of substitution between landand capital in the production of the Uoor area is zero. At a given point in time, housing unit size, theUoor-area ratio of housing, and population are all independent of the property tax system in place; so tootherefore is the residential area of the city and the boundary of urban development. In this special case,therefore, all property tax systems have no effect on the density and timing of development, and hencegenerate no deadweight loss. If the elasticity of substitution in housing production is non-zero, however,property taxation generates deadweight loss by inducing inefficient factor proportionsPstructural density.This line of reasonong leads to the conjecture that the deadweight loss due to a property tax system

is higher the greater the elasticity of demand for housing and the greater is the elasticity of substitutionbetween capital and land in the production of housing. The difficulty in formalizing the conjecture is indeciding what to hold 5xed while these elasticities are being varied.

�

20

20

( ) ( )r t Q K ipK

In analyzing the efficiency of alternative property tax systems with development controls and zoningregulations, it is important to recognize that they are imposed to deal with perceived market failure.

interest rate, no change in construction costs, zero pre-development land rent, and aconstant growth rate of Uoor rent. How does relaxing these assumptions affect our resultsqualitatively and quantitatively?

4. Our analysis ignored uncertainty, which is surely important in property develop-ment. Since Capozza and Li (1994) introduced stochasticity into the Arnott-Lewis model,one obvious approach is to extend their analysis to treat a variety of property value taxsystems.

5. We assumed that the developer has complete discretion concerning when and atwhat density to build. But in practice his choice is constrained by a variety of develop-ment controls and zoning regulations. If they are so strict that they result in the samedevelopment time and density with and without a particular property tax system, theproperty tax system is neutral.

6. In an earlier version of the paper, we contrasted our analysis of the property taxas a tax on value with the conventional analysis which treats the property tax as a taxon rent, especially with respect to measurement of deadweight loss. This topic meritsconsideration.

7. It is shown in Arnott (2002) that a tax on 9net site rent: (equal to zero prior todevelopment and after development) is neutral. Net site rent taxationis presumably not employed because net site rent is unobservable or observable onlyat prohibitive cost. Our analysis treated observability only implicitly. Perhaps a moreexplicit treatment would be fruitful.

In the introduction, we emphasized that the choice of property tax system entails atradeoff between conventional deadweight loss and administrative costs broadly speaking.At one extreme is a classical land value tax system, which is nonWdistortionary but verycostly to administer. Our paper focused on quantifying deadweight loss. As importantbut more difficult will be to quantify the other side of the tradeoff.

32

�

��

��

��

��

2

( )( )

( )( )

Appendix 1

�

�

�

�

�

�

�� � �

� � �

�

�

1

(1 )( )(1 )

+(1 )

( )(1 )

R ���

D � ��

��

R � ��

D �

� ���

���

��

��

i�

i�

sa

��

a b

a b

i �� �

� i �� �

�� i �� �

� i �� �

� �� �� � ��� �

� � �� � � �)

� � �

� � � �� �� ���� � � � ��

� � � �

� � � � �

b c

c

b c

c

biT a

iT b

s

s

T

s s

biT a

iT b

s

s

iT a

iT b s

i � T T

a b s s

s

s

s

i � T T

s

s

iT a

iT b s

s

(0) = (0)( ) +

(0) = (0) 1+

( ) +

(0) = (0)( ) ( )

( ( ) ( ) )

+

+

( )

( + ) ( + )

(0) = (0) 1( ) ( )

( ( ) ( ) )

+

+

( ) ( )

( ( ) ( ) )=

+

=1ln

++1

ln+

+

=1

(1 )ln

++ ln

+

=+

+

( ) ( )

( ( ) ( ) )=

+

+

Vi�

� i �

i �

i � �

V�i � i�

� i �

i �

i � �.

Vi r T Q K e

� r T Q K e

� �

i �

e i �

i � i � �

Vi r T Q K e

� r T Q K e

� �

i �.

r T Q K e

r T Q K e

i

i �e

T T�

i �

i

�

�

i �

i

i �

i � �

� �

i �

i�

i �

i � �

ei

i �

i � �

i �.

r T Q K e

r T Q K e

i

i �

i � �

i �.

(Not for publication)Relative Efficiency of the Canadian and Simple Property Tax Systems

We start by recording the formulae for revenue raised from the Canadian property taxsystem, and the deadweight loss:

(30)

(32)

To obtain the corresponding formulae for the simple tax system will require someadditional algebra. Rewrite (33) and (35), using (29):

(A1.1)

(A1.2)

From (36b) and (37):

(A1.3)

with

(A1.4)

so that

(A1.5)

Substituting (A1.5) into (A1.3) yields

(A1.6)

And substituting (A1.6) and (37) into (A1.1) and (A1.2) yields

33

0 0

1

���

���

�

D � ��

R ��

� ��

�

b s

s

s

b

s

s

s

s s

s

s

s

c

(1 )( )(1 )

(1 )( )(1 )

(1 )

� � �� � � � )

� � � �� � �� � � � )

i� �

� i �� �

i� �

� i �� �

s�

� s� �

(0) = (0) 1+

+

+

(0) = (0)+

+

+

( + ) ( + )

+

( + )

V� �

�

i

i �

i � �

i �.

Vi

i �

i � �

i �

� �

�

i �

� i � �

c r

p i �

i � �

c i �.

��

(A1.7)

(A1.8)

The relative efficiency of the two tax systems for a given set of parameter values canbe calculated as follows. Set and from (A1.7) and (A1.8) calculate the correspondingdeadweight loss and tax revenue. From (30) calculate the which raises the same amountof tax revenue and from (32) calculate the corresponding deadweight loss. Then comparethe deadweight losses.

34

+ +

�

′ �

�

�

�

∞ �

� �

� �

�

0

0

( )

Appendix 2

∫

� �

� �� �

� �ad valorem ad

valorem

�

�

�

� �

�

�� �

�� �

��

�

�

��

i �i

�i

i �i

i V �

i

i Vi

i �i

i �i

it

i � T

iT iT

S

K

S

V

S

K

S

V KS

SS

S

V S

IK

V K SS

S

( ) = =

( )

�( ) = ( )

: ( ) = 0

: ( ) = 0

�( ) = ( )+

+

+

= 0

�( ) = ( )+

+

+

= 0 =+

=+

= 0 = 0

=

= 0 =

( ) =

(1 + ) =

=+

r t e dtr

i ��.

Q K eKe D e ,

K,D �Q K D pKD.

D �Q Ki �

iD pK

K �Q K D pD ,

K,D �Q K Di �

i � �

i �

i �pKD .

� .

K,D �Q K Di �

i � �

i �

i �pKD.

� ���

i � �

��

i � �.

� �

��

i.

� � �

Q K D ��

i �.

� � �

� � �i �

i � �.

(For publication)Some Isomorphisms

Some insights can be gained by viewing our model as a static model, with pricesand quantities in present value terms. One unit of structure constructed today generatespresent discounted revenue of Interpret this as the exogenous

consumer price of structure. Accordingly, the quantity of structure produced on a unitof area of land P in present value terms P is , and the quantity of capitalemployed P in present value terms P is . De5ning the developerJs netrevenue or pro5t function in the absence of taxation is

(A2.1)

The corresponding 5rst-order conditions for pro5t-maximization are

(A2.2a)

(A2.2b)

which have straightforward interpretations.With taxation, from (20) the developerJs pro5t function is

(A2.3)

The isomorphisms arise when For this special case,

(A2.4)

Comparing (A2.1) and (A2.4), we obtain the following isomorphisms.

1. A property tax system with and is isomorphic to a pro5t

tax at rate This is the neutral tax system identi5ed in Arnott (2002).

2. A property tax system with and is isomorphic to a tax on the inputKD at rate

3. A property tax system with and P a Canadian property tax systemP is isomorphic to an tax on the output at rate The

tax drives a wedge between the producer and consumer price. Since the consumerprice is exogenous (and the demand function therefore perfectly elastic) ,

where is the producer price. From (A2.4), Combining these two

formulae establishes the result.

35

�

i �i�

′

′

� � � �

� �

S

c c c

Sc S

iT

c

c

c

c

S

c

�

R �R

� � ⇒ �

�

���

�

�

�

�

( )

(0) = ( ) = ( ) ( ) ( (1 + ) = )

( ) (0)

: ( ) + ( ) ( ) = 0 = =1

=( )

( )+

1

= 0 =1

( + )

=+

= =

= = 0 = =

= =

= =

;

q Q K D .

� �q � � � q � , � � � .

q � �

� q � � � q �� �

��

ε.

dq

d�qQ K

Q K

dK

d�

i �

i D

dD

d�.

dK

d�

dT

d� � i � �.

� �i �

i � �, � � , D e

dK

d�

dK

d�

d�

d�

dD

d�

dD

dT

dT

d�

d�

d�

iD

��.

ε�

q

dq

d�

i �

�,

��

i �� �.

i �

�i �

��.

This result allows us to provide an explanation, albeit a rather mechanical one, forthe results presented in Prop. 2. De5ne Then the tax revenue from theCanadian property tax system may be written as

using (A2.5)

where is the supply curve. Maximizing with respect to gives an expressionfor the tax-revenue-maximizing producer price:

(A2.6)

All that remains is to solve the elasticity of supply:

(A2.7)

From (23) and (27):

(A2.8)

Recalling that and gives

and (A2.9)

Combining (A2.7) and (A2.9) yields

(A2.10)

from which it follows that the revenue-maximizing tax rates are

and (A2.11)

Thus, the revenue-maximizing tax rate under the Canadian property tax system equalsthe growth rate of rents because:

i) the Canadian property tax system with an exogenous time path of rents is isomorphicto an output tax in a static model with perfectly elastic demand;

ii) the revenue-maximizing tax rate for an output tax in a static model with perfectlyelastic demand equals the inverse of the elasticity of supply;

iii) the elasticity of supply in the static model isomorphic to the dynamic model of the

Canadian property tax system is and

iv) an output tax rate of in the static model maps into a Canadian property tax

rate of

36

�V� .= 0

Unfortunately, the pre-development land tax rate enters the developerJs pro5t function,(A2.3), in a way that does not correspond to the way in which linear input, output orpro5t taxes enter the pro5t function in static models. As a result, there seems to be nosimple isomorphisms when

37

�

�

�

�

1

1

1

1

�

�

�

�

�

�

�

�

�

Appendix 3

( 0]

1

1

1

( 0]

( 0]

1

K

��

��

��

K

K

��

L

L

L

� D � R

D �

D � � � �

D � � �� �

�

D �

R

R�

� � �

� � � �

�

� � � � � �

� � � � � �� �

� �

� �� �

K

KK K

K � i,

K

K

L K K

iT

K K

K

K

L

K

K K

iT

L

K

K

K � i,

K � i,

K L

iT

T

L L

K

K T

K

L L

LK

TK

L L

� 0 0

( 0](0)

0(0)

0

(0)0

(0)=

+

+

1

+

=1

( + )

(0)=

+

+

( )

( + ) ( + )

=+ ( + )

(0)0

(0)0

(0)=

+

1

( + ) ( + )+ ( + )

( + ) ( + )

+( + )

( + ) ( + )

T > , � >

� ' i, ,d

d�

d

d�>

d

d�

d

d�

� �

i �p

�c

i � � � �idT

d�e .

dT

d� � i �.

d

d�

� �

i �p

�c

i � �

i � �

� � � i �e

p�c

i � �

�

� i �,

d

d�.

d

d�>

d

d�p

�c

i � �e

i �

�e

i � i � �

idT

d�

� �

i �

e i � �

i � i � �

�dT

d�

e i � �

i � i � �

(Not for publication)With an Efficient Differentiated Property Tax System, when

We prove this by showing that for while

From (51):

(A3.1)

From (49):

(A3.2)

Combining (A3.1) and (A3.2) yields

(A3.3)

so that

From (50)

(A3.4)

38

1

1

+

�

�

�

�

�

�

��

1

1

( 0]

��

L

L

�� L

K � i,

� �

� � � �

R�

� � � � �

�

� �

R

� � �

� � �

K L

iT

T

L L

K

K

L T

L L

L

iT K

K

T

L

K

K L L K

K L

(0)=

+

1

( + ) ( + )

( + )

( ) ( + )+

( + )

( + ) ( + )

=+ ( + )

+( + )

(0)0

( ) ( ) ( 0]0

( )

d

d�p

�c

i � �e

i �

�e

i � i � �

i � �

� i � i �i � e

i � i � �

p�c

i � �e

�

� i �

e

i �,

d

d�> .

� , � � > i � � i,

� < i � < i � .

Substituting in (A3.2) gives

(A3.5)

so that

Thus starting at (with ), increasing from a level into increases revenue and decreases deadweight loss. The model is not well-de5ned for

or

39

References

RegionalScience and Urban Economics

Journalof Political Economy

Journal of Political Economy

American Economic Review

Industrial Incentives: Competition among AmericanStates and Cities

Journalof Urban Economics

Urban Studies

LocalGovernment Tax and Land Use Policies in the United States: Understanding theLinks,

Principles of Economics

Journal of Urban Economics

Journalof Public Economics

National Tax Jour-nal

Illinois Real Estate Letter

Economics of the Property Tax

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[2] Arnott, R. (2002) 9Neutral Property Taxation: http://FMWWW.bc.edu/EC-V/Arnott.fac.html

[3] Arnott, R.J., and F.D. Lewis (1979) 9The Transition of Land to Urban Use:, Vol. 87, pp.161W169.

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[5] Capozza, D., and Y. Li (1994) 9The Intensity and Timing of Investment: The Caseof Land: , Vol. 84, pp. 889W904.

[6] Cannan, E. (1959) 9Minutes of Royal Commission on Local Taxation, 1899: reprintedin Readings in the Economics of Taxation, R. Musgrave and C. Shoup, eds. (Home-wood, IL:R.Irwin), 171W201.

[7] Fisher, S. and A.H. Peters (1998)(Kalamazoo, MI: Upjohn).

[8] Fujita, M. (1976) 9Spatial Patterns of Urban Growth: Optimum and Market:, Vol. 3, pp. 209W241.

[9] Hamilton, B.W. (1975) 9Zoning and Property Taxation in a System of Local Gov-ernments: , Vol. 12, pp. 205W211.

[10] Ladd, H.F. (1997) 9Theoretical Controversies: Land and Property Taxation:

Ch.2 (Cheltenham, U.K.: Edward Elgar).

[11] Marshall, A. , 9th ed., 1961, Appendix G (1961:MacMillan).

[12] McDonald, J. (1981) 9CapitalWLand Substitution in Urban Housing: A Survey ofEmpirical Estimates: , Vol.9, pp.190W221.

[13] Mieszkowski, P. (1972) 9The Property Tax: An Excise Tax or a Pro5t Tax ?:, Vol.1, pp. 73W96.

[14] Mills, D.E. (1981) 9The NonWneutrality of Land Value Taxation:, Vol. 34, pp. 125W129.

[15] Mills, E.S. (1998) 9Is Land Taxation Practical?: , Fall,pp. 1W 5.

[16] Netzer, D. (1966) (The Brookings Institution).

40

Land Value Taxation: Can It and Will It Work Today?

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Constructionand Real Estate Review

An International Survey of Taxes on Landand Buildings

[17] Netzer, D., Ed.(1998) (Cam-bridge, MA: Lincoln Institute).

[18] Shoup, D. (1970) 9The Optimal Timing of Urban Land Development:, Vol. 25, pp. 33W44.

[19] Skouras,A. (1978) 9The NonWneutrality of Land Taxation: , Vol.30,pp.113W134.

[20] Tideman, N.T. (1982) 9A Tax on Land Is Neutral: , Vol.35,pp. 109W111.

[21] Tideman, N. (undated) 9Taxing Land is Better than Neutral: Land Taxes, LandSpeculation and the Timing of Development: mimeo.

[22] Vickrey, W.S. (1970) 9De5ning Land Value for Taxation Purposes:, inby D.M. Holland, ed. (Milwaukee, WI: University of Wisconsin

Press).

[23] Wheaton, W. C. (1982) 9Urban Residential Growth under Perfect Foresight:. Vol. 12, p 1W21.

[24] Wong, K.C. (1999) 9The Evolution of Land Value Taxation in China:, Vol.3, pp. 1W4.

[25] Youngman, J.M. and J.H. Malme (1993)(Deventer, The Netherlands: Kluwer).

41