JYH-BANG JOU
Graduate Institute of National Development, National Taiwan University, No. 1 Roosevelt Rd. Sec. 4, Taipei 106,
Taiwan, R.O.C.
E-mail: [email protected]
TAN LEE (Corresponding Author)
Department of International Business, Yuan Ze University, No. 135 Yuan-Tung Rd., Chung-Li, Taoyuan 320,
Taiwan, R.O.C.
E-mail: [email protected]
Abstract
This article employs a real options framework to investigate the design of taxation on both land value and
development in a competitive real estate market. We assume that developed properties reduce open space, and
thereby harm urban residents. However, ignoring this negative externality, landowners will develop properties
sooner than is socially optimal. A regulator can correct this tendency by imposing a positive tax on development
or a negative tax on land value. Alternatively, the regulator can implement both instruments simultaneously, in
which case an increase in the tax rate on development will be accompanied by an increase in the tax rate on land
value, and vice versa.
Keywords: Negative Externality, Real Options, Optimal Taxation
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Introduction
Several recent articles investigate how taxation on the market value of vacant land and on the costs to develop such land affects choices regarding the timing of development.
However, few studies discuss the normative aspect of these policy instruments, that is, why the regulator employs them in the first place. To the best of our knowledge, the only theoretical article that focuses on this issue is Anderson (1993a).1
Anderson constructs a non-stochastic model in which an owner of vacant land extends benefits to urban residents through the provision of open space. Modeling these benefits as an increasing function of the cash inflow received by the owner, he shows that the regulator can induce the landowner to delay developing property through the use of a Pigouvian subsidy. In this article we investigate an issue similar to Anderson (1993a), but different from Anderson, we derive the policy-maker’s optimal property taxation in a stochastic environment.2
Specifically, we consider a perfectly competitive real estate industry that consists of homogeneous landowners.3 We assume that developed properties reduce open space and thereby harm urban residents. Following Anderson (1993a), we assume that this external cost increases as landowners receive more cash flow. Landowners will ignore this externality, and will therefore develop properties sooner than is socially optimal. The regulator can correct
1 Irwin and Bockstael (2004) also consider externalities involving open space. However, they focus on how a
“smart growth”policy (such as a policy that preserves open space) associated with these externalities affects planned development timing rather than on the design of optimal property taxation.
2 Anderson (1993a) suggests that land development imposes external costs associated with increased traffic congestion, higher density, and attendant problems.
3 In this article we assume that landowners are also developers. We therefore use both terms interchangeably in what follows.
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this tendency by implementing a single instrument such as a positive tax on land development or a negative tax (i.e., a subsidy) on land value. In the first case, the regulator should increase the tax rate on development if the negative externality rises; in the second case, the regulator should decrease the subsidy to land value if the negative externality falls, demand uncertainty increases, demand for developed properties is expected to grow at a higher rate, or the discount rate decreases. Alternatively, the regulator can simultaneously implement both policy instruments. In this case, if the regulator increases the tax rate on development, he should also increase the tax rate (i.e., decrease the subsidy rate) on land value, and vice versa.
Our article is closely related to the real options literature such as Dixit (1991) and especially Grenadier (1995) while both of these papers abstract from the issue of externalities, they solve the competitive equilibrium associated with the maximization problem faced by a social planner.4 Similar to Grenadier, we assume that land development requires an initial lump sum construction cost. At any point in time, landowners who have developed properties will rent their properties. The market clearing condition requires that the spot price adjusts so that current supply equals stochastic demand. If the industry’s prospects become sufficiently favorable, new developers will find it optimal to develop properties. The decision to enter the real estate industry is analogous to the decision to exercise a call option on a real estate asset where the exercise price is the cost of development: when the value of entering the industry rises to the level of the development cost, new developers will enter
4 See Capozza and Li (1994), who also employ real options analysis. However, they focus on a representative landowner and investigate how taxation on property values both before and after development affects the landowner’s choices regarding development timing and capital intensity.
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such that no excess profits will exist.
When property development exhibits negative externalities, however, the optimal development timing decision for the competitive real estate industry and that for the centralized economy are different because the former will ignore the negative externality, while the latter will internalize it. We assume that the decision rule for each is determined by a different kind of social planner: the “naive”social planner ignores the externality and solves for the competitive equilibrium, and the “sophisticated”social planner internalizes the externality and solves for the centralized economy. We then investigate how a regulator may employ a positive tax on development and/or a negative tax on land value to induce the naive social planner to develop properties in accordance with the timing that the sophisticated social planner would choose.
In addition to analyzing the design of optimal property taxation, we also investigate how property taxation affects a developer’s choice of development timing in the competitive equilibrium. We find that a developer will delay development if either the tax rate on land value decreases or the tax rate on development increases. Our results therefore provide further support to Anderson (1986), who abstracts from uncertainty. Given our article focuses only on the development timing choice, our results cannot be directly compared to those articles that allow for the simultaneous choices concerning both the timing and the density (or capital intensity) of land development, such as Arnott (2005), Arnott and Lewis (1979), McFarlane (1999), and Turnbull (1988a; 1988b).
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The remainder of this article is organized as follows. “Basic Assumptions”section presents the assumptions in our model. “Optimal Development Timing Choices”section solves the development timing choice for both the competitive real estate industry and the centralized economy. In particular, we investigate how taxation on land value and development affects the timing choice for developers in the real estate industry. “Optimal Taxation on Land Value and Development”section reports the comparative-statics results on how various exogenous forces affect the optimal levels of these two taxation instruments.
“Numerical Analysis”section employs plausible parameter values to do numerical analysis.
The last section concludes with caveats and suggestions for future research.
Basic Assumptions
In this section we build a model that extends Grenadier (1995). Consider a competitive real estate industry with a large number of landowners, where each landowner owns one unit of vacant land.5 We assume that the units are small enough and the number of landowners are large enough such that the current total supply of developed properties may be represented as a continuum whose mass at time t is
Q t ( )
.At each point in time, the rent per unit of developed property,
P t , which evolves
d( ) such that it clears the market, is of the constant-elasticity form( ) ( ) ( )b 1
P t
d X t Q t
, (1)5 The model will yield identical results if developers are permitted to own more than one unit of vacant land, provided no single developer yields significant market power.
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where
1 b 0
andX t ( )
represents a multiplicative demand shock that evolves according to a geometric Brownian motion:( ) ( ) ( ) ( )
dX t X t dt X t d t
, (2)where is the instantaneous expected percentage change in
X t ( )
per unit time,
is the instantaneous standard deviation per unit time, andd ( ) t
is an increment of a standard Wiener process. Such a market is thus characterized by evolving uncertainty in the state of demand for the developed property. We assume that development, which reduces open space, harms urban residents. Similar to Anderson (1993a), we assume that the external cost increases as the cash flow from developed properties increases. Consequently, from the viewpoint of a “sophisticated”social planner who takes this externality into account, the marginal value of an additional developed property is reduced to( ) (1 ) ( ), 0 1,
c d