Incentivizing residential land development

Abstract

The owners of undeveloped urban land are often blamed for restricting housing supply and thereby driving up house prices in the face of increasing demand. This article shows how greater variation in amenity values across a housing market reduces competition between developers and makes delaying development more attractive to landowners. Competition can be enhanced, and development of land accelerated, by reducing this variation. In particular, governments can increase housing supply in more desirable areas by taking actions that boost the amenity value of land in less desirable areas.

Keywords:

• Real estate
• housing supply
• urban development
• land banking
• real options

Acknowledgements

I gratefully acknowledge helpful comments from Chris Parker and two anonymous referees.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 However, recent research suggests that marginal reductions in supply constraints alone are unlikely to solve the housing affordability crisis (Anenberg & Kung, 2018).

2 This is also true for underdeveloped land. For example, the ability to delay investment reduced the supply elasticity of infill housing in the San Francisco Bay Area (Murphy, 2018).

3 For example, the UK government has conducted inquiries every few years into aspects of developer behavior (Barker, 2004; Callcutt, 2007; OFT, 2008; Letwin, 2018).

4 See Dixit and Pindyck (1994) and Guthrie (2009) for introductions to real options analysis and Titman (1985) for one way to estimate the option value of vacant land. Real options analysis has been used to model equilibrium in markets for urban land, starting with Capozza and Helsley (1990), who presented a model of development timing in which land closer to the central business district generates higher rental income than land further out. Subsequent authors have considered extensions including endogenous development intensity (Capozza & Li, 1994) and construction lags (Bar-Ilan & Strange, 1996).

5 Guthrie (2010) proves this using a model of equilibrium in real estate markets. Grenadier (2002) shows that when firms are identical and there are no restrictions on development policies, competition eliminates the option value.

6 Guthrie (2010) proves that option values are positive, and can be substantial, when land is heterogeneous and developers are atomistic. Grenadier (1996) analyzes the outcome of duopoly competition in a more general investment-timing game.

7 The model used here is based on the one in Dixit and Pindyck (1994, Chapter 9). Pawlina and Kort (2006) and Huisman and Kort (2015) modified this investment-timing model by allowing the two competing firms to have different investment costs. This article examines the effects of asymmetric benefits, which is more important for understanding real estate markets.

8 If the land is owner-occupied then it generates the same amount of imputed rent.

9 Large developers will have a more complicated objective function if the development of this unit of land affects the value of the rest of their portfolio. For example, development of this unit of land will reduce the market-clearing rent, which will reduce the value of other land (developed and undeveloped) owned by the developer in the same housing market. In this case, what matters is the effect of investment (by the developer or its competitor) on the value of the developer's portfolio in this housing market. Including such portfolio effects would complicate the model greatly as it would require specification of relevant parts of the developer's portfolio.

10 Derivations of the key equations in this section are contained in the appendix.

11 That is, if developer $i=1$ is the leader then developer $3-i=2$ is the follower. Similarly, if developer $i=2$ is the leader then developer $3-i=1$ is the follower.

12 The functional forms of $V_1\left(x\right)$ and $V_2\left(x\right)$ imply that the expected rate of return from holding undeveloped land equals $r+\beta \lambda .$ In contrast, once development is complete the expected rate of return is just $r+\lambda .$ As $\beta >1,$expected returns are higher while waiting to invest, which reflects the greater risk associated with waiting.

13 Note that even though the owner of the low-value land is indifferent between leading and following when $x=0.1470,$ once the high-value land has been developed, the owner of the low-value land will choose to wait much longer, until $x=0.2940,$ before developing its own land.

14 In equilibrium, the high-value land is not developed until the development payoff equals 140; the low-value land is not developed until the development payoff equals 270.

15 The leader’s payoff in the top graph will also fall slightly, reflecting the fact that the low-value land is developed sooner, which reduces the present value of the rental income generated by the land. This leads to a reduction in the option value of the high-value land, but does not affect the timing of development.

16 In terms of the model here, the risk premium $\lambda$ is increased until the leader’s payoff ${L_1(\widehat{x}}_1^L)$ in Equation (2)(2) $$L_i\left(x\right)=\left\{\begin{array}{c}\frac{q_i{D}_{1}x}{r+\lambda -\mu }+\left(\frac{q_i{D}_2{\widehat{x}}_{3-i}^F}{r+\lambda -\mu }-\frac{q_i{D}_1{\widehat{x}}_{3-i}^F}{r+\lambda -\mu }\right){\left(\frac{x}{{\widehat{x}}_{3-i}^F}\right)}^{\beta }-I \mathrm{i}\mathrm{f} x<{\widehat{x}}_{3-i}^F,\\ \frac{q_i{D}_{2}x}{r+\lambda -\mu }-I \mathrm{i}\mathrm{f} x\ge {\widehat{x}}_{3-i}^F.\end{array}\right.$$(2) equals zero. That is, the leader’s payoff for the high-value land equals zero when it is evaluated at the optimal development threshold, holding the follower’s development threshold constant at its actual level ${\widehat{x}}_2^F.$

17 Leishman (2015) describes the series of housing reviews in the UK during the first decade of this century and evaluates the effectiveness of the resulting policy changes.

18 See Meen (2005) for a discussion of the economic analysis underlying the Barker review.

19 Individual metropolitan areas also conduct their own reviews. For example, Molior (2012, 2014) examined the barriers to housing development in London for the Greater London Authority.

20 Barker (2004, p. 140) concluded that giving planning permission to a number of small sites is preferable to giving it to a single large site. Callcutt (2007, p. 193) recommended that ‘in disposing of large sites for housing development, the government and its agencies should wherever possible either break up a proportion of each site into smaller parcels for separate disposal or stipulate as a condition of sale that the primary purchaser should do so.’

21 For example, Nygaard and Meen (2013) find such a path dependency in London, estimating that 30% of the distribution of modern house prices can be explained by factors predating the Second World War.

Additional information

Notes on contributor

Graeme Guthrie is a financial economist whose current research interests include applications of real options analysis to problems in corporate finance, corporate governance, and real estate markets. He is the author of Real Options in Theory and Practice (2009) and The Firm Divided: Manager-Shareholder Conflict and the Fight for Control of the Modern Corporation (2017), both published by Oxford University Press.