An empirical examination of the timing of land conversions in the presence of farmland preservation programs.

Over the past decades, an increasing number of state and local governments have adopted incentive-based mechanisms in an attempt to manage the pace and pattern of urban growth and the conversion of agricultural land. Under one such mechanism, landowners receive payment for voluntarily agreeing to forego conversion and accept easements placed on their land. Since the first "purchase of development rights" (PDR) program was implemented in 1974, over fifty-three state and local governments in the United States have collectively spent over $2.6 billion in public funds to preserve 1.6 million acres (American Farmland Trust 2005a,b). In 2002 the Federal government authorized $597 million in matching funds for farmland preservation over the 2002-2007 period. PDR programs enjoy continued taxpayer support; in 2003 alone, $700 million in state and local ballot measures were passed to provide funding for farm and ranch land protection (Trust for Public Land 2005).

In urbanizing areas where landowners can often choose to reap immediate financial rewards through development, PDR programs offer a means to continue farming while receiving remuneration for their development rights. Given the significant costs involved in preserving farmland--which averages approximately $2,000 per acre nationally--government agencies are increasingly interested in the effectiveness of these programs. Two studies have considered their effects on rates of urban development using aggregate (county level and crop reporting district) data and found limited evidence that they slow conversions (Miller and Nickerson 2003; Lynch and Carpenter 2003). A few microlevel studies have suggested that PDR programs may actually hasten the development of adjacent parcels by making this land more valuable in residential use (e.g., Irwin 2002; Irwin and Bockstael 2001). To our knowledge no studies have explored how the very existence of an option to participate in a PDR program affects landowners' development decisions. That is, even if a landowner ultimately chooses not to preserve, the existence of an option to do so may alter the time at which conversion occurs. Real options theory suggests that this may be the case--and, in particular, that the existence of the PDR option may delay conversion decisions. If so, these programs may generate benefits (by retaining land in farming longer even if it is ultimately developed) beyond those provided by the farmland enrolled in the programs. (1)

In this article we use microlevel data on both the development and preservation of farmland to test whether the option of preserving farmland affects the timing of development. Our model of land conversion decisions is based on real options theory rather than on the traditional net present value rule. We find evidence supporting the theoretical prediction that a PDR program delays development decisions.

Real Options Models

Several authors have recognized that land development is equivalent to the exercise of an option (Dixit and Pindyck 1994; Capozza and Li 2001, 2002). The conditions defining a real option require that the investment is irreversible, that returns are uncertain, and that the decision to convert can be postponed. In contrast to real options theory, the net present value (NPV) rule for characterizing land conversion decisions ignores the implicit costs introduced by uncertainty and irreversibility. It predicts that land will be developed as soon as the present value of development, net of conversion costs, exceeds the present value of the current use. By relying entirely on a one-period rule, the NPV model implicitly assumes that an investment can be reversed if the market is less favorable in subsequent periods.

The real options story recognizes the effects of uncertainty and irreversibility by introducing a value to waiting, as more information emerges. Dixit and Pindyck (1994, Ch. 5) specify a problem in which net return, V, evolves over time according to a geometric Brownian motion as

(1) dV = [alpha]V dt + [sigma] V dz

where [alpha] is the rate of growth in expected returns, [sigma] is the standard error of the investment value, and dz is an increment of a Weiner process or the continuous time equivalent of a random walk. In keeping with the literature, we refer to [alpha] as the "drift" parameter and [sigma] as the "variance" parameter (even though [sigma] is actually the square root of the variance). The standard model takes [alpha] and [sigma] as constant, but studies suggest that real estate returns are inconsistent with this assumption, at least in the short run (Meese and Wallace 1994; Case and Shiller 1989). Allowing time-varying drift and variance parameters does not change the theoretical predictions, although the value of the option to wait may be lower (Heston 1993).

The NPV rule would predict conversion as soon as V(t) [greater than or equal to] I(t), where V(t) is defined as the value of development in time t minus the lost net revenues due to the nondeveloped use, in perpetuity. I(t) is defined as the infrastructure and regulatory costs of development in time t. Real options theory introduces a wedge, the value of the option to wait, between the net returns and costs. The real options decision rule predicts conversion as soon as

(2) V(t) - F(V) [greater than or equal to] I(t)

where F(V) is the value of the option. In standard real options theory, the value of the option to wait (i.e., to convert land in the future) is defined by:

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where T is the conversion time and [rho] is the discount rate. (2)

Dixit and Pindyck show that the solution to (3), which specifies the optimal development time, is increasing in both [alpha] and [sigma], so that increases in both drift and variance slow development. However, in a real-world setting, the underlying simple assumptions of the Dixit and Pindyck model may not hold. Others have suggested that the fear of preemption may reduce the impact of uncertainty and drive investment decisions back to the standard NPV rule (Williams 1993). Emerging empirical evidence in the real estate market lends support to the notion that greater competition may erode the effect of uncertainty on the timing of development (Shwartz and Torous 2004; Bulan, Mayer and Somerville 2004). Increasing returns to scale may also dampen impacts (Downing and Wallace 2005).

Our empirical investigation deals with a more complex real options problem--one in which land use conversion occurs in the presence of more than one investment alternative. Specifically, landowners can "invest" by developing their parcel or by selling their rights to develop (i.e., selling an easement). The primary goal of the empirical application is to test the hypothesis that the existence of the preservation option delays the development decision.

There is some a priori reason to expect such an effect. Capozza and Li (1994) consider varying time and capital intensity of development options in a real options model context. They show that having variable capital intensity raises the level of the "hurdle" and delays development decisions. Geltner, Riddiough, and Stojanovic's (1996) work is even more to the point. They model land use choice as a perpetual option where two mutually exclusive types of development (e.g., offices or apartments) are allowed. The authors find that multiple development options delay development decisions and that the more similarly valued the options, the more the development is delayed.

A Hazard Model of the Timing of Land Conversion

Despite theoretical progress on real options, empirical evidence of the aforementioned effects in the land use context is scant. One notable exception is Schatzki (2003) who finds that sunk costs and uncertainty in returns lowers the likelihood of land conversion from agriculture to forest in Georgia. Using a static model, he controls for the presence of multiple options (to convert to urban uses or to pasture) with variables measuring the percent of county land in alternative uses.

Many of the more traditional empirical articles on land conversion decisions, those based on NPV type rules, also use static empirical models. The most common approach is to specify the development decision as a discrete choice (e.g., Bockstael 1996; McMillen 1989; Kline and Alig 1999; Landis and Zhang 1998). This method provides insight into the effect of parcel attributes on the relative probabilities of conversion but does not account for the dynamic environment in which such decisions are made. In contrast, duration models are better able to analyze the timing of the development decision and are increasingly being applied in the land use context (e.g., Nickerson 2000; Irwin 2002; Irwin and Bockstael 2001; Hite, Sohngen, and Templeton 2003).

We use a duration model to analyze whether PDR programs delay development decisions. The duration model can be described in terms of the hazard function. Define T as the "failure" time at which the parcel makes the transition from the undeveloped state to the developed state. The hazard function, h(t), is the probability that the failure event (conversion) occurs in the time period between t and [DELTA]t, conditional on the fact that the failure has not yet occurred by t:

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The hazard can be interpreted as the rate at which failures (conversions) occur. Following convention, we specify the empirical model as the natural log of the hazard function:

(5) ln [h.sub.i](t) = [omega](t) + [x.sub.i][beta]